Science, Irving K. Barber Faculty of (Okanagan)
Chemistry, Department of (Okanagan)
DSpace
UBCO
Romero Montalvo, Eduardo Alejandro
Doctor of Philosophy - PhD
University of British Columbia
Water as a reaction medium for organic reactions has potential applications in different areas of chemistry. Consequently, aqueous organic chemistry has increasingly become relevant in the past few decades; one of these types of reactions, and the main topic of this thesis, is the “on water” reaction. This reaction involves the increased rate of reactions of selected organic reactions when they occur in the presence of an organic aqueous interface; such an increase in the kinetics of the reaction is relative to the same reaction in solventless or organic solvent conditions. Over the years, some models based on hydrogen bonding, proton transfer and dipole moment have been proposed. Still, there has yet to be a general agreement on the molecular origin of this phenomenon. In this thesis, we explored, through computational methods, the mechanism driving this unusual reactivity. It was found that the accelerated effect observed in “on water” reactions arises from a combination of different effects: hydrogen bonding at the interface stabilizes transition states with respect to pre-reaction complexes, and strong electric fields near the water-oil interface have a dominant effect on the reduction of energy barriers associated with “on water” reactions. Based on these findings, we propose a new mechanism for “on water” reactions. In addition, we present an explanation of the origin of the kinetic isotope effect that “on water” reactions display based on the difference in the macroscopic physical properties between D₂O and H₂O (kH/kD). This thesis offers insights into the still poorly understood chemistry of water in heterogeneous conditions; it provides a rationale for understanding chemical processes occurring near confined or interfacial water. The insights found in this thesis are relevant to other fields of chemistry, such as green chemistry, biochemistry, organic chemistry and atmospheric chemistry.
Elucidating the “On Water”Mechanism in Accelerated Reactionsin WaterbyEduardo Alejandro Romero MontalvoB.Sc. Hons., Universidad Nacional Auto´noma de Me´xico, 2014M.Sc. Hons., Universidad Nacional Auto´noma de Me´xico, 2016A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE COLLEGE OF GRADUATE STUDIES(Chemistry)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)October 2023© Eduardo Alejandro Romero Montalvo, 2023The following individuals certify that they have read, and recommend to the College of GraduateStudies for acceptance, a dissertation entitled:Elucidating the “On Water” Mechanism in Accelerated Reactions in Watersubmitted by Eduardo Alejandro Romero Montalvo in partial fulfilment of the requirementsof the degree of Doctor of Philosophy in Chemistry.Dr. Gino A. DiLabio, University of British ColumbiaSupervisorDr. Kevin M. Smith, University of British ColumbiaSupervisory Committee MemberDr. Robert Godin, University of British ColumbiaSupervisory Committee MemberDr. Jian Liu, University of British ColumbiaUniversity ExaminerDr. Stacey Wetmore, University of LethbridgeExternal ExamineriiAbstractWater as a reaction medium for organic reactions has potential applications in different areas ofchemistry. Consequently, aqueous organic chemistry has increasingly become relevant in the pastfew decades; one of these types of reactions, and the main topic of this thesis, is the “on water”reaction. This reaction involves the increased rate of reactions of selected organic reactions whenthey occur in the presence of an organic aqueous interface; such an increase in the kinetics of thereaction is relative to the same reaction in solventless or organic solvent conditions. Over the years,some models based on hydrogen bonding, proton transfer and dipole moment have been proposed.Still, there has yet to be a general agreement on the molecular origin of this phenomenon. In thisthesis, we explored, through computational methods, the mechanism driving this unusual reactivity.It was found that the accelerated effect observed in “on water” reactions arises from a combinationof different effects: hydrogen bonding at the interface stabilizes transition states with respect topre-reaction complexes, and strong electric fields near the water-oil interface have a dominant effecton the reduction of energy barriers associated with “on water” reactions. Based on these findings,we propose a new mechanism for “on water” reactions. In addition, we present an explanation ofthe origin of the kinetic isotope effect that “on water” reactions display based on the difference inthe macroscopic physical properties between D2O and H2O (kH/kD). This thesis offers insights intothe still poorly understood chemistry of water in heterogeneous conditions; it provides a rationalefor understanding chemical processes occurring near confined or interfacial water. The insightsfound in this thesis are relevant to other fields of chemistry, such as green chemistry, biochemistry,organic chemistry and atmospheric chemistry.iiiLay SummaryIn this thesis, we explore a phenomenon in chemistry known as the “on water” reaction thatoccurs in immiscible water-oil systems. When specific reactions happen at the boundaries of theseparations of water-oil mixtures, they occur faster than when carried out in traditional solventconditions. The reason for this increased speed has been debated, and various explanations havebeen proposed. Through computer simulations, this research found that this accelerated reactioncomes from a combination of effects; interactions involving hydrogen atoms near the boundariesof the separation of the water-oil systems help stabilize reacting molecules and, molecular electriceffects near the water-oil border promotes the acceleration of the chemical reactions. As a result ofour research, a new mechanism with potential applications to other areas of chemistry is proposedfor “on water” reactions.ivPrefaceThe work presented in this thesis work was carried out at The University of British Columbia- Okanagan Campus in Kelowna, BC. Results obtained during the progress of the Ph.D. programwere presented at the following conferences:1. Virtual symposium on theoretical and computational chemistry in Canada, speed talk: “Sam-pling and analyzing noncovalent interactions in water cluster - organic molecule complexes,”Romero-Montalvo, E. Concordia University (Virtual Host), July 19th-23rd, 2021.2. Canadian symposium on theoretical computational chemistry - CATC, invited talk for specialsession: “The on-water effect in organic reactions,” Romero-Montalvo, E. The University ofBritish Columbia - Okanagan Campus, June 27th - July 1st, 2022.3. 12th triennial congress of the world association of theoretical and computational chemists- WATOC, poster: “Benchmarking binding and barrier energies for modelling acceleratedorganic reactions via the on-water mechanism,” Romero-Montalvo, E.; DiLabio, G. The Uni-versity of British Columbia - Vancouver Campus, July 3rd - 8th, 2022.Chapter 3 of this thesis is based on the following article1. Romero-Montalvo, E.; DiLabio, G. A. “Computational study of hydrogen bond interactionsin water cluster-organic molecule complexes,” J. Phys. Chem. A 2021, 125, 3369-3377.Published on April 20th, 2021 (https://doi.org/10.1021/acs.jpca.1c01377).The article was reprinted (adapted) with permission from J. Phys. Chem. A 2021, 125, 3369-3377.Copyright© 2021 American Chemical Society. The adaptations were made for the purposesof writing this thesis. The original idea and conceptualization of the paper were done by Gino A.DiLabio. The design and planning of the research work were done by Eduardo Romero-Montalvo.The research work, analysis and curation of the data were also done by Eduardo Romero-Montalvo.The initial draft was written by Eduardo Romero-Montalvo and was reviewed and edited by GinoA. DiLabio. Supplementary information for this work can be found, free of charge, at the ACSwebpage indicated in the DOI link above. This notice is replicated at the beginning of Chapter 3.A research article based on Chapter 4 of this thesis is planned for publication. The idea andconceptualization of this chapter are the outcomes of a series of research meetings between Gino A.DiLabio and Eduardo Romero-Montalvo. We also received significant contributions from AlirezaSadeghifar regarding the molecular dynamics simulations in this thesis. Eduardo Romero-Montalvoplanned and performed all calculations for this chapter and analyzed, interpreted and curated thevdata. Gino A. DiLabio provided critical feedback by interpreting specific parts of the data inthis thesis and guiding the direction of the research in all steps of the thesis. Figures and tablessufficient to follow this dissertation are included within chapters or in the appendixes of this thesis.Data that is large in volume have been deposited in public repositories and are indicated with theircorresponding links in the thesis text when appropriate.A molecular dynamics code (MODYAN) was developed as part of the work of this thesis; theinitial code was written by Alireza Sadeghifar in FORTRAN. The code was subsequently migratedto Julia and expanded by Eduardo Romero-Montalvo. The code is still expanding and can be foundin the following GitHub repository: https://github.com/eromerom/MODYAN.Other collaborative works published during the progress of the program at The University ofBritish Columbia - Okanagan Campus include1. Noestheden, M.; Dennis, E. G.; Romero-Montalvo, E.; DiLabio, G. A.; Zandberg, W. F.“Detailed characterization of glycosylated sensory-active volatile phenols in smoke-exposedgrapes and wine,” Food Chem. 2018, 259, 147-156.2. Baschieri, A.; Valgimigli, L.; Gabbanini, S.; DiLabio, G.; Romero-Montalvo, E.; Amorati, R.“Extremely fast hydrogen atom transfer between nitroxides and HOO· radicals and implica-tion for catalytic coantioxidant systems,” J. Am. Chem. Soc. 2018, 140, 10354-10362.3. Bietti, M.; Cucinotta, E.; DiLabio, G. A.; Lanzalunga, O.; Lapi, A.; Mazzonna, M.; Romero-Montalvo, E.; Salamone, M. “Evaluation of polar effects in hydrogen atom transfer reactionsfrom activated phenols,” J. Org. Chem. 2019, 84, 1778-1786.4. Salamone, M.; Galeotti, M.; Romero-Montalvo, E.; van Santen, J. A.; Groff, B. D.; Mayer,J. M.; DiLabio, G. A.; Bietti, M. “Bimodal Evans-Polanyi relationships in hydrogen atomtransfer from C(sp3 )-H bonds to the cumyloxyl radical. A combined time-resolved kineticand computational study,” J. Am. Chem. Soc. 2021, 143, 11759-11776.viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxivDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxviChapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Organic Reactions Using Water as Solvent . . . . . . . . . . . . . . . . . . . . . . . . 11.2 The “On Water” Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 “On Water” Reactions and Green Chemistry . . . . . . . . . . . . . . . . . . . . . . 51.4 Proposed Mechanisms for OWRs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.5 Recent Proposals and Discussion on OWRs . . . . . . . . . . . . . . . . . . . . . . . 111.6 Organic Reactions Promoted by Electric Fields . . . . . . . . . . . . . . . . . . . . . 171.7 Research Motivation and Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Chapter 2: Theoretical Background and Methods . . . . . . . . . . . . . . . . . . . 222.1 Quantum Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.2 Quantum Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.2.1 The Electronic Hamiltonian and the Born-Oppenheimer Approximation . . . 252.2.2 The Electronic Wavefunction and the Hartree-Fock Method . . . . . . . . . . 262.2.3 Electronic Correlation and Post-HF Methods . . . . . . . . . . . . . . . . . . 312.2.4 Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37viiTABLE OF CONTENTS2.3 Tools in Quantum Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.3.1 Basis Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.3.2 Potential-Based Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.3.3 Geometry Optimizations and Thermochemistry . . . . . . . . . . . . . . . . . 442.3.4 Quantum Theory of Atoms in Molecules . . . . . . . . . . . . . . . . . . . . . 462.4 Classical Molecular Dynamics Simulations . . . . . . . . . . . . . . . . . . . . . . . . 48Chapter 3: Noncovalent Interactions in Aqueous Organic Media . . . . . . . . . . 533.1 Motivation to Study Noncovalent Interactions in the Context of Aqueous OrganicChemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.2 Other Methodologies and Our Computational Approach . . . . . . . . . . . . . . . . 543.3 Noncovalent Interactions in Aqueous Organic Media are Intricate . . . . . . . . . . . 61Chapter 4: Exploring the OWR Mechanism Using Computational Methods . . . 724.1 HB Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.1.1 Computational Approach for the Analysis of OWRs . . . . . . . . . . . . . . 744.1.2 The Effect of HBs in OWRs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.2 Electrostatic Effects in OWRs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 894.2.1 QM Calculations for the Study of the OWR Dipole Model . . . . . . . . . . . 894.2.2 MD Simulations for Aqueous Organic Systems . . . . . . . . . . . . . . . . . 954.2.3 Analysis of the MD simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 984.2.4 An Explanation of the Kinetic Isotope Effect in OWRs . . . . . . . . . . . . . 1054.3 PT Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1114.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113Chapter 5: Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145Appendix A: BEs for Organic Molecule - Water Cluster Complexes . . . . . . . . . . . . . 145Appendix B: OWRs Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152Nitrogen-Based Claisen Rearrangement . . . . . . . . . . . . . . . . . . . . . . . . . 152Oxygen-Based Claisen Rearrangement . . . . . . . . . . . . . . . . . . . . . . . . . . 156Nitrogen-Based Diels-Alder Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . 160Oxygen-Based Diels-Alder Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . 164Appendix C: Correlation Between Transferred Charges and EBs in OWR Models . . . . . 169Appendix D: Point Charge Models and Electric Fields . . . . . . . . . . . . . . . . . . . . 171Appendix E: Scalar Projections in Bulk and Interfacial Regions for OWR Models . . . . . 175viiiList of TablesTable 1.1 Rate constants in different solvent conditions for the Diels-Alder reactionbetween cyclopentadiene and butenone (at 250 nm and 20◦ C). The analy-sis of this reaction represents the foundation of aqueous organic chemistry.Reprinted (adapted) with permission from reference 12. Copyright © 1980American Chemical Society. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Table 1.2 Completion times for the reaction of Q with DMAD in various solvents.Reprinted (adapted) with permission from reference 19. Copyright © 2005Wiley. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Table 1.3 Comparison of solvent conditions for an aromatic Claisen rearrangement, per-formed at room temperature for 5 days. Reprinted (adapted) with permissionfrom reference 19. Copyright © 2005 Wiley. . . . . . . . . . . . . . . . . . . 4Table 2.1 Functions for popular exchange-correlation functionals. . . . . . . . . . . . . . 40Table 3.1 Names of the water clusters considered in this thesis. The structures of allthe water clusters shown here can be seen in Figures 1 and 2 of reference 176. 56Table 3.2 Benchmark binding energies of the most stable complexes between heptamersand all probes; in the presence and absence of vdW interactions and Abra-ham’s parameters193,194 for HB basicity. βH2 values for diethyl ether, THFand pyridazine were used, due to their structural similarity, for the dimethylether, oxirane and azomethane molecules, respectively. . . . . . . . . . . . . . 68Table 4.1 RMSD of atomic positions for the complex formed between the modeled reac-tions and the water cluster (H2O)10. Comparison between the best performingmethod (M05-D3/6-31+G**-BSIP) and the method used for our structures(B3LYP-D3(BJ)/6-31+G**-BSIP). The changes in atomic positions due toreleasing the constraint water molecules at the M05-D3/6-31+G**-BSIP levelare also shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Table 4.2 Correlations in charge transfer with the benchmark EBs. This table is asummary of the correlations shown in Figures C.1 and C.2, and adds thecorrelation of analogous plots but without the gas-phase data. . . . . . . . . . 89ixLIST OF TABLESTable 4.3 Number of organic molecules placed into the simulation box; these organicmolecules were evenly distributed between the top and bottom organic layersshown in Figure 4.19. In all boxes, the number of water molecules in thesimulation is 7197. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Table 4.4 Dipole moments utilized for the calculation of the electric fields in the simu-lation boxes of this thesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101xList of FiguresFigure 1.1 Marcus’ model for OWRs. Reprinted (adapted) with permission from refer-ence 21. Copyright © 2020 Wiley. . . . . . . . . . . . . . . . . . . . . . . . . 8Figure 1.2 (a) The biphasic fluidic platform Huck et al. used to study the OWR betweenQ andDEAD. Fo and Fw are the flow rates of the organic and water phases,respectively. (b) Pictures of the experiment when varying the flow rates ofthe organic and water phases. The water-organic surface area can be care-fully controlled by adjusting Fw/Fo. Reprinted (adapted) with permissionfrom reference 46. Copyright © 2012 Wiley. . . . . . . . . . . . . . . . . . . 9Figure 1.3 Acid-catalysis model with a completely transferred proton. Proton-transfermodels for OWRs. Reprinted (adapted) with permission from reference 21.Copyright © 2020 Wiley. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Figure 1.4 Gradual transition to OWRs with decreasing reactant water solubility. Reprinted(adapted) with permission from reference 17. Copyright © 2016 Royal So-ciety of Chemistry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Figure 1.5 “In water” and “on water” reactions. Solubility is represented with the letter“s.” Reprinted (adapted) with permission from reference 22. Copyright© 2015 American Chemical Society. . . . . . . . . . . . . . . . . . . . . . . . 13Figure 1.6 Comparison between (a), a typical bifunctional catalyst in synthetic organicchemistry and, (b) and (c), where water molecules reduce the barrier heightin the formation of H2SO4. The nucleophiles, electrophiles and the catalystsare displayed in red, blue and green, respectively. Reprinted (adapted) withpermission from reference 57. Copyright © 2017 Royal Society of Chemistry. 14Figure 1.7 Mukaiyama aldol reaction in OWR conditions. If X=F, the reaction is com-pleted in 10 hours (85% yield). If X is Cl or H, the reaction yield is negligibleafter 24 hours.59 Reprinted (adapted) with permission from reference 59.Copyright © 2014 Wiley. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Figure 1.8 “On water” mechanism model proposed by Kitanosono and Kobayashi. Reprinted(adapted) with permission from reference 21. Copyright © 2020 Wiley. . . . 16Figure 1.9 For a reaction to benefit from field catalysis, the external electric field mustalign with the bond (or bonds) that are being formed or broken.71 Reprinted(adapted) with permission from reference 71. Copyright © 2020 AmericanChemical Society. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18xiLIST OF FIGURESFigure 1.10 Interfacial water molecules display an excess of charge when compared tobulk water, this translates to an increased electric field at the water-air in-terface.39 Reprinted (adapted) with permission from reference 39. Copyright© 2022 Springer Nature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Figure 1.11 Proposed mechanism for OWRs based on hydrogen bonds and electric fields.The shaded blue area represents space region with strong electric fields. . . . 21Figure 3.1 Hexamer (6CC) of water from reference 176. Colour code, red: oxygen, andblue: hydrogen. Dashed lines indicate HB interactions. . . . . . . . . . . . . 55Figure 3.2 Summary of the screening process followed in selecting the most stable com-plexes analyzed in this work. We applied this procedure to each of thepossible 273 complexes (7 probes interacting with 39 water clusters). SPrefers to single-point energies using the indicated methods. . . . . . . . . . . 58Figure 3.3 Two-point extrapolation to the CBS extrapolation limit for one of the bind-ing energies between the decamer 10PP2 and methyl acetate. Our bench-mark binding energies are the average of the CP and non-CP binding en-ergies at the CBS extrapolation limit (DZ-TZ). Colour code, red: oxygen,blue: hydrogen, and magenta: carbon. Dashed lines indicate HB interactions. 61Figure 3.4 Two-point extrapolation to the CBS limit for one of the binding energies be-tween the hexamer 6CC and azomethane. Our benchmark binding energiesare the average of the CP and non-CP binding energies at the CBS extrap-olation limit (DZ-TZ). Colour code, red: oxygen, blue: hydrogen, magenta:carbon, and maroon: nitrogen. Dashed lines indicate HB interactions. . . . . 62Figure 3.5 Mean absolute errors for a diverse set of DFT functionals using 6-31+G**as basis sets with respect to our benchmark binding energies. MAE =1N∑ |Benchmark BE − BEDFT|, N runs for all the 2376 complexes. Thelegends D3 (red) and BSIP (orange) represent the use of empirical disper-sion and basis set incompleteness potentials. The legend BSIP-D3 (cyan) isthe combined use of both BSIP and D3 corrections and Functional (purple)represents the DFT method without the two corrections. . . . . . . . . . . . 63Figure 3.6 Profile of all binding energies for dimethyl ether and (H2O)n (with n = 1-10)at our benchmark level of theory. . . . . . . . . . . . . . . . . . . . . . . . . 64Figure 3.7 Classification of noncovalent interactions found in dimethyl ether-water clus-ter complexes. Colour code, red: oxygen, blue: hydrogen, and magenta: car-bon. Dotted lines indicate either HB or C−H · · · (H2O)n interactions. Seetext for definitions of the classifications. . . . . . . . . . . . . . . . . . . . . . 65Figure 3.8 Some of the noncovalent bonds defined in Figure 3.7 can gain additionalstability when combined with type vdW interactions. Colour code, red:oxygen, blue: hydrogen, and magenta: carbon. Dashed lines indicate eitherHB or C−H · · · (H2O)n interactions. . . . . . . . . . . . . . . . . . . . . . . 66xiiLIST OF FIGURESFigure 3.9 Benchmark binding energies for dimethyl ether and (H2O)n (with n = 1-10)classified according to Figures 3.7 and 3.8. . . . . . . . . . . . . . . . . . . . 66Figure 3.10 Benchmark binding energies profile of the most stable complexes found foreach organic molecule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Figure 3.11 The formation of the shown complex between cluster 7CH3 and dimethy-lamine leads to the strongest binding energy of all; the strong interactionoccurs via a DDDA interaction that is stabilized by vdW interactions. Thestrongest interaction among octamers and dimethylamine is also displayed;there is no additional vdW stabilization for this case. Colour code, red:oxygen, blue: hydrogen, magenta: carbon, and maroon: nitrogen. Dashedlines indicate either HB or C−H · · · (H2O)n interactions. . . . . . . . . . . . 69Figure 3.12 Benchmark binding energies for dimethyl ether and individual clusters aslabelled in Table 3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Figure 4.1 Representation of a hydrogen bond between two water molecules: the waterthat is acting as HB acceptor has a lone pair orbital that interacts with theσ∗ O−H antibonding orbital in the water molecule acting as HB donor. Onlythe relevant interacting orbitals are shown. . . . . . . . . . . . . . . . . . . . 74Figure 4.2 Schematic representation of a PT process between the water and acetonemolecules forming a hydroxide ion and a protonated acetone. A hydrogenbond is necessary for a proton transfer to occur, relative dipole orientationare also highly dependent on the formation of HBs. . . . . . . . . . . . . . . 74Figure 4.3 Model reactions for Claisen rearrangements in this thesis. X = O or NH.The labels R, TS, and P represent reactants, transition states, and products,respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75Figure 4.4 Model reactions for the Diels-Alder cycloadditions. X = O or NH. DielsAlderRXis a representation of the pre-reaction complex formed with diene and dienophilemolecules. The labels R, TS, and P represent reactants, transition states,and products, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75Figure 4.5 Mean absolute error (MAE) in reaction energy barriers for different DFTmethods using 6-31+G** as basis sets compared to our benchmark barrierenergies (formation of TSs, see reactions 4.1 and 4.2).MAE = 1N∑∣∣∣EbarrierDLPNO−CCSD(T)/CBS − EbarrierDFT ∣∣∣, where the sum goes over allcalculated energy barriers. The red and orange bars represent values usingempirical dispersion and basis set incompleteness potentials, respectively.The cyan bar combines the previous two, and the purple (DFT Functional)shows the errors in the absence of both. When empirical dispersion wasemployed, BJ-damping was included. . . . . . . . . . . . . . . . . . . . . . . 78xiiiLIST OF FIGURESFigure 4.6 Overlapped structures of DielsAlderTSO. (a) B3LYP-D3(BJ)/6-31+G**-BSIP vs. M05-D3/6-31+G**-BSIP (water clusters fixed), RMSD = 0.068 A˚.(b) M05-D3/6-31+G**-BSIP (water clusters fixed) vs. M05-D3/6-31+G**-BSIP (no constraints), RMSD = 0.134 A˚. . . . . . . . . . . . . . . . . . . . . 79Figure 4.7 Benchmark energy barriers for all calculations; (a) oxygen-based Claisenrearrangement, (b) oxygen-based Diels-Alder reaction, (c) nitrogen-basedClaisen rearrangement, (d) nitrogen-based Diels-Alder reaction. The greenline represents the corresponding cycloaddition in the absence of water,whereas the purple dots show the EBs of the same reactions as we add(H2O)n, n=1-10, to our systems. . . . . . . . . . . . . . . . . . . . . . . . . . 81Figure 4.8 The effect of using a implicit solvent model (SMD) in the nitrogen-basedClaisen rearrangement reaction with and without the hexamer of water. Theinclusion of explicit water molecules is necessary to reproduce the decreasein energy barriers. Calculations ran at the M05-D3/6-31+G**-BSIP level oftheory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82Figure 4.9 Binding energies for the pre-reaction complex and transition state of allmodel reactions at the M05-D3/6-31+G**-BSIP level. The binding ener-gies are defined as BE = E(R · · · (H2O)n)− E(R)− E((H2O)n). Where E(X)represents the electronic energy of system X. See Equation 4.3. (a) Oxygen-based Claisen rearrangement, (b) oxygen-based Diels-Alder reaction, (c)nitrogen-based Claisen rearrangement, and, (d) nitrogen-based Diels-Alderreaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Figure 4.10 DielsAlderTSN · · · (H2O)4. The N-H in the organic molecule donates an HBback to an oxygen in the water cluster, the interaction was confirmed by abond critical point between the hydrogen in the N-H group and the oxygenin (H2O)4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Figure 4.11 Charges of (H2O)n clusters (in atomic units) when they interact with thetransition states in all reaction models. The water clusters become negativelycharged when interacting with polarized TSs. Charges were calculated usingAIMAll and an M05-D3/6-31+G**-BSIP wavefunction. (a) Oxygen-basedClaisen rearrangement, (b) oxygen-based Diels-Alder reaction, (c) nitrogen-based Claisen rearrangement, and (d) nitrogen-based Diels-Alder reaction.The scale shows the zero value of charge (y-axis) in all cases, as a referenceof a reaction in the absence of water molecules. . . . . . . . . . . . . . . . . . 86Figure 4.12 Charges of the diene, dienophile and water clusters in DielsAlderTSN · · · (H2O)n.Charges were calculated using AIMAll and the M05-D3/6-31+G**-BSIPwavefunctions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87xivLIST OF FIGURESFigure 4.13 ClaisenTSN · · · (H2O)7. The C-H groups in the organic molecule back donateto oxygen atoms in the water cluster. The interactions were confirmed by abond critical point between the hydrogen atoms in the C-H groups and theoxygen atoms in (H2O)7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88Figure 4.14 Comparison in the reduction of energy barriers by explicit water molecules(fully quantum, in yellow) and implicit water molecules (point charges, inblue) for the reaction with ClaisenRNH. The red horizontal line representsthe reference reaction in the gas-phase. We employed M05-D3/6-31+G**-BSIP as the level of theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91Figure 4.15 Energy barrier modulation due to the magnitude of the charge in the oxygenatom in the water molecule. The trend is almost linear with the followingequation: EB = 5.16qO + 47.6, r2 = 0.995. The green horizontal line is theenergy barrier for the reference gas-phase reaction. This reaction is the OWRbetween ClaisenRNH and H2O. We employed M05-D3/6-31+G**-BSIP asthe level of theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Figure 4.16 Schematic representation of how we aligned the external electric field toour model system. Colour code: gray (carbon), white (hydrogen) and blue(nitrogen). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94Figure 4.17 Evaluation of the effect of an external electric field in the reactivity of thenitrogen-based Claisen rearrangement. The blue horizontal line representsthe EB in the absence of any external EField. We used M05-D3/6-31+G**-BSIP as the level of theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94Figure 4.18 Evaluation of the effect of an external electric field in the reactivity of theoxygen-based Diels-Alder reaction. The blue horizontal line represents theEB in the absence of any external EField. We used M05-D3/6-31+G**-BSIPas the level of theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Figure 4.19 Representation of the simulation boxes used in this thesis. The blue moleculesare organic molecules, while the red ones represent water molecules. Thelongest dimension of the box is aligned with the z-coordinate. The dimen-sions of the initial boxes are lx = ly = 6 nm, and lz = 24 nm. The topand bottom organic layers have lx = ly = 6 nm and lz = 9 nm as dimen-sions, each. The water layer in the middle has the following dimensions:lx = ly = lz = 6 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Figure 4.20 Screenshot of the welcome user interface prompt of one of MODYAN’s modules. 99Figure 4.21 Scalar projections into the C−O bonds of the organic molecules (ClaisenRO)in a region of the simulation box identified as bulk organic. The calculationof the electric fields and projections involves all other molecules of the systemin the box. The red dots represent average scalar projections. . . . . . . . . 102xvLIST OF FIGURESFigure 4.22 Scalar projections into the C−O of the organic molecules (ClaisenRO) in aregion of the simulation box identified as the interface. The calculation ofthe electric fields and projections involves all other molecules of the systemin the box. The red dots represent average scalar projections. . . . . . . . . 103Figure 4.23 Scalar projections into the perpendicular direction to the plane formed by thethree carbon atoms in the organic molecules (DienophileRO) in a region ofthe simulation box identified as bulk organic. The calculation of the electricfields and projections involves all other molecules of the system in the box.The red dots represent average scalar projections. . . . . . . . . . . . . . . . 104Figure 4.24 Scalar projections into the perpendicular direction to the plane formed bythe three carbon atoms in the organic molecules (DienophileRO) in a regionof the simulation box identified as interface. The calculation of the electricfields and projections involves all other molecules of the system in the box.The red dots represent average scalar projections. . . . . . . . . . . . . . . . 105Figure 4.25 Density profile for the simulation of ClaisenRNH with water molecules. . . . 106Figure 4.26 Density profile for the simulation of ClaisenRNH with heavy water molecules. 107Figure 4.27 Detailed penetration of H2O and D2O into the organic phase of ClaisenRNH.This graph displays the density of H2O and D2O, as shown in Figures 4.25and 4.26, but focusing on the first organic layer (0 < z < 8 nm) . . . . . . . 108Figure 4.28 Density profile for the simulation of DielsAlderRNH with water molecules. . . 108Figure 4.29 Density profile for the simulation of DielsAlderRNH with heavy water molecules.109Figure 4.30 (a) Counting H2O molecules in a bulk organic region (0 < z < 9 in thesimulation box) for the ClaisenRNH system. (b) Counting D2O molecules ina bulk organic region (0 < z < 9 in the simulation box) for the ClaisenRNHsystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110Figure 4.31 Probability density of the scalar project on the C−N bond in the simulationbox corresponding to the ClaisenRNH system. . . . . . . . . . . . . . . . . . 111Figure 4.32 The transition state ClaisenTSNH+ · · · (H2O)5(OH)− is connected to the un-protonated pre-reaction complex ClaisenRN · · · (H2O)6. Both structures wereoptimized at the M05-D3/6-31+G**-BSIP level of theory. . . . . . . . . . . . 113Figure 5.1 Proposed mechanism for OWRs based on hydrogen bonds and electric fields.The shaded blue area represents space region with strong electric fields. . . . 118Figure A.1 Profile of all binding energies for acetone and (H2O)n (with n = 1 - 10) atour benchmark level of theory. . . . . . . . . . . . . . . . . . . . . . . . . . . 145Figure A.2 Benchmark binding energies for acetone and individual clusters as labelledin Table 3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146Figure A.3 Profile of all binding energies for dimethylamine and (H2O)n (with n = 1- 10) at our benchmark level of theory. . . . . . . . . . . . . . . . . . . . . . 146xviLIST OF FIGURESFigure A.4 Benchmark binding energies for dimethylamine and individual clusters aslabelled in Table 3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147Figure A.5 Profile of all binding energies for azomethane and (H2O)n (with n = 1 -10) at our benchmark level of theory. . . . . . . . . . . . . . . . . . . . . . . 147Figure A.6 Benchmark binding energies for azomethane and individual clusters as la-belled in Table 3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148Figure A.7 Profile of all binding energies for methyl acetate and (H2O)n (with n = 1- 10) at our benchmark level of theory. . . . . . . . . . . . . . . . . . . . . . 148Figure A.8 Benchmark binding energies for methyl acetate and individual clusters aslabelled in Table 3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149Figure A.9 Profile of all binding energies for oxirane and (H2O)n (with n = 1 - 10) atour benchmark level of theory. . . . . . . . . . . . . . . . . . . . . . . . . . . 149Figure A.10 Benchmark binding energies for oxirane and individual clusters as labelledin Table 3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150Figure A.11 Profile of all binding energies for trimethylamine and (H2O)n (with n = 1- 10) at our benchmark level of theory. . . . . . . . . . . . . . . . . . . . . . 150Figure A.12 Benchmark binding energies for trimethylamine and individual clusters aslabelled in Table 3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151Figure B.1 Structure of the transition state. Gas phase reaction. . . . . . . . . . . . . . 152Figure B.2 Structure of the transition state. Reaction with the monomer of water. . . . 152Figure B.3 Structure of the transition state. Reaction with the dimer of water. . . . . . 153Figure B.4 Structure of the transition state. Reaction with the trimer of water. . . . . . 153Figure B.5 Structure of the transition state. Reaction with the tetramer of water. . . . 153Figure B.6 Structure of the transition state. Reaction with the pentamer of water. . . . 154Figure B.7 Structure of the transition state. Reaction with the hexamer of water. . . . . 154Figure B.8 Structure of the transition state. Reaction with the heptamer of water. . . . 154Figure B.9 Structure of the transition state. Reaction with the octamer of water. . . . . 155Figure B.10 Structure of the transition state. Reaction with the nonamer of water. . . . 155Figure B.11 Structure of the transition state. Reaction with the decamer of water. . . . . 156Figure B.12 Structure of the transition state. Gas phase reaction. . . . . . . . . . . . . . 156Figure B.13 Structure of the transition state. Reaction with the monomer of water. . . . 157Figure B.14 Structure of the transition state. Reaction with the dimer of water. . . . . . 157Figure B.15 Structure of the transition state. Reaction with the trimer of water. . . . . . 157Figure B.16 Structure of the transition state. Reaction with the tetramer of water. . . . 158Figure B.17 Structure of the transition state. Reaction with the pentamer of water. . . . 158Figure B.18 Structure of the transition state. Reaction with the hexamer of water. . . . . 158Figure B.19 Structure of the transition state. Reaction with the heptamer of water. . . . 159Figure B.20 Structure of the transition state. Reaction with the octamer of water. . . . . 159Figure B.21 Structure of the transition state. Reaction with the nonamer of water. . . . 159xviiLIST OF FIGURESFigure B.22 Structure of the transition state. Reaction with the decamer of water. . . . . 160Figure B.23 Structure of the transition state. Gas phase reaction. . . . . . . . . . . . . . 160Figure B.24 Structure of the transition state. Reaction with the monomer of water. . . . 161Figure B.25 Structure of the transition state. Reaction with the dimer of water. . . . . . 161Figure B.26 Structure of the transition state. Reaction with the trimer of water. . . . . . 161Figure B.27 Structure of the transition state. Reaction with the tetramer of water. . . . 162Figure B.28 Structure of the transition state. Reaction with the pentamer of water. . . . 162Figure B.29 Structure of the transition state. Reaction with the hexamer of water. . . . . 162Figure B.30 Structure of the transition state. Reaction with the heptamer of water. . . . 163Figure B.31 Structure of the transition state. Reaction with the octamer of water. . . . . 163Figure B.32 Structure of the transition state. Reaction with the nonamer of water. . . . 163Figure B.33 Structure of the transition state. Reaction with the decamer of water. . . . . 164Figure B.34 Structure of the transition state. Gas phase reaction. . . . . . . . . . . . . . 164Figure B.35 Structure of the transition state. Reaction with the monomer of water. . . . 165Figure B.36 Structure of the transition state. Reaction with the dimer of water. . . . . . 165Figure B.37 Structure of the transition state. Reaction with the trimer of water. . . . . . 165Figure B.38 Structure of the transition state. Reaction with the tetramer of water. . . . 166Figure B.39 Structure of the transition state. Reaction with the pentamer of water. . . . 166Figure B.40 Structure of the transition state. Reaction with the hexamer of water. . . . . 166Figure B.41 Structure of the transition state. Reaction with the heptamer of water. . . . 167Figure B.42 Structure of the transition state. Reaction with the octamer of water. . . . . 167Figure B.43 Structure of the transition state. Reaction with the nonamer of water. . . . 167Figure B.44 Structure of the transition state. Reaction with the decamer of water. . . . . 168Figure C.1 Benchmark energy barriers vs ∆q in the organic molecules for the Claisenrearrangement models. (a) Oxygen-based Claisen rearrangement (∆q =qClaisenTSO − qClaisenRO , trenline: EB = −293∆q + 37.2, r2 = 0.759) and(b) nitrogen-based Claisen rearrangement (∆q = qClaisenTSNH − qClaisenRNH ,trenline: EB = −108∆q + 43.1, r2 = 0.198). Charges (in a.u.) were cal-culated using AIMAll at the M05-D3/6-31+G**-BSIP level and the energybarriers correspond to our benchmark values. . . . . . . . . . . . . . . . . . . 169Figure C.2 Benchmark energy barriers vs q in the organic molecules for the Diels-Aldermodels. (a) oxygen-based Diels-Alder reaction (∆q = qDieneTSO − qDieneRO ,trenline: EB = −77.5∆q + 25.8, r2 = 0.871) and (b) nitrogen-based Diels-Alder reaction (∆q = qDieneTSNH − qDieneRNH , trenline: EB = −30.5∆q +18.9, r2 = 0.627). Charges (in a.u.) were calculated using AIMAll at theM05-D3/6-31+G**-BSIP level and the energy barriers correspond to ourbenchmark values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170Figure D.1 The effect of using point charges as water models on the nitrogen-basedClaisen rearrangement. TIP3P charges were employed (qO = −2qH = −0.834).171xviiiLIST OF FIGURESFigure D.2 The effect of using point charges as water models on the oxygen-based Claisenrearrangement. TIP3P charges were employed (qO = −2qH = −0.834). . . . . 171Figure D.3 The effect of using point charges as water models on the nitrogen-basedDiels-Alder reaction. TIP3P charges were employed (qO = −2qH = −0.834). 172Figure D.4 The effect of using point charges as water models on the oxygen-based Diels-Alder reaction. TIP3P charges were employed (qO = −2qH = −0.834). . . . . 172Figure D.5 The effect of applying an external electric field on the nitrogen-based Claisenrearrangement using different field magnitudes and directions. The C−Nbond is aligned with the z direction, the benzene ring is aligned to the xzplane. Ai = 1.08, Bi = 6.94, and Ci = 15.02; i = x, y or z, all field valuesreported in eV e−1 nm−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173Figure D.6 The effect of applying an external electric field on the oxygen-based Claisenrearrangement using different field magnitudes and directions. The C−Obond is aligned with the z direction, the benzene ring is aligned to the xzplane. Ai = 1.08, Bi = 6.94, and Ci = 15.02; i = x, y or z, all field valuesreported in eV e−1 nm−1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173Figure D.7 The effect of applying an external electric field on the nitrogen-based Diels-Alder reaction using different field magnitudes and directions. The C−Cbond in the dienophile is aligned with the z direction, the dienophile is alignedwith the xz plane. Ai = 1.08, Bi = 6.94, and Ci = 15.02; i = x, y or z, allfield values reported in eV e−1 nm−1 . . . . . . . . . . . . . . . . . . . . . . 174Figure D.8 The effect of applying an external electric field on the oxygen-based Diels-Alder reaction using different field magnitudes and directions. The C−Cbond in the dienophile is aligned with the z direction, the dienophile is alignedwith the xz plane. Ai = 1.08, Bi = 6.94, and Ci = 15.02; i = x, y or z, allfield values reported in eV e−1 nm−1 . . . . . . . . . . . . . . . . . . . . . . 174Figure E.1 Scalar projections into the C−O bonds of the organic molecules (ClaisenRO)in a region of the simulation box identified as bulk organic. The calculationof the electric fields and projections involves all other molecules of the systemin the box. The red dots represent average scalar projections. . . . . . . . . 175Figure E.2 Scalar projections into the C−O of the organic molecules (ClaisenRO) in aregion of the simulation box identified as the interface. The calculation ofthe electric fields and projections involves all other molecules of the systemin the box. The red dots represent average scalar projections. . . . . . . . . 176Figure E.3 Scalar projections into the C−N bonds of the organic molecules (ClaisenRNH)in a region of the simulation box identified as bulk organic. The calculationof the electric fields and projections involves all other molecules of the systemin the box. The red dots represent average scalar projections. . . . . . . . . 176xixLIST OF FIGURESFigure E.4 Scalar projections into the C−N of the organic molecules (ClaisenRNH) in aregion of the simulation box identified as the interface. The calculation ofthe electric fields and projections involves all other molecules of the systemin the box. The red dots represent average scalar projections. . . . . . . . . 177Figure E.5 Scalar projections into the perpendicular direction to the plane formed by thethree carbon atoms in the organic molecules (DienophileRO) in a region ofthe simulation box identified as bulk organic. The calculation of the electricfields and projections involves all other molecules of the system in the box.The red dots represent average scalar projections. . . . . . . . . . . . . . . . 177Figure E.6 Scalar projections into the perpendicular direction to the plane formed bythe three carbon atoms in the organic molecules (DienophileRO) in a regionof the simulation box identified as interface. The calculation of the electricfields and projections involves all other molecules of the system in the box.The red dots represent average scalar projections. . . . . . . . . . . . . . . . 178Figure E.7 Scalar projections into the perpendicular direction to the plane formed by thethree carbon atoms in the organic molecules (DienophileRNH) in a region ofthe simulation box identified as bulk organic. The calculation of the electricfields and projections involves all other molecules of the system in the box.The red dots represent average scalar projections. . . . . . . . . . . . . . . . 178Figure E.8 Scalar projections into the perpendicular direction to the plane formed bythe three carbon atoms in the organic molecules (DienophileRNH) in a regionof the simulation box identified as interface. The calculation of the electricfields and projections involves all other molecules of the system in the box.The red dots represent average scalar projections. . . . . . . . . . . . . . . . 179Figure E.9 (a) Counting H2O molecules in a bulk organic region (0 < z < 9 in thesimulation box) for the ClaisenRO system. (b) Counting D2O molecules ina bulk organic region (0 < z < 9 in the simulation box) for the ClaisenROsystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179Figure E.10 (a) Counting H2O molecules in a bulk organic region (0 < z < 9 in thesimulation box) for the ClaisenRNH system. (b) Counting D2O molecules ina bulk organic region (0 < z < 9 in the simulation box) for the ClaisenRNHsystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180Figure E.11 (a) Counting H2O molecules in a bulk organic region (0 < z < 9 in thesimulation box) for the DielsAlderRO system. (b) Counting D2Omolecules ina bulk organic region (0 < z < 9 in the simulation box) for the DielsAlderROsystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180xxLIST OF FIGURESFigure E.12 (a) Counting H2O molecules in a bulk organic region (0 < z < 9 in the simu-lation box) for the DielsAlderRNH system. (b) Counting D2O molecules in abulk organic region (0 < z < 9 in the simulation box) for the DielsAlderRNHsystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181Figure E.13 Probability density of the scalar project on the C−N bond in the simulationbox corresponding to the ClaisenRNH system. . . . . . . . . . . . . . . . . . 181Figure E.14 Probability density of the scalar project on the C−O bond in the simulationbox corresponding to the ClaisenRO system. . . . . . . . . . . . . . . . . . . 182Figure E.15 Probability density of the scalar project into the nˆCCC bond in the simulationbox corresponding to the DielsAlderRNH system. . . . . . . . . . . . . . . . . 182Figure E.16 Probability density of the scalar project into the nˆCCC direction in the sim-ulation box corresponding to the DielsAlderRO system. . . . . . . . . . . . . 183xxiList of Acronyms6-31+G**: Valence Double-Zeta Basis Set with s-Diffuse, d-Polarization, and p-Polarization.ACP: Atom-Centered Potential.aug-cc-pVDZ: Augmented Correlation Consistent Polarized Valence Double-Zeta Basis Set.aug-cc-pVTZ: Augmented Correlation Consistent Polarized Valence Triple-Zeta Basis Set.BE: Binding Energy.BDM: Bockris-Devanathan-Muller.BSIE: Basis Set Incompleteness Error.BSIP: Basis Set Incompleteness Potential.CBS: Complete Basis Set.CC: Coupled Cluster.CCSD(T): Coupled Cluster with Single, Double, and Perturbative Triple excitations.CI: Configuration Interaction.CP: Counterpoise.D3(BJ): Grimme’s Empirical Dispersion with Becke-Johnson’s Damping Function.DD: Double Donor.DDDA: Double Donor, Double Acceptor.DDSA: Double Donor, Single Acceptor.DEAD: Diethyl Azodicarboxylate.Density Functional Theory: DFT.DMAD: Dimethyl Azodicarboxylate.DMF: Dimethylformamide.DMSO: Dimethyl Sulfoxide.DLPNO: Domain-Based Local Pair Natural Orbital.ECP: Effective-Core Potentials.FF: Force Field.g16: Gaussian 16.GGA: Generalized Gradient Approximation.GTO: Gaussian-Type Orbitals.HB: Hydrogen Bonding or Hydrogen Bond.HF: Hartree-Fock.HP: Hartree Product.xxiiKIE: Kinetic Isotope Effect.KS: Kohn-Sham.LDA: Local Density Approximation.MAE: Mean Absolute Error.MD: Molecular Dynamics.MINIs: Minimal Basis Set.MP2: Second Order Møller-Plesset.non-CP: non-Counterpoise.OWR: “On Water” Reaction.PBC: Periodic Boundary Conditions.PES: Potential Energy Surface.PT: Proton Transfer.Q: Quadricyclane.QC: Quantum Chemistry.QM: Quantum Mechanics.QM/MM: Quantum Mechanics/Molecular Mechanics.QTAIM: Quantum Theory of Atoms in Molecules.RI: Resolution of the Identity.SCF: Self-Consistent Field.SD: Slater Determinant.SDSA: Single Donor, Single Acceptor.SI: International System of Units (Syste`me International).SP: Single Point.STO: Slater-Type Orbitals.THF: Tetrahydrofuran.TS: Transition State.UFF: Universal Force Field.vdW: van der Waals.xxiiiAcknowledgementsI want to start by thanking my Ph.D. supervisor, Gino A. DiLabio. Words cannot expresshow grateful I am to Gino for all these years of constant encouragement, wise advice and supportregarding research and life outside the lab. I thank Gino for fostering an exciting and friendlyenvironment in his lab, wherein I always felt at home. I am immensely grateful for several enrichingdiscussions and for always finding a positive angle to my research. Your vision and optimism helpedme “counterpoise” my recurrent states of confusion and pessimism; your guidance was vital tocompleting this project. Most importantly, I am most grateful for the opportunity to obtain alifelong membership in the DiLabio group.I also want to thank Dr. Kevin Smith and Dr. Robert Godin for years of valuable feedbackand suggestions during my doctoral supervisory committee meetings. Your questions, observationsand insights helped me shape this thesis in its current form and ensured that the direction ofthis research was always on track. I would like to extend my gratitude to Dr. Stacey Wetmorefor agreeing to act as external examiner and Dr. Jian Liu for accepting to be the universityexaminer. I am thankful to the faculty and staff of UBCO (former and present), who deeply careabout students and constantly make the university and the chemistry department a better place:Dr. Alberto Otero-de-la-Roza, Dr. Emilian Tuca, Dr. Wesley Zandberg, Dr. Robert Szilagyi,Dr. Jennifer Robison, Dr. Trudy Kavanagh, Dr. Francisco Pen˜a, Charlene Wehrmann, MicheleCannon, Ieva Zigg, Lindsay Odne and Karen Krysko; thank you for your kindness, support andprofessionalism.I thank the members of the DiLabio Lab and neighbouring labs for being a source of academicand emotional support. Notably, I am deeply thankful to Zhipeng Pei, Nitin, Hossein Khalilian,Alireza Sadeghifar and Viki Kumar Prasad for becoming friends for life.I acknowledge CONACyT-Mexico for providing me with financial support during the 2017-2021period under the scholarship number 308773/472432. I also thank UBC for financial aid throughteaching assistantships and fellowships. I thank the Digital Research Alliance of Canada andUBC’s advanced research computing services, for providing access to high-performance computingresources for the completion of this thesis.I am grateful for the support of my mexican friends: Ulises Jime´nez, Guillermo Romo, FernandoRobles, Gabriel Herna´ndez, Oliver Funabazama, Alberto Ferna´ndez, Miguel Rosales, GuillermoMoreno, Roberto Meza, Jesu´s Garduza, Marlon Herna´ndez, Fredy Hirata, Itzel Condado, LuisMart´ınez and the memory of my dear friend Aldo Facundo. A special mention to all my mentorsthat, with the years, became close friends: Dr. Toma´s Rocha, Dr. Christian Ferna´ndez, Dr. ManuelxxivGuevara, Dr. Jorge Gonza´lez and M.Sc. Edith Ca´rdenas.I would like to pay my respects by remembering and thanking family members that, sadly,passed away while I was completing my degree. Gerardo Romero Salas, Catalina Yoshizaki Aniceto,Alberto Montalvo Yoshizaki and Mayra Garc´ıa Pineda. Thank you for the shared memories andmoments we spent together. In particular, I am heartily grateful to Uncle Alberto for introducingme to physics in middle school and sparking my interest in science. Also, I thank my mom-in-law,Mayra, for receiving me in her home and always treating me like a son; I am blessed to be part ofyour family and I thank you, from the bottom of my heart, for raising an incredible woman, mywife. Thanks for all the happy moments we shared, especially the food you used to prepare and therecipes you loved to share with family on weekends. Thank you for teaching us that family comesfirst.I thank my parents, Jesu´s Romero Domı´nguez and Xo´chitl Montalvo Yoshizaki, for raising meto be resilient and for always supporting my dreams. Thank you for all the love and encouragement;I hope you feel proud of what I am building, and I pray for your well-being so that we continue toshare moments like this in the future. It is my desire one day to repay the kindness and dedicationyou always gave to your children.I am grateful for abuelita Mina, my big brother Chuch´ın, my big sister Mitzue, my nephew Leoand my niece Mitsuri, for making me feel that no matter how bad things may become, we are notalone.Finally, I am eternally grateful to my wife Fabiola, my son Mat´ıas, and my daughter Hana.Thank you for helping me realize what is important in life and for giving me reasons to become abetter husband, dad and man. Thank you for your patience and the sacrifices you made so that Icould conclude my degree. This doctoral degree undoubtedly belongs to the four of us. Please knowthat completing my Ph.D. degree is one of the most challenging tasks I have ever done; withoutyour love and dedication, this work would have been impossible to complete. De corazo´n, gracias.xxvDedicationPara Hana.Gracias por venir al mundo.xxviChapter 1IntroductionUrea, found in mammalian urine, was first reported to be obtained from a non-living precur-sor in water media in 1828 by Friedrich Wo¨hler; the production of this compound from ammoniacyanate is considered by many as the starting point of modern organic chemistry.1 A historicallook at the early organic synthesis work during the 19th century reveals that much of the earlywork in organic synthesis used water as a solvent. The list of organic reactions in water is large,but important examples include the Lieben haloform reaction,2 the Curtius rearrangement,3,4 theHofmann degradation,5 the Sandmeyer reaction,6 the Baeyer-Villiger oxidation,7 among other pi-oneering reactions. In the early days of organic synthesis, water was the obvious choice for solventdue to its polar properties and ubiquity. However, in the early 1900’s, the success of Grignard’sreagent8 and the subsequent development of similar and water-labile organometallic compounds,along with the expansion of the 20th century’s petroleum industry and their solvent derivatives,led to the exponential growth of complex organic synthesis procedures that, for the most part,a useorganic solvents.10 Many of those developed procedures are used today in modern organic synthesisprocedures. Despite the relevance of water in biochemical processes, it seems that its use in organicchemistry is now a part of the forgotten history of chemical synthesis.111.1 Organic Reactions Using Water as SolventAlthough most biochemical processes occur in H2O, the potential of chemical synthesis usingwater as solvent was only rediscovered by the pioneering work of Breslow and coworkers fourdecades ago.12–15 In a series of seminal papers published during the 1980s, they discovered theextraordinary effect that water possesses in accelerating Diels-Alder reactions; 700-fold in rateconstants were observed compared to reactions using organic solvents.12 This effect was ascribedaWith some exceptions, see reference 9 for an example.11.2. THE “ON WATER” REACTIONto the hydrophobic association of nonpolar molecules in aqueous solutions. They added lithiumchloride, a salt that boosts hydrophobic effects, to the cyclopentadiene and butenone reactionmixture to explore the hypothesis. Kinetic data were obtained and compared for this reaction indistinct solvent conditions (see Table 1.1). The data showed a pronounced increase in the rate ofreaction upon the addition of LiCl to the reaction systems using water as the solvent, as predicted bythe hydrophobic effect hypothesis. In a subsequent study,13 the opposite effect was observed whenadding C(NH2)3ClO4, which decreases hydrophobic effects. This observation was also consistentwith the proposed explanation of the effect.Solvent Additional Component k2 × 105 (M−1s−1)Isooctane None 5.94MeOH None 75.5H2O None 4400H2O LiCl (4.86 M) 10800Table 1.1: Rate constants in different solvent conditions for the Diels-Alder reaction between cy-clopentadiene and butenone (at 250 nm and 20◦ C). The analysis of this reaction represents thefoundation of aqueous organic chemistry. Reprinted (adapted) with permission from reference 12.Copyright © 1980 American Chemical Society.Breslow and colleagues used the hydrophobic effect hypothesis to make crucial contributionsto synthetic chemistry,12–15 setting the foundations of aqueous organic chemistry as a new fieldthat exploits the use of the cheap and ubiquitous water solvent for green and synthetic chemistryprocedures.1.2 The “On Water” ReactionIt has been generally accepted, that in order for substances to react, they should be soluble inthe reaction media.16 This is particularly problematic in the case of water because many nonpolarmolecules are insoluble or, worse, labile in water.17 For this reason, organic co-solvents have stillbeen employed for efficient transformations in aqueous solutions.18 In 2005, however, Sharpless andcoworkers reported an impressive acceleration of cycloaddition reactions involving water-insolublereagents in aqueous suspension.19 They coined the term “on water” reactions (OWRs) to makea clear distinction between those reactions happening in aqueous solution (“in water” for soluble21.2. THE “ON WATER” REACTIONreactants) and those occurring in the water-organic suspension (“on water” for insoluble reactants).In the years following, several reactions were reported to undergo rate acceleration via OWRs, asit is listed in the review article shown in reference 20.The first OWR to be studied was the cycloaddition between quadricyclane (Q) and dimethylazodicarboxylate (DMAD). Table 1.2 compares the completion times for this reaction in differentsolvents. Notice that the reaction is classified as “in solvent” (homogeneous) and as “on solvent”(heterogeneous) conditions to analyze the effect of the interface on the reaction rate. The data forthe reactions in the homogeneous reactions has the following trend in reaction rates: MeOH/H2O(3:1) > MeOH > DMSO > CH3CN ≈ CH2Cl2 > EtOAc ≈ toluene. These results suggest thathydrogen bonding, charge stabilization, and dipolar effects play a significant role in enhancing thereaction rates for solubilized reagents. For the MeOH/H2O mixtures, the interface between Q plusDMAD and the MeOH/H2O 1:1 or MeOH/H2O 1:3 mixtures (“on solvent” systems), produces a24-fold increase in completion times compared to the “in solvent” system (MeOH/H2O 3:1). Thiseffect is independent of the methanol concentration in heterogeneous conditions; that is, the effectspresent in the homogeneous reaction systems are absent once the interface is formed.Nonetheless, heterogeneity is not sufficient to produce the decreases in the time to completion ofthe reaction: 36 hours are necessary to complete the reaction in the perfluorohexane heterogeneoussystem, considerably longer than the ten minutes that are required for the OWR. This result alsoillustrates the vital role that hydrogen bonding (HB) and/or proton transfer (PT) plays in thisphenomenon, an idea confirmed by contrasting the reaction rates on D2O and H2O; the reactionis slower on deuterated water than in the case of normal “on water” conditions. If a chemicalreaction is accelerated when forming an aqueous emulsion with water, it is said to present an “onwater” character. For example, the Claisen rearrangement shown in Table 1.3 has “on water”character since it experiences an increase in the conversion percentage when performed as an OWRcompared to the reactions in commonly used solvents. This reaction was executed in differentsolvent conditions for 120 hours at room temperature. The data demonstrate that increasing thepolarity of the solvent improves the reaction progress; however, the OWR is much faster than the“in solvent” and neat systems.As previously mentioned, OWRs have been reported to occur in many organic experimen-tal procedures. A review by Chanda and Fokin20 gathers examples of “on water” reactivity in31.2. THE “ON WATER” REACTIONQ DMAD ProductSolvent [Q] = [DMAD] (M) Time to completionToluene (homogeneous) 2 >120 hEtOAc (homogeneous) 2 >120 hCH3CN (homogeneous) 2 84 hCH2Cl2 (homogeneous) 2 72 hDMSO (homogeneous) 2 36 hMeOH (homogeneous) 2 18 hneat 4.53 48 hon D2O (heterogeneous) 4.53 45 minon C6F14 (heterogeneous) 4.53 36 hon H2O (heterogeneous) 4.53 10 minMeOH/H2O (3:1, homogeneous) 2 4 hMeOH/H2O (1:1, heterogeneous) 4.53 10 minMeOH/H2O (1:3, heterogeneous) 4.53 10 minTable 1.2: Completion times for the reaction of Q with DMAD in various solvents. Reprinted(adapted) with permission from reference 19. Copyright © 2005 Wiley.ClO 23°C120 hClOHSolvent Conversion [%]Toluene 16DMF 21CH3CN 27MeOH 56neat 73on H2O 100Table 1.3: Comparison of solvent conditions for an aromatic Claisen rearrangement, performed atroom temperature for 5 days. Reprinted (adapted) with permission from reference 19. Copyright© 2005 Wiley.41.3. “ON WATER” REACTIONS AND GREEN CHEMISTRYeleven different types of reactions; specifically in Diels-Alder reactions, 1,3-dipolar cycloadditions,cycloadditions of azodicarboxylates, Claisen rearrangements, Passerini and Ugi reactions, nucle-ophilic openings of three-membered rings, nucleophilic substitutions, transformations catalyzed bytransition metals, metal-free carbon-carbon bond-forming processes, bromination reactions, andoxidation-reduction reactions. Also, recent reviews have focused their attention on the potential ofOWRs for innovative, environmentally-friendly techniques in organic chemistry.16,17,21–251.3 “On Water” Reactions and Green ChemistryAnother feature of OWRs is that the effect is persistent even for reactants dissolved in water-immiscible solvents;19 this is particularly useful for solid reagents that cannot form emulsions withwater. Nonetheless, and due to environmental concerns, the trend in recent years has focused onmoving towards aqueous organic chemistry procedures that avoid the use of any organic solvent.In the specific case of OWRs, the utilization of at least one reactant that is either liquid or whosemelting point is lower than the boiling point of water is necessary to attain emulsification withoutusing other solvents.17In the context of aqueous organic chemistry, some of the principles of green chemistry proposethe following as ideal characteristics of green processes in chemistry:b1. Wherever practicable, synthetic methodologies should be designed to use and generate sub-stances that possess little or no toxicity to human health and the environment.2. The use of auxiliary substances (e.g., solvents, separation agents, etc.) should be madeunnecessary wherever possible and innocuous when used.3. Energy requirements should be recognized for their environmental and economic impacts andshould be minimized. Synthetic methods should be conducted at ambient temperature andpressure.4. A raw material or feedstock should be renewable rather than depleting wherever technicallyand economically practicable.bReprinted (adapted) with permission from reference 26. Copyright© 2002 American Chemical Society.51.3. “ON WATER” REACTIONS AND GREEN CHEMISTRY5. Unnecessary derivatization (blocking group, protection/deprotection, temporary modificationof physical/chemical processes) should be avoided whenever possible.6. Substances and the form of a substance used in a chemical process should be chosen so as tominimize the potential for chemical accidents, including releases, explosions, and fires.“In water” reactions are model candidates for environmentally benign reactions. However, theexploration and comprehension of the chemical reactivity in aqueous solution are still in develop-ment27 and face significant experimental challenges. For instance, some reactants are unstable inthe presence of water, and nonpolar molecules are usually poorly soluble in water. In the lattercase, the use of co-solvents and additional chemical reactions to attach polar groups to the organicsubstrates are common to increase the solubility of reagents in water; nonetheless, doing so goesagainst principles 2 and 5 of green chemistry (listed above). On the other hand, OWRs do notrequire the solubilization of the reagents in water. Also, since reagents in OWRs are insoluble inwater, the purification process of products involves only phase separation or filtration. Moreover,OWRs often generate single products from cycloadditions or condensations, and many of themoccur in mild conditions (room temperature and pressure) and in a short time.28 In other words,OWRs fulfill many of the principles of green chemistry. Therefore, a deeper understanding of OWRswill contribute to the development of more sustainable chemistry procedures. The central goal ofthis thesis is to provide a deeper understanding of OWRs.Gaining insight into the behaviour of water molecules at interfaces, such as those in OWRs,has significant implications in other areas of chemistry. For example, atmospheric chemistry inves-tigations have shown that volatile organic molecules have an affinity for absorption to the surfaceof water droplets in the troposphere, impacting air quality in polluted areas.29,30 Likewise, it hasbeen proposed that chemical evolution might have been accelerated in prebiotic earth due to rapidreactions in clouds.31 Certainly, the role of heterogeneous water chemistry in biochemistry is stillbeing explored and offers explanations for poorly understood phenomena.32 For instance, somestudies have recently suggested that small droplets of water in cells assist biochemical processesthat otherwise are slow or thermodynamically unfavourable,33 and other studies highlight the im-portance of liquid-liquid separation inside eukaryotic cells for the regulation of critical processessuch as RNA metabolism, ribosome biogenesis, DNA damage response, and signal transduction.3461.4. PROPOSED MECHANISMS FOR OWRSOther examples include the biosynthesis of ladder toxins by algal blooms. These toxins are pro-duced in the presence of water with a specific stereochemistry and regioselectivity via a mechanismthat is not yet fully understood.35–38 Due to the ubiquity of water on earth and in living organisms,chemical reactions in the presence of heterogeneous water are of critical importance as it is presentin many natural processes and, it is starting to get more common to be employed in chemistry labsas a reaction medium.24,25 Also, the unusual electrical properties of water interfaces have recentlygarnered interest as potential catalytic systems.39 For the reasons mentioned in this paragraph, itis essential to deepen our understanding of the chemical reactivity of water under heterogeneousconditions.1.4 Proposed Mechanisms for OWRsThere has yet to be developed a coherent theory of the molecular level origins of the effectsobserved in OWRs.20 Initially, Sharpless and coworkers were puzzled by the “on water” effect andcould not provide a definitive explanation. They suggested that hydrophobic effects and hydro-gen bonding near the interface may cause acceleration in reaction rates.19 Shortly after, Jung andMarcus theoretically studied the problem40 by building a model based on the experimental obser-vation that approximately 25% of the surface water molecules have free −OH groups. Quantummechanical simulations of the reaction between Q and DMAD showed that molecular interactionsinvolving these “dangling” −OH groups played a critical role in stabilizing the transition state,resulting in an accelerated rate of reaction in comparison with the neat and “in water” models.Figure 1.1 depicts a simplified version of this model, in which hydrogen bonding between the organicand water phases differentially stabilizes the transition state relative to reactants.Jung and Marcus used a three-water molecule model in their simulations to describe the ac-celeration effect in OWRs, providing an explanation based on energy barrier reductions. However,modelling the interface in OWRs using only three water molecules as a representation of the actualexperimental setting does not reflect condensed phase environments. Therefore, a more complexsystem involving thousands of water molecules was proposed by Thomas and coworkers.41 In theirwork, quantum mechanics/molecular mechanics (QM/MM) Monte Carlo simulations in gas andaqueous conditions were used to explore OWRs. Contrary to the findings of Jung and Marcus,71.4. PROPOSED MECHANISMS FOR OWRSFigure 1.1: Marcus’ model for OWRs. Reprinted (adapted) with permission from reference 21.Copyright © 2020 Wiley.hydrogen bonds at the interface were not found of significant relevance to the increased reactivityin the “on water” effect. Instead, Thomas et al. explained that hydrophobic interactions in wa-ter solution cause an increase in the reaction rates of OWRs. This hydrophobic effect, a criticalfactor in many biological and chemical processes, arises from the tendency of water molecules toexclude nonpolar substances. These findings agree with the initial observations made by Breslowfor reactions “in water” but requires reactants to be soluble in water.12,13Broadly, computational studies on OWRs include reported analyses using QM, QM/MM orCarr Parrinello Molecular Dynamics.40,42–44 These investigations point to hydrogen bonding in theproximity of the interface as the driving force of the “on water” effect. Recent quantum mechanicalcalculations confirmed the role of hydrogen bonding in OWRs by studying small reaction modelsand applying an energy decomposition scheme. The authors rationalized the catalytic effect interms of a charge transfer event between water molecules and organic molecules.45Similarly, only a small number of experimental kinetic investigations on OWRs have been con-ducted. Huck and coworkers46 analyzed the “on water” effect using biphasic fluidic platforms tostudy the reaction between Q and diethyl azodicarboxylate (DEAD), one of the OWR cycload-ditions reported by Sharpless.19 The employed experimental setup, which is shown in Figure 1.2,allows for controlled variation of the oil-water interface area; it was found that increasing the in-terface area produces a linear growth in the conversion percent of the reaction for a given reactiontime. Additional experiments using deuterated water instead of H2O shows a ratio of reaction rateconstants (kH/kD) of 1.1-1.2. Similar experiments loading water into porous silica to control the81.4. PROPOSED MECHANISMS FOR OWRSFigure 1.2: (a) The biphasic fluidic platform Huck et al. used to study the OWR between Q andDEAD. Fo and Fw are the flow rates of the organic and water phases, respectively. (b) Picturesof the experiment when varying the flow rates of the organic and water phases. The water-organicsurface area can be carefully controlled by adjusting Fw/Fo. Reprinted (adapted) with permissionfrom reference 46. Copyright © 2012 Wiley.surface of reaction in OWRs also point to a phenomenon occurring at the water-organic interfacewith a small kH/kD ratio of 1.1.47 When this ratio is close to unity, the reaction is not signif-icantly affected by substituting water for heavy water. We refer to these processes as reactionswith small deuterium kinetic isotope effect (KIE). For the Q+DEAD system, a KIE close to onestrongly suggests that proton transfer processes are not involved in the rate-limiting step of thereaction. The results from the microfluidic experiments suggest that the mechanism occurs via theHB stabilization model of Marcus and Jung.The Marcus model does not explain why some OWRs are considerably slower if heavy wateris used instead of water. This observation led to the hypothesis that proton transfer is involvedin the mechanism of “on water” reactions.48 Figure 1.3 displays the proposed mechanism in which91.4. PROPOSED MECHANISMS FOR OWRSFigure 1.3: Acid-catalysis model with a completely transferred proton. Proton-transfer models forOWRs. Reprinted (adapted) with permission from reference 21. Copyright © 2020 Wiley.water molecules in the aqueous phase transfer a proton to the reactants in the organic phase. Theauthors describe that OH– ions remain at the water surface while the reagents are transformed intoproducts via an acid-catalysis cycle.49 They also argue that the HB stabilization mechanism is notfeasible because dangling −OH groups would, in fact, inhibit the reaction by trapping and immo-bilizing molecules at the interface. The immobilization of reactants at the interface, as explainedby the proponents of the proton transfer mechanism, would prevent reactants from converting intoproducts at the interface.In a 2017 study,50 experimentalists reproduced the cycloaddition between Q and DEAD in“on droplet” assays. The electrospray ionization experiments, performed by Zare and coworkers,generated reaction mixture droplets of around 5 µm. They then quantified the progress of thereaction using mass spectroscopy analysis. The results showed an acceleration factor of 100 timesof “on droplet” runs compared to “on water” conditions; in the context of these experiments, “ondroplet” refers to reactions happening at the surface of water-oil droplets that are much smallerthan the droplets generated by friction in a traditional OWR in a flask with stirring. In “on droplet”reactions, a deuterium KIE of 5 was found. The observed kinetic isotope effect led the authors toconclude that the reaction mechanism must involve a proton transfer reaction.101.5. RECENT PROPOSALS AND DISCUSSION ON OWRS1.5 Recent Proposals and Discussion on OWRsA kH/kD kinetic isotope effect larger than one is often associated with proton transfer reactions;therefore, large KIEs align with a proton transfer (PT) mechanism for reaction acceleration inOWRs.48,51 Nonetheless, the PT mechanism has elements to doubt its validity. For example, itassumes the absorption of hydroxide ions on the presumably basic surface of the water phase.Such an assumption is based on the debated observation that surface water has a higher pH thanbulk water.52–55 Also, it implies the presence of protonated molecules in the organic phase (seeFigure 1.3). While it is reasonable to conceive that a proton transfer from the water moleculesto the organic molecules is possible, a protonated and positively charged molecule will likely haveincreased solubility in water. In such a case, the reaction would proceed mainly as an “in water”(hydrophobic effects) reaction and not as an OWR. Finally, the PT mechanism can explain whysome OWRs display a large KIE but fails to explain reactions with KIE values close to unity.In order to explain the observed discrepancies in KIEs in OWRs, and, in an effort to make aclear distinction between OWRs and “in water” reactions, the solubility of the reagents has beenused as a classification tool. Lower solubility values represent reactions conducted primarily “onwater” whereas higher soluble reagents react in bulk water,17 see Figure 1.4. In an experimentalstudy, Zou and Qu56 modified the solubility of reagents involved in OWRs by attaching increasinglylarger aliphatic chains to the substrates. They found that some reactions were independent of thesolubility of the reactant. In contrast, other reaction rates showed a dependence on reactantsolubility. Those experiments in which the reaction rate was nearly independent of the solubilityof the reagents would likely proceed as pure OWRs, and those showing a rate dependence on thesolubility would proceed as “in water” reactions. For reactions occurring simultaneously via “onwater” and “in water” reactions, the analysis of KIE becomes more complex.It is hard to use solubility as a criterion for classifying organic reactions in the presence of waterbecause, regardless of the solubility of the reactants, molecules can access (to a greater or lesserextent) bulk water. Hence, some reactions may benefit mainly from “on water” catalysis, whileothers may react through a blend of “in water”, “on water” and neat reactivities. For example,for a reactant with a solubility of ≈ 10−5 M, accessing “in water” reactivity would be rare. Onthe other hand, contributions from the three reactivities can be present for a reagent with higher111.5. RECENT PROPOSALS AND DISCUSSION ON OWRSFigure 1.4: Gradual transition to OWRs with decreasing reactant water solubility. Reprinted(adapted) with permission from reference 17. Copyright © 2016 Royal Society of Chemistry.solubility. To avoid confusion, we will refer to OWRs as the collection of processes occurring atthe interface as initially conceived by Sharpless and coworkers.19 Because there is no such thingas absolute insolubility, slightly to sparingly soluble reactants might undergo both “in water” and“on water” catalysis, as depicted in Figure 1.4; this combination of effects makes the study ofOWRs experimentally difficult. For example, Figure 1.5 shows how variations in the solubility ofthe dienophile in Huisgen cycloadditions could induce a reaction to occur via an “in water” or an“on water” mechanism.22 The reactions studied in reference 22, as shown in Figure 1.5, displays anendo:exo ratio of (42:1) with a strong preference for the endo product when using a dienophile witha solubility (s) of 0.27 mol L−1. This ratio is explained in terms of the hydrophobic associationof molecules in bulk water. In contrast, if a dienophile with s = 0.016 molL−1, the endo:exo ratiodecreases to (8.2:1), suggesting that the molecules can no longer access “in water” reactivity. For areaction occurring at the interface (OWR), the organic molecules can approach the water interfacefrom different orientations and the endo:exo ratio decreases.As already explored in this chapter, an increasing number of organic reactions happening in thepresence of water have consistently been reported in the literature in recent decades23–25,27 and theline between homogeneous and heterogeneous reactions is hard to draw. While Butler and Coyne’ssolubility-based classification of reactions17 may differentiate between “in water” and “on water”reactivity in some cases, the classification is hard to use for reactions with multiple componentswith different solubilities. The dearth of accurate data available for the solubility of immisciblereagents makes it difficult to determine to what extent a reaction occurs via an “in water” or “onwater” mechanism. Terms such as “on water”, “at water”, and “aqueous,” for example, have been121.5. RECENT PROPOSALS AND DISCUSSION ON OWRS8.2:142 : 1 Figure 1.5: “In water” and “on water” reactions. Solubility is represented with the letter “s.”Reprinted (adapted) with permission from reference 22. Copyright © 2015 American ChemicalSociety.used to describe organic reactions in a water medium without any clear definition, thus addingto the confusion around the “on water” mechanism discussion. The lack of clarity on OWRsmotivated Kitanosono and Kobayashi21 to name all the collective of organic reactions involvingwater as “reactions in water” and then subclassify them into different categories. Under theirclassification, the entirely homogeneous “in water” reactions and OWRs are encompassed, alongwith other cases where the reaction mixtures contain solids, surfactants or catalysts. Within thiscontext, the authors suggest that the term “on water” mechanism should be used only when theuse of water as a heterogeneous reaction medium results in an increased rate in comparison withthat in organic solvents or neat conditions; this is the vision that we will adopt for the rest of thethesis.Kitanosono and Kobayashi included the concept of catalyst21 in their classification of reactionsoccurring in aqueous media. They argued that this was an essential missing piece in the studyand understanding of reactions in aqueous media. It is true that the cycloadditions reported in200519 do not explicitly use the word catalyst; however, their broad definition of OWRs as insolublereactants stirred in aqueous emulsions or suspensions without the addition of any organic cosolventimplicitly involves reactions using catalysts, such as the reactions catalyzed by transition metalsreviewed by Chanda and Fokin.20 The catalyst-free reactions that benefit from the effects of thewater-oil interface, within Kitanosono’s classification, can be regarded as an accelerated reactions inwhich interfacial water molecules act as catalysts. This view is supported by recent computational131.5. RECENT PROPOSALS AND DISCUSSION ON OWRSFigure 1.6: Comparison between (a), a typical bifunctional catalyst in synthetic organic chemistryand, (b) and (c), where water molecules reduce the barrier height in the formation of H2SO4.The nucleophiles, electrophiles and the catalysts are displayed in red, blue and green, respectively.Reprinted (adapted) with permission from reference 57. Copyright© 2017 Royal Society of Chem-istry.studies where water molecules were shown to behave as bifunctional catalysts due to their abilityto reduce barrier heights in the formation of acid rain or the hydrolysis of oxiranes.57,58 Figure 1.6shows how water molecules, highlighted in green, behave similarly to a bifunctional organocatalyst,which is an organic molecule with at least two functional groups which interact with substrates tohelp promote reactions. Hence, for OWRs, even in the absence of organic or metallic catalysts,the original definition of OWRs is still compatible with the concept of catalyst if we look at watermolecules as catalysts. In this work, water molecules are seen as catalysts.Reactions in the literature are often reported as OWRs because they use the general definitionproposed by Sharpless and coworkers.19 In other words, if an acceleration effect (relative to the neator organic solvent reactions) is observed when carrying out the reaction in a water-oil emulsion, it isan OWR. This broad classification causes problems and leads to a lack of clarity when explaining theorigin of the rate acceleration effect. The apparent rate acceleration of some reactions in aqueousemulsions can be attributed to factors unrelated to the interface, such as side-reaction suppression,18and still be classified as an OWR. In an attempt to clarify the definition and correct classificationof OWRs, Kitanosono and Kobayashi define the “on water” mechanism as a process relying onhydrogen bonding at the water-oil interface, causing an acceleration effect in the reactions whencompared to their counterparts in organic solvents or neat conditions. To illustrate this, Figure1.7 displays a Mukaiyama aldol reaction carried out in a diverse set of solvent conditions.59 Inthis study, the authors found that the presence of fluorine in the substrates, a hydrogen bondingacceptor, is necessary to observe rate acceleration in heterogeneous systems. This “on water”mechanism definition is more precise and eliminates the possibility of misclassifying OWRs that141.5. RECENT PROPOSALS AND DISCUSSION ON OWRSFigure 1.7: Mukaiyama aldol reaction in OWR conditions. If X=F, the reaction is completed in10 hours (85% yield). If X is Cl or H, the reaction yield is negligible after 24 hours.59 Reprinted(adapted) with permission from reference 59. Copyright © 2014 Wiley.are accelerated due to other effects. To summarize, an OWR is an accelerated reaction, relativeto the neat or organic solvent conditions, that occurs via an “on water” mechanism as defined byKitanosono and Kobayashi.“In water” reactions have widely been explored;60–62 the effects governing their reactivity aredescribed in terms of activation of pre-reaction complexes due to hydrophobic association of organicmolecules, which tend to aggregate in water solution. On the other hand, studies of organic reactionsin water emulsions,46,47,50,63,64 have proven that the water-oil interface is responsible for the rateacceleration effect and, to the best of our knowledge, just two models trying to explain the “onwater” mechanism were discussed in the literature over the past years.40,48 In Figure 1.1, thedangling −OH model explains the acceleration effect through differential stabilization of transitionstates over reactants via hydrogen bonding. In contrast, Figure 1.3 displays the proton-transfermodel, which attempts to explain the relatively high kinetic isotope effect (KIE), kH/kD, that someaccelerated reactions show.Although it is clear that the rate acceleration effects originate in the water-oil interface, todate, there is no agreement on, or clear understanding of, the molecular origin of the “on water”mechanism. In particular, the discrepancies in the observed KIE in different reactions and differentexperimental setups of the same reaction cast doubt on both the HB and the PT models. Variousexamples of accelerated “reactions in water”, which likely benefit from the “on water” effect, showKIE values that range from 1.01 to 5. Specifically, it is argued that the dangling model is incom-patible with the presence of catalysts and unable to explain the KIE.21 On the other hand, theproton-transfer mechanism contains serious deficiencies. For example, it cannot explain reactionsin which the KIE is absent, and it is not compatible with the use of basic substrates or acid/basecatalysts.21 Most importantly, the proton-transfer mechanism is founded on the assumption that151.5. RECENT PROPOSALS AND DISCUSSION ON OWRSFigure 1.8: “On water” mechanism model proposed by Kitanosono and Kobayashi. Reprinted(adapted) with permission from reference 21. Copyright © 2020 Wiley.the water surface is basic, an idea that was proven wrong in 2012.65 These inconsistencies led tothe proposal of a new “on water” mechanism model, shown in Figure 1.8. In this new model,the authors describe:c “interfacial water molecules would undergo partial polarization due to a lossof balance between donation and acceptance of hydrogen bonding via the Grotthuss mechanism atthe interface. Collective dipole orientation fluctuations would recognize reactants and catalysts ina fixed orientation through weak interactions and facilitate the formation of highly oriented tran-sition states.” 21 The model also describes three water layers: water molecules oriented to releaseprotons toward the oil phase (inner Helmholtz layer), those surrounded by a secondary layer (outerHelmholtz layer), and bulk water. An explanation of how organic molecules respond to the col-lection of water dipoles is provided to describe the KIE in OWRs. However, it is unclear howthe model differentiates the reactivity seen in OWRs from that of “on heavy water” reactions. Inparticular, the model does not provide an explanation of the role of each of the water layers orwhy the first layer releases protons toward the oil phase. The Kitanosono and Kobayashi model isinspired by a theoretical and experimental study of the interaction between water molecules andceramides,66 and the Bockris-Devanathan-Muller (BDM) model for solid-fluid systems.67To the best of our knowledge, the model for the “on water” mechanism by Kitanosono andKobayashi has not been explored, either experimentally or theoretically. It is noted that the BDMcReprinted (adapted) with permission from reference 21. Copyright© 2020 Wiley.161.6. ORGANIC REACTIONS PROMOTED BY ELECTRIC FIELDSmodel, which is often applied to solid-fluid interfaces to study the adsorption of solvents intoelectrodes, may not reflect the actual dynamical conditions of OWRs. In a laboratory setting, thewater-oil interface is constantly perturbed by the continuous movement of a stirred reaction andmight not necessarily maintain a multilayered structure over the course of the reaction.Returning to the initially proposed mechanism, the dangling−OHmodel is not inconsistent withthe presence of a catalyst. Nothing prevents the further stabilization of reactant-catalyst transitionstates by hydrogen bonding at the water-oil interface. Besides, it is worth mentioning that, inthe context of OWRs, the macroscopic physical properties of H2O and D2O have not been widelydiscussed in the literature, except for the original paper by Jung and Marcus.40 They explained,within the dangling −OH model context, that a KIE of 5-7 is usually associated with protontransfer reactions or larger if there is H-tunneling. However, instead of focusing on the possibilityof a H+ transfer, they suggested that the isotope effect in some reactions could arise from thehigher viscosity of heavy water, causing a change in the surface of water droplets in the emulsion.Another overlooked aspect of the “on water” mechanism discussion is that many of the reported“on water” accelerated organic reactions can occur via multiple steps. In a multi-step reaction,the slowest step of the mechanism often determines the kinetics of the reaction; but it can also bethe case where a reaction has multiple slow steps, complicating the study of OWRs. Identifyingthe rate-limiting step of an OWR is crucial to study the mechanism properly. To illustrate thispoint, a PT reaction is necessary for one of the steps in the Copper(II)-catalyzed addition reactionsdepicted in reference 68; while one would expect a KIE greater than 1, the reaction shows a KIEof 1.01. This result can be explained by understanding that the reaction rate-limiting step doesnot involve such a proton-transfer step, a fact clearly explained by the authors.68 In short, thevariety of KIE values in OWRs can also be rationalized in terms of a composite effect in complexmechanisms. Therefore, the model reactions to be tested for OWRs should have a well-definedrate-limiting reaction step.1.6 Organic Reactions Promoted by Electric FieldsBefore discussing the research motivation and hypothesis of this thesis, an overview of a topicseemingly unrelated to OWRs will be presented.171.6. ORGANIC REACTIONS PROMOTED BY ELECTRIC FIELDSFigure 1.9: For a reaction to benefit from field catalysis, the external electric field must align withthe bond (or bonds) that are being formed or broken.71 Reprinted (adapted) with permission fromreference 71. Copyright © 2020 American Chemical Society.In 2010, the research group of Sason Shaik showed, through quantum mechanical calculations,that an oriented external electric field applied to the Diels-Alder reaction can lower its energybarrier, suggesting that electric fields can function as a catalyst.69 This was corroborated yearslater using scanning tunnelling microscopy. In this experimental investigation,70 the authors studiedDiels-Alder reactions at the single-molecule level and confirmed that external fields could catalyzethe formation of carbon-carbon bonds in organic reactions, a feature believed to be achievable onlyfor redox systems.So that an electric field can efficiently reduce the energy barriers in an organic reaction, sucha field must align with bonds being formed or broken, as depicted in Figure 1.9. Unfortunately,in practice, it is difficult to control and align an electric field with an organic molecule in solutionbecause the strong directionality of the field is quenched.70 A controlled local environment is neces-sary, such as the one some enzymes utilize to catalyze reactions, where active sites use electrostaticeffects to harness electric field catalysis in an effective manner.72 Another example of the use ofelectric fields to control reactivity is given in reference 73, where the authors were able to controlthe direction of the growth of organic nanostructures in a silicon surface by applying a constantexternal field into the reaction surface. In summary, under certain conditions, it is possible toharness field catalysis by creating strong local electric fields with charged catalysts, substrates andfunctional groups.In recent years, there has been an increasing interest in studying the properties of interfa-cial water, in specific how water surfaces respond to external electric fields74,75 and how electricfields naturally arise at water interfaces.76,77 The chemistry of interfacial water molecules has been181.7. RESEARCH MOTIVATION AND HYPOTHESISFigure 1.10: Interfacial water molecules display an excess of charge when compared to bulk water,this translates to an increased electric field at the water-air interface.39 Reprinted (adapted) withpermission from reference 39. Copyright © 2022 Springer Nature.compared to the effects observed in reactions in confined environments (e.g. micellar catalysis,reactions in porous materials and nanostructures, etc.),78 where partial solvation leads to strongelectrostatic effects. Also, in the past few years, there has been growing interest in understandingthe relationship between the strong field effect at water interfaces and its ability to accelerate re-actions. In particular, Teresa Head-Gordon and her research group computationally estimated themagnitude and direction of the electric fields at the air-water interface in microdroplets models.39The computed electric fields displayed a strong and localized perpendicular orientational preferencenear the water-air interface and an excess of charge density in the same region (see Figure 1.10).The authors suggested that the features of the electric field at the interface result in a type ofelectrostatic pre-organization at the interface that facilitates the alignment of reactant moleculeswith the electric field in a way that could drive faster chemical reactions at the air-water interface.These results suggest that the development of oil-water interfaces could create electrostatic fieldsthat catalyze OWRs.1.7 Research Motivation and HypothesisAccording to the current literature, OWRs may experience higher rates through the utilizationof hydrogen bonds, proton transfer reactions, dipole orientations, or charge transfers. To thiscomplexity, there are added contradictory data regarding the KIE in OWRs (contrast references46 and 50) and computational investigations which have not reached an agreement regarding theorigin of the OWR effect.39–41,45 Even in light of the preceding, we can state the following:191.7. RESEARCH MOTIVATION AND HYPOTHESIS1. Reactions showing “on water” acceleration involve organic molecules that can engage in hy-drogen bonding with water.2. Water interfaces have dangling−OH bonds (i.e. −OH bonds that are not involved in hydrogenbonds); therefore, there is an opportunity for hydrogen bonding to differentially stabilize TSsat the interface.3. The formation of a hydrogen bond is a prerequisite for a proton transfer reaction.4. Water interfaces generate large electric fields; electric fields may significantly influence reac-tivity.Hence, it is hypothesized that the acceleration effect in OWRs relates to both hydrogen bondingstabilization of transition states and the presence of strong electric fields at the water-oil interface.Hydrogen bonding at the interface holds reactants in close proximity to the electric field, therebyallowing the electric fields to induce further stabilization of the transition state. A schematic rep-resentation of this mechanism is depicted in Figure 1.11. Our hypothesis is aligned with the obser-vation that approximately 25% of surface water molecules contain a dangling −OH group towardsthe hydrophobic phase,79,80 a feature suggesting that hydrogen bonding interactions between theorganic molecules and the water phase are possible. It is also proposed that the apparent deuteriumKIE arises from physical (i.e. viscosity) differences between H2O and D2O, as originally describedby Jung and Marcus.40 The isotope effect arises from differences in the physical properties of D2Oand H2O; water is roughly 25% less viscous than heavy water; therefore, the D2O will require morework to generate an emulsion with the same reactive-surface area than regular water. With regardsto the PT mechanism, there are reasons to doubt it; however, a proton transfer reaction, if possible,should necessarily originate from an initial hydrogen bonding.As described in this chapter, OWRs permeate different areas of chemistry; their relevance inunderstanding new reactivities is crucial, especially in the areas of biochemistry, atmospheric andgreen chemistry. Also, due to the challenges involved in studying water-oil systems experimentally,computational methods are a promising means of providing insights into the “on water” mechanism.The main goal of this thesis is the study and elucidation of the complex aspects of the reactionmechanisms involving OWRs in organic chemistry, taking the hydrogen bond between organic201.7. RESEARCH MOTIVATION AND HYPOTHESISFigure 1.11: Proposed mechanism for OWRs based on hydrogen bonds and electric fields. Theshaded blue area represents space region with strong electric fields.and water molecules as central to OWRs. Hydrogen bonds serve as channels for charge transfer,and their formation induces preferential orientation: hence, molecular alignment in the electricfield of the reaction medium for catalysis. For the described goals of this thesis, we employedcomputational chemistry tools such as electronic structure methods and molecular mechanics, asdescribed in the next section. The results of this thesis provide essential insights into the poorlyunderstood chemistry of heterogeneous water systems.21Chapter 2Theoretical Background and MethodsThe present chapter deals with the theory and the computational tools used in this thesis tostudy the “on water” mechanism. We do so by first exploring the generalities of quantum mechanics(QM) and then moving into classical molecular dynamics (MD).2.1 Quantum MechanicsAt the end of the 19th century, the black body radiation experiment proved to be pivotalin the history of physics; it represented a phenomenon that could not be explained in terms ofthe available science. At that time, important milestones in science were achieved. The successfulapplication of Newton’s laws by Hamilton and Lagrange for the prediction of planetary movements,the complete and still valid foundations of thermodynamics, Maxwell’s prediction of the wave-likenature of light, among other remarkable works, made many scientists believe that most of thefundamental features of nature were fully understood.81 Nonetheless, the physics of those days, orclassical physics as they are known nowadays, were insufficient to describe the black body radiationproblem.82 Classical physics predicted that the intensity of the black body radiation would divergeat high frequencies; meanwhile, experimental measurements disagreed by showing an asymmetricalGaussian behaviour of the radiation’s intensity as a function of the frequency. To explain thisodd result, Max Planck introduced the hypothesis that atoms can only emit energy in the form ofdefined energy packages, hν, where h is Planck’s constant and ν is the frequency of the radiation.83The quantization of energy not only reproduced the radiation spectra of the black body but wasalso the first step toward the development of the quantum theory.Quantum mechanics was built over the first thirty years of the 20th century. It is often referredto as the theory that describes phenomena at the level of electrons, nuclei, atoms, and moleculesor, more generally, where classical mechanics otherwise fails. F.S. Levin goes further and defines222.1. QUANTUM MECHANICSquantum mechanics as the theoretical framework that describes physical phenomena in situationsin which Planck’s constant is not negligible.84 This theory is formulated in a set of postulates, andits central point relies upon the Scho¨dinger equation (SE).85,86 The SE for a single particle of massm in one dimension has the following form:iℏ∂∂tΨ(x, t) = Ĥ (x, t)Ψ (x, t) , (2.1)whereĤ = − ℏ22m∂2∂x2+ V (x, t) (2.2)represents the Hamiltonian operator, with ℏ = h/2π. Ψ (x, t) is the wavefunction of the system,which according to the first postulate of quantum mechanics, fully describes the state of the sys-tem.82 While Ψ (x, t) does not have physical meaning itself, its statical interpretation allows us topredict that the probability of finding a particle in an interval of space is87∫ ba|Ψ(x, t)|2 dx = A, (2.3)where A is proportional to the probability of finding the particle between a and b at a certain timet. For a normalized wavefunction, if a = −∞ and b = ∞, then A = 1. The fact that Ψ (x, t) issquare-integrable means that the particle can be found with certainty over all the space.For a particle of mass m under a time-independent potential V (x), we can write a wavefunctionsuch that83Ψ(x, t) = f (t)ψ (x) . (2.4)By substitution of Equation 2.4 into Equation 2.1, we get f (t) = exp(−iEt/ℏ) and the time-independent Schro¨dinger equation:[− ℏ22md2dx2+ V (x)]︸ ︷︷ ︸Ĥ(x)ψ (x) = Eψ (x) . (2.5)232.2. QUANTUM CHEMISTRYWhere E is the energy of the system. An immediate consequence is that|Ψ(x, t)|2 = |ψ (x)|2 , (2.6)which implies that the probability density remains unchanged over time. Systems behaving inthis manner are known as stationary states and arise from considering potential energies that areindependent of time, such as those present in molecular systems. It turns out that the wavefunctionsof atoms and molecules are stationary states that define the electronic structure of matter, as willbe discussed in the next section. From now on, when we refer to the Schro¨dinger equation, we willbe referring to the time-independent version of it.2.2 Quantum ChemistryIt is possible to represent an atom or molecule as a collection of N electrons (i) and M nuclei(A). We can use the coordinates ri and RA to describe the positions of electrons and nuclei,respectively. Then, the Schro¨dinger equation can be written asĤψ ({ri} , {RA}) = Eψ ({ri} , {RA}) , (2.7)with the Hamiltonian defined by (in SI units)Ĥ = −N∑iℏ22me∇2i︸ ︷︷ ︸T̂e−M∑Aℏ22mA∇2A︸ ︷︷ ︸T̂n−N∑iM∑Ae2ZA4πε0riA︸ ︷︷ ︸V̂en+N∑iN∑j>ie24πε0rij︸ ︷︷ ︸V̂ee+M∑AM∑B>Ae2ZAZB4πε0rAB︸ ︷︷ ︸V̂nn. (2.8)In this equation, me is the mass of an electron, mA the mass of a nucleus A, ∇2α the Laplacian ofparticle α (i or A), ε0 the vacuum permittivity, e the electron charge, ZA the nuclear charge associ-ated to the nucleus A, and rαβ the distance between particles α and β; for example, for an electroni and nucleus A, riA = |ri −RA|. Equation 2.7 is known as the non-relativistic time-independentSchro¨dinger equation and takes into account the kinetic energies of electrons and nuclei (T̂e and T̂n,respectively), as well as the potential energy terms related to electron-nucleus attractions (V̂en),electron-electron repulsions (V̂ee), and nucleus-nucleus repulsions (V̂nn). All of these terms are242.2. QUANTUM CHEMISTRYidentified in Equation 2.8. In certain situations, this Hamiltonian will need additional terms,88 forinstance, in molecular systems with significant relativistic effects or in cases where the system isunder the influence of an external field.The center of quantum chemistry (QC) is Equation 2.7, for which an exact solution can onlybe achieved for monoelectronic atoms and molecules.89 In a way, QC can be regarded as thefield that finds approximate solutions to the polyelectronic Schro¨dinger equation and applies themto relevant problems in chemistry. This endeavor is a numerical task that is highly demanding,so most initial applications were limited to systems with only a few atoms and electrons undercrude approximations; naturally, this discipline continues to evolve in parallel with the evolutionof computers.Quantum chemistry is often employed to complement or explain experimental results and fre-quently provides insight into phenomena where experiments are not feasible. Nowadays, QCmethodologies are routinely used to predict molecular structures, spectroscopic properties, reactionthermodynamics, and kinetics, to mention a few properties. The following subsections introduceand discuss some of the approximations to the Schro¨dinger equation beyond monoelectronic sys-tems; these methodologies constitute the base of QC and are utilized in this work to explore theOWR mechanism in this thesis.2.2.1 The Electronic Hamiltonian and the Born-Oppenheimer ApproximationIn atoms or molecules, electrons move much faster than the nuclei because the former is muchlighter than the latter. To a certain degree, the movement of electrons can be deemed independentof the nuclei motion. Thus, the Hamiltonian in Equation 2.8 can be separated in nuclear andelectronic terms, i.e. Ĥ = Ĥe + Ĥn, whereĤe = −12N∑i∇2i −N∑iM∑AZAriA+N∑iN∑j>i1rij, (2.9)is the electronic Hamiltonian in atomic units, and Ĥn = T̂n + V̂nn, as per indicated in Equation2.8. Ĥe considers electrons moving around fixed nuclei. This process of artificially separatingthe movement of nuclei and electrons is known as the Born-Oppenheimer approximation,90 andreduces the polyelectronic (N) and polynuclear (M) Schro¨dinger equation from an (N+M)-particle252.2. QUANTUM CHEMISTRYproblem to an N -particle problem. Equation 2.7 with Ĥe then becomesĤe |ψe⟩ = Ee |ψe⟩ , (2.10)where we now adopt Dirac’s notation.91 The wavefunction, ψe, explicitly depends only on thecoordinates of the electrons. Since the nuclei are not moving, the repulsion between them is aconstant term that can be added to the electronic energy to obtain the total energy of the system:Etot = Ee +M∑AM∑B>AZAZBrAB. (2.11)If we solve the electronic Schro¨dinger equation for a system with more than one nucleus andsubsequently evaluate Equation 2.11, we will obtain Etot for a single geometry of the system. Byrepeating this process for different spacial arrangements of the nuclei until all possible geometriesare explored, we define the potential energy surface (PES), an important concept in computationalchemistry that helps us find optimal structures (minima or transition states) for arbitrary molecules.Because valuable information for chemists is available within ψe, much of the efforts in quantumchemistry are put into solving Equation 2.10. In general, we can assume that the Born-Oppenheimerapproximation is valid: in H2, for example, use of the approximation introduces an error in thetotal electronic energy on the order of 10−4 atomic units. The error becomes smaller as the nuclearmasses increase.922.2.2 The Electronic Wavefunction and the Hartree-Fock MethodThe electronic Hamiltonian described in Equation 2.9 can be rewritten asĤe =N∑iĥ (ri)︸ ︷︷ ︸monoelectronic+N∑iN∑j>iĝ (ri, rj)︸ ︷︷ ︸bielectronic, (2.12)where we have separated the operator into their one and two-electron terms. Namely, inĥ (ri) = −12∇2i −M∑AZAriA, (2.13)262.2. QUANTUM CHEMISTRYandĝ (ri, rj) =1rij=1|ri − rj | . (2.14)The latter represents the electron-electron repulsion, a problem for which an exact solution has yetto be found. If the electron-electron repulsion is neglected, the Schro¨dinger equation becomes aseparable eigenfunction problem where solutions have the formĥ (ri)ψi (ri) = ϵiψi (ri) , (2.15)where ψi (ri) is a spatial orbital with an associated energy ϵi. However, to fully describe the natureof an electron, it is necessary to introduce its spin coordinate:ĥ (ri)ψi (ri)σ (ωi) = ϵiψi (ri)σ (ωi) , (2.16)with σ (ωi) = α (ωi) or β (ωi), representing the orthonormal functions spin “up” and spin “down,”respectively. For an arbitrary i number of spatial orbitals, it is possible to build twice as manyfunctions as follows{χj (rj , ωj)} =ψ j2+ 12(rj)α (ωj) if j is oddψ j2(rj)β (ωj) if j is even,(2.17)where, j runs from 1 to 2i. χj are known as spin orbitals, and they are also eigenfunctions of themonoelectronic operator in the electronic Hamiltonian, i.e.ĥ (i) |χj (i)⟩ = ϵj |χj (i)⟩ , (2.18)adopting Dirac’s notation.91 The equations presented in this subsection represent the exact solutionto the Schro¨dinger equation for the hydrogen atom and can be applied to atoms and molecules withonly one electron, obtaining near-experimental accuracy. For polyelectronic systems, neglectingelectron-electron repulsion leads to an inadequate description of electronic structure. The resultingspin orbitals, however, constitute a starting point for constructing approximate wavefunctions thatpartially recover the contributions of Equation 2.14, as will be shown in the following paragraphsfor the Hartree-Fock method.272.2. QUANTUM CHEMISTRYFor a collection of N electrons, we can place electron 1 in the spin orbital χ1, electron 2 in χ2,electron 3 in χ3, and so forth until the last electron N is in the spin orbital χN . The multiplicationof these occupied spin orbitals leads to a N -electron wavefunction that has the following form∣∣ψHPe 〉 = N∏i|χi⟩ , (2.19)this wavefunction is known as the Hartree product (HP).93 The HP represents a system withindependent electrons that do not interact with each other.∣∣ψHPe 〉 is also an eigenfunction ofthe monoelectronic HamiltonianN∑iĥ (i) with an eigenvalue equal to the adding of all of the spinorbital energies: ϵ1+ ϵ2+ · · ·+ ϵN . The HP has the deficiency of not being antisymmetric upon theinterchange of space and spin coordinates of two given electrons; that is, the Hartree product doesnot change its sign when any two electrons exchange their spatial and spin coordinates, leading todistinguishing between electrons.Building upon the HP, different physicists working on the foundations of QM independentlyproposed the use of determinants for polyelectronic wavefunctions:94–96∣∣ψSDe 〉 = (N !)− 12 det |χ1χ2 . . . χN | = |χ1χ2 . . . χN ⟩ , (2.20)where SD stands for Slater determinant after one of the proponents97 of using determinants forbuilding electronic wavefunctions. The factor involving N before the determinant is a normalizationconstant; it is usually implied and∣∣ψSDe 〉 is often just written as it is shown in the right-hand side ofEquation 2.20. Determinants have the property of changing their sign upon the exchange of rows:this is equivalent to exchanging the space and spin coordinates of any two electrons,|. . . χm . . . χn . . . ⟩ = − |. . . χn . . . χm . . . ⟩ . (2.21)In other words, a Slater determinant is an antisymmetric wavefunction as required by quantummechanics. A determinant with two identical rows has a value of zero; if two electrons occupy thesame spin orbital, the wavefunction becomes zero, which is a generalization of Pauli’s exclusionprinciple.98 The Slater Determinant is the simplest antisymmetric wavefunction for an N -electronsystem.282.2. QUANTUM CHEMISTRYNow, the Variation Principle, a central theorem in quantum chemistry, states that any approx-imate wavefunction, such as a Slater determinant, will have an expected value for the Hamiltonianthat is higher than the exact ground state energy. A detailed derivation of the previous statementcan be found in references 87 and 89. The Hartree-Fock (HF) energy then is defined as the expectedvalue of the electronic Hamiltonian using a Slater determinant as the trial function, as shown inthe following equation,EHF =〈ψSDe∣∣∣Ĥe∣∣∣ψSDe 〉=N∑i〈χi (1)∣∣∣ĥ (1)∣∣∣χi (1)〉+12N∑iN∑j[〈χi (1)∣∣∣Ĵj (1)∣∣∣χi (1)〉− 〈χi (1) ∣∣∣K̂j (1)∣∣∣χi (1)〉] .(2.22)By taking advantage of the indistinguishability of electrons, the sums in the previous equation aredone over spin orbital rather than over electrons. The Coulomb operator, Ĵj (1), is defined by itsaction into a spin orbital:Ĵj (1) |χi (1)⟩ = ⟨χj (2) |ĝ (1, 2)|χj (2)⟩ |χi (1)⟩ . (2.23)The interpretation of this operator relies on the form of the operator, which averages the electronicrepulsion of an electron in a spin orbital i with the rest of the electrons in the other spin orbitals.The name of the operator comes from the resemblance with the classical term associated withCoulombic electrostatic potentials. Likewise, K̂j (1) is an operator that, when acting into a spinorbital is written asK̂j (1) |χi (1)⟩ = ⟨χj (2) |ĝ (1, 2)|χi (2)⟩ |χj (1)⟩ . (2.24)Unlike the coulomb operator, this operator does not have a classical analog and arises from theantisymmetric nature of the Slater determinant. This operator is referred to as the exchangeoperator since it involves swapping the spin orbitals for electrons 1 and 2 on the right of thebielectronic operator in the coulomb operator.The HF is then, according to the Variational Principle, an upper bound to the exact electronic292.2. QUANTUM CHEMISTRYenergy, Ee,EHF ≥〈ψe∣∣∣Ĥe∣∣∣ψe〉 = Ee, (2.25)where ψe is the exact wavefunction. Under the Variational Principle, minimizing EHF by systemat-ically improving the spin orbitals will improve the approximate wavefunction. For this endeavour,the employment of Lagrange multipliers is used:L [{χi}] = EHF [{χi}]−N∑iN∑jϵij (⟨χi | χj⟩ − δij) . (2.26)Since we are minimizing the energy subject to the condition of the spin orbitals being orthonormal,i.e. ⟨χi | χj⟩ = δij , the second term in the right-hand side of Equation 2.26 will be zero. Thus,the Lagrangian, L, a functional of the spin orbitals, will share the same minima as the HF energy.Setting δL = 0 leads tof̂ |χi⟩ = ϵi |χi⟩ , (2.27)where f̂ is known as the Fock operator,f̂ = ĥ+∑j[Ĵj − K̂j]. (2.28)Equation 2.27 is a pseudo-eigenvalue problem where the Fock operator depends on the same spinorbitals, χi, that we are trying to find. In order to solve such an equation, an iterative method isnecessary. This procedure is called self-consistent field (SCF).99Attempting to directly solve Equation 2.27 through a numerical method is not practical. Forthis reason, Roothaan100 and Hall101 introduced the use of a known finite set of basis functions,ϕν , to build the spin orbitals. That is|χi⟩ =∑νCµi |ϕν⟩ , (2.29)where Cµi are the coefficients for the expansion of χi.Equation 2.27 becomesf̂∑νCνi |ϕν⟩ = ϵi∑νCνi |ϕν⟩ . (2.30)302.2. QUANTUM CHEMISTRYProjecting the ket ⟨ϕµ| into this equation leads to∑νCνi〈ϕµ∣∣∣f̂ ∣∣∣ϕν〉︸ ︷︷ ︸Fµν= ϵi∑νCνi ⟨ϕµ | ϕν⟩︸ ︷︷ ︸Sµν, (2.31)where Fµν and Sµν are elements of the Fock and overlap matrices, respectively. The previousequation is compactly written in its matrix form asFC = SCϵ. (2.32)This set of equations can be solved using standard matrix techniques;89 the SCF problem is re-duced from calculating the actual spin orbitals to optimizing a set of coefficients in the matrix Cuntil the iteration converges, then the spin orbitals are trivially generated by means of Equation2.29. Nowadays, this approach is widely used in generic electronic structure software102,103 andconstitutes a starting point for more sophisticated methods to solving the electronic structure ofpolyelectronic systems.2.2.3 Electronic Correlation and Post-HF MethodsOptimizing a Slater determinant wavefunction through a self-consistent field method is oftenreferred to as the Hartree-Fock method. The resulting wavefunction has its limitations; first of all,the basis set employed to span the spin orbitals is a finite set where ideally, a complete (i.e. infinite)basis set should be used. In terms of computational resources, only a finite basis set can be feasiblyemployed in calculations, so there is commonly an error associated with the incompleteness of thebasis set functions, the Basis Set Incompleteness Error (BSIE).104 Using an SD wavefunction is thesimplest way to describe the antisymmetric wavefunction of a polyelectronic system, but it has itslimitations. In ψSDe , it can be shown that the movement of electrons with parallel spin is correlated,whereas the movement with opposite spins is not. Even in the scenario where we utilize a completebasis set (CBS), the inherent nature of Slater determinants, that partially recovers the interactionbetween electrons in an average way, would not lead to the exact electronic energy. Therefore, thecorrelation energy, Ecorr, is defined as the difference between the exact energy and the HF energy312.2. QUANTUM CHEMISTRYat the CBS limitEcorr = Eexact − EHF/CBS. (2.33)The Hartree-Fock approach serves as the starting point for subsequent methods to estimate the cor-relation energy. Computational techniques for calculating the correlation energy using the Hartree-Fock wavefunction are named post-HF methods. In the following paragraphs, some of these post-HFmethods will be discussed. Specifically, the Møller-Plesset perturbation theory,105,106 the config-uration interaction method,107,108 and the coupled-cluster theory109,110 will be described. Theformulations of the foregoing theories are well-known and can be found in many books on quantumchemistry, such as those in references 88, 89 and 92One of the procedures to estimate Ecorr employs Rayleigh and Schro¨dinger’s perturbation theory.Under this mathematical procedure, the complete Hamiltonian, the “perturbed” one, is written asĤλ = Ĥ + λĤ′. (2.34)Here, λ is a parameter controlling the perturbation (Ĥ ′), and the unperturbed Hamiltonian, Ĥ hassolutions we already know:Ĥ∣∣∣ψ(0)〉 = Λ(0) ∣∣∣ψ(0)〉 . (2.35)However, we are interested in the solutions to the perturbed state,Ĥλ |ψλ⟩ = Λ |ψλ⟩ . (2.36)An approximate solution to this equation can be obtained by expressing the perturbed Hamiltonianin terms of equation 2.34, and expanding ψλ and Λ in their corresponding Taylor series:(Ĥ + λĤ ′) ∞∑i=0λi∣∣∣ψ(i)〉 = ( ∞∑i=0λiΛ(i)) ∞∑i=0λi∣∣∣ψ(i)〉 . (2.37)Grouping terms with common λi coefficients give us equation 2.35 and, for k > 0, it leads to the322.2. QUANTUM CHEMISTRYfollowing general equation,Ĥ∣∣∣ψ(k)〉+ Ĥ ′ ∣∣∣ψ(k−1)〉 = k∑j=0Λ(j)∣∣∣ψ(k−j)〉 . (2.38)By imposing the intermediate normalization,〈ψλ | ψ(0)〉= 1, which implies〈ψ(i) | ψ(0)〉 = δi0, weobtainΛ(0) =〈ψ(0) | Ĥ | ψ(0)〉, (2.39)which we already know from equation 2.35, andΛ(k) =〈ψ(0) | Ĥ ′ | ψ(k−1)〉, (2.40)which depends on the perturbation.In Møller-Plesset perturbation theory, Ĥ is selected to be the sum of the Fock operators for allelectrons,Ĥ =N∑if̂ (i) =N∑iĥ (i) + N∑j[Ĵj (i)− K̂j (i)] , (2.41)using the HF as the reference wavefunction, the eigenvalue of this equation is just the sum of theenergy of each occupied spin orbital,Ĥ∣∣ψSDe 〉 =(N∑iϵi)∣∣ψSDe 〉 . (2.42)By setting the perturbation equal to the difference between the perturbed Hamiltonian in Equation2.41 and the electronic Hamiltonian asĤ ′ =N∑i N∑j>iĝ (i, j)−N∑j[Ĵj (i)− K̂j (i)] = Ĥe − Ĥ, (2.43)we find approximate solutions to the eigenfunctions of Ĥe. Using equations 2.39 and 2.40 conductsus to the next results:E(0) =〈ψSDe | Ĥ | ψSDe〉=N∑iϵi, (2.44)332.2. QUANTUM CHEMISTRYa known value, and the correction to first orderE(1) =〈ψSDe | Ĥ ′ | ψSDe〉=〈ψSDe | Ĥe − Ĥ | ψSDe〉= EHF −N∑iϵi. (2.45)The final zeroth and first-order corrections are given byEMP0 = E(0) =N∑iϵi, (2.46)andEMP1 = E(0) + E(1) = EHF, (2.47)respectively. These outcomes reveal that correlation energy is accounted for starting from thesecond-order correction, that is,EMP2 = EHF + E(2), (2.48)withE(2) =14occ∑abvirt∑rs∣∣∣〈χa (1)χb (2) | ĝ (1, 2)(1− P̂12) | χr (1)χs (2)〉∣∣∣2ϵa + ϵb − ϵr − ϵs , (2.49)where P̂12 is a permutation operator that exchanges electrons 1 and 2; a, b, . . . represent occupiedspin orbitals, and r, s, . . . virtual ones (unoccupied). Perturbation theory applied to polyelectronicsystems has the disadvantage of not being variational, so overestimating the total electronic energyis possible. Also, since a perturbation theory approach works best if the perturbation is negligible,there is no guarantee that the energy will converge at higher perturbation orders with a finite basisset.111 It also becomes prohibitively expensive as we go beyond the forth-order perturbation.Now, it is convenient to introduce the concept of excited determinants. A wavefunction ex-pressed as an SD in its ground state can be written as∣∣ψSDe 〉 = |. . . χaχb . . . ⟩ . (2.50)If we promote an electron from an occupied orbital a to a virtual orbital r, we get∣∣raψSDe〉=∣∣. . . χ(a→r)χb . . . 〉 , (2.51)342.2. QUANTUM CHEMISTRYwhich is a single excited determinant. Similarly, by promoting two electrons, we obtain∣∣rsabψSDe〉=∣∣. . . χ(a→r)χ(b→s) . . . 〉 , (2.52)representing a double excited determinant.Another post-HF technique, the configuration interaction (CI) method, uses a linear combina-tion of excited determinants, using the HF wavefunction again as a reference, i.e.∣∣ψCIe 〉 = c0 ∣∣ψSDe 〉+ occ∑avirt∑rcra∣∣raψSDe〉+occ∑aocc∑b>avirt∑rvirt∑s>rcrsab∣∣rsabψSDe〉+ . . . ; (2.53)this trial function is variational, and its energy can be minimized subject to the condition thatthe wavefunction is normalized. As we did for minimizing the HF energy, a Lagrange multipliersprocedure can be followed for CI:L =〈ψCIe | Ĥe | ψCIe〉− ECI(〈ψCIe | ψCIe〉− 1) . (2.54)While conceptually simple, CI is hard to implement due to its high computationally cost. Intheory, with a complete basis set, the full CI method generates the exact electronic energy; however,practical considerations limit CI methods to their truncated (e.g. only single or double excitations)versions.88,89,92An alternative to representing excited determinants is to use cluster operators,T̂ =N∑iT̂i (2.55)Applying the first-order cluster operator to a reference SD generates a linear combination of single-excited determinants:T̂1∣∣ψSDe 〉 = occ∑avirt∑rcra∣∣raψSDe〉. (2.56)Likewise, T̂2 produces all double-excited determinants,T̂2∣∣ψSDe 〉 = occ∑aocc∑b>avirt∑rvirt∑s>rcrsab∣∣rsabψSDe〉. (2.57)352.2. QUANTUM CHEMISTRYWe can then write the full CI wavefunction in a more compact form,∣∣ψCIe 〉 =(1̂ +N∑iT̂i)∣∣ψSDe 〉 , (2.58)where N is the number of electrons in the system. At this point, we introduce the coupled cluster(CC) wavefunction: ∣∣ψCCe 〉 = exp(T̂) ∣∣ψSDe 〉 , (2.59)the exponential operator in this equation has the following form in its Taylor expansion,exp(T̂)= 1̂ + T̂ +12!T̂ 2 +13!T̂ 3 + · · · =∞∑k=01k!T̂ k. (2.60)Both the CI and CC wavefunctions are equivalent in a complete basis set and represent theexact solution to the electronic problem. Nonetheless, they are both computationally unfeasible intheir full forms. A more detailed expansion of the Taylor expansion shown in the previous equationleads toexp(T̂)=1̂ + T̂1 +(T̂2 +12!T̂ 21)+(T̂3 + T̂2T̂1 +13!T̂ 31)+(T̂4 + T̂3T̂1 +12!T̂ 22 +12!T̂2T̂21 +14!T̂ 41)+ . . . ,(2.61)where the first and second terms of the expansion give us the reference wavefunction (HF) andall single excitations as defined for CI, respectively. The rest of the terms have been grouped inparentheses; for the first parenthesis, we have the T̂2 that we saw in the configuration interactionsmethod; however, an additional term involving a product (T̂1)(T̂1) appears; the former term repre-sents a connected excitation and the latter is regarded as a disconnected operator. The CC energycan be obtained by projecting the reference state into the coupled cluster Hamiltonian,ECC =〈ψSDe | Ĥe | ψCCe〉. (2.62)Coupled cluster is computationally costly. It can only be applied to molecular systems with upto about 20 atoms. Nevertheless, when combined with large basis sets, CC with single and double362.2. QUANTUM CHEMISTRYexcitations, plus perturbative triple excitations — commonly known as CCSD(T),112 can reproduceexperimental observables with chemical accuracy.113 It is frequently used in the generation of high-quality computational data. For this reason, the coupled cluster method is often referred to as thegold standard of electronic structure methods.2.2.4 Density Functional TheoryUp to this point, we have focused our attention on finding approximate wavefunctions in anattempt to solve the non-relativistic Scho¨dinger equation under the Born-Oppenheimer approxima-tion. This effort helps us recover part of the correlation energy that ultimately allows us to makequantitative predictions, but often at a high computational cost. An option that balances accuracyand calculation expense is density functional theory (DFT),114,115 which uses the electron densityinstead of the wavefunction. In a general form, the electron density isρ (r1) = N∫ ∫· · ·∫|ψe (r1, σ1, r2, σ2, . . . , rN , σN )|2 dσ1dr2dσ2 . . . drNdσN , (2.63)ρ (r1) is a function that takes spatial coordinates and provides the probability of finding an electronin an element of volume dr1. The electron density is obtained by integrating all of the spincoordinates and all but the spatial coordinates of electron 1. Integrating the electron densityover the spatial coordinates of electron 1 returns the total number of electrons in the system:N =∫ρ (r1) dr1. (2.64)Since electrons are indistinguishable, the electron density can be defined using electrons 2, 3, orany electron. However, r1 = r and ρ (r1) = ρ (r) provides a more compact notation.It is possible to utilize electron density in the formulation and calculation of electronic structurein polyelectronic molecular systems thanks to Hohenberg and Kohn’s theorems.116 On a qualita-tive level, the first theorem establishes that electron density uniquely determines the Hamiltonianoperator and hence connects the ρ (r) with the wavefunction in a one-to-one correspondence. Thistheorem has the critical implication that determining the electron density of the system allowsfor the determination of all of the properties of the system. The second theorem is a Variational372.2. QUANTUM CHEMISTRYPrinciple for the electron density. In short, this theorem dictates that a trial ρ (r) will lead to anupper bound energy with respect to the energy associated with the exact density.Under DFT, the total electronic energy depends on how we express the electron density of thesystem. In other words, the DFT energy is determined by the function of ρ (r) and it is said to bea functional of the electron density. Unfortunately, the formulation of DFT delivers no indicationof what the energy functional should look like; thus, we do not have an available and systematicway to improve the electron density for more accurate energies. One way to proceed is to dividethe energy functional into separate contributions, that is,EDFTexact [ρ (r)] = Te [ρ (r)] + Ven [ρ (r)] + Vee [ρ (r)] , (2.65)in which the first functional on the right-hand side of the equation is the kinetic energy of theelectron functional. The second functional recovers contributions from the attractions betweenelectrons and the nuclei,Ven [ρ (r)] = −M∑A∫ZA|RA − r|ρ (r) dr. (2.66)The third functional involves electron-electron repulsions and can be further divided into Coulomb(J) and exchange (K) functionals:Vee [ρ (r)] = J [ρ (r)] +K[ρ (r)], (2.67)J [ρ (r)] =12∫∫ρ(r)ρ (r′)|r− r′| drdr′. (2.68)Note that equations 2.66 and 2.68 have a direct form obtained from their analogous classical termsbased on the electron density, while the exchange functional does not have a defined form.Directly attempting to find functional forms for all the previous equations is impractical. Tack-ling this issue in the form of the Kohn-Sham117 (KS) approach involves the use of a reference SD,where the introduced orbitals generate a field of non-interacting electrons with a given density givenbyρSD (r) =N∑i⟨χi | χi⟩ , (2.69)this electron density is subject to reproduce the exact density of the system. The KS energy382.2. QUANTUM CHEMISTRYfunctional then is written asEDFTKS [ρ(r)] =TSD [ρ(r)] + Ven [ρ(r)] + J [ρ(r)] + Exc [ρ(r)]=N∑i〈χi∣∣∣∣−12∇2i∣∣∣∣χi〉− N∑iM∑A〈χi∣∣∣∣ ZA|ri − rA|∣∣∣∣χi〉+N∑i〈χi∣∣∣∣12∫ρ (r′)|ri − r′|dr′∣∣∣∣χi〉+ Exc[ρ(r)].(2.70)Using this set of trial orbitals for estimating the kinetic energy functional does not recover allof the kinetic energy of the system. It is often observed in the literature that all unaccountedcontributions are expressed as separate terms and merged into the exchange-correlation functional,Exc[ρ] = (Te[ρ (r)]− TSD[ρ (r)]) + (Vee[ρ (r)]− J [ρ (r)]) . (2.71)Exc does not have a definitive functional; nevertheless, expressing it in terms of the generic Te andVee terms recovers the exact DFT energy and shows us that the exchange-correlation functionalcontains information about the kinetic energy and the repulsion between electrons. Further workon the equations leads us to the Kohn-Sham equations:hKSi |χi⟩ = ϵi |χi⟩ (2.72)were the one-electron operator, hKSi , is given byhKSi = −12∇2i −M∑AZA|ri − rA| +∫ρ (r′)|ri − r′|dr′ + Vxc. (2.73)here, Vxc = ∂Exc/∂ρ.In the literature, orbital-based DFT methods are widely popular for calculating molecularproperties due to their reduced computational cost and relatively accurate results when comparedto traditional wavefunction methods.118 In analogy with the Hartree-Fock method, KS-DFT issolved iteratively and at a reasonable computational cost with the added advantage that it recoverssome of the missing electron correlation that is completely absent from the HF method. While thetheory is exact, there is no systematic approach to defining the exchange-correlation functional yet.392.2. QUANTUM CHEMISTRYIn its general form, Exc can be written asExc [ρ (r)] =∫ρ (r) εγxc[ρ (r) , ρ′ (r) , ρ′′ (r) , . . .]dr. (2.74)where γ is just an arbitrary index to classify the functionals according to the information found inTable 2.1.γ Functions in εγxcLDA (Local Density Approximation) ρ (r)GGA (Generalized Gradient Approximation) ρ (r) ,∇ρ (r)meta-GGA ρ (r) ,∇ρ (r) ,∇2ρ (r) or τ (r)Table 2.1: Functions for popular exchange-correlation functionals.Incorporating the electron density, its gradient and Laplacian, and the kinetic energy density (τ)into Equation 2.74 allows for higher flexibility in the functional form and accounts for the inhomo-geneity in the electron density, which is critical in improving the description of molecular systems.Various DFT approximations incorporate such functions to different degrees. In the simplest ofthe cases, the local-density approximation (LDA) calculates the exchange-correlation energy usingonly ρ (r); it is based on the premise that the system behaves like a uniform electron gas.116,117This approximation leads to accurate results in solid-state chemistry but fails to describe molecularsystems.119 Another approximation, the generalized-gradient approximation (GGA), integrates thegradient of the electron density with the local density when determining the exchange-correlationenergy. GGA functionals provide a better assessment of the local electron density and provide abetter description of properties when compared to LDA. Examples of GGA functionals include thePerdew-Burke-Ernzerhof (PBE),120 Perdew-Wang 1986 (PW86),121 Becke 1986b (B86b),122 andthe Becke 1988 (B88)123 functionals. Beyond GGA functionals, we find the meta-GGA functionals,which use a more advanced functional definition employing the Laplacian of the density and τ .An example of this type of functional is the Tao-Perdew-Staroverov-Scuseria (TPSS)124 and thefamily of Minnesota functionals.125–127 LDA, GGA and meta-GGA are called semilocal or purefunctionals because the exchange-correlation energy in a given point depends only on the electrondensity properties evaluated in the same point.119 A summary of the functionals described hereincan be found in Table 2.1.402.2. QUANTUM CHEMISTRYAxel Becke demonstrated that adding a fraction of the exact exchange, as calculated in Hartree-Fock theory but employing Kohn-Sham orbitals, leads to an improved description of molecularthermochemistry.128 Popular functionals built in this way are known as hybrid functionals andextremely popular examples include the B3LYP129,130 and PBE0131,132 functionals. A particulartype of hybrid functional is range-separated hybrid functionals. These functionals dissect theelectron-electron interaction into short and long-range contributions. This distinction betweenshort and long-range allows for the appropriate long-range behaviour of the exchange-correlationpotential. Among the range-separated hybrid functionals, ωB97,133 CAM-B3LYP,134 and LC-ωPBE135,136 are popular. Due to the incorporation of the exact exchange into hybrid and long-rangefunctional, these functionals are not semilocal.The DFT community is very active in developing new forms for the exchange-correlation func-tional. However, due to its indeterminate mathematical expression, it is unclear whether improve-ments in the DFT energy with respect to high-level wavefunction energies are a consequence ofheavily parametrized functionals. Some authors have shown that in striving to get more accurateelectronic energies, we are getting farther from the exact electron density.137Another drawback of DFT methodologies is their inability to account for dispersion interactionsfully. A straightforward way to estimate the missing dispersion energy is via a semi-empiricalmethod, namelyEDFTCorrected = EDFTKS + ED3(BJ)Disp , (2.75)where D3 refers to Grimme’s approach to calculating dispersion energies,138 BJ indicates the use ofthe Becke-Johnson damping functions.139,140 This dispersion correction has the following expressionED3(BJ)disp = −12∑A ̸=B(s6CAB6R6AB +[f(R0AB)]6 + s8 CAB8R8AB +[f(R0AB)]8), (2.76)wheref(R0AB)= a1R0AB + a2. (2.77)Here, CAB6 and CAB8 are the sixth and eighth-order dispersion coefficients for atoms A and B,respectively. RAB is the interatomic distance between atoms A and B. R0AB is a constant valuedepending on the dispersion coefficients, s6 and s8 are empirical-determined parameters, whereas412.3. TOOLS IN QUANTUM CHEMISTRYa1 and a2 are fitted parameters.141 Including empirical dispersion for DFT calculations is criticalfor accurately modelling noncovalent interactions and has now become a common incorporation toroutine density functional theory computations.1422.3 Tools in Quantum ChemistryThis section deals with a collection of various methodologies and techniques that are oftenused in quantum chemistry calculations. The intention of this section is to explain in more detailthe concept of basis sets and introduce how potential-based methodologies are used in QC. Also,we explore how thermochemistry is calculated from an electronic structure calculation. Finally, apopular analysis of the electronic density is also explained.2.3.1 Basis SetsThe basis sets introduced in Equation 2.29 are mathematical functions that are used to representatomic orbitals. In their simplest form, they can be written as92ϕSTOν = NYl,m (θ, φ) rn−1 exp (−ζr) , (2.78)where N is a normalization constant, Yl,m is the angular part of the function, and the rest of theequation represents the radial part. These are the so-called Slater-type orbitals (STO) and arethe exact solutions to the electronic Hamiltonian for the hydrogen atom. Here, the n, l, and mare integers, the quantum numbers that naturally arise from solving the Schro¨dinger equation forhydrogen-like systems. ζ is a constant exponent part of the radial function. These basis sets arerarely used in practice because there is no analytical formula for solving the integrals appearingduring the SCF part of the calculations, so efficient numerical approaches are needed for this step.As a more efficient alternative, quantum chemists use Gaussian basis sets to generate the spinorbitals:143ϕGTOν = NYl,m (θ, φ) r2n−2−l exp(−ζr2) . (2.79)These basis sets are known as Gaussian-type orbitals (GTO), and the parameters and variables havethe same meaning as in STOs. The main advantage of GTOs over STOs is their analytical form422.3. TOOLS IN QUANTUM CHEMISTRYto compute integrals and the Gaussian product theorem.89 Using Gaussian-type orbitals simplifiesand accelerates the SCF procedure considerably and is what modern electronic structure programsoften employ for molecular calculations. GTOs, however, decay faster than STOs. Also, they donot adequately reproduce the molecular orbital in the vicinity of the atomic nuclei. This issue isaddressed by using a linear combination of GTOs as atomic orbital,ϕCGTOµ =k∑i=1ciµϕGTOi , (2.80)commonly known as contracted Gaussian-Type orbitals (CGTO), which alleviates some of theshortcomings of GTO by improving the description of an electron near and far from the atomicnuclei.2.3.2 Potential-Based ApproachesElectrons near the nuclei (core electrons) are often deemed not as relevant to chemical phe-nomena as valence electrons. To a certain degree, this statement is true since, in contrast to coreelectrons, electrons in the outer shells directly participate in chemical bonding. Thus, as an approx-imation, we can replace the core electrons in a polyelectronic system with potential functions119,144V̂ECP = Vlmax+1 (r) +lmax∑l=0l∑m=−1|Ylm⟩Vl (r) ⟨Ylm| , (2.81)which are atom-centred potentials known as effective-core potentials (ECPs), as they replace coreelectrons with Gaussian-type potentials:Vl (r) =1r2k∑i=1clirnli exp(−ζlir2) . (2.82)Here, Ylm have the same meaning as in equations 2.78 and 2.79. The coefficients, cli, are parametersto be fitted, nli is an integer for the power of the radial part of the function, and ζli is an adjustableexponent for the Gaussian function. The standard parametrization of ECPs starts with Vlmax+1 ,for which it is custom to write this term as a separate term in the expansion.By placing Gaussian-type functions (ECPs) instead of core electrons into the Hamiltonian, the432.3. TOOLS IN QUANTUM CHEMISTRYcomputational cost is reduced without significantly compromising the mathematical descriptionof valence electrons. Though ECPs were initially utilized for substituting core electrons in heavyelements, atom-centred potentials (ACPs) with a similar form as Equation 2.83 can be exploitedto modify the potential where all electrons move in the system. These potentials are particularlyuseful to compensate for the errors of failing to have a complete basis set; so forV̂BSIP =M∑A[V Almax+1 (rA) +lmax∑l=0l∑m=−l∣∣Y Alm〉V Al (rA) 〈Y Alm∣∣], (2.83)where BSIP refers to the acronym Basis Sets Incompleteness Potentials.145 These functions areatom-dependent, and the coefficients are parametrized to correct the deficiencies of a given methoddue to the incomplete basis set error. The individual terms are also a linear combination of Gaussianfunctions,V Al (ra) =k∑i=1cAli exp(−ζAli r2A) . (2.84)ACPs are very flexible and can be parametrized to alleviate the shortcomings of many quantumchemistry methods. For example, ACPs have been used to correct the lack of accurate descriptionof dispersion interactions in DFT methods,146,147 and improve the prediction of thermochemicalproperties, among other potential applications.148 ACPs can do this with minimal added compu-tational cost.2.3.3 Geometry Optimizations and ThermochemistryUnder the Born-Oppenheimer approximation, the total energy of the system depends para-metrically on the nuclear coordinates. The PES, as introduced in subsection 2.2.1, is defined bycalculating Etot for all (in theory) nuclear arrangements. Finding stationary points in the potentialenergy surface is crucial to quantum chemistry as it allows us to calculate optimized geometries forlocal minima and transition states — collectively referred to as stationary states on the PES. Oncethe stationary states of interest are located, it is possible to calculate properties that are useful tochemists, such as reaction energies, activation energies, bond dissociation energies, etc.The general procedure for finding stationary states is as follows. For simplicity, let us assumethat Etot = E. In general, we can express all nuclear coordinates of an arbitrary system as a vector,442.3. TOOLS IN QUANTUM CHEMISTRYthat is, x† = (x1, x2, . . . , x3N ) in its transposed form. By producing a small change in the nuclearcoordinates from x to x1, we can then write the energy of the system in the new coordinates as aTaylor series around the original position,89E (x1) = E (x) + d†g (x) +12d†H (x)d+ . . . . (2.85)In this equation, the displacement of the nuclei is given by d = (x1 − x). The gradient and Hessianmatrices (not to be confused with the Hamiltonian) are defined by their matrix elements:gi =∂E (x)∂xi, (2.86)andHij =∂E (x)∂xi∂xj, (2.87)respectively. A stationary point is found when the zero vector is returned when the gradient isevaluated. In other words, if x = xS (the nuclear coordinates are at a stationary point), theng (xS) = 0. Different procedures start from Equation 2.85 to locate stationary points; they arecommonly implemented in quantum chemistry software packages.Once a stationary point is found, it can be characterized using the mass-weighed Hessian92Fij =1√mimjHij , (2.88)which essentially is the same Hessian but scaled by a mass factor of the nuclei involved.The eigenvalues of the matrix shown in Equation 2.88, λi, are related to the vibration frequenciesof the normal modes of the molecule at a given stationary point by:νi =12πλ12i . (2.89)If all of the vibrational modes in this equation are positive, we can characterize the stationarypoint as a minimum on the PES. A negative eigenvalue from the Hessian matrix generates animaginary vibrational mode whose presence, along with the other vibrational modes being positiveand real, indicates that a transition state has been found (saddle point in the PES), provided that452.3. TOOLS IN QUANTUM CHEMISTRYthe gradient of the energy with respect to the geometry is also zero.Now, with an approximate description of the electronic structure of molecular polyelectronic sys-tems and a recipe for locating meaningful molecular structures, we can use statical mechanics81,149to connect the outcomes of quantum mechanics and thermodynamics. In statical mechanics andunder the ideal gas approximation, a partition function in its canonical form is used to link thequantum states of a collection of particles to macroscopic properties; it has the formQ =qNN !, (2.90)where Q is a function of the number of moles, volume and temperature. The function q is themolecular partition function and can be separated into its translational, rotational, vibrational andelectronic components:q = (qtrans) (qrot) (qvib) (qelec) . (2.91)It can be shown that the entropy and internal energy of a system can be calculated, in the gasphase, from the relationsS = NkB +NkB ln( qN)+NkBT(∂ ln q∂T)V, (2.92)andU = NkBT2(∂ ln q∂T)V. (2.93)Then the enthalpy and Gibbs free energies are obtained from their definitions;H = U + pV, (2.94)G = H − TS. (2.95)2.3.4 Quantum Theory of Atoms in MoleculesBader’s group developed the quantum theory of atoms in molecules (QTAIM)150,151 at McMas-ter University out of the necessity of clearly defining chemical concepts such as a chemical bond orfunctional group through an experimental observable, the electron density. In short, QTAIM is a462.3. TOOLS IN QUANTUM CHEMISTRYrigorous partition scheme based on ρ(r); its formulation is based on the analysis of critical pointsin the electron density, i.e. where∇ρ (rc) = 0. (2.96)When the electron density gradient vanishes, a critical point is identified. Such critical points canbe characterized in terms of its 3× 3 Hessian matrixHij =∂2ρ (r)∂xi∂xj, (2.97)where i = 1, 2 or 3 and j = 1, 2 or 3. Depending on signs of the three eigenvalues of the Hessianmatrix, it is possible to link the critical point to an element of chemical structure. For example,if all eigenvalues are negative (positive), the critical point is a maximum (minimum) in the threedirections of the coordinates, which is indicative of a nuclear critical point (cage critical point).For intermediate cases, we would identify a bond critical point (two negative plus one positiveeigenvalues) and a ring critical point (two positive plus one negative eigenvalues). This theory alsodefines a bond path as a gradient flux line that connects two nuclear critical points. They furthersuggest that the presence of a bond path and a bond critical point between two nuclei indicatesthat both atoms are bonded, though this definition of chemical bond has been questioned in thepast few decades.152,153In addition to providing a clear definition of elements of chemical structure, QTAIM also pro-vides a partition definition based on the so-called zero flux condition∇ρ (r) · n (r) = 0. (2.98)In this equation, n (r) is a unitary vector that is normal to the “surface” of the atoms. This relationimplicitly defines the interatomic surfaces within the molecule, such as a basin where none of the∇ρ(r) vectors cross. These basins are known as Bader atoms.Under this partition scheme, it is possible to calculate atom-based properties within the molecule.For example, the number of electrons in the basin identified as atom A would simply beNA =∫Aρ (r) dr, (2.99)472.4. CLASSICAL MOLECULAR DYNAMICS SIMULATIONSand its charge would be calculated asqA = ZA −NA. (2.100)Grouping several atoms to calculate contributions from functional groups is possible under thisformalism.Once the partition is defined, the expected value of an arbitrary observable can be decomposedinto atomic contributions. QTAIM has been widely used in the literature over the years, mainlybecause of the atom-based data that can be retrieved from it. However, it has the drawback ofrelying heavily on the quality of the calculated electron density, which often requires the calculationof high-level theory wavefunctions to build reliable electron densities. Because QTAIM generatesa consistent set of data, some recent studies have used properties obtained from QTAIM, such ascharges, to generate training data for machine learning models successfully.1542.4 Classical Molecular Dynamics SimulationsIn the previous sections of this chapter, we focused on the theory involving quantum mechanics,which applies only to small systems where calculations are computationally achievable. In thissection, we introduce the basics for simulations at a larger scale using molecular dynamics.In classical molecular dynamics (MD), atoms or molecules are studied by numerically solvingNewton’s equations of motion. The temporal evolution of the configuration of the system is ana-lyzed, and micro and macroscopic data are retrieved from the simulations. The simulation size forMD is in the order of hundreds or thousands of atoms; a force field (FF) method is necessary. FFmethods are also called molecular mechanics. Under this approach, the energy of the system for agiven nuclear arrangement is parametrically expressed in terms of the atoms. Since there is no infor-mation regarding the electronic structure of the atoms, explicit information about bonds and other482.4. CLASSICAL MOLECULAR DYNAMICS SIMULATIONSgeometrical parameters must be given. A force field is often divided into contributions:92,155,156EFF = Estretch + Ebending + Etorsion + EvdW + Eelectrostatic + Ecross=∑bondski2(li − li,0)2 +∑angleski2(θi − θi,0)2 +∑torsionsVn2[1 + cos (nω − γ)]+∑i∑j>i(4ϵij[(σijrij)12−(σijrij)6])+∑i∑j>i+qiqj4πε0rij+ Ecross.(2.101)The nuclear position of all atoms determines the energy of the system. The stretch term, Estretch,models the energy associated with the bonds in the system. It reflects the change in energy ofa specific bond with length li with respect to their reference length li,0 and is modelled using aharmonic potential. The second term, Ebending, similarly uses a harmonic potential to describethe deviation of valence angles from their reference values. The third term models the torsionalangles (Etorsion). The term EvdW employs a Lennard-Jones potential for describing van der Waalsinteractions. The fifth term, Eelectrostatic, is the classical Coulomb potential term for calculating theelectrostatic interactions. The last term (Ecross) is the cross term; not all FFs include this term.This term has a form that depends on the nature of the problem; it involves the coupling of two ormore of the other terms. The parameters in Equation 2.101 are fitted to reproduce experimentalresults and to higher levels of theory when feasible.Classical molecular dynamics are based on the ergodic hypothesis, which states that⟨P ⟩ = limτ→∞1τ∫ τ0P (t) dt = limS→∞1SS∑i=1Pi. (2.102)The interpretation of this equation is that, for any property P , the average of a small number ofparticles over a long time is equivalent to averaging a large number of particles over a short period.This hypothesis allows us to obtain properties from atomic or molecular ensemble averages easily.For example, the internal energy is obtained by simply averaging the energies of each particle:U = ⟨E⟩ = 1SS∑i=1Ei. (2.103)492.4. CLASSICAL MOLECULAR DYNAMICS SIMULATIONSThen, it follows that the heat capacity of the system is computed asCV =(∂U∂T)V=〈E2〉− ⟨E⟩2kBT 2. (2.104)Other properties can also be computed by averaging from the ensemble.As previously mentioned, classical molecular dynamics are based on numerically solving New-ton’s laws of motion; the second law statesFxi = mid2xidt2, (2.105)which represents the force applied to a particle i along the coordinate xi.There exist many numerical methods for solving Equation 2.105. Herein, we will explore afinite difference technique, which divides the integration into several small stages and separatesthem by an arbitrary amount of time, δt. Then a Taylor series expansion is employed to calculatethe position for the next step,r (t+ δt) = r (t) + (δt)v (t) +δt22!a (t) +δt33!b (t) + . . . , (2.106)where the vectors r, v, a, and b are the position, velocity, acceleration and third derivative withrespect to time of the positions, which likewise have their own Taylor series expansion:v (t+ δt) = v (t) + (δt)a (t) +δt22!b (t) + . . . , (2.107)anda (t+ δt) = a (t) + (δt)b (t) + . . . . (2.108)The following relation is obtained by using a previous step (t−δt) in its Taylor series expansionand adding it to Equation 2.106r (t+ δt) = 2r (t)− r (t− δt) + δt2a (t) . (2.109)This approach is known as the Verlet algorithm.157 The velocities do not appear explicitly; however,502.4. CLASSICAL MOLECULAR DYNAMICS SIMULATIONSthey can be calculated byv (t) =r (t+ δt)− r (t− δt)2δt. (2.110)Implementing this algorithm is straightforward and does not require much computational power.Numerous other algorithms for calculating steps in MD simulations rely on Verlet’s algorithm.During an MD simulation, it is essential to have a means to control the temperature andpressure of the system. A simple method for temperature management is to scale the velocities ofthe particles after each step.158 If T (t) is the temperature of the system at a given time, and Tbathis the desired temperature, the change in temperature after each step is∆T =δtτ[Tbath − T (t)] , (2.111)where τ is a coupling parameter. The scaling factor for the velocities is given byλv = 1 +δtτ[TbathT (t)− 1], (2.112)where the velocities are multiplied by the factor λ1/2v to control the temperature. Note that thescaling factor becomes zero if the bath and actual temperatures are the same.Similarly, a scaling factor is employed to control the pressure158 of a simulation. The associatedequations are comparable to those for handling the temperature, namelydP (t)dt=1τP[Pbath − P (t)] , (2.113)andλp = 1 + κδtτP[Pbath − P (t)] . (2.114)For the pressure, we scale the coordinates of the particles and the dimensions of the box. We do soby using λ1/3p as a scaling factor to adjust the pressure by changing the volume of the simulationbox.Molecular dynamics simulations provide a robust and computationally feasible means to obtaininsight into the properties of large (in the order of hundreds and thousands of particles) atomic andmolecular systems.155 For reaching a level of simulation that is representative of bulk properties,512.4. CLASSICAL MOLECULAR DYNAMICS SIMULATIONSMD simulations make use of periodic boundary conditions (PBC). Implementing PBC consists ofdefining a unit cell, often called the simulation box, and replicating it in all directions. Particlesare free to move between replicas of the unit cell; when a particle exits a given box, an identicalparticle enters the box from the opposite direction.156 Implementing periodic boundary conditionsensures that artifacts, such as creating artificial vacuum-particle surfaces, are avoided during thesimulations. PBC MD simulations are widely applied in modelling biochemical systems involvingenzymes and proteins, in the rationalization of materials, and in condensed phase simulations. Inour case, it is employed to analyze the properties of a water-oil interface model in the order ofthousands of molecules, which is not possible to study employing QM approaches.52Chapter 3Noncovalent Interactions in AqueousOrganic MediaThis chapter is based on the following article1. Romero-Montalvo, E.; DiLabio, G. A. “Computational study of hydrogen bond interactionsin water cluster-organic molecule complexes,” J. Phys. Chem. A 2021, 125, 3369-3377.Published on April 20th, 2021 (https://doi.org/10.1021/acs.jpca.1c01377).The article was reprinted (adapted) with permission from J. Phys. Chem. A 2021, 125, 3369-3377.Copyright© 2021 American Chemical Society (reference 57 in this thesis). The adaptationswere made for the purposes of writing this thesis. The original idea and conceptualization of thepaper were done by Gino A. DiLabio. The design and planning of the research work were done byEduardo Romero-Montalvo. The research work, analysis and curation of the data were also doneby Eduardo Romero-Montalvo. The initial draft was written by Eduardo Romero-Montalvo andwas reviewed and edited by Gino A. DiLabio. Supplementary information for this work can befound, free of charge, at the ACS webpage indicated in the DOI link above. This notice is alsoincluded in the preface of this thesis.3.1 Motivation to Study Noncovalent Interactions in theContext of Aqueous Organic ChemistryUnderstanding hydrogen bonding (HB) interactions between organic molecules and water moleculesis central to unravelling the poorly understood chemistry occurring in aqueous organic media, in-cluding OWRs, which have been hypothesized to undergo HB stabilization.40 Also, several chemicalprocesses relevant to biology and chemistry involve water cluster-organic substrate interactions, as533.2. OTHER METHODOLOGIES AND OUR COMPUTATIONAL APPROACHdescribed in the introduction of this thesis. Considering the significance of hydrogen bonding inthis thesis, the present chapter focuses on their accurate description using quantum mechanicalmethodologies.Over the years, there has been extensive research on HBs in water clusters. Cooperative effects,as described by Xantheas and collaborators,159–163 are well-known and have been widely studied inthe literature.164–168 Cooperative effects increase with the number of water molecules in the cluster.The size of water clusters and the environment of their hydrogen bonds play a crucial role indetermining their overall stability and strength. The nature of the HB donor and acceptor, alongwith their surrounding molecules, have been used to describe noncovalent interactions in small waterclusters. Previous studies have explored this aspect in detail.169,170 Regarding molecular systemsinvolving organic molecules and water molecules, until recently,171 there were no comprehensiveinvestigations analyzing the different interactions arising when forming complexes with organicmolecules and water clusters of various sizes.In modelling reactions in aqueous organic media, some works employing quantum chemistry cal-culations rely on small representations of molecular systems with only a few water molecules.40,172,173While these investigations often lead to a correct qualitative description of chemical reactions, theyfail to capture the complexity of HBs in these molecular systems, completely neglecting the roleof water cluster size in accurately describing HB interactions with organic molecules. In orderto develop our understanding of OWRs, we begin our research by analyzing noncovalent interac-tions present in organic molecule-water cluster complexes. This chapter explores the interactionstrengths of water clusters of varying sizes with organic HB acceptors/donors.3.2 Other Methodologies and Our Computational ApproachWhen performing highly accurate quantum mechanical calculations, we are limited by the sizeof the molecular system. In the case of water clusters, such modelling can be accomplished onlyfor small water clusters.174,175 Nonetheless, small models can frequently produce insightful datafor solving chemical problems. For this thesis, our first goal was to understand the behaviour ofnoncovalent interactions between organic molecules and water clusters of increasing size. Havingthis information is crucial when constructing models for OWRs.543.2. OTHER METHODOLOGIES AND OUR COMPUTATIONAL APPROACHFigure 3.1: Hexamer (6CC) of water from reference 176. Colour code, red: oxygen, and blue:hydrogen. Dashed lines indicate HB interactions.Highly accurate QM methods have been used to determine the structures of water clustersranging from the monomer to the decamer.176 These water cluster structures were used for thepresent work and are summarized in Table 3.1. An example of one of the hexamers of water isdisplayed in Figure 3.1. Temelso et al. generated these structures at the RI-MP2177,178/aug-cc-pVDZ179 level of theory, making them appropriate for benchmarking purposes. In terms of theorganic molecules, the following seven organic molecules were selected: acetone, dimethyl ether,oxirane, methyl acetate, azomethane, dimethylamine, and trimethylamine. These systems werepicked because of their structural similarities to organic substrates involved in OWRs.20 The organicmolecules were pre-optimized at B3LYP129,130,180/6-31+G** using Gaussian 16 (g16).102 We usedthese organic molecules as probes to study the HB donating/accepting capabilities of −OH groupsin the water clusters displayed in Table 3.1.The possible configurations of the complexes formed by the interactions between the probes andwater clusters of various sizes, described in the previous paragraphs, grow with the size of the waterclusters. The large number of possible complexes arises because as the number of water moleculesincreases in the cluster, the number of available −OH donor groups also increase. In order to samplerepresentative configurations of the complexes, we generated thousands of structures and followeda screening method to retrieve meaningful molecular configurations. The approach we followed forthe generation of the probe-water cluster structures is as follows. First, we fixed the coordinates ofthe water clusters obtained from reference 176 and allowed the pre-optimized organic molecules to553.2. OTHER METHODOLOGIES AND OUR COMPUTATIONAL APPROACHCluster size, n Labels1 Monomer2 2Cs3 3UUD, 3UUU4 4Ci, 4PY, 4S45 5CA-A, 5CA-B, 5CA-C,5CYC, 5FR-A, 5FR-B,5FR-C6 6BAG, 6BK-1, 6BK-2,6CA, 6CB-1, 6CB-2,6CC, 6PR7 7BI1, 7BI2, 7CA1,7CA2, 7CH1, 7CH2,7CH3, 7HM1, 7PR1,7PR2, 7PR38 8D2d, 8S49 9D2dDD, 9S4DA10 10PP1, 10PP2Table 3.1: Names of the water clusters considered in this thesis. The structures of all the waterclusters shown here can be seen in Figures 1 and 2 of reference 176.563.2. OTHER METHODOLOGIES AND OUR COMPUTATIONAL APPROACHmove freely around the water clusters. For doing so, we employed a random generator of structureswhich led to obtaining up to 2000 structures per water cluster-probe complex. The module genmerfrom the Molclus software,181 which allows us to generate random molecular configurations, was em-ployed for this purpose. Next, we performed single-point (SP) calculations on these structures andenergy-ranked them using the UFF force-field,182 and eliminated the 1000 least stable complexes(step I). In step II, SP energies of the remaining 1000 compounds using HF-D3(BJ)/MINIs-ACP148were used for reordering the structures based on their electronic energy. The 500 least stable config-urations were removed from the set. Similarly, step III involved the calculation of SP energies of theremaining 500 complexes using B3LYP-D3(BJ)129,130,138–141,180/6-31+G**-BSIP,145 reordering thestructures by energy and eliminating the 250 least stable structures. Step II employs atom-centeredpotentials (ACPs) that are designed to mitigate the effects of incomplete correlation, incompletebasis sets, and other errors associated with the HF-D3(BJ)/MINIs approach.148 Step III used theB3LYP-D3(BJ)129,130,138–141,180/6-31+G**-BSIP145 level of theory to complete single-point ener-gies; in this step, we also employed a type of ACPs known as basis set incompleteness potentials(BSIPs), which are designed to reduce the effects of incomplete basis sets used with conventionaldensity-functional theory (DFT) based methods.145 In all steps, the software g16 was employed.Figure 3.2 shows a summary of the screening process explained in this paragraph.The preceding screening resulted in a set of 250 configurations per organic molecule-watercluster complex. These energy-ranked configurations were divided into ten bins containing 25conformers each. These groups of 25 complexes were also energy ranked; bin 1 contains the 25most stable systems, bin 2 the following 25 most stable ones, and so on. This approach allowsfor a meaningful sampling of configurations involving not only strong interactions but also weakerinteractions. The most stable complex from each bin was selected to get 10 structures per complex.In these final structures, the organic molecules within the complexes were optimized at B3LYP-D3(BJ)129,130,138–141,180/6-31+G**-BSIP145 using g16; in all cases, the structures of the waterclusters within the complexes were kept fixed at those obtained by Temelso and coworkers.176 Sincewe have 7 organic molecules, 38 water clusters plus the monomer of water, and 10 configurationsper complex, our data set consists of 7×39×10 = 2730 structures. The approach followed in ourwork has the advantage of using high-level structures. However, since the water clusters are fixed,their structures will not relax upon the formation of noncovalent interactions. Hence, the calculated573.2. OTHER METHODOLOGIES AND OUR COMPUTATIONAL APPROACHFigure 3.2: Summary of the screening process followed in selecting the most stable complexesanalyzed in this work. We applied this procedure to each of the possible 273 complexes (7 probesinteracting with 39 water clusters). SP refers to single-point energies using the indicated methods.binding energies will all be upper bounds.When optimizing structures, it is possible that some of them are very close to the same minimumin the PES, leading to configurations with almost identical structures in the data set. In order tosolve this issue, the COMPARE feature, implemented in the program Critic2,183,184 was used. Thissoftware calculates the root-mean-square deviation (RMSD) of the atomic positions of two givengeometries; we considered a pair of structures with an RMSD value lower than 1 A˚ to be redundantand proceeded to delete one of them. We checked each pair of organic molecule-water clustercomplexes to ensure our dataset had no redundant geometries. After comparing and discardingredundant structures, we obtained 2376 non-redundant organic probe-water cluster structures. Thiselaborate screening method, while complex, ensures that strong interactions from the dangling −OHto the organic molecules are present and other weaker interactions, like those involving C−H HBdonors and dispersion interactions, are also taken into account. Molecular visualization of thecomplexes was performed using the software Chemcraft.185High-level benchmark binding energy calculations were obtained using DLPNO-CCSD(T)186583.2. OTHER METHODOLOGIES AND OUR COMPUTATIONAL APPROACHwith aug-cc-pVDZ and aug-cc-pVTZ basis sets,179 represented as DZ and TZ, respectively.d Asimilar technique to the one proposed by MacKie and DiLabio187 was used for the extrapolation tothe CBS limit of binding energies. To achieve this, we calculated the counterpoise (CP) correctedbinding energies (BECP)188,189 of the complexes asBECP =[EComplexComplex (Complex)− EComplexComplex ((H2O)n)− EComplexComplex (R)]+[ERComplex (R)− ERR (R)],(3.1)where the general nomenclature, Ebasismolecule (X), represents the electronic energy of species X (R fororganic molecules, (H2O)n for a water cluster of size n, and complex for the organic molecule-watercluster complex), at the geometry specified by the subscript and using the basis set displayed in thesuperscript. As an example, the term ERComplex (R) represents the electronic energy of an organicmolecule at its geometry in a complex using the organic molecule basis sets. Note that Equation3.1 can also be written asBECP = ECPint (Complex) + ERdef (R) , (3.2)in which ECPint (Complex) = EComplexComplex (Complex) − EComplexComplex ((H2O)n) − EComplexComplex (R), and the de-formation energy of the organic molecule, ERdef (R) equals ERComplex (R)−ERR (R). The deformationenergies of the water clusters (E(H2O)nComplex ((H2O)n)−E(H2O)n(H2O)n ((H2O)n)) are zero because we are usingfrozen structures for them throughout. The non-counterpoise (non-CP) energies (∆Enon−CPBE ) areBEnon−CP = EComplexComplex (Complex)−[E(H2O)n(H2O)n((H2O)n) + ERR (R)]. (3.3)We used the ORCA103 package for the calculation of the DLPNO-CCSD(T) energies. Equations3.2 and 3.3 were evaluated for both basis sets, DZ and TZ. A two-point extrapolation (DZ-TZ) tothe CBS limit, based on the El = A + B/(l + 1/2)4 formula, was applied.190 In this equation, Arepresents the extrapolated energy, B is a constant, and l = 2 and 3 for DZ and TZ, respectively.Once the energies at the DZ and TZ levels are obtained, a set of 2 equations from which AdFor all performed DLPNO-CCSD(T) calculations in this thesis, the auxiliary basis sets aug-cc-pVNZ/C, with N= D or T, were used. Also the keywords TightSCF and TightPNO were employed to ensure the accuracy of the QMcalculations.593.2. OTHER METHODOLOGIES AND OUR COMPUTATIONAL APPROACHand B are determined is used to estimate the CBS energy. The average of the CP and non-CPapproaches was also computed as BEiave =(BEiCP +BEinon−CP)/2, with i = DZ, TZ, and DZ-TZ.Our benchmark binding energies are defined as the average of the CP and non-CP binding energiesat the CBS extrapolation limit (BEDZ−TZave ), we will refer to this energy as the benchmark bindingenergy (or benchmark BE). Previous research has demonstrated that CP BEs tend to convergeto the complete basis set limit from above, while the non-CP BEs converge from below.160,187Therefore, averaging the two quantities generally results in quicker convergence to the CBS limit.These average binding energies quickly converge to the CBS limit for most noncovalent interactionsin our organic molecule-water cluster complexes. A selected example of the convergence of BEiave isdepicted in Figure 3.3. However, the convergence of the average of the CP and non-CP BEs is notalways ideal, for example, Figure 3.4 shows one of those examples in which the binding energiesof a complex formed between azomethane and the hexamer 6CC are displayed. For this example,the non-CP binding energies show little variation with the basis set. Is it important to note that,Figures 3.3 and 3.4 represent extreme cases. Despite the presence of some systems displaying abehaviour similar to that in Figure 3.4, more than 97% of the 2376 BEs we calculated herein showbetter convergence of the averaged BEs than the CP and non-CP BEs. The complete set of graphsshowing the CBS extrapolation limit for all complexes is large, and it is included in the supportinginformation of our published work on the matter (see reference 171).We evaluated the performance of a set of DFT methods120,123,125–127,132,134,191,192 against ourbenchmark binding energies. The result of this exercise is reported in Figure 3.5. This graphshows the mean absolute error (MAE) for each DFT approach; B3LYP-D3(BJ)/6-31+G**-BSIP,which we used as part of our procedure to generate the complex structures, has a 0.44 kcal/molMAE value, which suggests that the method was suitable for the structure optimization step ofour calculations. We also note that BLYP-D3(BJ)/6-31+G**-BSIP and M05/6-31+G** reproducethe binding energies most closely amongst all of the DFT approaches assessed (MAEs of 0.25 and0.26 kcal/mol, respectively). Our analysis of noncovalent interactions in the next section uses thebenchmark energies; however, assessing the performance of a variety of DFT methodologies providesvalue to those members of the computational chemistry community searching for a suitable DFTmethod for modelling noncovalent interactions in aqueous organic media.603.3. NONCOVALENT INTERACTIONS IN AQUEOUS ORGANIC MEDIA ARE INTRICATEFigure 3.3: Two-point extrapolation to the CBS extrapolation limit for one of the binding energiesbetween the decamer 10PP2 and methyl acetate. Our benchmark binding energies are the averageof the CP and non-CP binding energies at the CBS extrapolation limit (DZ-TZ). Colour code, red:oxygen, blue: hydrogen, and magenta: carbon. Dashed lines indicate HB interactions.3.3 Noncovalent Interactions in Aqueous Organic Media areIntricateIn the previous section, we described how to obtain a large set of water cluster-probe configura-tions at a high level of theory (DLPNO-CCSD(T)/CBS). Figure 3.6 shows all of these benchmarkbinding energies (BEs) obtained for the dimethyl ether molecule and all of the different water clus-ters. Dimethyl ether is a symmetrical molecule and represents the simplest from the set of organicmolecules considered in this chapter. For this reason, the discussion here will be focused on thisparticular molecule. The BE data cover an energy range of -0.19 kcal/mol to -8.42 kcal/mol. Acareful inspection of the structures of the complexes associated with Figure 3.6 led us to identifysix different classifications of noncovalent interactions, as shown in Figure 3.7. The vdW label rep-resents all weak interactions that do not involve an −OH group from the water clusters donatingan HB to the probes; dispersion, dipole-dipole, and C−H · · · (H2O)n interactions are included inthe vdW category. The Monomer type corresponds to the H2O molecule donating a hydrogenbond to the heteroatoms in the organic molecules. In the case of the water dimer, there are two613.3. NONCOVALENT INTERACTIONS IN AQUEOUS ORGANIC MEDIA ARE INTRICATEFigure 3.4: Two-point extrapolation to the CBS limit for one of the binding energies between thehexamer 6CC and azomethane. Our benchmark binding energies are the average of the CP andnon-CP binding energies at the CBS extrapolation limit (DZ-TZ). Colour code, red: oxygen, blue:hydrogen, magenta: carbon, and maroon: nitrogen. Dashed lines indicate HB interactions.possibilities: DD, when the water molecule is a double HB donor (one HB donated to the probeand one donated to the other water molecule), and SDSA if it is both a single donor (HB to theprobe) and an acceptor of an HB (from the other water molecule). There are only two types of HBswhen considering water clusters from the trimer to the decamer: DDSA, in which the donatingwater is a double donor and a single acceptor of HB, and DDDA, where the water molecule actsas a double HB donor and double acceptor. This classification is applicable to the rest of thecomplexes formed with all probes. Analogous graphs for the remainder of the organic moleculescan be found at the end of this thesis (Appendix A). They all display a similar pattern and thesame type of noncovalent interactions. The only exception is dimethylamine, which presents anadditional interaction when the organic molecule donates an HB (N−H) to an oxygen atom in awater cluster; this interaction is usually found to contribute ca. -2 kcal/mol to -3 kcal/mol to theBE.The vdW interactions portrayed in Figure 3.7 can occur with, and increase the strengths of,other types of interactions, especially theDDDA andDDSA types. The majority of vdW+DDDA623.3. NONCOVALENT INTERACTIONS IN AQUEOUS ORGANIC MEDIA ARE INTRICATE 0 0.5 1 1.5 2 2.5 3BLYP B3LYP CAM-B3LYP M05 M05-2X M06 M06-2X PBE PBE0DFT FunctionalD3BSIPBSIP-D3MAE (kcal/mol)MethodFigure 3.5: Mean absolute errors for a diverse set of DFT functionals using 6-31+G** as basis setswith respect to our benchmark binding energies. MAE = 1N∑ |Benchmark BE− BEDFT|, N runsfor all the 2376 complexes. The legends D3 (red) and BSIP (orange) represent the use of empiricaldispersion and basis set incompleteness potentials. The legend BSIP-D3 (cyan) is the combineduse of both BSIP and D3 corrections and Functional (purple) represents the DFT method withoutthe two corrections.and vdW+DDSA interactions are obtained in larger clusters; in most cases, the water clusterslarger than the trimer are able to accommodate secondary interactions between aliphatic hydrogensand the water cluster. However, in some cases, a vdW+SDSA type complex can be observed,as shown in Figure 3.8. Plotting the benchmark BEs using this classification of noncovalent inter-actions results in Figure 3.9. From this graph, and taking the most stable complex in each case,type vdW emerges as the weakest of the organic molecules-water cluster complex interactions be-cause it involves primarily dispersion, C−H · · · (H2O)n, and dipole-dipole interactions. For theHBs present in the monomer and dimer clusters, the following order of BE strength is observed:DD<Monomer<SDSA<vdW+SDSA. The weakest of these interactions is the DD since itforms a hydrogen bond with the probe through a water molecule that is acting as a double HB633.3. NONCOVALENT INTERACTIONS IN AQUEOUS ORGANIC MEDIA ARE INTRICATE-9.0-8.0-7.0-6.0-5.0-4.0-3.0-2.0-1.00.0 1 2 3 4 5 6 7 8 9 10Binding energy (kcal/mol)(H2O)nFigure 3.6: Profile of all binding energies for dimethyl ether and (H2O)n (with n = 1-10) at ourbenchmark level of theory.donor. As Figure 3.7 depicts, the water donating an HB to the organic molecule is also donatingan HB to a neighbouring molecule of water: accepting electronic density from both molecules andreducing the HB donating capabilities of the central water. For SDSA and vdW+SDSA, thewater molecule donating an HB to the probe is also acting as an HB acceptor of another watermolecule. This is the well-known “cooperative” effect in hydrogen bonding:159–163 The water boundto the probe is electron deficient because it is donating electron density to a neighbouring watermolecule, making the former water better able to accept electron density from the organic molecule.This effect is also at play in the vdW+SDSA systems, which interactions are further enhancedby the secondary vdW interactions. The monomer, which lacks neighbour water molecules actingas HB acceptors or donors, falls between the two dimer cases.Figure 3.8 displays the following order of BE strength for the trimer to the decamer of the waterclusters: DDSA < DDDA < vdW+DDSA < vdW+DDDA. In these cases, all interactions643.3. NONCOVALENT INTERACTIONS IN AQUEOUS ORGANIC MEDIA ARE INTRICATEvdW Monomer DD SDSADDSA DDDAFigure 3.7: Classification of noncovalent interactions found in dimethyl ether-water cluster com-plexes. Colour code, red: oxygen, blue: hydrogen, and magenta: carbon. Dotted lines indicateeither HB or C−H · · · (H2O)n interactions. See text for definitions of the classifications.involve a water molecule acting as a double hydrogen bond donor to a different water molecule andthe organic molecule, and the water accepting a single HB from a neighbouring water (DDSA)or the water accepting two HBs from two neighbouring waters (DDDA). For the same argumentsgiven in the dimer example discussed in the previous paragraph, a water molecule accepting moreHBs from neighbouring waters is a better HB donor than one accepting fewer HBs. ThereforeDDDA motifs result in stronger BEs than DDSA. Likewise, vdW+DDDA represents a morestable interaction with respect to vdW+DDSA, with extra stability due to the secondary vdW653.3. NONCOVALENT INTERACTIONS IN AQUEOUS ORGANIC MEDIA ARE INTRICATEvdW+DDDA vdW+DDSA vdW+SDSAFigure 3.8: Some of the noncovalent bonds defined in Figure 3.7 can gain additional stability whencombined with type vdW interactions. Colour code, red: oxygen, blue: hydrogen, and magenta:carbon. Dashed lines indicate either HB or C−H · · · (H2O)n interactions.-9.0-8.0-7.0-6.0-5.0-4.0-3.0-2.0-1.00.0vdW DDMonomerDDSADDDASDSAvdW+SDSAvdW+DDSAvdW+DDDABinding energy (kcal/mol)Figure 3.9: Benchmark binding energies for dimethyl ether and (H2O)n (with n = 1-10) classifiedaccording to Figures 3.7 and 3.8.interactions. Similar hierarchies, based on the donating and acceptor capabilities of water, havebeen proposed in the past to classify hydrogen bonds within water clusters.169,170663.3. NONCOVALENT INTERACTIONS IN AQUEOUS ORGANIC MEDIA ARE INTRICATE-11.0-10.0-9.0-8.0-7.0-6.0-5.0 1 2 3 4 5 6 7 8 9 10Binding energy (kcal/mol)(H2O)ndimethyl etheroxiranemethyl acetateacetoneazomethanetrimethylaminedimethylamineFigure 3.10: Benchmark binding energies profile of the most stable complexes found for eachorganic molecule.The analysis of the most stable complex of each water cluster with each of the organic moleculesshows that the profile of benchmark BEs (Figure 3.10) has an irregular trend with increasing n in(H2O)n without appearing to reach an asymptote by n−10. To explain this trend in the curves, wenoted that the water cluster displaying the strongest HB interactions belongs to the water heptamer- this is the largest water cluster presenting a book-like shape, which allow for vdW+DDDAtype interactions. Of the 11 heptamer structures we obtained from the literature,176 six are openstructures (i.e. they do not form cages or prisms). In contrast, the structures of the octamer,nonamer, and decamer include only 6 structures in total, all of which have cage-like structures inwhich further stabilization via vdW interactions is absent or not optimal. Figure 3.11 illustratesthis using complexes formed between (H2O)n and dimethylamine. These findings suggest that themagnitude of the BEs obtained with the heptamer is likely to be quite close to the maximum HBstrengths for this type of system.673.3. NONCOVALENT INTERACTIONS IN AQUEOUS ORGANIC MEDIA ARE INTRICATEProbe Benchmark BE (kcal/mol) Benchmark BE (kcal/mol) βH2heptamer+vdW heptamerDimethyl ether -8.42 -7.35 0.45Oxirane -8.88 -7.58 0.48Methyl acetate -8.99 -8.05 0.45Acetone -9.41 -7.65 0.49Azomethane -10.19 -8.86 0.64Trimethylamine -10.75 -9.91 0.67Dimethylamine -10.76 -9.77 0.66Table 3.2: Benchmark binding energies of the most stable complexes between heptamers and allprobes; in the presence and absence of vdW interactions and Abraham’s parameters193,194 forHB basicity. βH2 values for diethyl ether, THF and pyridazine were used, due to their structuralsimilarity, for the dimethyl ether, oxirane and azomethane molecules, respectively.The type of organic molecule is also a significant factor in determining the strength of theHB binding. Table 3.2 displays the benchmark binding energies for the most stable heptamercomplexes per organic molecule, with and without vdW interactions along with their correspondingAbraham’s HB basicity parameters.193,194 This parameter βH2 indicates the ability of a specificmolecule to accept a hydrogen bond; in their scale, Abraham’s HB basicity parameters place non-basic compounds like alkane at zero and more basic molecules at higher values. The data showsthat the nitrogen-based probes produce the more stable complexes of the set. These BEs followthe trend expected based on Abraham’s HB basicity scale. Table 3.2 also shows that nitrogen-containing molecules are more basic than oxygen-based probes, which indicates that nitrogen is abetter HB acceptor than oxygen; this is in agreement with the heptamer+vdW values in the sametable. For dimethyl ether, oxirane, methyl acetate, and acetone with BEs of -8.42, -8.88, -8.99,and -9.41 kcal/mol, respectively, the βH2 values increase, except for oxirane, monotonically overthe series from 0.45 to 0.50. For the nitrogen-containing probes azomethane, trimethylamine, anddimethylamine, with BEs of -10.19, -10.75, and -10.76 kcal/mol respectively, the βH2 are 0.64 (usingpyridazine to represent azomethane), 0.67 (using Et3N), and 0.70 (using Et2NH). Interestingly, theBE values in Table 3.2 do not correlate very well with Abraham’s parameters in the absence ofvdW. Also, the difference between heptamer and heptamer+vdW binding energies vary by 0.84 to1.76 kcal/mol, depending on the probe; for example, acetone benefits most from vdW stabilizationprobably due to their acidic alpha hydrogens.683.3. NONCOVALENT INTERACTIONS IN AQUEOUS ORGANIC MEDIA ARE INTRICATE7CH3 - dimethylamine complex (vdW+DDDA)BE = -10.76 kcal/mol8S4 - dimethylamine complex (DDDA)BE = -9.17 kcal/molFigure 3.11: The formation of the shown complex between cluster 7CH3 and dimethylamine leadsto the strongest binding energy of all; the strong interaction occurs via a DDDA interaction thatis stabilized by vdW interactions. The strongest interaction among octamers and dimethylamineis also displayed; there is no additional vdW stabilization for this case. Colour code, red: oxygen,blue: hydrogen, magenta: carbon, and maroon: nitrogen. Dashed lines indicate either HB orC−H · · · (H2O)n interactions.-9.0-8.0-7.0-6.0-5.0-4.0-3.0-2.0-1.00.0Monomer2Cs3UUD3UUU4Ci4Py4S45CAA5CAB5CAC5CYC5FRA5FRB5FRC6BAG6BK16BK26CA6CB16CB26CC6PR7BI17BI27CA17CA27CH17CH27CH37HM17PR17PR27PR38D2d 8S49D2dDD9S4DA10PP110PP2Binding energy (kcal/mol)Figure 3.12: Benchmark binding energies for dimethyl ether and individual clusters as labelled inTable 3.1.Finally, the benchmark binding energies per individual clusters for the dimethyl ether (Figure3.12) show a similar distribution of the BE from the pentamer to the decamer. Some complexes forthe 6BAG, 7CH3, and 7PR2 clusters are more stable than the rest complexes; this situation can693.3. NONCOVALENT INTERACTIONS IN AQUEOUS ORGANIC MEDIA ARE INTRICATEbe explained in terms of vdW stabilization. Again, since the (H2O)8-10 systems are all cage-like,the vdW stabilization is not present or not as favourable as in the open water cluster complexes.Setting aside the methyl acetate, which is the less symmetrical and the most structurally complexof the probes, all organic molecules show a similar distribution of binding energies (see AppendixA).We can expect that aqueous organic chemistry reactions involving the moieties present in ourorganic molecules would behave similarly when interacting with water molecules. Real water-organic complexes will involve significant dynamics in HB formation between the organic moleculesand the water systems with which they interact, resulting in fluctuations in BE over time. Wesuspect that the maximum strength of the BEs achievable will likely be relatively close to thosecalculated for the probe-(H2O)7.It is important to note that the present results are representative of interactions occurring inthe gas-phase, for which entropic effects are important. That is, the formation of large complexesis not favoured due to the rapid decrease of entropy with cluster size. However, in aqueous media,the formation of large (H2O)n systems is enthalpically promoted because of the formation of largeHB networks so that organic molecules can interact with the already available free −OH groups.Hence, we expect that the results presented herein will guide computational chemists to build morerepresentative models of organic reactions occurring in aqueous media. For example, in the useof implicit solvent models, sometimes the inclusion of a few explicit water molecules is required,and, according to our results, a single monomer of water interacting with a heteroatom in a probeunderestimates the potential stabilizing effects that may arise in situations where larger waterclusters may be involved, even transiently (see Fig. 3.10).In summary, the analysis of noncovalent interactions between organic molecules and waterclusters presented in this chapter provides an understanding of the kinds of interactions that mightbe occurring in aqueous organic phenomena. It was found that, while contact between a heteroatomin the organic molecules and an −OH group from the cluster is required for a strong interaction,additional interactions from aliphatic hydrogens can provide extra stabilization to the complexes.We showed that the nature of the water molecule interacting with the organic species, whether it isacting as a single or double HB acceptor or donor, determines the strength of the binding energies ofthe complexes. In addition, the nature of the HB acceptor in the organic molecule is an important703.3. NONCOVALENT INTERACTIONS IN AQUEOUS ORGANIC MEDIA ARE INTRICATEdeterminant of HB strengths. Also, the presence of multiple HB acceptors in the organic moleculescan lead to a more complex distribution of the BEs. For instance, methyl acetate can engagein many of the classes of interactions identified in this work. Within the context of OWRs, thewide range of binding energies displayed between all the organic molecules and the water clustershighlights the many ways organic molecules can form stable complexes when interacting with waterclusters; this implies that there is an opportunity for organic reactants in the oil phase to stronglyinteract with −OH from water molecules in the aqueous phase in an OWR.These results suggest that organic molecules with HB acceptors in their structures can attachto the water interface via strong noncovalent interactions and undergo “on water” catalysis; suchinteractions would also allow for charge transfer processes to occur between the aqueous and organicphases. Hydrogen bonding at the interface would also help fix the organic molecules in specificorientations, relative to the interface, potentially enabling electric field catalysis. Finally andoverall, this chapter also illustrates the intricate nature of reactions in the presence of aqueousmedia. It provides a novel benchmark data set for organic molecule-water cluster binding energiesthat can be used to assess computational methods that describe noncovalent interactions.71Chapter 4Exploring the OWR MechanismUsing Computational MethodsAs described in the introduction of this thesis, independent experiments supporting eitherthe dangling −OH or the proton-transfer mechanism have been reported in the literature.46,50These contradictory reports reflect how both theories cannot describe the wide range of acceleratedreactions occurring via the “on water” mechanism. The most recent model21 tries to address theseissues by proposing that interfacial water molecules create collective dipole orientations that dictatethe relative positions of reactants and transition states. For simplicity, we will refer to the proposedOWRmechanisms as HB, PT and dipole models. Clearly, elucidating the OWRmechanism requiresmore analysis from both experimental and theoretical perspectives.In the previous chapter, we demonstrated that organic molecules containing HB acceptors havethe potential to form strong interactions with water molecules. Such strong interactions betweenorganic and water molecules at the interface are central to the HB mechanism and, at the sametime, are a necessary step for a proton-transfer process. In addition, noncovalent interactions atthe water-oil interface can increase the amount of time organic molecules spend there. In otherwords, our results up to this point suggest that elements of the three proposed mechanisms maybe operating simultaneously.In the present chapter, we explore the proposed OWR mechanisms using computational meth-ods. To this end, we evaluated the effects present in complexes formed between small water clusters(H2O)n, with n = 1-10, and organic molecules. The analyzed interactions mainly involve HBs fromthe water clusters to the organic molecules modulating the energy barriers of Diels-Alder cycload-ditions and Claisen rearrangements. These reaction models are suitable because they representclassic examples of organic reactions displaying an “on water” character;20 in addition, they each724.1. HB MECHANISMshow a rate-limiting step of reaction that is well-defined. We also evaluated the effect of the collec-tive dipoles in our reaction models. For this purpose, we employed (in addition to QM methods)molecular dynamics simulations to understand the behaviour of aqueous-organic systems in thecondensed phase. Attempts to explore the PT mechanism were made but with little success. In thefollowing sections, we describe our exploration of the proposed mechanisms for OWRs in detail.4.1 HB MechanismThe International Union of Pure and Applied Chemistry defines hydrogen bonding as an attrac-tive interaction involving a hydrogen atom and an atom or group of atoms. A hydrogen bond hasthe generic X−H · · ·Y − Z form, where the dots represent the HB.195 In this molecular complex,X−H is the HB donor and X is more electronegative than H and Y − Z is the HB acceptor, whichis rich in electrons. The attractive forces involved in HBs are mainly electrostatic but also includesthose arising from charge transfer due to orbital overlap. Dispersion interactions also play a rolein hydrogen bonding, although to a minor degree compared to electrostatic and charge transferinteractions. Figure 4.1 displays a representation of the hydrogen bond in the water dimer; uponthe formation of the HB, the lone pair orbital in the water on the right (HB acceptor) interacts withthe σ∗ antibonding O−H orbital in the water molecule on the left (HB donor). As a consequence,σ∗ becomes populated and the O−H bond elongates. The weakening of this bond manifests asa red shift in its stretching IR frequency. In the following subsections, we explore the effects ofhydrogen bonding and its charge transfer and electrostatic components in OWRs.To the best of our knowledge, current quantum chemistry literature exploring the effect ofhydrogen bonding in OWRs involves only a few water molecules to represent these complex sys-tems.40,172,173 In the previous chapter, we analyzed the impact of the size of water clusters on thebinding energies of organic molecule-water cluster complexes; in this chapter, we evaluate the effectof water clusters of different sizes in accelerating OWRs by analyzing how the presence of suchclusters affect the energy barriers of model “on water” reactions. Again, while the three proposedmechanisms for OWRs have been reported as independent phenomena, they are necessarily related.To illustrate this, Figure 4.2 shows how an HB is required in order for a proton transfer to occur.Likewise, the relative orientations described in the dipole model strictly depend on the hydrogen734.1. HB MECHANISMFigure 4.1: Representation of a hydrogen bond between two water molecules: the water that isacting as HB acceptor has a lone pair orbital that interacts with the σ∗ O−H antibonding orbitalin the water molecule acting as HB donor. Only the relevant interacting orbitals are shown.Figure 4.2: Schematic representation of a PT process between the water and acetone moleculesforming a hydroxide ion and a protonated acetone. A hydrogen bond is necessary for a protontransfer to occur, relative dipole orientation are also highly dependent on the formation of HBs.bond network formed at the oil-water interface. Hence, hydrogen bonding must play a central rolein the reactivity of “on water” reactions.4.1.1 Computational Approach for the Analysis of OWRsMany of the reported “on water” reactions in the literature involve pericyclic reactions withsubstrates containing oxygen or nitrogen;19–22 hydrogen bonds will form between the water clusters(acting as HB donors) and these heteroatoms in the organic molecules (accepting HBs), accordingto the HB mechanism and as demonstrated in the previous chapter.40 Consequently, we exploredthe Claisen rearrangements and Diels-Alder cycloadditions displayed in Figures 4.3 and 4.4, re-spectively. Organic reactions, such as Diels-Alder cycloadditions, have been studied in40,172,173and outside196,197 of the context of aqueous organic reactions using DFT by employing the B3LYPfunctional129,130,180 with the 6-31+G** basis set.198,199 In the absence of empirical dispersion andwith small basis sets, error cancellation often leads to results that agree with experimental databut for the wrong reasons. Due to this situation, we decided to incorporate empirical disper-sion corrections into OWRs modelling, which is important for the accurate description of organicsystems.142 Hence, we used B3LYP129,130,180-D3(BJ)138–141/6-31+G**-BSIP145 to optimize thestructures shown in Figures 4.3 and 4.4, employing Gaussian 16.102 This methodology was usedin the previous chapter in the analysis of noncovalent interactions and was also validated against744.1. HB MECHANISMFigure 4.3: Model reactions for Claisen rearrangements in this thesis. X = O or NH. The labels R,TS, and P represent reactants, transition states, and products, respectively.Figure 4.4: Model reactions for the Diels-Alder cycloadditions. X = O or NH. DielsAlderRX is arepresentation of the pre-reaction complex formed with diene and dienophile molecules. The labelsR, TS, and P represent reactants, transition states, and products, respectively.high-level quantum chemistry methods. In this case, though, we used the confab 200 utility from theOpen Babel201 program to generate initial guesses for the reactants and products, and we reliedon chemical intuition for obtaining the transition states.The full understanding of the structural features of bulk water is still an open question inscience;202 their representation in chemical modelling is complicated and has represented an activetopic of research over the years.203–205 However, comprehensive investigations employing high-levelwave-function methods on small water cluster structures are available in the literature.174–176 Inthe same fashion as our analysis of noncovalent interactions in aqueous organic settings, we tookselected structures from the water clusters data set by Temelso176 et al., from the monomer tothe decamer. These (H2O)1−10 structures, which have been used for benchmarking purposes, wereoptimized at the RI-MP2177,178/aug-cc-pVDZ179 level. We again fixed these water clusters at thegeometries determined by Temelso for all of our calculations; all of our structure optimizationsand conformer search strategies involved constraining the water cluster molecules to their reportedbenchmark structures. We then optimized the organic molecules from Figures 4.3 and 4.4, at theB3LYP-D3(BJ)/6-31+G**-BSIP level of theory, in the presence of the frozen structures of the754.1. HB MECHANISMwater clusters to calculate the barriers associated with the following reactions:ClaisenRX · · · (H2O)n → ClaisenTSX · · · (H2O)n, (4.1)DielsAlderRX · · · (H2O)n → DielsAlderTSX · · · (H2O)n, (4.2)where n = 1-10 and X = O or NH (see Figures 4.3 and 4.4 for additional definitions). To generateinitial structures for these reactions, we utilized MacroModel206 as implemented by Schro¨dingerInc.207 in the Maestro software.208 With the water clusters fixed to their benchmark structures,a mixed torsional/large-scale low-mode sampling search combined with OPLS209 force-field opti-mization were carried out for each complex in reactions 4.1 and 4.2. We used optimized organicmolecules at B3LYP-D3(BJ)/6-31+G**-BSIP for these conformational searches. However, we hadto additionally constrain the relevant atomic distances in the transition state systems in order topreserve the important reactivity features of the Claisen and Diels-Alder reactions; i.e., we fixed theatomic distances associated to bonds being formed and broken in the gas-phase TS structures. Withthe outputs from the conformational searches of Maestro, we re-optimized the organic moleculesin the organic molecule-water cluster complexes employing B3LYP-D3(BJ)/6-31+G**-BSIP. Fromthe generated conformers in the previous step, we kept the energetically lowest-lying structure. Wethen calculated the energies along the Intrinsic Reaction Coordinate (IRC), employing the samelevel of theory calculations, to generate guesses for the optimization of the pre and post-reactioncomplexes connected to the TSs.The selection of the (H2O)n systems to form our complexes was planned by considering theresults of Chapter 3.171 In addition to the cluster size, we demonstrated that the type of dangling−OH bond, the nature of the accepting HB molecule, and dispersion interactions involving -CHgroups can all contribute to the binding energies of an organic molecule-water cluster complex. Inlight of these insights, we ensured that the selected water clusters for this work could form stablecomplexes with organic molecules. Also, we employed the same method used for the optimizationof the organic molecules in the complexes as in the previous chapter, B3LYP-D3(BJ)/6-31+G**(MAE of 0.44 kcal/mol for binding energies with respect to DLPNO-CCSD(T)/CBS, see Chapter3), followed by single point (SP) energy computations on the optimized structures of the chemical764.1. HB MECHANISMspecies displayed in reactions 4.1 and 4.2 using a DLPNO-CCSD(T)186/CBS190 two-point aug-cc-pVDZ and aug-cc-pVTZ179 extrapolation scheme. The ORCA103 software was employed forthis calculation step. AIMAll210 was employed for the QTAIM calculations, and Chemcraft185 tovisualize molecular systems. Figures displaying the structures of transition states and informationregarding Cartesian coordinates and energies can be found in Appendix B.We used the DLPNO-CCSD(T)/CBS barrier energies associated with the formation of transi-tion states for Reactions 4.1 and 4.2 for benchmarking purposes. An evaluation of the BLYP,123,130CAM-B3LYP,134 M05,125 M05-2X,126 M06,127 M06-2X,127 PBE,120,191 and PBE0,132,192 function-als with the 6-31+G** basis set was carried out. The effect of including empirical dispersioncorrections and BSIPs was considered as well. Our evaluation shows that M05-D3/6-31+G**-BSIPperforms best with an MAE of 0.86 kcal/mol with respect to our benchmark data. The complete setof mean absolute errors can be seen in Figure 4.5. These results agree with recent reports showingthat pericyclic reactions are best described by hybrid functionals with dispersion corrections.211B3LYP-D3(BJ)/6-31+G**-BSIP, the method employed to generate the structures of the com-plexes, is not the best performing functional according to Figure 4.5. Also, fixing the water clustersto their benchmark structures might raise questions regarding changes in the constrained modelsupon the relaxation of the structures. In order to address these issues, we performed a validationof the methodology. For that purpose, first, we re-optimized the organic part of four transitionstates from reactions 4.1 and 4.2 with (H2O)10 but employed the best performing method (M05-D3/6-31+G**-BSIP). Then, we re-optimized the same systems at the same level of theory but nowreleased the constraints we previously imposed on the structures of the water clusters. The resultsof this exercise are shown in Table 4.1 and Figure 4.6. The root-mean-square deviation (RMSD) ofthe atomic positions of the complexes shows that the variations in the atomic positions of the com-plexes are minimal when switching between DFT methods; this validates our obtained structuresat the B3LYP-D3(BJ)/6-31+G**-BSIP level of theory. Figure 4.6(b) also shows that the RMSDvalues increase modestly after releasing the structure constraints, and the connectivities in the HBnetwork in the organic molecule-water cluster complex remain the same as those in the constrainedcomplex, thus validating our computational approach. For computational studies using DFT forthe analysis of reactions in the presence of water, we recommend and use M05-D3/6-31+G**-BSIPas level of theory, as this method generates energy barriers with errors lower than 1 kcal/mol with774.1. HB MECHANISM 0 1 2 3 4 5 6 7 8 9 10 11 12BLYP B3LYP CAM-B3LYP M05 M05-2X M06 M06-2X PBE PBE0DFT FunctionalD3BSIPBSIP-D3MAE (kcal/mol)MethodFigure 4.5: Mean absolute error (MAE) in reaction energy barriers for different DFT methodsusing 6-31+G** as basis sets compared to our benchmark barrier energies (formation of TSs, seereactions 4.1 and 4.2).MAE = 1N∑∣∣∣EbarrierDLPNO−CCSD(T)/CBS − EbarrierDFT ∣∣∣, where the sum goes over all calculated energybarriers. The red and orange bars represent values using empirical dispersion and basis set incom-pleteness potentials, respectively. The cyan bar combines the previous two, and the purple (DFTFunctional) shows the errors in the absence of both. When empirical dispersion was employed,BJ-damping was included.respect to DLPNO/CBS for both, binding energies and energy barriers.4.1.2 The Effect of HBs in OWRsChapter 3 showed that the strongest interactions often arise when the HB donor to the organicmolecule is a water molecule that accepts two HBs from neighbouring water molecules. Also,a secondary interaction was shown to provide extra stabilization to the complexes. In light ofthese results, we were able to select and design complexes with optimal interactions between thewater molecules and the organic molecules for this thesis. On the other hand, fixing the water784.1. HB MECHANISMB3LYP-D3(BJ) M05-D3 (water clusters fixed)Complex vs. vs.M05-D3 M05-D3 (no constraints)RMSD (A˚) RMSD (A˚)ClaisenTSNH 0.062 0.326ClaisenTSO 0.090 0.163DielsAlderTSNH 0.083 0.172DielsAlderTSO 0.068 0.134Table 4.1: RMSD of atomic positions for the complex formed between the modeled reactions andthe water cluster (H2O)10. Comparison between the best performing method (M05-D3/6-31+G**-BSIP) and the method used for our structures (B3LYP-D3(BJ)/6-31+G**-BSIP). The changes inatomic positions due to releasing the constraint water molecules at the M05-D3/6-31+G**-BSIPlevel are also shown.Figure 4.6: Overlapped structures of DielsAlderTSO. (a) B3LYP-D3(BJ)/6-31+G**-BSIP vs.M05-D3/6-31+G**-BSIP (water clusters fixed), RMSD = 0.068 A˚. (b) M05-D3/6-31+G**-BSIP(water clusters fixed) vs. M05-D3/6-31+G**-BSIP (no constraints), RMSD = 0.134 A˚.794.1. HB MECHANISMmolecules to their high-level structures permitted us to test the effect of HBs on the energetics ofthese reaction barriers directly. Freezing the water cluster structures has limitations as a model;however, it provides certain technical advantages and helps us avoid issues in large-sized complexesinvolving many water molecules. For example, proton transfer between water molecules can occurdue to cooperative effects in water clusters via the Grotthuss mechanism.212 This side reactionis undesired for the purposes of this chapter because it would impede our ability to analyze thepure effect of HBs on the energy barriers. Similarly, molecular rearrangements within the reactionmodels along the reaction path would lead to the potential solvation of the organic molecules. Theseeffects have the potential to mask the pure effect of hydrogen bonding in the energy barriers ofthe reactions studied herein. Our approximate model of “on water” reactions is much simpler thanthe real representation of the reaction. However, to gain more fundamental insights into the OWRmechanism, we designed our model and methodology to focus on the critical aspects of OWRswithin the HB model, hydrogen bonding between water clusters and organic molecules.The presence of noncovalent interactions between the water clusters and the organic moleculeshas a critical impact on the energy barriers of the reaction models. Our computed energy barriers(EBs) at our benchmark level (DLPNO-CCSD(T)/CBS) demonstrates that there is a reduction inthe energy barriers as a consequence of adding water molecules to the molecular complexes; thisenergy reduction is observed in all cases. Figure 4.7 summarizes the energy barriers associated withthe formation of TSs in reactions 4.1 and 4.2; the green line represents the EBs in the absence ofwater, while the purple dots depict the barriers when water clusters interact with the reactant(s)and the TSs. For all cases, the barriers in the presence of (H2O)n fall below the green lines,meaning that the interactions between the water HB-donating molecules in the clusters and theHB-accepting heteroatoms in the organic molecules produce a noticeable reduction of EBs in thecycloadditions presented in this work. As a reference, the electronic energy barrier for the reactionbetween cyclopentadiene and nitroethylene, with −NO2 being a strong electron-withdrawing groupthat promotes Diels-Alder reactions, is 12.1 kcal/mol at the B3LYP/6-31G* level of theory.213This value is comparable with the values obtained for our oxygen-based Diels-Alder reaction of13-14 kcal/mol in the presence of (H2O)n (see Figure 4.7(b)). These results suggest that hydrogenbonds from the water clusters to the organic substrates have an effect that reduces EBs as a strongelectron-withdrawing group similarly does for Diels-Alder cycloadditions. To further illustrate this,804.1. HB MECHANISM31.032.033.034.035.036.037.038.039.0 1 2 3 4 5 6 7 8 9 10Energy barrier (kcal/mol)Cluster size(a)12.013.014.015.016.017.018.019.0 1 2 3 4 5 6 7 8 9 10Energy barrier (kcal/mol)Cluster size(b)39.040.041.042.043.044.045.046.047.0 1 2 3 4 5 6 7 8 9 10Energy barrier (kcal/mol)Cluster size(c)14.515.015.516.016.517.0 1 2 3 4 5 6 7 8 9 10Energy barrier (kcal/mol)Cluster size(d)Figure 4.7: Benchmark energy barriers for all calculations; (a) oxygen-based Claisen rearrangement,(b) oxygen-based Diels-Alder reaction, (c) nitrogen-based Claisen rearrangement, (d) nitrogen-based Diels-Alder reaction. The green line represents the corresponding cycloaddition in the absenceof water, whereas the purple dots show the EBs of the same reactions as we add (H2O)n, n=1-10,to our systems.by making use of Eyring’s Equation214 at 298.15 K, a 100-fold increase in the kinetic constant of theaccelerated reaction requires only a reduction of 2.73 kcal/mol in the energy barrier. This impliesthat most of the reactions catalyzed by water shown in Figure 4.7 would present accelerationsgreater than 100 times the original reference gas-phase reaction; the only exception is the trimercase of nitrogen-based Claisen rearrangement (see Figure 4.7(c)) and the nitrogen-based Diels-Alderreaction models (see Figure 4.7(d)), which still display a reduction in EB energies, although of amore modest magnitude in both cases. The reported experimental activation energies are 19.7814.1. HB MECHANISM 41 42 43 44 45 46 47 48 49No water With (H2O)6gas phasebenzenewaterEbarrier (kcal mol-1)Figure 4.8: The effect of using a implicit solvent model (SMD) in the nitrogen-based Claisenrearrangement reaction with and without the hexamer of water. The inclusion of explicit watermolecules is necessary to reproduce the decrease in energy barriers. Calculations ran at the M05-D3/6-31+G**-BSIP level of theory.kcal/mol and 30.6 kcal/mol for the oxygen-based Diels-Alder reaction215 and the oxygen-basedClaisen rearrangement,216 respectively. The calculated benchmark EBs for the oxygen-based Diels-Alder is 18.4 kcal/mol, which is relatively close to the experimental value. On the other hand, thebenchmark EB for the oxygen-based Claisen rearrangement is 38.0 kcal/mol. It is important tonote that the Arrhenius activation energies are phenomenological. Although they are related tothe energy barriers, they are highly dependent on the conditions of the experimental setting. Still,the experimental activation energies suggest that our benchmark BEs convincingly illustrate theeffects of HBs on OWRs.We also emphasize that including explicit water molecules in organic reactions is necessary formodelling reactions such as OWRs, as depicted in Figure 4.8. In this graph, the energy barriersfor the nitrogen-based Claisen rearrangement reacting in the presence and absence of the waterhexamer is displayed; in both cases an implicit solvent model (SMD)217 for water and benzeneis applied. The plot shows that the inclusion of an implicit solvent model is not sufficient to824.1. HB MECHANISM-20.0-18.0-16.0-14.0-12.0-10.0-8.0-6.0-4.0 1 2 3 4 5 6 7 8 9 10Binding energy (kcal/mol)(H2O)nPre-reaction complexTS(a)-17.0-16.0-15.0-14.0-13.0-12.0-11.0-10.0-9.0-8.0-7.0 1 2 3 4 5 6 7 8 9 10Binding energy (kcal/mol)(H2O)nPre-reaction complexTS(b)-16.0-15.0-14.0-13.0-12.0-11.0-10.0-9.0-8.0-7.0-6.0 1 2 3 4 5 6 7 8 9 10Binding energy (kcal/mol)(H2O)nPre-reaction complexTS(c)-16.0-15.0-14.0-13.0-12.0-11.0-10.0-9.0 1 2 3 4 5 6 7 8 9 10Binding energy (kcal/mol)(H2O)nPre-reaction complexTS(d)Figure 4.9: Binding energies for the pre-reaction complex and transition state of allmodel reactions at the M05-D3/6-31+G**-BSIP level. The binding energies are defined asBE = E(R · · · (H2O)n)− E(R)− E((H2O)n). Where E(X) represents the electronic energy of sys-tem X. See Equation 4.3. (a) Oxygen-based Claisen rearrangement, (b) oxygen-based Diels-Alderreaction, (c) nitrogen-based Claisen rearrangement, and, (d) nitrogen-based Diels-Alder reaction.reproduce the energy barrier reduction that is obtained by using the explicit water molecules.Most importantly, the plot also shows that the energy barrier lowering is persistent even in thepresence of a large dielectric medium. These results highlight the importance of explicit solventmodels in computational chemistry in the context of OWRs. Reaction phenomena that are missedby implicit solvent models can be recovered using explicit solvent models.Jung and Marcus’ theory of dangling −OH bonds proposes that reactants interact more weaklywith the (H2O)n oligomers than transition states in OWRs; otherwise, we would not see a reduc-834.1. HB MECHANISMtion in the energy barriers and the characteristic acceleration effect of these reactions. Thus, weproceeded to evaluate the binding energies (BEs) of pre-reaction complexes and transitions stateswith water clusters, that is, to compute the electronic energy associated with the reactionsR + (H2O)n → R · · · (H2O)n, (4.3)at the M05-D3/6-31+G**-BSIP level of theory. Here, R represents a pre-reaction complex or a TSshown in reactions 4.1 and 4.2, and n = 1-10. These calculations show that, in general, these transi-tion states have larger BEs than their corresponding pre-reaction complexes in all reactions. Figure4.9(b) compares such binding energies for DielsAlderRO · · · (H2O)n and DielsAlderTSO · · · (H2O)n,from the monomer (n=1) to the decamer. The graphs for the other reactions can be found in Fig-ure 4.9; most of them show similar behaviour. The only exceptions are the tetramer and nonamercases of the nitrogen-based Diels-Alder reaction (see Figure 4.9(d)). In these reactions, both thepre-reaction complexes and transition states have BEs that are similar, showing that the TS doesnot have an extra stabilization via hydrogen bonding compared to the pre-reaction complex. Theseresults are consistent with those shown in Figure 4.7(d), where these two systems are the ones withless reduction in their EBs. These findings support the hypothesis of HB mechanism40 for “on wa-ter” reactions, which explains that TSs interacting more strongly with the water clusters, relativeto the pre-reaction complexes, is the cause of the EB reduction and the origin of the acceleratedreactivity in OWRs.The data displayed in Figure 4.7(b) show that the water effect for the oxygen-based Diels-Alder reaction is produced approximately in the same magnitude regardless of the number ofwater molecules present in the (H2O)n cluster. In other words, the reduction in their energybarriers seems to be uniformly independent of the size of the water cluster that participates in thereaction, with a reduction from 4.5 to 5.6 kcal/mol upon the addition of the water models. Similarfindings were obtained for the case of the oxygen-based Claisen rearrangement (Figure 4.7(a)),with reductions in the EBs from 4.1 to 5.6 kcal/mol. In both oxygen-based reactions, the EBreductions translate to an increase in the reaction rate constant of 3 to 4 orders of magnitude. Forboth nitrogen-based reactions, the variations in the reduction of EBs are larger; by examining thecase of DielsAlderTSN · · · (H2O)4 complex (Figure 4.7(d)), which only reduces its energy barrier by844.1. HB MECHANISMFigure 4.10: DielsAlderTSN · · · (H2O)4. The N-H in the organic molecule donates an HB back toan oxygen in the water cluster, the interaction was confirmed by a bond critical point between thehydrogen in the N-H group and the oxygen in (H2O)4.0.2 kcal/mol with respect to the gas-phase reaction, we notice that the nitrogen atom is not onlyaccepting an HB from the water cluster, but it is also donating its −NH to a neighboring oxygenatom in (H2O)4 (see Figure 4.10). Normally, when a hydrogen bond is formed, the HB acceptor,the nitrogen in this case, donates electron density to the HB-donor (the dangling −OH in the watercluster); this leads to a stabilization of the TS via an electron transfer from the organic moleculeto the water cluster, as shown in Figure 4.11. However, since the nitrogen in the DielsAlderTSNmolecule interacting with the tetramer of water is also donating its −NH to an oxygen atom in thewater cluster, it transfers electron density from the water tetramer back to the organic moleculeproducing a redistribution of the electron density within the complex. These effects are illustratedin detail in Figure 4.12, where the charges of the diene, dienophile and (H2O)n in the transitionstates are displayed as a function of water cluster size. In this figure, it is observed that the chargeof the diene and dienophile, in the tetramer complex, is less positive and negative, respectively,when compared to the charges of other complexes of different cluster size in the same figure. Thisexample and the nonamer of water interacting with DielsAlderTSN stand out as anomalous casesof distribution of electron density. The overall effect, in both cases, is a smaller reduction in thereaction EB compared to all other reactions.Other systems, such as ClaisenTSn · · · (H2O)7 (Figure 4.13), can form intricate combinationsof noncovalent interactions involving −CH · · ·OH2, even displaying the presence of bond criti-cal points. These findings confirm our previous conclusions on the importance and ubiquityof this weak interaction in forming organic molecule-water cluster complexes,171 and it also re-854.1. HB MECHANISM-0.050-0.045-0.040-0.035-0.030-0.025-0.020-0.015 1 2 3 4 5 6 7 8 9 10qn in (H2O)n(a)-0.050-0.045-0.040-0.035-0.030-0.025-0.020-0.015 1 2 3 4 5 6 7 8 9 10qn in (H2O)n(b)-0.060-0.055-0.050-0.045-0.040-0.035-0.030 1 2 3 4 5 6 7 8 9 10qn in (H2O)n(c)-0.060-0.055-0.050-0.045-0.040-0.035-0.030 1 2 3 4 5 6 7 8 9 10qn in (H2O)n(d)Figure 4.11: Charges of (H2O)n clusters (in atomic units) when they interact with the transitionstates in all reaction models. The water clusters become negatively charged when interacting withpolarized TSs. Charges were calculated using AIMAll and an M05-D3/6-31+G**-BSIP wavefunc-tion. (a) Oxygen-based Claisen rearrangement, (b) oxygen-based Diels-Alder reaction, (c) nitrogen-based Claisen rearrangement, and (d) nitrogen-based Diels-Alder reaction. The scale shows the zerovalue of charge (y-axis) in all cases, as a reference of a reaction in the absence of water molecules.veals that their study is more complex than originally assumed. Except for the already discussedDiels−AlderTSN · · · (H2O)4 complex, analysis of structural features of the other nitrogen-basedsystems does not directly conduct us to an explanation of their irregular behaviour displayed insome of the energy barrier plots.Prior studies213 have demonstrated that, for various Diels-Alder reactions, the charge transfer(CT) between diene and dienophile and their electronic activation energy of cycloaddition are864.1. HB MECHANISM-0.15-0.10-0.050.000.050.100.150.20 1 2 3 4 5 6 7 8 9 10qn in (H2O)nDieneDienophile(H2O)nFigure 4.12: Charges of the diene, dienophile and water clusters in DielsAlderTSN · · · (H2O)n.Charges were calculated using AIMAll and the M05-D3/6-31+G**-BSIP wavefunctions.correlated. On those same lines, the charges in Figures 4.11 and 4.12 modestly resemble the plotsin Figure 4.7. For instance, the trimer and heptamer of the nitrogen-based Claisen rearrangementrepresent the lowest values of charge transferred to water clusters in Figure 4.11(c), these transferredcharges seem to correspond with the lowest EBs in Figure 4.7(c). This situation is similar to howthe charges in Figure 4.12 explain the tetramer and the nonamer cases in Figure 4.7(d) for thenitrogen-based Diels-Alder reaction. These observations are reasonable since it is expected that,upon the formation of a hydrogen bond, orbital overlap between acceptors and donors of HBs willoccur leading to charge transfer.In light of the previous statements, we searched for correlation relationships between the chargetransfer in our systems and their corresponding energy barriers. For doing so, we employed AIMcharges obtained from the analysis of M05-D3/6-31+G**-BSIP wavefunctions and energy barriersat the DLPNO-CCSD(T)/CBS level. We found that, in general, correlation is poor. However,874.1. HB MECHANISMFigure 4.13: ClaisenTSN · · · (H2O)7. The C-H groups in the organic molecule back donate to oxygenatoms in the water cluster. The interactions were confirmed by a bond critical point between thehydrogen atoms in the C-H groups and the oxygen atoms in (H2O)7.in the case of the Claisen rearrangements, it was observed that the EBs correlate best with thecharge transferred to the whole organic molecules in complexes. On the other hand, Diels-Alderbarriers correlate best using the transferred charges to the diene within the organic molecule-watercluster complexes. The correlation for both oxygen-based reactions is relatively good, with valuesof r2 = 0.759 and r2 = 0.871 for the Claisen and Diels-Alder reactions, respectively. In contrast,the correlation is poor for the nitrogen-based models, with values of r2 = 0.198 (Claisen) andr2 = 0.627 (Diels-Alder). It is important to note that these correlations are heavily influencedby the gas-phase data (n = 0 in (H2O)n), which, upon removal from the dataset, produces poorcorrelations in all reactions. See Table 4.2 for a summary of all the correlations discussed in thisparagraph and Figures C.1 and C.2 in Appendix C for the linear fitting generated for the calculationof the correlation coefficients. Analyzing the charge transferred to individual atoms, specific watermolecules or other moieties in the organic molecules along the reaction path did not improve thecorrelations between the EBs and the transferred charges.According to the results in Table 4.2, the correlation for the OWR models (data without thegas-phase EB) is very poor in all cases, suggesting that, for the reactions analyzed in this thesis,CT does not explain the barrier reduction effect in “on water” reactions. While there is some884.2. ELECTROSTATIC EFFECTS IN OWRSSystem r2 (all data) r2 (all data without gas-phase barriers)Oxygen-based Claisen rearrangement 0.759 0.045Nitrogen-based Claisen rearrangement 0.198 0.094Oxygen-based Diels-Alder reaction 0.871 0.058Nitrogen-based Diels-Alder reaction 0.627 0.435Table 4.2: Correlations in charge transfer with the benchmark EBs. This table is a summary of thecorrelations shown in Figures C.1 and C.2, and adds the correlation of analogous plots but withoutthe gas-phase data.correspondence between charge transferred and EBs, as discussed in this subsection, orbital overlapand its associated charge transfer are not sufficient to explain the nature of the acceleration effectin “on water” reactions.4.2 Electrostatic Effects in OWRsIn the past five years, studies showcasing the role of strong electric fields at water interfaces andits role in the reactivity of chemical processes have represented an active research topic.39,69,71,218,219While not explicitly stated in the original dipole model by the authors, we hypothesized that thecollective dipoles at the water-oil interface would generate a strong and directed electric field. Inthe following subsections, we incorporate these ideas of catalysis due to a strong oriented electricfield and explore its effects in the context of OWRs.4.2.1 QM Calculations for the Study of the OWR Dipole ModelA dipole moment appears because of polarization of electron density in a molecule due todifferences in the electronegativity between atoms. It represents the polarity of a molecule due tocharge separation and is a vector quantity represented by88µsystem =∑i∈systemqiri, (4.4)where µsystem is the dipole moment vector of the system, qi is the charge of atom i within thesystem, and ri is the distance between the atom i and a reference. Notice that, for neutral systems,the dipole moment is independent of the reference; so, in most cases, the origin is selected forconvenience. Also, since the dipole moment is a vector, it can be the case where a molecule with894.2. ELECTROSTATIC EFFECTS IN OWRSpolar bonds has a net zero dipole, such as carbon dioxide. In summary, µsystem gives us informationabout the charge separation in molecular systems.A simple but effective way to test the effect of the collective dipoles and, at the same time,eliminate the charge transfer effects in our systems is substituting the explicit water molecules inour model OWRs with point charges. We took the optimized structures from the model OWRsemployed in the previous section of this chapter. Then the oxygens and hydrogens of the watermolecules in the complexes were substituted by point charges such that qO = −2qH = −0.834 a.u.Then we proceeded to perform single-point QM calculations on these systems at the M05-D3/6-31+G**-BSIP level. The selection of the point charges for the water molecules is not arbitrary: theyrepresent the charges that the model TIP3P (Transferable Intermolecular Potential with 3 Points)uses to simulate liquid water in molecular dynamics. This model has been employed widely in theMD community and has been carefully tailored to reproduce macroscopic experimental propertiessuch as density.220 The results of using this point charge model for water molecules are displayed inFigure 4.14 for the nitrogen-based Claisen rearrangement. The rest of the reaction models, whichdisplay similar behaviour, can be found in Appendix D.Figure 4.14 also includes the EB reductions from including explicit water clusters, as we didin the HB mechanism section (see Figure 4.7). It is observed, that in most cases, the use of pointcharges as water models reproduce the trend in EB reductions observed with the explicit (H2O)nmolecules, relative to the unassisted reaction in the gas-phase. In other words, the presence of acollection of charges in the vicinity of an organic reaction has the potential to modulate the energybarriers, at least in the case of the cycloadditions studied in this thesis. The results here suggest thatthe EB lowering effect observed is primarily due to the charge distribution in the water molecules,and that the orbital overlap component and concomitant charge transfer of the HB only modulatesthe barrier heights to a minor extent. Most remarkably, the point charge models can reproducethe benchmark EBs from the QM water-explicit models in Figure 4.7 with a mean absolute error(MAE) value of 0.9 kcal/mol. This result implies strongly that OWRs are a phenomenon that isdriven by the distribution of charges in the water clusters.In order to analyze the effect of the magnitude of the point charges in the modulation of EBsin OWRs, we took the model reaction between ClaisenRNH and the monomer of water. Then wechanged the magnitude of the oxygen charges from the TIP3P values to qO = −2qH = 0.834 a.u.,904.2. ELECTROSTATIC EFFECTS IN OWRS40.041.042.043.044.045.046.047.048.049.0 1 2 3 4 5 6 7 8 9 10Energy barrier (kcal/mol)n in (H2O)nPoint Charge (H2O)nExplicit (H2O)nFigure 4.14: Comparison in the reduction of energy barriers by explicit water molecules (fullyquantum, in yellow) and implicit water molecules (point charges, in blue) for the reaction withClaisenRNH. The red horizontal line represents the reference reaction in the gas-phase. We em-ployed M05-D3/6-31+G**-BSIP as the level of theory.using intervals of 0.1 a.u., while keeping qH = −qO/2. By inspection of Equation 4.4 we notethat, for charge values such that qO = −2qH > 0, the vector µH2O points to the opposite directionwith respect to its original orientation. This exercise allowed us to analyze the effect of the energybarriers due to the magnitude of the point charges. It also permitted us to evaluate the effect ofthe direction of the water dipole on EBs in our model systems. Figure 4.15 shows a near-linearrelationship between the magnitude of the water dipole and the energy barriers: the larger themagnitude of the point charges (or the larger the dipole), the larger the reduction in the energybarrier. We also note that once the charges of the oxygen atom become positive and the chargesof hydrogen negative, there is an opposite effect; an increase in the energy barrier relative to thegas-phase reference (green horizontal line in Figure 4.15). The analysis presented in this and theprevious paragraph emphasizes the importance of the direction and magnitude of the dipoles inmodulating EBs in “on water” reactions.Now, an arbitrary distribution of charges in space generates an electric field. For a given point914.2. ELECTROSTATIC EFFECTS IN OWRS42.043.044.045.046.047.048.049.050.051.052.0-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8Energy barrier (kcal/mol)q in oxygen from water (a.u.)Figure 4.15: Energy barrier modulation due to the magnitude of the charge in the oxygen atomin the water molecule. The trend is almost linear with the following equation: EB = 5.16qO +47.6, r2 = 0.995. The green horizontal line is the energy barrier for the reference gas-phase reaction.This reaction is the OWR between ClaisenRNH and H2O. We employed M05-D3/6-31+G**-BSIPas the level of theory.in space and a collection of i charges, the electric field is defined by221EField =14πε0∑iqirˆ0ir20i. (4.5)In this equation, qi is the charge of particle i, rˆ0i is the unitary vector from the ith charge to thepoint we are calculating EField, and r0i is the magnitude of distance vector between the referencepoint and charge i. If we place a test charge in the point of space where we calculate the electricfield, it is then possible to calculate the electric force exerted on the test charge due to the othercharges asF = qtestEField. (4.6)The dipoles of molecules have been observed to align with external electric fields.70 Additionally,it has been demonstrated that an external field can assist the formation of carbon-carbon bonds,71924.2. ELECTROSTATIC EFFECTS IN OWRSeffectively catalyzing organic reactions. In light of our results where the water point charges reduceEBs, we applied an external electric field to our OWR models to study its effect on the energybarriers. The constant external electric field was aligned to the C−N bond, as shown in 4.16. Wecalculated the energy barriers of this reaction using three different magnitudes of EField. Namely1.08, 6.94, and 15.02 eV e−1 nm−1; these quantities represent electric fields in n-hexane, water, andat the water-air interface, according to references 222 and 223. In the n-hexane and water cases,222the electric field was estimated by MD simulations. The values represent the projection of theelectric field into the C−O bond of a single acetophenone molecule surrounded n-hexane or water.In the case of the water-air interface,223 the value represents the peak EField value as determined byab initio molecular dynamics calculations. We report the effect that these electric field values haveon the EBs in the nitrogen-based Claisen rearrangement in Figure 4.17 and confirm that an orientedexternal electric field can reduce the energy barrier of the model OWR. The reduction in the EBsis proportional to the magnitude of the electric field and, in line with the findings of Shaik,71 theelectric field best catalyzes a reaction if its direction is aligned with bonds that are formed or brokenduring the reaction, or in this case, being modified from single to double bond. In our case, wefound that aligning EField with the C−N bond in the nitrogen-based Claisen rearrangement hadthe most dramatic effect in reducing the EBs. Another example is shown in Figure 4.18, where theoxygen-based Diels-Alder reaction was exposed to the same external electric fields, but this timealigning the field towards the direction of the C−C bonds being formed between the diene andthe dienophile. The general effect is the same as the one observed in the nitrogen-based Claisenrearrangement; a stronger electric field reduces more the energy barrier of the reaction. Moredetailed graphs for EB calculations with electric fields oriented towards other directions for allof the OWR models is reported in Appendix D. There, we observe different effects (decrease orincrease) in the energy barriers depending on how the electric fields align with bonds undergoingtransformations. The EB lowerings obtained from the QM calculations (Figure 4.7) correspond toEB reductions with applied fields that fall in the range of 1 to 7 eV e−1 nm−1.It is important to note that the water-air value (15.02 eV e−1 nm−1) represents a peak value.Different papers report electric field values for water interfaces ranging from 1 to 15 eV e−1 nm−1.77Teresa Head-Gordon and coworkers argue that there is a 1.6 eV e−1 nm−1 increase in the strengthof the EField at the water interface compared to bulk water,39 while Martins-Costa and Ruiz-Lo´pez934.2. ELECTROSTATIC EFFECTS IN OWRSFigure 4.16: Schematic representation of how we aligned the external electric field to our modelsystem. Colour code: gray (carbon), white (hydrogen) and blue (nitrogen). 20 25 30 35 40 45 501.08 (n-hexane) 6.94 (water) 15.02 (water-air)Ebarrier (kcal mol-1)Field Magnitude (eV e-1 nm-1)Figure 4.17: Evaluation of the effect of an external electric field in the reactivity of the nitrogen-based Claisen rearrangement. The blue horizontal line represents the EB in the absence of anyexternal EField. We used M05-D3/6-31+G**-BSIP as the level of theory.claim that the electric field is lower at the interface than in bulk.224 The consensus, though, is thatthe electrical properties of water interfaces are different from those observed in bulk water due thepresence of dangling −OH groups. There are many ways to estimate electric fields, but to this day,it remains an active field of research due to its complexity.225944.2. ELECTROSTATIC EFFECTS IN OWRS 2 4 6 8 10 12 14 16 18 201.08 (n-hexane) 6.94 (water) 15.02 (water-air)Ebarrier (kcal mol-1)Field Magnitude (eV e-1 nm-1)Figure 4.18: Evaluation of the effect of an external electric field in the reactivity of the oxygen-based Diels-Alder reaction. The blue horizontal line represents the EB in the absence of any externalEField. We used M05-D3/6-31+G**-BSIP as the level of theory.The data presented in this thesis subsection demonstrates that a collection of charges and electricfields can efficiently modulate the reactivity of model OWRs, reproducing the acceleration effectcaused by the “on water” mechanism. The next question we tried to address was whether organicmolecules in OWR systems would be subject to strong and oriented electric fields. Do organicsubstrates near the water-oil interface in “on water” reactions benefit from strong and highlyoriented electric fields? We explore this question in the following subsection through moleculardynamics simulations.4.2.2 MD Simulations for Aqueous Organic SystemsBeyond the construction and validation of our small OWR models, where QM calculations wereapplied on molecular systems on the order of tens of atoms, and, in order to estimate the electricfield at the aqueous interface of a more representative OWR system, we used a molecular dynamicssimulation protocol with thousands of molecules; we did this intending to recover any effect due tobulk molecules that might be absent in the small QM models. The simulation protocol used herein954.2. ELECTROSTATIC EFFECTS IN OWRSis based on a recent study on the interfacial properties of a system consisting of octanol and watermolecules.226 The authors of this investigation carefully analyzed the effect of using different forcefields and simulation box dimensions. They validated their methodology by comparing calculatedsurface tension values to experimental data. In the following paragraphs, we will describe, in detail,this simulation protocol and how we adapted it to our OWR molecules. We used GROMACS227(version 2021.2) for the molecular dynamics simulations. The programs VMD228 and PyMol229were used for visualization purposes.First, we generated initial configurations of the simulation boxes using Packmol.230 This soft-ware allowed us to build reasonable starting configurations and molecule distributions for oursimulation boxes without getting too high in energy configurations or molecules that were too closeto each other. We obtained 4 simulation boxes corresponding to the chemical reactants ClaisenRXand DielsAlderRX, where X is either O or NH. The orientation and dimensions of these boxes arerepresented in Figure 4.19. They are composed of three layers: an organic layer at the bottom ofz, followed by a middle water layer, and a top organic layer. The number of molecules in each caseis summarized in Table 4.3; in each case, the number of molecules was selected to reproduce thedensity of the organic and water phases. Subsequently, we proceeded by performing standard andgood practices in MD simulations: energy minimization, equilibration and production runs. In allsteps, we used a cutoff radius of 1.6 nm for both the electrostatic and van der Waals interactionsalong with the particle-mesh Ewald sum treatment231 of long-range electrostatics, as suggested inthe benchmark study in reference 226. We employed the OPLS-AA209 force field for the organicmolecules; the parameters were generated by the online service provided by the Jorgensen groupat Yale University,232–234 and we used TIP3P as water model.220,235 For the minimization steps,we used the steepest descent algorithm as implemented in GROMACS,227 using 0.001 nm and 30.0kJ mol−1 nm−1 as step size and convergence criterion for the minimization, respectively. In allcases, we set 500000 as the maximum number of steps. After the minimization of energy of oursimulation boxes, we applied the following equilibration protocol to each of the simulation boxes:(1) 40 ns of simulation run for pre-equilibration of the system at a constant number of moles (N),pressure (P) and temperature (T) using a Berendsen thermostat and barostat;158 in shorter words,40 ns of NPT pre-equilibration run. (2) Then 40 ns of NPT equilibration but using the Nose´-Hoover thermostat236–238 and the Parrinello-Rahman barostat.239–241 (3) Subsequently, we ran an964.2. ELECTROSTATIC EFFECTS IN OWRSFigure 4.19: Representation of the simulation boxes used in this thesis. The blue molecules areorganic molecules, while the red ones represent water molecules. The longest dimension of the boxis aligned with the z-coordinate. The dimensions of the initial boxes are lx = ly = 6 nm, andlz = 24 nm. The top and bottom organic layers have lx = ly = 6 nm and lz = 9 nm as dimensions,each. The water layer in the middle has the following dimensions: lx = ly = lz = 6 nm.Simulated system Number of molecules in the simulation boxClaisenRO 2844ClaisenRNH 2878DielsAlderRO 2400 (diene) + 2400 (dienophile)DielsAlderRNH 2400 (diene) + 2400 (dienophile)Table 4.3: Number of organic molecules placed into the simulation box; these organic moleculeswere evenly distributed between the top and bottom organic layers shown in Figure 4.19. In allboxes, the number of water molecules in the simulation is 7197.additional 40 ns of NVT equilibration using the Nose´-Hoover thermostat. (4) We finally ran theproduction simulation, which is the same protocol as in (3) but for 20 ns. These steps constitute theprotocol recommended by Kumar and coworkers for reproducing experimental interfacial tensionsin water-octanol systems;226 we had, however, to add a pre-equilibration in step (1) due to theinstability of the simulations in steps (2) and (3).The protocol described in the previous paragraph has been tested against experimental surfacetensions of water-oil systems. We, however, tested the methodology by generating a system such asthe one shown in Figure 4.19 but using aniline as the organic molecule. By extracting informationfrom the production run (step 4 above), we can calculate the surface tension, γ (t), with the974.2. ELECTROSTATIC EFFECTS IN OWRSformula242γ (t) =lz2[Pzz (t)− Pxx (t) + Pyy (t)2], (4.7)where lz is the length of the simulation box in the z direction, and Pii (t) with ii = xx, yy or zzare the components of the pressure in the x, y and z directions, respectively. This equation isimplemented in GROMACS227 and permitted us to obtain an average of γ equal to 8.29 mN/m,over the 20 ns of the production run. The obtained averaged value for the surface tension is higherthan the reported experimental γ value of 5.77 mN/m.243,244 This result is consistent with theextensive benchmark simulations performed by Kumar and coworkers,226 where higher values forsurface tensions of water-octanol systems, compared to the experimental values, were also obtainedbut validated by means of heat of vaporizations. While our calculated γ values are not in excellentagreement with experiments, they do suggest that the simulation protocol reasonably describes ourOWR systems.4.2.3 Analysis of the MD simulationsThe calculation of the electric field generated by the molecules in MD simulations is generallynot implemented in standard computational software, at least in a way that is customizable andtailored to our goals. Other authors studying electric fields caused by molecules in simulations havehad to develop their own codes.39,222 In our case, we built a new Julia-based code, MODYAN,245that processes the outputs of simulations from GROMACS.227 This code has the capabilities ofcounting molecules, slicing the simulation box to analyze specific regions of the system, calculatingradial distribution functions, and finding partially solvated molecules, among other capabilities.Figure 4.20 presents a screenshot of the user interface prompt. The coding of the program isa long-term project developed at UBCO that is pending publication. It is currently hosted inGitHub in a public repository and can be accessed at https://github.com/eromerom/MODYAN.GROMACS files for all the systems can be found in the same repository.We implemented Equation 4.5 in our Julia code and built a routine to calculate EField in themiddle point of any two arbitrary atoms, i and j, of a given organic molecule. The vector connectingthese two atoms is given bydij = ri − rj . (4.8)984.2. ELECTROSTATIC EFFECTS IN OWRSFigure 4.20: Screenshot of the welcome user interface prompt of one of MODYAN’s modules.Where ri and rj are the position vectors of the atoms i and j, respectively. Then, the projectionof the electric field into the bond formed between atoms i and j is calculated byProjection =EField · dijd2ijdij , (4.9)where dij is the magnitude of the distance vector in Equation 4.8. We now define the scalarprojection of Equation 4.9,Scalar Projection =−|Projection|; if 180◦ > α > 90◦,|Projection|; if 90◦ > α > 0,(4.10)where α is the angle between the vectors EField and dij . The scalar projection in Equation 4.10is the signed magnitude of the projection; i.e., if the angle between the electric field and the bondbetween atoms i and j is larger than 90◦, then the projected electric field is pointing into theopposite direction of the distance vector of the atoms. Then the scalar projection becomes the994.2. ELECTROSTATIC EFFECTS IN OWRSnegative value of the magnitude of the projection shown in Equation 4.9. If the angle between thedistance vector and EField is less than 90◦, the projection is then pointing towards the same directionof the distance vector; in this case, the scalar projection is simply the magnitude of the projection.This implementation allows us to evaluate how much of the electric field in the simulation boxaligns with a bond of interest. We did not take into account the charges of the organic moleculecontaining i and j in the calculation of EField because the electric field that an isolated moleculeexperiences in the vacuum due to its environment is zero. The rest of the other molecules of thesystem, organic and water, were used in the calculation of the electric fields. We can directly applyEquation 4.9 to our Claisen rearrangement systems because the bonds we want to align with theelectric field are C−O and C−N, for the ClaisenRO and ClaisenRNH molecules, respectively. Thecases of the Diels-Alder reactions are more complicated because we are interested in the directionof the forming C−C bonds between the diene and dienophile molecules; in order to analyze theprojections of EField into such direction, we created a normal unitary vector to the plane generatedby the three carbon atoms in the dienophile, C−C−C in DienophileRNH or DienophileRO. Thisnormal unitary vector, nˆCCC, can be used to generate projections for the Diels-Alder systems asfollowsProjection = (EField · nˆCCC) nˆCCC, (4.11)then, the scalar projection can be calculated by means of Equation 4.10, too.Another important advantage of using MODYAN is its ability to scale the charges employed inthe calculation of the fields; this is particularly useful because, while MD force fields are typicallyparametrized to reproduce macroscopic properties such as density or enthalpies of vaporization,they are prone to misrepresent molecular properties such as dipole moments. In the particular caseof the TIP3P water model, it predicts a |µH2O| value of 2.37 D compared to its experimental 1.8546D dipole reported in the literature.246 Given the importance of dipole moments on the potential forfield-induced catalysis, we scaled the charges so that they represent either an experimental |µsystem|value or a dipole calculated at the MP2/aug-cc-pVTZ level of theory. The latter QM calculationmethod has been used in the calculation of dipole moments, leading to accurate results whencompared to experimental values.247 For example, MP2/aug-cc-pVTZ predicts a dipole moment of3.1915 D for the DienophileRO molecule, which is in good agreement with the experimental 3.1171004.2. ELECTROSTATIC EFFECTS IN OWRSSystem |µsystem| (D) SourceClaisenRO 1.4106 MP2/aug-cc-pVTZClaisenRNH 1.6664 MP2/aug-cc-pVTZDieneRO = DieneRNH 0.0629 MP2/aug-cc-pVTZDienophileRO 3.1915 MP2/aug-cc-pVTZDienophileRNH 1.6868 MP2/aug-cc-pVTZH2O 1.8546 Experiment246D2O 1.8558 Experiment246Table 4.4: Dipole moments utilized for the calculation of the electric fields in the simulation boxesof this thesis.D value for the same system.248 Table 4.4 displays the dipoles employed in the calculation of EFieldin the simulation boxes of our systems.By making use of our software, we dissected the simulation boxes: 24 slices parallel to thexy plane, as defined in Figure 4.19, were made so that we could differentiate between regionscorresponding to the bulk organic phase and the interface. Each of these slices has a thicknessof approximately 1 nm.e In these regions, we calculated the scalar projections of electric fields inbonds and directions of interest. Figure 4.21 shows the scalar projection of the electric field onClaisenRO bulk molecules (slice number 24 at the top of the simulation box) along its C-O bond asa function of simulation time. We selected to project EField in this bond direction because, in ourQM models, we found that the alignment of an electric field along this bond had a critical impactin modulating EBs.As expected, the distribution of the scalar projections in a bulk organic region throughout the20 ns of the simulation displays a symmetrical behaviour with values that oscillate around zero andwith near-zero values for the average of the fields. Repeating the same exercise but for a region ofthe simulation box identified as the interface (slice number 16, which includes the region betweenz = 15 nm and z = 16 nm) generates Figure 4.22. In this graph, we observe a broader distribution,with ranging field values of -6 to 6 eV e−1 nm−1 (with a few cases going beyond this range) ofthe scalar projections, compared to the -3 to 3 eV e−1 nm−1 range observed in bulk phase. Thisbroader range in EField implies that organic molecules near the interface are accessing higher valuesof EField with respect to the organic molecules in the bulk region. The plots also show that theaverage values of the fields near the interface are no longer close to zero as in the case of bulk organiceThis value oscillates from 0.98 to 0.99 nm due to changes in the dimensions of the boxes during the NPTequilibration steps.1014.2. ELECTROSTATIC EFFECTS IN OWRSFigure 4.21: Scalar projections into the C−O bonds of the organic molecules (ClaisenRO) in aregion of the simulation box identified as bulk organic. The calculation of the electric fields andprojections involves all other molecules of the system in the box. The red dots represent averagescalar projections.phase. These results demonstrate that, at least for the oxygen-based Claisen rearrangement, theelectric field values experienced by organic molecules near the water-oil interface are larger thanthose in the bulk organic phase. Conversely, Figures 4.23 and 4.24 display no significant differencesbetween the scalar projections for the DielsAlderRO system in the bulk and interfacial regions.The electric fields, in this case, are projected into the direction that is perpendicular to the planedefined by the three carbon atoms (C−C−C) in the dienophile molecule, which according to ourQM calculations, is the direction where the system has the most dramatic reduction in EBs. Itis important to note, that the cases of the oxygen-based Claisen rearrangement and the oxygen-based Diels-Alder reactions are extreme cases; the former shows a clear distinction in the electricfields between the bulk and interface regions while the latter depicts virtually no differences, interms of the electric field range, between the same two regions. The plots that corresponds tothe rest of the systems are shown in Appendix E; they show the same differences between thebulk and interfacial regions that are observed in the ClaisenRO system, but to a lesser extent.Interestingly, the field differences between bulk and interfacial organic molecules appear only if the1024.2. ELECTROSTATIC EFFECTS IN OWRSFigure 4.22: Scalar projections into the C−O of the organic molecules (ClaisenRO) in a region ofthe simulation box identified as the interface. The calculation of the electric fields and projectionsinvolves all other molecules of the system in the box. The red dots represent average scalar projec-tions.dipole moment of the HB acceptor in the organic systems is lower than the water dipole; which isthe case of all systems but DielsAlderRO. This is consistent with the first reported OWR, wherethe dipoles of the reactants are small compared to the dipole of water; with values of 0.01989D and 0.0031 D for Q249 and DMAD,f respectively. These observations make sense from theperspective of field dampening, which occurs due to water and organic molecules having similardipoles that act to mitigate electric fields near the interface. The previous results also suggest thatthe field catalysis properties of a water-oil interface are more dominant if the dipole moments of themolecules in the organic phase are small compared to |µH2O|, relative to water-oil interfaces with|µorganic| ≈ |µH2O| where, conversely, field effects must be minimal. Catalysis, if observed in thiscase, would be mainly produced by HB effects; an effect similar to that shown for the water implicitsolvent calculations (see Figure 4.8) is expected for the energy barriers. Also, it is important torecognize that the solubility of reactants is correlated with the dipole moment and the size of theorganic molecules;250 hence, as the dipole moment of the organic reactant increases and its sizefCalculated using MP2/aug-cc-pVTZ as the level of theory.1034.2. ELECTROSTATIC EFFECTS IN OWRSFigure 4.23: Scalar projections into the perpendicular direction to the plane formed by the threecarbon atoms in the organic molecules (DienophileRO) in a region of the simulation box identifiedas bulk organic. The calculation of the electric fields and projections involves all other moleculesof the system in the box. The red dots represent average scalar projections.decreases, solvation in the water phase is enhanced. Solvated organic systems will not undergo “onwater” acceleration (as discussed in Section 1.5 in this thesis) but they would primarily occur asan “in water” reaction. It is difficult to ascertain at what point our systems transitions from “onwater” to “in water” reactivity.We previously demonstrated that an oriented electric field caused by water molecules can reduceEBs. In this subsection, we showed that organic molecules with dipole moments lower than thewater dipole can experience larger values of electric fields near the interface; thus, it is possible tostate that these organic molecules, in the context of OWRs, benefit from the stronger electric fieldsat the interface to reduce its EBs and undergo accelerated reactivity.Another immediate observations we can make, as it will be explored in the next section, isthat the water-oil interface is not a 2-dimensional and well-defined area in the simulation box as isdepicted often in the literature; instead, it is a region of space where the density of water (or theorganic phase) decreases steadily from its bulk value. It is a diffuse region of transition between theorganic and water phases. For water-air interfaces, the interface is defined as the Gibbs dividing1044.2. ELECTROSTATIC EFFECTS IN OWRSFigure 4.24: Scalar projections into the perpendicular direction to the plane formed by the threecarbon atoms in the organic molecules (DienophileRO) in a region of the simulation box identifiedas interface. The calculation of the electric fields and projections involves all other molecules of thesystem in the box. The red dots represent average scalar projections.surface (GDS),30 which represents, for an interface parallel to the xy plane, the z value at whichthe density of bulk water becomes half. This definition is problematic for organic-water systems, asthere is some penetration of the water molecules into the organic phase (and vice versa). Therefore,we explored interfaces as the 3D space region of transition between the two phases.4.2.4 An Explanation of the Kinetic Isotope Effect in OWRsIn addition to the work described in the previous subsection, we ran the corresponding simula-tions of the same organic systems but using a heavy water model, TIP3P-HW,251 to describe D2Omolecules. We followed the same protocol for minimization, equilibration and production runs.Figure 4.25 shows the density profile of the simulation of the nitrogen-based Claisen rearrangementreactant, ClaisenRNH, with water molecules using the TIP3P model.A version of Figure 4.25 but for the heavy water model is displayed in Figure 4.26. It can beobserved that, qualitatively, the heavy water molecules penetrate less than H2O, suggesting thatsystems composed of organic molecules and heavy water molecules have less interfacial area of1054.2. ELECTROSTATIC EFFECTS IN OWRSFigure 4.25: Density profile for the simulation of ClaisenRNH with water molecules.reaction. These data are consistent with the macroscopic properties of D2O, which is inherentlymore dense and viscous than regular water.40 Also, when the penetration of organic molecules andwater increases, the differences between the D2O and H2O systems become more pronounced, as itis shown in Figures 4.28 and 4.29 for the Diels-Alder reactant DielsAlderRNH. In these graphs, thesimulation using water shows a larger penetration of the organic molecules into the water phasewhen compared to the simulation in D2O. Again, these results indicate that the interfacial area inthe water-organic systems are larger than those of the D2O-organic systems, suggesting that theformer will see enhanced OWR reaction rates than the latter. These observations also point tosignificant differences in the physical distribution of molecules between the heavy water and watersystems, providing a possible explanation for the different KIE observed in OWRs, as originallyproposed by Jung and Marcus, being a kinetic isotope effect with a physical origin.40It can be argued that the differences in water and D2O penetration into the organic phase aresimply due to the different densities for H2O and heavy water. For these reasons, instead of focusingon density values, we counted molecules in bulk organic regions in the simulation boxes. Figures4.30(a) and 4.30(b) count H2O and D2O molecules for the nitrogen-based Claisen rearrangement1064.2. ELECTROSTATIC EFFECTS IN OWRSFigure 4.26: Density profile for the simulation of ClaisenRNH with heavy water molecules.system; it is observed that there are more water molecules in the organic phase than heavy watermolecules in its corresponding box. These results confirm that the penetration, and hence, theinterfacial area between the water-oil interface, is larger for H2O than for D2O under the samesimulation conditions. These results, again, point to a possible physical origin of the KIE inOWRs. Plots counting H2O and D2O molecules for all other systems can be found in AppendixE; in general, water molecules penetrate more the bulk organic phase than heavy water, in allcases. The differences between the D2O and H2O systems are more evident for the nitrogen-basedsimulations than for the oxygen-based ones because nitrogen-based molecules allow hundreds ofwater (or heavy water) molecules in the bulk organic phase, compared to the oxygen-based systemswhich allow only tens of water (or heavy water) molecules in the same box region. These lastobservations also suggest that the nature of the HB acceptor (nitrogen or oxygen, in this case) canchange the way in which organic and water molecules interact (as discussed in Chapter 3); differentHB acceptors in the organic phase lead to different penetrations of water into the organic phase.From our simulations, we observe that the presence of a stronger HB acceptor (nitrogen) leads to ahigher interfacial area when compared to the oxygen-based systems, presumably, due to a stronger1074.2. ELECTROSTATIC EFFECTS IN OWRS10.020.030.040.050.060.070.080.090.0100.0110.0 0 1 2 3 4 5 6 7 8Density (kg/m3)z (nm)H2OD2OFigure 4.27: Detailed penetration of H2O and D2O into the organic phase of ClaisenRNH. Thisgraph displays the density of H2O and D2O, as shown in Figures 4.25 and 4.26, but focusing onthe first organic layer (0 < z < 8 nm)Figure 4.28: Density profile for the simulation of DielsAlderRNH with water molecules.1084.2. ELECTROSTATIC EFFECTS IN OWRSFigure 4.29: Density profile for the simulation of DielsAlderRNH with heavy water molecules.HB interactions between the organic and aqueous phases in the former compared to the latter.By making use of the electric fields calculated in the previous section, it is also possible toobserve differences between D2O and H2O systems in the electric field projections. For example,we took the whole simulation box for the nitrogen-based Claisen rearrangement and proceeded toto calculate the probability density of finding organic molecules experiencing different values of thescalar projections, as described previously in this chapter. These probabilities are reported in Figure4.31; the plot shows that the population of molecules with scalar projections near to zero is higherfor the heavy water model than that of the H2O model; also, the tails of the heavy water modeldecay faster as we approach larger values of electric fields in comparison to the H2O model, whichdisplays a larger population of organic molecules accessing larger values of EField. Hence, OWRshave the potential of exploiting field catalysis effects more than its heavy water counterpart for thenitrogen-based Claisen rearrangement. The simulation box containing DielsAlderRNH molecules(see Figure E.15 in Appendix E) displays a similar behaviour with organic molecules accessinglarger field values in the water model simulation in comparison to the D2O system. The oxygen-based simulations do not display significant differences in the electric field projections between the1094.2. ELECTROSTATIC EFFECTS IN OWRS(a) (b)Figure 4.30: (a) Counting H2O molecules in a bulk organic region (0 < z < 9 in the simulationbox) for the ClaisenRNH system. (b) Counting D2O molecules in a bulk organic region (0 < z < 9in the simulation box) for the ClaisenRNH system.H2O and D2O models. These plots, which can be found in Appendix E, suggest that the larger thepenetration of the aqueous phase into the organic phase, the larger the differences in the projectedelectric fields between the H2O and D2O models.In summary, there are indications that, due to the distinct physical properties of water andheavy water, there will be differences in the interfacial area of reaction of H2O-organic and D2O-organic systems. Specifically, since heavy water systems have less interfacial area of reaction thanreactions using H2O, “on D2O” reactions will proceed more slowly whether catalysis occurs dueto H-bonding, electric field effects or a combination of the two. These differences in the interfacialarea between water and heavy water systems also depend on the nature of the HB acceptor inthe organic phase; stronger HB acceptors promote more penetration of the aqueous phase into theorganic one, enlarging the differences between the H2O and D2O models. Weaker HB acceptorsproduce less penetration and the differences between the water and heavy water become smaller.Also, some organic molecules (half of our systems, the nitrogen-based molecules) in an “on water”setting may have a small kinetic advantage with respect to “on heavy water” systems due to fieldcatalysis. The result presented in this section complements the hypothesis that KIEs in OWRs arisefrom physical effects and also offers alternative explanations to the variety of kinetic isotope effectsobserved in OWRs. These conclusions regarding the KIE observed in OWRs are indicative andcannot be compared directly with experimental results; as explained by Nguyen and coworkers,471104.3. PT MECHANISMFigure 4.31: Probability density of the scalar project on the C−N bond in the simulation boxcorresponding to the ClaisenRNH system.the reproducibility of interfacial areas of reaction in “on water” systems is complicated as theytend to vary largely with the experimental settings. In the same study, the authors proved thatkinetic isotope effects in OWRs are quenched if the interfacial area of reaction is carefully controlled;which they achieve by loading reactants in mesoporous silica nanoparticles of known surface. Theseexperimental results also point to a KIE effect due to different interfacial areas of reaction betweenD2O and H2O in uncontrolled surface conditions, such as those present in an organic synthesis lab.4.3 PT MechanismIn the previous section, we demonstrated that the electric field generated from the collectivedipoles and partial water charges in small OWR models can effectively change the reactivity oforganic reactions by modulating EBs. It was also shown that the electric field experienced by organicmolecules near the water-oil interface can be larger than those experienced in bulk conditions. Inaddition, we suggest and provide data to support the notion that kinetic isotope effects in OWRsarise from the physical differences between water and heavy water, the nature of the HB acceptor1114.3. PT MECHANISMin the organic phase, and field effects. In this section, we discussed the followed approach for theexploration of the PT mechanism.The proton transfer mechanism tries to address the kinetic isotope effect (KIE) observed insome reactions when using deuterated water instead of H2O. Hydrogen bonds in deuterated waterinvolve a lower zero-point vibrational energy compared to HBs in water, producing more stablecomplexes for the former than the latter (at least at low temperatures).252–254 However, at roomtemperature, forming a hydrogen-bonded complex in water is more entropically favoured comparedto its counterpart in deuterated systems. This entropic effect drives the free energy of formation ofcomplexes of the form (H2O)n and (D2O)n to be similar at room temperature;255 hence, a kineticisotope effect close to unity is expected for processes involving the formation of hydrogen bonds. Weestimated, by means of the Eyring equation and under our approximation of frozen water clusters,that the kH/kD value for our oxygen-based Claisen rearrangement models were all close to 1.0; withan average value, across all molecular complexes, of 0.99. On the other hand, when a proton istransferred, a KIE from 5 to 7 is observed experimentally,40 and even larger values are obtained iftunnelling effects are present.256–259 For these reasons, the presence of KIEs on the order of 5 insome OWRs led to the proposal of the PT mechanism.48Attempts were made to explore the possibility of a proton transfer reaction within the contextof our OWR models. The employed approach to this end consisted of using the structures of thecomplexes obtained in Section 4.1, where we analyzed the effect if HBs on EBs. We used thesestructures as a starting point, followed by the use of chemical intuition to promote PT processesfor all reactions. However, the organic molecules of our models easily lose the promoted protonto the negatively charged [(H2O)n−1(OH)]− clusters. This issue makes finding the desired OWRtransition states a difficult task, even when using an implicit solvent model. Nevertheless, invery few cases, it was possible to locate TSs. Figure 4.32 displays a protonated transition state,ClaisenTSNH+ · · · (H2O)5(OH)−, connected to an unprotonated pre-reaction complex, in one step,with an associated reaction energy barrier of 57.45 kcal/mol at the M05-D3/6-31+G**-BSIP level oftheory. Efforts to connect this TS with a protonated pre-reaction complex were unsuccessful; also,we notice that the reference gas-phase energy barrier, at the same level of theory, is 50.62 kcal/mol,meaning that the protonated version of the reaction is, in fact, less favourable than the gas-phaseunassisted reaction. This situation and the fact that the protonated organic species are unstable1124.4. SUMMARYFigure 4.32: The transition state ClaisenTSNH+ · · · (H2O)5(OH)− is connected to the unprotonatedpre-reaction complex ClaisenRN · · · (H2O)6. Both structures were optimized at the M05-D3/6-31+G**-BSIP level of theory.suggest that the proton-transfer mechanism is less viable than the HB mechanism, at least in ourmodel systems. We note, however, that this can be an artifact of the size of the presented modelsherein; the large charges that appear upon the formation of OH− are not stabilized enough by theneighbouring water molecules or by implicit solvent models. In a real system with thousands ofwater molecules, the zwitterion species might be stable enough to permit PT reactivity; nonetheless,this introduces other challenges from the modelling perspective, as discussed at the beginning ofthis chapter.4.4 SummaryThe analysis of OWR models shown in this thesis supports the hypothesis that noncovalentinteractions stabilize transition states in OWRs. Our data indicate that hydrogen bonding fromthe dangling −OH bonds in the water clusters to the organic molecules reduces the energy barriersof the reactions studied in this thesis. We found poor correlations between charge transfer and thecalculated energy barriers in all of our OWR models. This situation highlights that charge transfer,an active phenomenon that arises upon the formation of HBs, fails to explain the acceleration effectsobserved in OWRs. The application of an external electric field, aligned with bonds undergoingtransformations in our OWR models, also produces energy barrier reductions in the gas-phasereactions studied in this thesis, in the same order and beyond the EB lowerings observed in theOWR models with HBs. Subsequently, we found that a charge point model for water molecules in1134.4. SUMMARYOWR models reproduces the energy barrier reductions observed in the HB QM models, suggestingthat the distribution of charges in the boundaries of the water-oil interface and its natural electricfield have a dominant effect in the modulation of energy barriers in OWRs. Next, by means of MDsimulations, we found that electric field effects in OWRs are stronger if the dipole moment of theorganic molecule in the oil phase is low compared to the dipole of the water molecule; this impliesthat OWRs should be more accelerated by field effects if the dipoles of the molecules composing theorganic phase approach to zero. On the other hand, fields effects would be minimized if the dipoleof the organic phase molecules are similar to the dipoles of water because of field dampening effects;in this case, OWRs would be accelerated by HB effects alone. It is important to note that, even atan interface with a damped electric field, the presence of HBs between organic and water moleculeswill still present some OWR catalysis. This EB lowering occurs because, as we demonstrated in ourexplicit QM models (see Figure 4.7), a single water molecule in OWRs can produce a significantreduction in the EBs of OWR models due to the near proximity of the organic molecule to thecharge distribution of the interacting water molecule. We expect this effect to be present in allorganic-water cluster HB complexes in OWRs; electric field effects are strongest at short distances.Hence, hydrogen bonding interactions remain central due to their relevant role in the orientationand short range effects observed in OWRs. Finally, we provided some indications that the KIEobserved in OWRs arises from the different physical properties of D2O and H2O, the nature of theHB acceptor in the organic phase, and mild differences in the projected electric fields.114Chapter 5Conclusions and OutlookIn this thesis, we employed a series of computational techniques: quantum chemistry calcula-tions and molecular dynamics simulations with the goal of unravelling the intricate chemistry ofaccelerated reactions “on water.” We began our analysis with small model systems in the order oftens of atoms and finalized our study with simulations involving thousands of molecules. Noncova-lent interactions, energy barriers, charge transfer effects, proton transfer reactions, dipoles, pointcharge distribution, and electric field effects were carefully examined in our testing of three OWRmechanisms reported in the literature.We used the Claisen rearrangement and the Diels-Alder cycloaddition as model reactions forOWRs. We arrive at the following conclusions:− Noncovalent interactions in organic molecule-water cluster complexes are diverse and complex;intricate combinations of noncovalent interactions can easily arise in such complexes as thesize of the organic and water cluster increases. Hence, noncovalent interactions present in aOWR must be complex.− Interactions between organic molecules and water clusters are strong; then, there is the poten-tial of strong interactions happening at the aqueous-organic phases in OWRs. The strengthof the interaction in organic molecule-water cluster complexes correlates with Abraham’s ba-sicity parameters; the more basic an HB acceptor is, the stronger the HB it will form withwater clusters. This must also be the case in an OWR; reactants containing more basic HBacceptors should interact more strongly with the water phase when compared with reactantswith low basicity.− The formation of hydrogen bonds between water clusters and organic molecules in our modelreactions significantly reduces energy barriers in all of the OWR models analyzed in this115thesis. HB differentially stabilizes transition states relative to pre-reaction complexes whichexplains the accelerated effect observed in OWRs.− There is a charge transfer component associated with HB that poorly correlates with theHB reduction in EBs. This implies that CT, although present in OWRs, is not driving theaccelerated reactivity in “on water” reactions.− An oriented external electric field can modulate the energetics of organic reactions. The effectis larger if the external field is aligned with bonds that are being broken or formed duringthe course reaction. We confirmed that, for our gas-phase systems, aligning an electric fieldwith the C−X bonds in the case of the Claisen rearrangements and the forming C−C bondsfor the Diels-Alder reactions has the most dramatic reduction in EBs.− A collection of point charges representing water molecules and their dipoles can effectivelyreduce energy barriers, similarly to how HBs reduce EBs in OWR models. Changing thedirection of the dipoles (changing the sign of the point charges) increases the barriers, sug-gesting that the direction of the dipoles plays an important role in the modulation of EBs inOWRs.− The point charge models reproduce well the reduction in EBs in the absence of HBs, high-lighting the relevance of electrostatic effects in our QM models and indicating that, even inour small HB models, the field effects are dominant in the reducing the EBs. In other words,the fact that the QM hydrogen bond EB plots looks very similar as the point charge plotsindicates that the dominant factor in the energy barrier lowering is the electric field and notorbital overlap.− Organic molecules near a water interface may experience larger electric fields than thoseorganic molecules in bulk phase, as long as the dipole of the organic molecule is low comparedto the water dipole. In such case, reactants at the interface can benefit more from electricfield catalysis than those in the bulk phase.− Our simulations suggest that if the organic phase in OWRs is composed by molecules with adipole such that µorganic ≈ µH2O, electric field effects are quenched due to field dampening.In that scenario, only lowering caused by HB bonding will be observed.116− In our condensed phase simulations, we found indications that physical differences betweenH2O and D2O lead to lower interfacial area of reaction for the heavy water models, whichtranslates in less “on D2O” reactive sites and slower reactions compared to reactions us-ing H2O. Other factors, such as the nature of the HB acceptor in the organic phase andmild differences in the field projections seem to also contribute in the emergence of KIE inOWRs. The experimental literature shows that the KIE in OWRs is highly dependent on theinterfacial area of reaction.− We were unable to obtain evidence that a proton transfer mechanism is operating and accel-erating OWRs, at least for the reactions analyzed in this thesis.On the basis of the foregoing observations, we propose that real OWR systems incorporatecomponents of the HB and dipole models. As outlined in the introduction of this thesis, we proposethat, hydrogen bonds remain central to OWRs because they are necessary to orient reacting organicmolecules at the interface, favourably aligning them with the strong electric field present in thatregion. Using the Arrhenius equation, k = A exp (−∆E/RT ), we can qualitatively connect thereductions in energy barriers due to the HBs and electric fields with the ∆E term. The effects ofhydrogen bonding interactions might also be reflected in the pre-exponential factor, A, which isrelated to the frequency of collisions between reactants; the attractive nature of HBs can increasethe probability of reactants of aligning and colliding in favourable ways so that an accelerationin the reactivity is observed. Our model amends the Marcus model by adding elements of theelectric field catalysis from Shaik69,71 and Coote’s work;70 it is illustrated graphically in Figure5.1. Although we do not have evidence that support the PT mechanism for the model reactionsstudied in this thesis, we do not discard it for other OWR reactions, such as epoxide openings,58where proton transfer may play a role in the acceleration effect of OWRs.The results presented in this thesis strongly point to a phenomenon dominated by electrostaticeffects; our quantum mechanical OWR models showed that a point charge distribution representa-tion of water molecules suffices to explain the lowering in energy barriers of “on water” reactions.Hydrogen bonding interactions are critical to this because they orient local water molecules nearthe reactants so that the dipole field of those waters can affect EB lowering. In addition, our molec-ular dynamics simulations predict strong and oriented electric field values near the aqueous-organic117Figure 5.1: Proposed mechanism for OWRs based on hydrogen bonds and electric fields. Theshaded blue area represents space region with strong electric fields.interface in some cases, providing opportunities for organic reagents to exploit field catalysis effects.Nonetheless, the MD component of the thesis has its limitations as it does not consider how thereactions proceed along the full reaction pathway. Hence, future work on OWRs should focus in theconfirmation of the QM findings in this thesis but at a larger scale; this can be achieved by buildingQM/MM models for “on water” reactions where the reaction and its immediate surroundings aremodeled quantum mechanically (QM region) and the rest of the system is modeled using a forcefield. Another option is the employment of a reactive force field, such as ReaxFF,260 which is ableto account for bond breaking and forming during the course of MD simulation.In this thesis, we found that field catalysis is enhanced if the dipole of the organic molecule inthe oil phase is close to zero; that is, electrostatic effects are maximum when ∆µ = µH2O−µorganic ≈µH2O. Another way to see this effect is that, the larger the ∆µ value, the larger the catalysis byelectric fields; hence, field effects can also be increased by changing the nature of the solvent actingas water. For example Hajra and coworkers261 reported the ring opening of spiroazidirine oxindoleusing trifluoroethanol as reaction medium, obtaining results that were similar to the reaction oc-curing in “on water” conditions. So, to experimentally test our theoretical observations, we wouldneed to analyze the kinetics of “on solvent” reactions, where we limit the use of solvents that areimmiscible with reactants, so that an interface, such as the one in OWRs, can be formed. Exploringdifferent solvents with distinct dipole moment values would test our theoretical predictions.Studying the chemistry of water in non-traditional conditions has several potential applications118outside the “on water” phenomena. For example, it can lead to a better understanding of wateraerosol processes occurring in the atmosphere, it can be applied for the design of micellar chemistry,or it can be used to explain the unusual properties of water near hydrophobic regions in cells or, inconfined carbon nanotubes. 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K. “Can organic chemists cut waste by switching to water?https://cen.acs.org/environment/green-chemistry/organic-chemists-cut-waste-switching-water/101/i23”, (accessed on August 31st, 2023).144AppendixAppendix A: BEs for Organic Molecule - Water ClusterComplexesIn this appendix, the binding energies plots for acetone, oxirane, methyl acetate, azomethane,dimethylamine, and trimethylamine as a function of water cluster size and per individual watercluster are presented. All structures and energies can be found in the supporting information ofreference 171, as indicated in the preface of this thesis.-10.0-9.0-8.0-7.0-6.0-5.0-4.0-3.0-2.0-1.00.0 1 2 3 4 5 6 7 8 9 10Binding energy (kcal/mol)(H2O)nFigure A.1: Profile of all binding energies for acetone and (H2O)n (with n = 1 - 10) at ourbenchmark level of theory.145-10.0-9.0-8.0-7.0-6.0-5.0-4.0-3.0-2.0-1.00.0Monomer2Cs3UUD3UUU4Ci4Py4S45CAA5CAB5CAC5CYC5FRA5FRB5FRC6BAG6BK16BK26CA6CB16CB26CC6PR7BI17BI27CA17CA27CH17CH27CH37HM17PR17PR27PR38D2d8S49D2dDD9S4DA10PP110PP2Binding energy (kcal/mol)Figure A.2: Benchmark binding energies for acetone and individual clusters as labelled in Table3.1.-12.0-10.0-8.0-6.0-4.0-2.00.0 1 2 3 4 5 6 7 8 9 10Binding energy (kcal/mol)(H2O)nFigure A.3: Profile of all binding energies for dimethylamine and (H2O)n (with n = 1 - 10) atour benchmark level of theory.146-12.0-10.0-8.0-6.0-4.0-2.00.0Monomer2Cs3UUD3UUU4Ci4Py4S45CAA5CAB5CAC5CYC5FRA5FRB5FRC6BAG6BK16BK26CA6CB16CB26CC6PR7BI17BI27CA17CA27CH17CH27CH37HM17PR17PR27PR38D2d8S49D2dDD9S4DA10PP110PP2Binding energy (kcal/mol)Figure A.4: Benchmark binding energies for dimethylamine and individual clusters as labelledin Table 3.1.-11.0-10.0-9.0-8.0-7.0-6.0-5.0-4.0-3.0-2.0-1.0 1 2 3 4 5 6 7 8 9 10Binding energy (kcal/mol)(H2O)nFigure A.5: Profile of all binding energies for azomethane and (H2O)n (with n = 1 - 10) at ourbenchmark level of theory.147-11.0-10.0-9.0-8.0-7.0-6.0-5.0-4.0-3.0-2.0-1.0Monomer2Cs3UUD3UUU4Ci4Py4S45CAA5CAB5CAC5CYC5FRA5FRB5FRC6BAG6BK16BK26CA6CB16CB26CC6PR7BI17BI27CA17CA27CH17CH27CH37HM17PR17PR27PR38D2d8S49D2dDD9S4DA10PP110PP2Binding energy (kcal/mol)Figure A.6: Benchmark binding energies for azomethane and individual clusters as labelled inTable 3.1.-10.0-9.0-8.0-7.0-6.0-5.0-4.0-3.0-2.0-1.00.0 1 2 3 4 5 6 7 8 9 10Binding energy (kcal/mol)(H2O)nFigure A.7: Profile of all binding energies for methyl acetate and (H2O)n (with n = 1 - 10) atour benchmark level of theory.148-10.0-9.0-8.0-7.0-6.0-5.0-4.0-3.0-2.0-1.00.0Monomer2Cs3UUD3UUU4Ci4Py4S45CAA5CAB5CAC5CYC5FRA5FRB5FRC6BAG6BK16BK26CA6CB16CB26CC6PR7BI17BI27CA17CA27CH17CH27CH37HM17PR17PR27PR38D2d8S49D2dDD9S4DA10PP110PP2Binding energy (kcal/mol)Figure A.8: Benchmark binding energies for methyl acetate and individual clusters as labelledin Table 3.1.-9.0-8.0-7.0-6.0-5.0-4.0-3.0-2.0-1.0 1 2 3 4 5 6 7 8 9 10Binding energy (kcal/mol)(H2O)nFigure A.9: Profile of all binding energies for oxirane and (H2O)n (with n = 1 - 10) at ourbenchmark level of theory.149-9.0-8.0-7.0-6.0-5.0-4.0-3.0-2.0-1.0Monomer2Cs3UUD3UUU4Ci4Py4S45CAA5CAB5CAC5CYC5FRA5FRB5FRC6BAG6BK16BK26CA6CB16CB26CC6PR7BI17BI27CA17CA27CH17CH27CH37HM17PR17PR27PR38D2d 8S49D2dDD9S4DA10PP110PP2Binding energy (kcal/mol)Figure A.10: Benchmark binding energies for oxirane and individual clusters as labelled in Table3.1.-12.0-10.0-8.0-6.0-4.0-2.00.0 1 2 3 4 5 6 7 8 9 10Binding energy (kcal/mol)(H2O)nFigure A.11: Profile of all binding energies for trimethylamine and (H2O)n (with n = 1 - 10) atour benchmark level of theory.150-12.0-10.0-8.0-6.0-4.0-2.00.0Monomer2Cs3UUD3UUU4Ci4Py4S45CAA5CAB5CAC5CYC5FRA5FRB5FRC6BAG6BK16BK26CA6CB16CB26CC6PR7BI17BI27CA17CA27CH17CH27CH37HM17PR17PR27PR38D2d8S49D2dDD9S4DA10PP110PP2Binding energy (kcal/mol)Figure A.12: Benchmark binding energies for trimethylamine and individual clusters as labelledin Table 3.1.151Appendix B: OWRs ModelsThis appendix contains figures containing the structures of the transition states of all OWRsmodel reactions considered for the quantum mechanical calculations. Files containing benchmarkenergies and XYZ files for pre-reaction complexes, TSs, and post-reaction complexes can be foundin the figshare repository at https://doi.org/10.6084/m9.figshare.23963166.v1.Nitrogen-Based Claisen RearrangementIn this section, we show the model reactions corresponding to the ClaisenTSNH systems andtheir corresponding complexes formed when interacting with water clusters from the monomer tothe decamer systems.Figure B.1: Structure of the transition state. Gas phase reaction.Figure B.2: Structure of the transition state. Reaction with the monomer of water.152Figure B.3: Structure of the transition state. Reaction with the dimer of water.Figure B.4: Structure of the transition state. Reaction with the trimer of water.Figure B.5: Structure of the transition state. Reaction with the tetramer of water.153Figure B.6: Structure of the transition state. Reaction with the pentamer of water.Figure B.7: Structure of the transition state. Reaction with the hexamer of water.Figure B.8: Structure of the transition state. Reaction with the heptamer of water.154Figure B.9: Structure of the transition state. Reaction with the octamer of water.Figure B.10: Structure of the transition state. Reaction with the nonamer of water.155Figure B.11: Structure of the transition state. Reaction with the decamer of water.Oxygen-Based Claisen RearrangementIn this section, we show the model reactions corresponding to the ClaisenTSO systems and theircorresponding complexes formed when interacting with water clusters from the monomer to thedecamer systems.Figure B.12: Structure of the transition state. Gas phase reaction.156Figure B.13: Structure of the transition state. Reaction with the monomer of water.Figure B.14: Structure of the transition state. Reaction with the dimer of water.Figure B.15: Structure of the transition state. Reaction with the trimer of water.157Figure B.16: Structure of the transition state. Reaction with the tetramer of water.Figure B.17: Structure of the transition state. Reaction with the pentamer of water.Figure B.18: Structure of the transition state. Reaction with the hexamer of water.158Figure B.19: Structure of the transition state. Reaction with the heptamer of water.Figure B.20: Structure of the transition state. Reaction with the octamer of water.Figure B.21: Structure of the transition state. Reaction with the nonamer of water.159Figure B.22: Structure of the transition state. Reaction with the decamer of water.Nitrogen-Based Diels-Alder ReactionIn this section, we show the model reactions corresponding to the DielsAlderTSNH systems andtheir corresponding complexes formed when interacting with water clusters from the monomer tothe decamer systems.Figure B.23: Structure of the transition state. Gas phase reaction.160Figure B.24: Structure of the transition state. Reaction with the monomer of water.Figure B.25: Structure of the transition state. Reaction with the dimer of water.Figure B.26: Structure of the transition state. Reaction with the trimer of water.161Figure B.27: Structure of the transition state. Reaction with the tetramer of water.Figure B.28: Structure of the transition state. Reaction with the pentamer of water.Figure B.29: Structure of the transition state. Reaction with the hexamer of water.162Figure B.30: Structure of the transition state. Reaction with the heptamer of water.Figure B.31: Structure of the transition state. Reaction with the octamer of water.Figure B.32: Structure of the transition state. Reaction with the nonamer of water.163Figure B.33: Structure of the transition state. Reaction with the decamer of water.Oxygen-Based Diels-Alder ReactionIn this section, we show the model reactions corresponding to the DielsAlderTSO systems andtheir corresponding complexes formed when interacting with water clusters from the monomer tothe decamer systems.Figure B.34: Structure of the transition state. Gas phase reaction.164Figure B.35: Structure of the transition state. Reaction with the monomer of water.Figure B.36: Structure of the transition state. Reaction with the dimer of water.Figure B.37: Structure of the transition state. Reaction with the trimer of water.165Figure B.38: Structure of the transition state. Reaction with the tetramer of water.Figure B.39: Structure of the transition state. Reaction with the pentamer of water.Figure B.40: Structure of the transition state. Reaction with the hexamer of water.166Figure B.41: Structure of the transition state. Reaction with the heptamer of water.Figure B.42: Structure of the transition state. Reaction with the octamer of water.Figure B.43: Structure of the transition state. Reaction with the nonamer of water.167Figure B.44: Structure of the transition state. Reaction with the decamer of water.168Appendix C: Correlation Between Transferred Charges and EBsin OWR ModelsThis appendix contains plots displaying how the correlation between charge transferred in ourOWR models and EBs are driven by the gas-phase data. Level of theory details are included inthe caption of the figures.32.033.034.035.036.037.038.039.00.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016Energy Barrier (kcal/mol)∆q 0123456 78910(a)40.041.042.043.044.045.046.0-0.01 -0.005 0 0.005 0.01 0.015Energy Barrier (kcal/mol)∆q012345678910(b)Figure C.1: Benchmark energy barriers vs ∆q in the organic molecules for the Claisen rear-rangement models. (a) Oxygen-based Claisen rearrangement (∆q = qClaisenTSO − qClaisenRO ,trenline: EB = −293∆q + 37.2, r2 = 0.759) and (b) nitrogen-based Claisen rearrangement(∆q = qClaisenTSNH − qClaisenRNH , trenline: EB = −108∆q + 43.1, r2 = 0.198). Charges (ina.u.) were calculated using AIMAll at the M05-D3/6-31+G**-BSIP level and the energy barrierscorrespond to our benchmark values.16912.013.014.015.016.017.018.019.0 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17Energy Barrier (kcal/mol)∆q012345678910(a)14.614.815.015.215.415.615.816.016.216.416.6 0.07 0.08 0.09 0.1 0.11 0.12 0.13Energy Barrier (kcal/mol)∆q012345678910(b)Figure C.2: Benchmark energy barriers vs q in the organic molecules for the Diels-Alder models.(a) oxygen-based Diels-Alder reaction (∆q = qDieneTSO − qDieneRO , trenline: EB = −77.5∆q +25.8, r2 = 0.871) and (b) nitrogen-based Diels-Alder reaction (∆q = qDieneTSNH − qDieneRNH ,trenline: EB = −30.5∆q + 18.9, r2 = 0.627). Charges (in a.u.) were calculated using AIMAll atthe M05-D3/6-31+G**-BSIP level and the energy barriers correspond to our benchmark values.170Appendix D: Point Charge Models and Electric FieldsThis appendix include graphs about the effect of point charges in the energy barriers of themodels described in Chapter 4, section 2.1 for all “on water” model reactions. It also includes theeffect of an external field applied on the same models. All energy barriers were calculated at theM05-D3/6-31+G**-BSIP level of theory.40.041.042.043.044.045.046.047.048.049.0 1 2 3 4 5 6 7 8 9 10Energy barrier (kcal/mol)n in (H2O)nPoint Charge (H2O)nExplicit (H2O)nFigure D.1: The effect of using point charges as water models on the nitrogen-based Claisen rear-rangement. TIP3P charges were employed (qO = −2qH = −0.834).30.031.032.033.034.035.036.037.038.039.0 1 2 3 4 5 6 7 8 9 10Energy barrier (kcal/mol)n in (H2O)nPoint Charge (H2O)nExplicit (H2O)nFigure D.2: The effect of using point charges as water models on the oxygen-based Claisen rear-rangement. TIP3P charges were employed (qO = −2qH = −0.834).17115.016.017.018.0 1 2 3 4 5 6 7 8 9 10Energy barrier (kcal/mol)n in (H2O)nPoint Charge (H2O)nExplicit (H2O)nFigure D.3: The effect of using point charges as water models on the nitrogen-based Diels-Alderreaction. TIP3P charges were employed (qO = −2qH = −0.834).12.013.014.015.016.017.018.019.020.0 1 2 3 4 5 6 7 8 9 10Energy barrier (kcal/mol)n in (H2O)nPoint Charge (H2O)nExplicit (H2O)nFigure D.4: The effect of using point charges as water models on the oxygen-based Diels-Alderreaction. TIP3P charges were employed (qO = −2qH = −0.834).172 25 30 35 40 45 50 55 60 65Ax Bx Cx Ay By Cy Az Bz Cz(-)(+)Ebarrier (kcal mol-1)Direction and Magnitude of FieldFigure D.5: The effect of applying an external electric field on the nitrogen-based Claisen rear-rangement using different field magnitudes and directions. The C−N bond is aligned with the zdirection, the benzene ring is aligned to the xz plane. Ai = 1.08, Bi = 6.94, and Ci = 15.02;i = x, y or z, all field values reported in eV e−1 nm−1 10 15 20 25 30 35 40 45 50 55 60Ax Bx Cx Ay By Cy Az Bz Cz(-)(+)Ebarrier (kcal mol-1)Direction and Magnitude of FieldFigure D.6: The effect of applying an external electric field on the oxygen-based Claisen rearrange-ment using different field magnitudes and directions. The C−O bond is aligned with the z direction,the benzene ring is aligned to the xz plane. Ai = 1.08, Bi = 6.94, and Ci = 15.02; i = x, y or z, allfield values reported in eV e−1 nm−1173 6 8 10 12 14 16 18 20 22 24Ax Bx Cx Ay By Cy Az Bz Cz(-)(+)Ebarrier (kcal mol-1)Direction and Magnitude of FieldFigure D.7: The effect of applying an external electric field on the nitrogen-based Diels-Alderreaction using different field magnitudes and directions. The C−C bond in the dienophile is alignedwith the z direction, the dienophile is aligned with the xz plane. Ai = 1.08, Bi = 6.94, andCi = 15.02; i = x, y or z, all field values reported in eV e−1 nm−1 0 5 10 15 20 25 30Ax Bx Cx Ay By Cy Az Bz Cz(-)(+)Ebarrier (kcal mol-1)Direction and Magnitude of FieldFigure D.8: The effect of applying an external electric field on the oxygen-based Diels-Alder reactionusing different field magnitudes and directions. The C−C bond in the dienophile is aligned withthe z direction, the dienophile is aligned with the xz plane. Ai = 1.08, Bi = 6.94, and Ci = 15.02;i = x, y or z, all field values reported in eV e−1 nm−1174Appendix E: Scalar Projections in Bulk and Interfacial Regionsfor OWR ModelsThis appendix contains graphs of the scalar projections calculated in parts of the simulationboxes identified as bulk organic and interfacial water-organic regions. It also contains plots compar-ing the number of H2O and D2O molecules that penetrate the organic phase. This appendix alsocontains the comparison of the scalar projections obtained using heavy water and water simulations.Figure E.1: Scalar projections into the C−O bonds of the organic molecules (ClaisenRO) in aregion of the simulation box identified as bulk organic. The calculation of the electric fields andprojections involves all other molecules of the system in the box. The red dots represent averagescalar projections.175Figure E.2: Scalar projections into the C−O of the organic molecules (ClaisenRO) in a region ofthe simulation box identified as the interface. The calculation of the electric fields and projectionsinvolves all other molecules of the system in the box. The red dots represent average scalar projec-tions.Figure E.3: Scalar projections into the C−N bonds of the organic molecules (ClaisenRNH) in aregion of the simulation box identified as bulk organic. The calculation of the electric fields andprojections involves all other molecules of the system in the box. The red dots represent averagescalar projections.176Figure E.4: Scalar projections into the C−N of the organic molecules (ClaisenRNH) in a region ofthe simulation box identified as the interface. The calculation of the electric fields and projectionsinvolves all other molecules of the system in the box. The red dots represent average scalar projec-tions.Figure E.5: Scalar projections into the perpendicular direction to the plane formed by the threecarbon atoms in the organic molecules (DienophileRO) in a region of the simulation box identifiedas bulk organic. The calculation of the electric fields and projections involves all other moleculesof the system in the box. The red dots represent average scalar projections.177Figure E.6: Scalar projections into the perpendicular direction to the plane formed by the threecarbon atoms in the organic molecules (DienophileRO) in a region of the simulation box identifiedas interface. The calculation of the electric fields and projections involves all other molecules of thesystem in the box. The red dots represent average scalar projections.Figure E.7: Scalar projections into the perpendicular direction to the plane formed by the threecarbon atoms in the organic molecules (DienophileRNH) in a region of the simulation box identifiedas bulk organic. The calculation of the electric fields and projections involves all other moleculesof the system in the box. The red dots represent average scalar projections.178Figure E.8: Scalar projections into the perpendicular direction to the plane formed by the threecarbon atoms in the organic molecules (DienophileRNH) in a region of the simulation box identifiedas interface. The calculation of the electric fields and projections involves all other molecules of thesystem in the box. The red dots represent average scalar projections.(a) (b)Figure E.9: (a) Counting H2O molecules in a bulk organic region (0 < z < 9 in the simulation box)for the ClaisenRO system. (b) Counting D2O molecules in a bulk organic region (0 < z < 9 in thesimulation box) for the ClaisenRO system.179(a) (b)Figure E.10: (a) Counting H2O molecules in a bulk organic region (0 < z < 9 in the simulationbox) for the ClaisenRNH system. (b) Counting D2O molecules in a bulk organic region (0 < z < 9in the simulation box) for the ClaisenRNH system.(a) (b)Figure E.11: (a) Counting H2O molecules in a bulk organic region (0 < z < 9 in the simulationbox) for the DielsAlderRO system. (b) Counting D2O molecules in a bulk organic region (0 < z <9 in the simulation box) for the DielsAlderRO system.180(a) (b)Figure E.12: (a) Counting H2O molecules in a bulk organic region (0 < z < 9 in the simulationbox) for the DielsAlderRNH system. (b) Counting D2O molecules in a bulk organic region (0 < z <9 in the simulation box) for the DielsAlderRNH system.Figure E.13: Probability density of the scalar project on the C−N bond in the simulation boxcorresponding to the ClaisenRNH system.181Figure E.14: Probability density of the scalar project on the C−O bond in the simulation boxcorresponding to the ClaisenRO system.Figure E.15: Probability density of the scalar project into the nˆCCC bond in the simulation boxcorresponding to the DielsAlderRNH system.182Figure E.16: Probability density of the scalar project into the nˆCCC direction in the simulation boxcorresponding to the DielsAlderRO system.183
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Elucidating the "on water" mechanism in accelerated reactions in water
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