Science, Irving K. Barber Faculty of (Okanagan)
Chemistry, Department of (Okanagan)
DSpace
UBCO
Pei, Zhipeng
Master of Science - MSc
University of British Columbia
A polymer cross-linker is a chemical agent that can create covalent bonds between the molecular chains that comprise a polymeric material. Recently, a novel, versatile, bis-diazirine based polymer cross-linker was reported,1 but its cross-linking efficacy is relatively low and can be improved. Moreover, the details of the mechanism of cross-linking has not been reported. In this thesis, we use state-of-art computational chemistry methods to explore how carbenes derived from bis-diazirines engage in cross-linking and identify the factors that affect the cross-linking efficacy. The computational results show that bis-diazirines do not form bis-carbenes in a concerted fashion upon thermal activation. Instead, the carbene centers are generated sequentially. The use of substituents on the carbene center (i.e. p-X-C6H4-C̈-R) and para to the carbene center can significantly influence the electronic state of carbenes, as well as the barrier heights associated with carbene formation and carbene insertion. Therefore, substitution provides a general strategy to control the reactivity of the cross-linker. We also explore how tether units and different ring structures may impact cross-linker performance, and possible carbene side- and self-reactions. To the best of our knowledge, this is the first computational study on this type of polymer cross-linker, and the results provide guidance and insights for improving cross-linking performance systematically. The data obtained were used to propose a next-generation diazirine-based polymer cross-linker.
Ab Initio Studies of Novel Polymer Cross-Linkers by Zhipeng Pei B.Sc., The Australian National Univerisity, 2017 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE COLLEGE OF GRADUATE STUDIES (Chemistry) THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan) April 2021 © Zhipeng Pei, 2021 ii The following individuals certify that they have read, and recommend to the College of Graduate Studies for acceptance, a thesis/dissertation entitled: Ab Initio Studies of Novel Polymer Cross-Linkers submitted by Zhipeng Pei in partial fulfillment of the requirements of the degree of Master of Science Gino DiLabio, Department of Chemistry, Irving K. Barber Faculty of Science Supervisor Frederic Menard, Department of Chemistry, Irving K. Barber Faculty of Science Supervisory Committee Member Kevin Smith, Department of Chemistry, Irving K. Barber Faculty of Science Supervisory Committee Member Kevin Golovin, School of Engineering, Faculty of Applied Science University Examiner iii Abstract A polymer cross-linker is a chemical agent that can create covalent bonds between the molecular chains that comprise a polymeric material. Recently, a novel, versatile, bis-diazirine based polymer cross-linker was reported,1 but its cross-linking efficacy is relatively low and can be improved. Moreover, the details of the mechanism of cross-linking has not been reported. In this thesis, we use state-of-art computational chemistry methods to explore how carbenes derived from bis-diazirines engage in cross-linking and identify the factors that affect the cross-linking efficacy. The computational results show that bis-diazirines do not form bis-carbenes in a concerted fashion upon thermal activation. Instead, the carbene centers are generated sequentially. The use of substituents on the carbene center (i.e. p-X-C6H4-C̈-R) and para to the carbene center can significantly influence the electronic state of carbenes, as well as the barrier heights associated with carbene formation and carbene insertion. Therefore, substitution provides a general strategy to control the reactivity of the cross-linker. We also explore how tether units and different ring structures may impact cross-linker performance, and possible carbene side- and self-reactions. To the best of our knowledge, this is the first computational study on this type of polymer cross-linker, and the results provide guidance and insights for improving cross-linking performance systematically. The data obtained were used to propose a next-generation diazirine-based polymer cross-linker. iv Lay Summary A polymer cross-linker is a glue-like compound designed to introduce strong bonds between adjacent polymer chains and create a network within the polymeric material that alters its physical properties. Cross-linking polymers can lead to increased mechanical strength and the resulting material can be used, for example, to build stronger and lighter ballistic protection armor. In this work, we use computer simulations to understand the properties of a new type of polymer cross-linker that is able to link materials that are normally not “glue-able”. The results of the simulations provide insights into the chemical behavior of the cross-linker and allow for the design of more effective cross-linkers. v Preface The research work in this thesis were conducted by Zhipeng Pei. This thesis was supervised by Prof. Gino DiLabio at the Department of Chemistry, University of British Columbia, Okanagan Campus. This project involved some collaboration with Prof. Jeremy Wulff from the Department of Chemistry, University of Victoria. As outlined below, part of this thesis has been published in research journals with the indication of the author’s contributions. Simhadri, C.; Bi, L.; Lepage, M. L.; Takaffoli, M.; Pei, Z.; Musolino, S. F.; Milani, A. S.; DiLabio, G. A.; Wulff, J. E. Flexible Polyfluorinated Bis-Diazirines as Molecular Adhesives. Chem. Sci. 2021, 12 (11), 4147–4153. Contribution: My contribution in this paper includes: (1) Performing the computational study for elucidating the dominant insertion mechanism, and (2) studying the self-reaction of cross-linkers. Results from this thesis will appear in one or more future, peer-reviewed scientific publications. vi Table of Contents Abstract ------------------------------------------------------------------------------------------------ iii Lay Summary -----------------------------------------------------------------------------------------iv Preface -------------------------------------------------------------------------------------------------- v Table of Contents -------------------------------------------------------------------------------------vi List of Tables ------------------------------------------------------------------------------------------ix List of Figures -----------------------------------------------------------------------------------------xi List of Schemes -------------------------------------------------------------------------------------- xiv List of Symbols and Abbreviations -------------------------------------------------------------- xv Acknowledgments --------------------------------------------------------------------------------- xvii Dedication ------------------------------------------------------------------------------------------ xviii Chapter 1: Introduction --------------------------------------------------------------------------- 1 1.1 Polymeric Materials .................................................................................................1 1.2 Polymer Cross-Linkers ............................................................................................2 1.2.1 Background----------------------------------------------------------------------------- 2 1.2.2 Traditional and Novel Cross-Linkers ----------------------------------------------- 3 1.3 Carbenes ...................................................................................................................5 1.3.1 Background on Carbenes ------------------------------------------------------------- 5 1.3.2 Electronic States of Carbenes -------------------------------------------------------- 6 1.3.3 Precursors and Carbene Formation ------------------------------------------------- 9 vii 1.3.4 X-Y bond Insertion ------------------------------------------------------------------- 12 1.4 Research Questions ................................................................................................14 Chapter 2: Theoretical Background ----------------------------------------------------------- 16 2.1 Hartree-Fock Theory ..............................................................................................16 2.2 Basis Sets ...............................................................................................................19 2.3 Coupled-Cluster Theory.........................................................................................22 2.4 Multi-Configurational Self-Consistent Field Theory.............................................25 2.5 Density Functional Theory ....................................................................................28 2.6 Geometry and Frequency .......................................................................................32 2.7 Thermochemistry ...................................................................................................33 Chapter 3: Methodology ------------------------------------------------------------------------- 36 Chapter 4: Mechanistic Profile ----------------------------------------------------------------- 38 4.1 Methylene Insertion into Methane .........................................................................38 4.2 Cross-Linking Reaction Energy Profile .................................................................41 4.3 Different Ring Structure and Tether Unit ..............................................................45 Chapter 5: Bis-Carbenes ------------------------------------------------------------------------- 50 5.1 Substituent Effect on Single Carbene Singlet-Triplet Gap ....................................50 5.2 para and meta Bis-Carbene Ground States ............................................................54 Chapter 6: Exploring Cross-Linking Efficacy of Cross-Linkers ------------------------ 60 6.1 Carbene Formation Barrier ....................................................................................60 viii 6.2 Reaction Free Energy of Carbene Formation ........................................................70 6.3 Carbene Insertion Barriers .....................................................................................76 6.3.1 C-H Insertion -------------------------------------------------------------------------- 76 6.3.2 C-F Insertion -------------------------------------------------------------------------- 81 6.3.3 Fluorination of the Ring ------------------------------------------------------------- 84 Chapter 7: Conclusion ---------------------------------------------------------------------------- 87 Bibliography ------------------------------------------------------------------------------------------ 92 Appendix -------------------------------------------------------------------------------------------- 102 ix List of Tables Table 4.1. Summary of the calculated singlet-triplet (S-T) gaps of methylene and its insertion barrier heights to methane by M06-2X-D3 and CCSD(T)/CBS. Energetic terms including Eel, E0, H, S, and G are reported. All geometries and thermal corrections were obtained from M06-2X-D3/6-31G** in gas phase. The temperatures used are 50K, 298K, and 400K, and the pressure is 1 atm. The units are kJ/mol. -------------------------------------------------------------- 39 Table 4.2. Summary of the calculated free energy (298K, 1 atm) carbene S-T gaps and reaction barriers for concerted carbene formation, diazo formation from a diazirine, carbene formation from a diazo intermediate, singlet insertion to methane, and triplet carbene hydrogen abstraction from methane in kJ/mol. All geometries and thermal corrections were obtained from M06-2X-D3/6-31G** except for the bold italic values were from CASPT2(12,12)/6-31G**//M06L/6-31G**. -------------------------------------------------------------------------------- 46 Table 4.3. Summary of the calculated free energy (298K, 1 atm) S-T gaps and reaction barriers of singlet insertion to and triplet carbene hydrogen abstraction from methane (CH4) or the central CH2 of propane (C3H8) in kJ/mol. All geometries and thermal corrections were obtained from M06-2X-D3/6-31G**. ---------------------------------------------------------------------------- 48 Table 5.1. Calculated electronic energy S-T splitting with available experimental data. All geometries and free energy contributions (298K, 1atm) were from M06-2X-D3/def2-TZVP, except for B3LYP data that were optimized separately at B3LYP-D3BJ/def2-TZVP. The energetic calculations of CASSCF used cc-pVTZ basis set, and DLPNO-CCSD(T) used cc-pV(D-T)Z CBS. The units are kJ/mol. ---------------------------------------------------------------- 51 Table 5.2. Summary of calculated electronic energies of various electronic states relative to the closed-shell singlet state (define as zero) in selected p-phenylenebis(carbene)s. All geometries were from M06-2X-D3/def2-TZVP, except for B3LYP data were optimized separately at B3LYP-D3BJ/def2-TZVP. CCSD(T) calculations used cc-pVTZ basis set. The units are in kJ/mol. ----------------------------------------------------------------------------------------------------- 56 x Table 5.3. Summary of calculated electronic energies of various electronic states relative to the closed-shell singlet state (define as zero) in selected m-phenylenebis(carbene)s. All geometries were from M06-2X-D3/def2-TZVP, except for B3LYP data was optimized separately at B3LYP-D3BJ/def2-TZVP. CCSD(T) calculations used cc-pVTZ basis set. The units are in kJ/mol. ----------------------------------------------------------------------------------------------------- 57 Table 6.1. Summary of the selected para-substituents X shown in Figure. 6.2, and their corresponding σp+ constants.95 ------------------------------------------------------------------------- 62 Table 6.2. Summary of the calculated free energy (298K, 1atm) S-T splittings of R=CF3, F, Cl, and OMe carbenes using DLPNO-CCSD(T)/CBS//M06-2X-D3/6-31G**. (D-T)CBS stands for cc-pV(D-T)Z, and (T-Q) stands for cc-pV(T-Q)Z. The units are in kJ/mol. ---------------- 75 Table 6.3. Summary of the calculated free energy barrier (298K, 1atm) for singlet C-F insertion shown in Fig. 6.9 using M06-2X-D3/6-31G**. The units are in kJ/mol. ------------------------ 82 Table 6.4. Summary of the calculated free energy barrier (298K, 1atm) for the triplet C-F abstraction shown in Fig. 6.9 using M06-2X-D3/6-31G**. The units are in kJ/mol. ---------- 83 Table 6.5. Calculated enthalpy and free-energy (298K, 1atm) reaction barriers of model carbene to hexafluorobenzene or benzene using M06-2X-D3/6-31G**. The units are in kJ/mol. Reproduced from ref[83] with permission from the Royal Society of Chemistry. ------------- 86 Table A.1. Summary of the calculated free energy (298K, 1atm) S-T gaps and barriers of carbene formation, singlet carbene insertion, and triplet carbene abstraction using M06-2X-D3/6-31G** for R=CF3, F, Cl, and OMe. The central C-H bond in propane is targeted for insertion or abstraction reaction modeling. The units are in kJ/mol. --------------------------- 102 Table A.2. Summary of the calculated (298K, 1atm) isodesmic fee energies (of the parent reaction or TS reaction) and reaction free energy (of the singlet carbene or triplet carbene) using M06-2X-D3/6-31G** for R=CF3, F, Cl, and OMe. The units are in kJ/mol. ---------- 103 xi List of Figures Figure 1.1. Illustration of cross-linking polymer chains using a chemical cross-linker. A (green) and B (red) are two polymer chains, and the cross-linker is represented as a blue band with star-shaped ends. The star represents a chemical moiety that can covalently bond to a polymer strand. ------------------------------------------------------------------------------------------------------- 2 Figure 1.2. Illustration of various strategies to cross-link polymers: (a). Diels-Alder cycloaddition between two pendant moieties to cross-link polypropylene (PP-X).9 (b). Formaldehyde dimethyl acetal as a cross-linker through Friedel-Crafts reaction to obtain microporous polymers.10 (c). Bis-diazirine cross-linking of polyethylene (PE). The chemistry of bis-diazirines is studied in this thesis.1 ------------------------------------------------------------- 4 Figure 1.3. Illustration of carbene orbitals. The different colors represent different phases of the orbitals. The left is the hybridized sp2-σ carbon-centered orbital, and the right is a largely unhybridized 2p-π carbon orbital. ---------------------------------------------------------------------- 7 Figure 1.4. Illustration of electron-withdrawing (left) and electron-donating (right) effects on carbenes. The red arrow indicates the shift of electrons. -------------------------------------------- 9 Figure 1.5. Scheme of interconversion of diazirine, diazo, and carbene. The interconversion barrier heights are determined by substituents R1 and R2. ----------------------------------------- 10 Figure 1.6. Singlet carbene will be formed first regardless of the precursor for photolysis of 3H-diazirine.37 However, under photolysis of excited diazomethane, the open-shell singlet carbene is predicted rather than closed-shell carbene.36 -------------------------------------------- 11 Figure 1.7. Mechanism of singlet or triplet carbene insertions into X-Y. The singlet insertion mechanism is concerted and has a ring TS complex. The triplet carbene will proceed via abstraction reaction, followed by radical recombination. ------------------------------------------ 13 Figure 1.8. Schematic orbital description of two phases in the concerted singlet insertion into X-Y bond. Firstly, the empty of 2p-π orbital of carbene attacks the filled X-Y bonding orbital. xii An internal, relative rotation then allows the nucleophilic attack of carbene lone pair to X-Y antibonding orbital, which completes the insertion. ------------------------------------------------ 14 Figure 2.1. Molecular orbital diagram of 1O2 based on only O 2p orbitals. One σ and two π orbitals are filled first, while the remaining electron pair (red color) can either occupy the degenerated π*a or π*b orbitals. ------------------------------------------------------------------------- 26 Figure 2.2. Schematic illustrations of CASSCF(2,2) (left) and CASSCF(6,4) (right). The blue box with a dash-line defines the active space in which all possible electrons configurations are generated. ------------------------------------------------------------------------------------------------- 27 Figure 2.3. Jacob’s ladder for DFT exchange-correlation functionals. The lowest rung is the LDA and the second highest is the double-hybrid functionals. The cost increases going up the ladder, while the accuracy ideally (but does not necessarily) follows the same trend. -------- 30 Figure 4.1. The carbon center A on the ring can be replaced by a nitrogen atom. Under thermal activation, the nitrogen substituted ring produces more diazo intermediates than the carbon ring as observed by experiments.1 --------------------------------------------------------------------- 45 Figure 4.2. Illustration of the first generation (Gen 1) and the second generation (Gen 2) cross-linkers. The joint that connects two rings is defined as a tether unit. Gen 2b has a double-length tether unit than Gen 2a. --------------------------------------------------------------------------------- 47 Figure 5.1. Selected singlet carbene systems for S-T splitting studies. (8) is the simplified system for the cross-linker 2A. ------------------------------------------------------------------------ 50 Figure 5.2. Illustration of possible resonance forms in meta- or para-phenylenebis(carbene) compounds. ----------------------------------------------------------------------------------------------- 55 Figure 6.1. The plot of experimental Tonset versus the calculated reaction free energy barrier (298K, 1atm) using M06-2X-D3/6-31G** for the carbene formation step. The model carbene precursor is inset. The plot is modified based on unpublished data from Wulff and co-workers with permissions.94 The units are in °C and kJ/mol. ------------------------------------------------ 61 xiii Figure 6.2. Selected R groups and para-substituents X used in this chapter (see Table 6.1 for their corresponding σp+ values). The carbene formation shown is under thermal activation. 62 Figure 6.3. Plot of the calculated reaction free energy barrier (298K, 1atm) versus σp+ of the para-substituents using M06-2X-D3/6-31G** for the concerted carbene formation. The units are in kJ/mol. --------------------------------------------------------------------------------------------- 63 Figure 6.4. Illustration of the isodesmic schemes for studying the influence of X substituents for the parent reaction (top) and the TS reaction (bottom). ---------------------------------------- 65 Figure 6.5. Plots of the isodesmic free energy (298K, 1atm) versus σp+ of the para-substituents for the parent reaction (top) and the TS reaction (bottom) using M06-2X-D3/6-31G**. The units are in kJ/mol. --------------------------------------------------------------------------------------- 67 Figure 6.6. Plots of the calculated carbene formation reaction free energy (298K, 1atm) versus σp+ of the X substituents using M06-2X-D3/6-31G**. Dash line is when the triplet carbene is formed, and the solid line is when the singlet carbene is formed. The units are in kJ/mol. (a). R=CF3, (b). R=F, (c). R=Cl, and (d). R=OMe. ------------------------------------------------------ 71 Figure 6.7. Illustration of C-H insertion (or abstraction) from our model carbenes. The central C-H bond in propane is targeted for insertion reaction modeling. -------------------------------- 78 Figure 6.8. Plots of the calculated free energy barriers (298K, 1atm) versus σp+ of the X substituents using M06-2X-D3/6-31G** for singlet insertion (or triplet abstraction). The solid line represents the singlet insertion, and the dashed line represents the triplet abstraction. The units are in kJ/mol. --------------------------------------------------------------------------------------- 78 Figure 6.9. Illustration of C-F insertion (or abstraction) from our model R=CF3 carbenes. The targeted substrates used are 2-fluoropropane, 2,2-difluoropropane, and perfluoropropane. -- 82 Figure 6.10. Possible reactions between carbene and benzene, and model carbene with benzene derivatives used for the study (in the square). Reproduced from ref[83] with permission from the Royal Society of Chemistry. ----------------------------------------------------------------------- 85 Figure 7.1. Structure of the cross-linker Gen 3a (top) and proposed Gen 4 (bottom). --------- 91 xiv List of Schemes Scheme 4.1. Free energy profile (298K, 1 atm) of the bis-diazirine to carbene formation. All geometries and thermal corrections were obtained from M06-2X-D3/6-31G** except for purple italic values, which were from CASPT2(12,12)/6-31G**//M06L/6-31G**. The red and purple values are reaction barriers, and green values are the S-T gap, where S is singlet and T is triplet. The units are kJ/mol. ------------------------------------------------------------------------- 42 Scheme 4.2. Free energy profile for singlet carbene insertion and triplet carbene abstraction pathways. All geometries and thermal corrections were obtained from M06-2X-D3/6-31G**. The green value is the S-T gap, and red values are free energy barriers associated with each step. The units are kJ/mol. ------------------------------------------------------------------------------ 44 xv List of Symbols and Abbreviations AO atomic orbital BDE bond dissociation enthaply CASSCF complete active space self-consistent field CBS complete basis set CGTF contracted Gaussian type function CC coupled-cluster PAL photoaffinity labeling PE-X cross-linked polyethylene PP-X cross-linked polypropylene DFT density functional theory EDG electron-donating group EWG electron-withdrawing group xvi GTF Gaussian type function HF Hartree-Fock HDPE high-density polyethylene HK Hohenberg-Kohn ISC intersystem crossing LDPE low-density polyethylene MO molecular orbital MCSCF multi-configurational self-consistent field PES potential energy surface QM quantum mechanic SE Schrödinger equation TS transition state ZPE zero-point energy xvii Acknowledgments First and foremost, I would like to express my sincere gratitude to my supervisor Prof. Gino DiLabio for offering me this very interesting project and for his insightful guidance throughout my M.Sc. study. I still could not forget that I came to this group with little computational background on the first day, but I have gained extensive knowledge today from your mentoring. I want to thank you for your patience in helping me with the thesis writing and train me as a better researcher. I would also like to thank all the current and past members of the DiLabio group for all their help and assistance. Thank you to Prof. Kevin Smith and Prof. Fred Menard for serving as my committee members and provide valuable suggestions during my progress. I want to say thank you to all our collaborators from the Wulff group at UVic for their diligent work and useful discussions. This has been a very enjoyable collaboration experience. I would also like to thank my previous supervisor Prof. Michelle Coote at ANU, who will also be my Ph.D. supervisor. Without her encouragement, I would never think of pursuing computational chemistry in my career. Finally, I need to thank all my loves for their solid supports and for providing me the freedom to pursue my interest. This work was financially supported, in part, by the Canadian Department of National Defence, through contract CFPMN1-026. xviii Dedication 感谢我的爷爷和奶奶。充满理想的老一辈知识分子，我科研之路上的引路人。 1 Chapter 1: Introduction 1.1 Polymeric Materials Polymers are macromolecules that consist of a large number of repeating units. Polymeric materials are everywhere in our daily life. From plastic bags to the coatings of airplanes, they have greatly facilitated and advanced modern technology.2 Polymers are not only synthesized but also naturally occur in biological systems. Therefore, polymers are ubiquitous and indispensable. One significant feature of polymeric materials is their versatility. Distinct thermal and mechanical properties of polymers can be conferred by altering the nature of the monomer unit. For instance, nylon 6,6 is a linear polymer that is mechanically anisotropic and has high elasticity. Kevlar is a polymer composed of hydrogen-bonded, substituted aromatic rings. It has very high mechanical strength and is widely used to make ballistic protection armor.3 During polymerization, the monomer units can be assembled in a variety of ways, leading to polymers with different shapes (e.g. linear, star, cross-linked) and different properties. The differences between low-density polyethylene (LDPE) and high-density polyethylene (HDPE) provide an illustrative example.4 Since LDPE is more branched than HDPE, its chains are more weakly interconnected, and so LDPE has a lower tensile strength than HDPE. Chemical agents may also increase the connectivity between molecular chains, thereby offering a relatively simple mechanism for tuning the strength and other properties of a polymer. 2 1.2 Polymer Cross-Linkers 1.2.1 Background A polymer cross-linker is an agent that can create covalent bonds between the molecular chains that comprise a polymeric material (Figure 1.1). Cross-linking is an effective way of altering or improving the mechanical and thermal properties of polymers. For example, cross-linking can convert a flexible thermoplastic linear polymer into a rigid thermoset,1 which has a better thermal resistance. Vulcanization, which uses a sulfur-based cross-linker, is used to increase the durability of rubber.5 Cross-linked polyethylene (PE-X) is commonly used for plumbing and can also be extended to medical6 and electrical applications.7 Figure 1.1. Illustration of cross-linking polymer chains using a chemical cross-linker. A (green) and B (red) are two polymer chains, and the cross-linker is represented as a blue band with star-shaped ends. The star represents a chemical moiety that can covalently bond to a polymer strand. Non-covalent interactions can also be used to form weak physical cross-links in polymers. One simple example is the “slime” that is often made as part of a chemistry demonstration via gelation of polyvinyl alcohol with borax.8 3 The degree of cross-linking plays a key role in the properties of a polymer. A high degree of cross-linking results, in most cases, in a more rigid but possibly more brittle polymer. On the other hand, a low degree of cross-linking may result in a polymer that forms a softer material but retains much of the original thermoplastic nature. Each of these materials will have a specific application depending on the desired properties one wishes to attain. Hence, the potential to control the degree of cross-linking is key when considering the development of new polymer materials. 1.2.2 Traditional and Novel Cross-Linkers We here present a few previous explorations of chemical polymer cross-linkers to demonstrate a few general strategies and their shortcomings. This background will also illustrate the need for novel cross-linkers. Chung and co-workers prepared cross-linked polypropylene (PP-X) using a styrene framework for connections, and the cross-linking is accomplished through a Diels-Alder cycloaddition between two pendant moieties (Figure 1.2 (a)).9 Tan and co-workers used formaldehyde dimethyl acetal as a cross-linker through Friedel-Crafts reaction to obtain microporous polymers (Figure 1.2 (b)).10 Both methods require special functional groups to proceed, so these methods are not appropriate to synthesize cross-linked polyethylene (PE-X). Generally, using such typical chemical reactions to achieve cross-linking is highly limited by the identity of functional groups and bonds, which reduces the applicability of these approaches. 4 Figure 1.2. Illustration of various strategies to cross-link polymers: (a). Diels-Alder cycloaddition between two pendant moieties to cross-link polypropylene (PP-X).9 (b). Formaldehyde dimethyl acetal as a cross-linker through Friedel-Crafts reaction to obtain microporous polymers.10 (c). Bis-diazirine cross-linking of polyethylene (PE). The chemistry of bis-diazirines is studied in this thesis.1 The preparation of PE-X can be further classified as peroxide cross-linking (PE-Xa), silane cross-linking (PE-Xb), irradiation cross-linking (PE-Xc), and azo cross-linking (PE-Xd).11 For instance, PE-Xc is produced by electron beam radiation;12 however, the intense radiation could result in embrittlement of materials.13 Main drawbacks of this procedure are associated with the generation of a radical center by exposure to high energy radiation, which results in uncontrolled side reactions and thereby making it difficult to tune the mechanical properties of the polymers.1 Lastly, all of the above-mentioned methods require the use of specialized equipment, highly reactive chemicals that require special storage/shipping, and the use of extreme reaction conditions. This makes these methods financially and environmentally costly. To address some of the limitations described above, Wulff and co-workers reported a novel polymer cross-linker using a bis-diazirine framework (Figure 1.2 (c)).1 Under thermal activation or photoactivation, carbene centers are formed by extrusion of N2 gas. The carbenes then undergo insertion into the C-H bonds present in the polymer. Because the cross-linker has 5 two carbene centers, it can interconnect two polymer chains to achieve cross-linking under relatively mild reaction conditions. Importantly, no special functional groups on the polymer are required for the cross-linker to be effective. Due to the lack of requirements on polymers and the mild reaction conditions used, Wulff’s novel bis-diazirine cross-linking approach shows great potentials in cross-linking polymeric materials. However, the detailed mechanism by which this cross-linking process occurs has yet to be clarified. The motivation for this thesis project is to develop an understanding of the thermochemistry and mechanisms associated with bis-diazirine cross-linkers. The insights derived from the modeling work presented in this thesis will help elucidate how better carbene cross-linkers can be designed. 1.3 Carbenes 1.3.1 Background on Carbenes Carbenes are molecules with a divalent carbon center, that is, a carbon surrounded by six electrons.14 These carbon centers are electronically deficient and highly reactive.15 Their general form can be described as R1CR2, and methylene (CH2) is the simplest example. Ultrafast time-resolved spectroscopy has led to significant advances in understanding carbene chemistry, as described in the excellent review from Platz.16 Also, Platz and others have made good use of computational chemistry techniques, along with their experiments, to help understand carbene behavior.15,17 6 The fact that carbenes possess two valence electrons distributed in two non-bonding orbitals means that they can, in principle, manifest different spin states. They may have a closed-shell singlet state when the two electrons are paired together in one orbital, an open-shell triplet state when the electrons have parallel spins in two orbitals, or an open-shell singlet state when antiparallel electrons occupy two orbitals. The reactivity and reaction pathways of carbenes depend on the nature of their spin states.18 In general, the cross-linking efficacy is expected to be intimately related to insertion barriers associated with a carbene and is inversely related to the stability of the carbene.1,19 In order to maximize this efficacy, it is therefore crucial to understand the electronic states of carbenes and how each state may undergo different reaction mechanisms with substrate polymers. A detailed discussion of how to modify the electronic state of a carbene is presented in the next subsection. 1.3.2 Electronic States of Carbenes The two non-bonding valence electrons in carbenes may occupy two orbitals. One is the hybridized sp2-σ carbon-centered orbital, and the other is a largely unhybridized 2p-π carbon orbital (Figure 1.3). There are three ways to accommodate two electrons into these two orbitals: σ2π0, σ1π1 (same spin), and σ1π1 (opposite spin). Hoffmann, Borden, and co-workers reported the possibility of σ0π2 ground state configuration, but this is not commonly accessible.20 Additionally, the open-shell singlet σ1π1 possesses stronger Coulombic repulsion than the corresponding triplet counterpart, and the triplet is always lower in energy by Hund’s rule.20,21 (Hund’s rule is applicable here because the two orbitals are atom-centered.) 7 Consequently, the two most accessible ground states will be closed-shell singlet (σ2π0) and open-shell triplet (σ1π1). The energetic difference between them is defined as ∆EST. In this thesis, a negative value indicates the singlet state is lower in energy (more stable) than the triplet. Figure 1.3. Illustration of carbene orbitals. The different colors represent different phases of the orbitals. The left is the hybridized sp2-σ carbon-centered orbital, and the right is a largely unhybridized 2p-π carbon orbital. In 1932, Mulliken found that methylene has two low-lying electronic states.22 Herzberg later concluded that the methylene ground state is the triplet.23 Experimentalists at the time believed methylene possessed a linear geometry,24 while the theoretical scientists proposed that the structure is bent.25 In 1970s, the bent structure was proven to be the correct one, and the calculated ∆EST agreed well with the experimental value of 9 kcal/mol.26 The resolution of the dispute established the importance of using theoretical chemistry methods for studying carbene chemistry. The ground state of carbenes depends on the energetic gap between their two orbitals. If the gap is large enough, the tendency to achieve maximum multiplicity is diminished by the repulsion associated with electron pairing, which will produce a singlet state. Therefore, varying the R1-C-R2 angle or substituents, which affects orbital energy through hybridization or electron-donating/withdrawing groups, respectively, is an effective strategy to achieve the desired electronic configuration in carbenes. For instance, perfect sp2 hybridization retains 120° 8 as the bond angle. Hence, most singlet carbenes have R1-C-R2 angles close to 120°, and therefore sp2 hybridization at the carbon center. In contrast, triplet carbenes tend to have larger R1-C-R2 angles due to the extra contribution from partially filled 2p-π orbital to minimize the electronic repulsion, so the triplet carbene deviates from perfect sp2 hybridization.15 Cyclopropylidene, which has an R1-C-R2 angle close to 60°, possesses a singlet ground state with ∆EST= -13.8 kcal/mol.27 However, its non-cyclized counterpart dimethylcarbene has a much lower gap of -1.4 kcal/mol.28 The different ∆EST can be ascribed to the fact that cyclopropylidene has a much smaller R1-C-R2 angle, which results in more s character on carbene center.17 This will increase the energetic gap between sp2-σ and 2p-π orbital, so a singlet state is favored. Substituent effects on ∆EST may be larger than structural effects. Since singlet carbene has an empty 2p-π orbital as well as a doubly filled sp2-σ orbital, it can behave as both an electrophile and a nucleophile. These orbitals may interact with substituents through mesomeric (resonance) or inductive effects. For example, lone pairs of electrons on substituents that conjugate with the empty 2p-π orbital through π donation will stabilize the singlet carbene (Figure 1.4). Similarly, but to a lesser extent, the overall energy of the singlet carbene may be lowered by introducing a σ-acceptor on the carbene. For example, fluorine atom substituent can synergistically stabilize a carbene’s lone pair and destabilize its empty 2p-π orbital, resulting in a closed-shell singlet carbene that is lower in energy than the triplet. ∆EST for FCH is reported as -14.9 kcal/mol,29 and -54 kcal/mol for F2C,30 compared to +9 kcal/mol for methylene. 9 Arduengo carbenes are N-heterocyclic species. These have two adjacent nitrogen atoms that can strongly donate to the empty 2p-π orbital of a carbene, resulting in a very-stable singlet state. Therefore, such carbenes can be even isolated as a pure compound, which contradicts its tradition as a reactive intermediate.31 Figure 1.4. Illustration of electron-withdrawing (left) and electron-donating (right) effects on carbenes. The red arrow indicates the shift of electrons. 1.3.3 Precursors and Carbene Formation Carbenes are typically formed from diazirine or diazo precursor compounds32 through photo or thermal activation leading to the loss of N2. Diazo species can interconvert with diazirines, and carbenes formed can be trapped by ambient N2, converting back to a precursor (Figure 1.5). The energy barriers associated with this interconversion are dependent on the nature of the substituents present, hence the final composition of products can be solely carbenes or a mixture with diazo species.33 The conditions of activation of precursors also affect the outcome of carbene formation. Under photolysis, the so-called rearrangement in the excited state (RIES) can lead to the formation of a number of reactive and non-reactive products.34 RIES processes increase the complexities of reactions promoted by photolysis, making reaction outcomes difficult to predict. 10 Figure 1.5. Scheme of interconversion of diazirine, diazo, and carbene. The interconversion barrier heights are determined by substituents R1 and R2. Both heat and light activation have advantages and disadvantages. For the thermal process, the reaction will only follow one potential energy surface (PES),17 and the closed-shell singlet carbene will be obtained first. The singlet carbenes may further relax through intersystem crossing (ISC) to form the triplet (Figure 1.6). The ISC rate may be slow enough to allow the singlet carbene to react before converting to a triplet state.35 However, due to the high reactivity of carbenes, possible side reactions with solvent molecules may occur. Photochemical reactions require less energy and can be used on materials with low melting points such as paraffin. Photoactivation can be used in cases where heat will result in shape distortion and/or mechanical strength loss, which in turn may impact the applications of the polymer. One shortcoming of photolysis is that the excited states of the carbene cross-linker may participate in reactions via RIES and create unwanted products. Additionally, it was reported that excited diazomethane produced an open-shell singlet carbene under UV irradiation rather than the traditional closed-shell carbene.36 This demonstrates that extra complexities may arise via the photoactivation route. 11 Figure 1.6. Singlet carbene will be formed first regardless of the precursor for photolysis of 3H-diazirine.37 However, under photolysis of excited diazomethane, the open-shell singlet carbene is predicted rather than closed-shell carbene.36 Since diazirines are effective photo-precursors of carbenes, they are widely used in photoaffinity labeling (PAL). PAL uses a chemical probe that can connect targeted covalent ligands to the biological substrates (e.g. proteins) under photoactivation,38,39 and this approach was firstly proposed by Westheimer and co-workers in the 1960s.40 Compared to other photoreactive groups such as benzophenones and phenylazides, phenyldiazirines have several advantages including: (1). The longer wavelength of irradiation (about 360 nm) than proteins can absorb (about 280 and 200 nm), so there is no damage to biological macromolecules. (2). A comparatively short period of irradiation. (3). Carbenes are more chemically reactive than nitrenes, which are produced via phenylazides. Trifluoromethylaryldiazirines are one of the most commonly used photoaffinity groups for their high chemical stability, inertness to acidic or basic solutions, little long-lived diazo intermediates, and resistance to nucleophiles. In Chapter 6, we will provide detailed discussions on how to systematically tune the ground state of the carbenes that formed from trifluoromethylaryldiazirines and their insertion barriers. PAL techniques have been greatly applied in drug discovery, neurochemistry, anti-cancer agents, etc. (see ref[38] and ref[39] for comprehensive reviews on PAL) 12 1.3.4 X-Y bond Insertion Carbenes are known for effectively inserting into X-Y bonds such as C-H bonds.41 Both singlet and triplet carbenes can react with substrates but do so via different pathways (Figure 1.7). Singlet carbene reactions proceed by a concerted mechanism through a three-membered ring transition state complex and the reaction can result in stereospecific products. On the other hand, the triplet carbene will initially engage in an abstraction reaction which generates two radical species. The radical intermediates will most likely rapidly recombine to give the insertion product. However, the stepwise mechanism will affect the reaction outcome in two ways. Firstly, the intermediate will relax its geometry as time passes; this means the product will not be stereospecific but stereoselective. Second, the intermediate may undergo other reactions prior to recombination (like radical rearrangements), generating unwanted side products. For instance, polyethylene chains that involve radical centers can engage in backbiting followed by β-scission to shorten the polymer chain. Backbiting is when a radical center on the polyethylene chain abstracts a hydrogen atom that is a few bonds away and produces a new radical center.42 β-scission is the cleavage of the bond that is adjacent to the radical center, resulting in an olefin and a chain with the radical end as products. These structural changes may, in turn, affect the thermal or mechanical properties of materials. Therefore, minimizing the concentration of radical intermediates is key to minimizing such side reactions. 13 Figure 1.7. Mechanism of singlet or triplet carbene insertions into X-Y. The singlet insertion mechanism is concerted and has a ring TS complex. The triplet carbene will proceed via abstraction reaction, followed by radical recombination. Since the singlet insertion pathway is stereospecific, it is advantageous to produce desired chiral structures and, hence, it has attracted attention for a comprehensive mechanistic study. Schaefer and co-workers43 reported that singlet methylene insertion into H2 does not follow the least motion pathway (i.e. a pathway along which the reacting atoms move the least), which would involve the carbene attacking the H2 bonding orbital along a perpendicular trajectory. This trajectory is orbital symmetry forbidden based on the Woodward-Hoffmann principle,44 and would therefore be expected to have a large barrier height. However, experimental observations indicate that the reaction is barrier-less. A computational study resolved the discrepancy, and the mechanism follows a concerted non-least-motion pathway.45 It was suggested that the reaction proceeds through two phases (Figure 1.8).46–49 The first phase is an electrophilic attack from the empty 2p-π orbital of the carbene to the filled X-Y (e.g. H-H or C-H) bonding orbital, after which, there is a nucleophilic attack from the filled sp2-σ orbital on the carbene to X-Y antibonding orbital. Additional simulation work showed that a similar concerted but asynchronous process was found for methylene and silylene insertion 14 into different substrates.49 The TS structures found have the substrate X-Y bond undergoing insertion oriented such that both orbital interactions described above occur simultaneously.49,50 Moreover, it also indicates that the electrophilic step is key to determine the reaction barrier. This research provides insights for tuning carbene reactivity through substituent effects, which will be discussed below. Figure 1.8. Schematic orbital description of two phases in the concerted singlet insertion into X-Y bond. Firstly, the empty of 2p-π orbital of carbene attacks the filled X-Y bonding orbital. An internal, relative rotation then allows the nucleophilic attack of carbene lone pair to X-Y antibonding orbital, which completes the insertion. 1.4 Research Questions It has been shown that bis-diazirine based cross-linkers may exhibit superior versatility compared to other cross-linking approaches,1 but more work needs to be done to understand their chemistry. There are many questions that need to be answered, including the thermochemistry associated with the bis-carbene formation processes, the impacts of structural and substituent effects on bis-carbene electronic states, and how these effects control insertion reactions. 15 This thesis explores how carbenes work as a novel cross-linker for soft materials using state-of-the-art quantum mechanical methods. We provide a comprehensive mechanistic profile, explore structural influences, and investigate the contributing factors at each reaction step, from carbene formation to substrate insertion. Finally, we propose a systematic approach to design the cross-linkers with higher efficacy and broader applicability. 16 Chapter 2: Theoretical Background This chapter provides a general overview of the theory behind the computational methods used in this work. Here, we briefly present the Hartree-Fock theory and its derivatives, basis sets, and nowadays popular density functional theory approximations.51,52 An understanding of the material in this section is not required in order to appreciate the chemistry under investigation, and a reader uninterested in the theoretical background may skip this chapter. 2.1 Hartree-Fock Theory The Schrödinger equation (SE, Eq. 2.1) can only be solved exactly for simple model systems containing only one electron. Therefore, certain approximations must be introduced in order to allow us to apply the Schrödinger equation to chemically interesting systems. In Eq. 2.1, ?̂? is the Hamiltonian operator that contains all energetic information. Ψ is the wavefunction, and E is the total energy. ?̂?Ψ = 𝐸Ψ (2.1) The Born-Oppenheimer approximation is one of the cornerstones approximation used.53 Since nuclei move much slower than electrons, the SE can be separated into a nuclear part and an electronic part. 17 ?̂?𝑒𝑙Ψ𝑒𝑙 = 𝐸𝑒𝑙Ψ𝑒𝑙 (2.2) The electronic SE (Eq. 2.2) can then be solved and the nuclear-nuclear repulsion can be added into electronic energy to obtain the system energy. In Eq. 2.2, the Hamiltonian, the energy, and the wavefunction now depend on electrons. The electronic SE dramatically simplifies the solutions to the full SE and allows us to explore chemical reactions along potential energy surfaces (PES). Solving the electronic SE still requires approximate approaches. The simplest approximate method is called the Hartree-Fock (HF) approximation.54,55 In HF theory, the wavefunction is constructed as a Slater determinant.56 The mathematics of determinant operations naturally allows the constructed wavefunction to be appropriately antisymmetric and for the Pauli exclusion principle to be obeyed. ?̂?𝑖𝜑𝑖 = 𝜀𝑖𝜑𝑖 (2.3) The HF approximation uses a Fock operator ?̂?𝑖 (Eq. 2.3), which is an effective one-electron Hamiltonian. In Eq. 2.3, 𝜑𝑖 is the HF orbital and 𝜀𝑖 is the energy of the HF orbital. In this way, a multi-electronic Hamiltonian is simplified into single electron terms plus a more complex effective potential term: ?̂?𝑖 = −12𝛻𝑖2 − ∑𝑀𝐴𝑍𝐴𝑟𝑖𝐴+ 𝑉𝐻𝐹(𝑖) (2.4) 18 where the Fock operator is constructed with the electron kinetic energy term −12𝛻𝑖2 , the electron-nuclei attraction −∑𝑀𝐴𝑍𝐴𝑟𝑖𝐴 , and electron-electron interaction 𝑉𝐻𝐹(𝑖) (Eq. 2.4). The first two terms are straightforward to calculate while the last one cannot be defined exactly. The total HF energy is expressed as follows: 𝐸𝐻𝐹 = 2 ∑ 𝜀0,𝑖 + ∑ ∑(2𝐽𝑖𝑗 − ?̂?𝑖𝑗)𝑁/2𝑗=1𝑁/2𝑖=1𝑁/2𝑖=1 (2.5) where N is the number of electrons, 𝜀0,𝑖 is the energy of the ith orbital without considering electron-electron repulsion, and 𝐽 and ?̂? constitute 𝑉𝐻𝐹(𝑖) that will be discussed below. The 𝜀0,𝑖 in Eq. 2.5 is based on the electron kinetic energy term and electron-nuclei attraction from Eq. 2.4, which neglects non-separable electron-electron interactions. In the context of the HF theory, 𝑉𝐻𝐹(𝑖) is defined by two operators: the Coulomb operator 𝐽 and the exchange operator ?̂? . The Coulomb operator can be viewed as classic electrostatic interaction between electrons, while the exchange operator is purely from quantum mechanics and lacks a simple physical interpretation. ?̂? can be considered as a correction to 𝐽 due to the Pauli Exclusion Principle, in which case two electrons with a same spin cannot occupy a same orbital. Both 𝐽 and ?̂? only have approximate solutions based on the static electron densities within a chemical system. Consequently, the instantaneous electron correlation, so-called dynamic correlation, is missing from the HF theory. Although the correlation energy only represents a small percentage of total electronic energy, the inclusion of correlation is required in order to accurately predict the properties of chemical systems. 19 The HF calculation is also called the self-consistent field (SCF) calculation. At the starting point of an HF calculation, the wave function for the system is unknown. A guess wave function must be generated to begin the process. The solution of the HF equations produces a new wave function, which is then fed back into the HF equations as a better wavefunction guess. This procedure is repeated until the wavefunction in the last two consecutive cycles is identical (hence “self-consistent”). The SCF approach is underpinned by the Variational Principle, which states that a better wavefunction will always produce a lower (and therefore better) energy than an inferior wavefunction. Therefore, the convergence in the SCF procedure can be determined when the energy of the system does not change from one step to the next. In summary, the HF method is an approximate theory to solve the SE but cannot account for dynamic correlation. The HF method is the starting point for many other modern and more accurate computational methodologies. The HF method can be improved upon by the inclusion of correlation through so-called post-HF methods. These methods use HF as a starting point and improve energies and wavefunctions through the application of other quantum theories. 2.2 Basis Sets When we refer to the “level of theory” in a calculation, there are two components: method and basis set. The aforementioned HF is a method, which must be combined with the basis set in order to build the wavefunction Ψ. A nearly exact solution to the SE can be obtained 20 if we use an infinitely large basis set (or complete basis set, CBS) and if we expand the HF wavefunction by including electronic configurations arising from the excitation of all electrons into all possible orbitals. Neither of these is feasible. Fortunately, convergence towards the CBS limit occurs quite quickly, meaning that finite basis sets can be effectively employed in computational chemistry calculations. Regardless of the method employed, most calculations scale with (at least) the third power of the number of functions that comprise the basis set. Most basis sets used are comprised of Gaussian type functions (GTFs): 𝜙𝛼,𝑙,𝑚,𝑛𝐺𝑇𝐹 (𝑟) = 𝑁𝑥𝑙𝑦𝑚𝑧𝑛𝑒−𝜁(𝑟−𝑅𝐴)2 (2.6) where N is the normalization coefficient, and 𝜁 is the Gaussian exponent. The sum of l, m and n corresponds to the angular momentum of orbitals. The sum equals 1 for s-type orbitals, 2 for p-type, and so on. In Eq. 2.6, x, y, and z are Cartesian coordinates, 𝑅𝐴 is the nuclear coordinate, and 𝑟 is the radius. The quadratic component in GTF facilitates integration operations that are needed for quantum mechanical calculations. However, GTFs do not have the proper form at nuclei. This means that several GTFs are required in order to get a good representation of an orbital. An efficient approach is to use a linear combination of GTFs to construct a contracted Gaussian type function (CGTF) as follows: 𝜙𝐶𝐺𝑇𝐹(𝑟) = ∑ 𝑐𝑖𝑖𝜙𝐺𝑇𝐹(𝑟) (2.7) In Eq. 2.7, the 𝑐𝑖 is the contraction coefficient, and the number of GTFs in CGTF defines the degree of contraction. The smallest basis set is the minimal (or single-𝜁) basis set, where each atomic orbital (AO) is described by one CGTF. Minimal basis sets are not widely 21 used because they provide a poor description of molecular wavefunctions. Most calculations utilize basis sets of at least double-𝜁 quality. The Pople-style extended basis sets57 are amongst of the most popular basis sets in use. A typical Pople-style basis set is 6-31G, a double-𝜁 basis set, is described here to illustrate how these kinds of basis sets are structured. The number 6 indicates that there one CGTF, consisting of 6 GTFs, used to describe each core AO (usually the 1s orbital). The number 31 after the dash refers to the use of a 3-function CGTF and a second single GTF for each valence AO. Therefore, these basis sets are also called split valence double zeta basis sets. Pople adopted two functions for valence orbitals to provide the flexibility needed to model chemical properties (which are mostly dependent on the description of the valence electronic structure), and one highly contracted CGTFs (i.e. one contracted basis function) to ensure a good description of core electrons, which is important for total energy calculations. In chemical bonding, the AOs from each atom may polarize to form the molecular orbitals (MOs). Using basis functions that have angular momentum values one higher than the valence AOs (e.g. a d-type GTF for carbon) provides the required flexibility for polarization. A notation is 6-31G* or 6-31G(d), where * or (d) refers to the addition of a set of d functions on, for example, first-row, non-hydrogen elements. Adding an extra asterisk 6-31G**, or equivalently 6-31G(d,p), indicates an additional p-type polarization functions is added to hydrogen atoms, which is essential for describing hydrogen bonding. Anionic systems have highly diffuse orbitals. Therefore, diffuse functions are required for appropriate descriptions of anionic properties, such as electron affinity. Diffuse functions are typically small exponent GTFs added to each of the valence shells (e.g. 2s and 2p in carbon). 22 Diffuse functions added to non-hydrogen atoms are indicated with a “+”, as in 6-31+G. “++” as in 6-31++G means that diffuse functions are added to all atoms. The complete basis set (CBS) limit was discussed above. While it is not possible to reach this limit in practice, it is possible to get very close to the limit using extrapolation schemes. The Dunning family of basis sets, which are referred to as correlation consistent basis sets, are typically used for extrapolation to the complete basis set limit.58 Their nomenclature has the form cc-pVnZ where “Vn” refers to the number of CGTFs per valence orbital, “p” refers to the inclusion of polarization functions, and “cc” signifies correlation consistent. The addition of an “aug” prefix corresponds to the addition of diffuse functions on all atoms. When extrapolating to the CBS limit, for example by using aug-cc-pVTZ and aug-cc-pVQZ basis sets, the nomenclature is aug-cc-pV(T-Q)Z. The CBS extrapolation scheme used for this thesis is presented in Chapter 3. Another commonly used type of basis set in DFT is referred to as Ahlrichs def2 basis sets.59 The structure of these basis sets is similar to the Pople-style sets, and the performance of def2-SVP (split valence polarized) is similar to 6-31G**. Ahlrichs basis sets can be augmented with an additional set of polarization (e.g. def2-SVPP) or diffuse function (e.g def2-SVPD). 2.3 Coupled-Cluster Theory Recall that the HF wavefunction is produced under the approximation that electron repulsion is the result of the interactions involving average densities of electrons. The 23 consequence of this assumption is that HF wavefunctions and energies do not include the important effects of electron correlation. Post-HF methods incorporate correlation by expanding the wavefunction by incorporating excited electronic state configurations that are generated by promoting electrons into unoccupied orbitals. Ideally, the expansion would use configurations generated by promoting all electrons into all possible orbitals. However, the number of configurations N generated in this way increases factorially with the size of the chemical system (see Section 2.4 Eq. 2.12), where N will rapidly grow as n (number of electrons) and m (number of orbitals) increase. Therefore, using all configurations is impossible except for the smallest molecules and AO basis sets. Therefore, approximate correlation methods must be employed. One of the most popular post-HF methods is the coupled-cluster (CC) theory. The CC theory improves the HF wavefunction by expanding it to include excited state electronic configurations that arise through Eq. 2.8. Ψ = 𝑒?̂?Ψ𝐻𝐹 (2.8) The CC method generates wavefunctions by expanding the HF wavefunction using 𝑒?̂?𝑁 term (Eq. 2.9, 2.10). ?̂?𝑁 is the excitation operator which is related to the promotion of N electrons from occupied to virtual orbitals (Eq. 2.10). For example, ?̂?2 involves the promotion of two electrons, and 𝑒?̂?2 considers all combinations related to double excitations. 𝑒?̂?2 not only includes the fundamental double excitation (?̂?2), but also comprises products of excitation operators such as a quadruple (?̂?22!). 24 𝑒?̂? = 1 + ?̂? +?̂?22!+?̂?33! ⋅⋅⋅ (2.9) ?̂? = ?̂?1 + ?̂?2 + ?̂?3 ⋅⋅⋅ +?̂?𝑁 (2.10) As discussed above, it is not feasible to take into account all possible excited configurations, so only truncated models can be practically used. If only single (?̂?1) and double (?̂?2) excitations are considered (a truncated Taylor expansion at N=2), then the method is abbreviated as CCSD. If the additional triple excitations (?̂?3) are involved (a truncated Taylor expansion at N=3), the approach is now obtained as CCSDT. Similarly, the inclusion quadruple excitations leads to CCSDTQ. The higher the order of excitations, the more correlation energy will be included in the final energy, but the more time-consuming the calculations will be. The CCSD approach can be quite demanding in terms of computational resources, and CCSDT can only apply to small chemical systems (e.g. under 10 first- and second-row atoms). Nevertheless, the configurations arising from ?̂?3 are vital to ensure the high accuracy hence cannot be neglected. An approximation used to alleviate the high computational cost associated with the triples without strongly impacting accuracy is to employ perturbative triples instead of real iterative ones. This approach is abbreviated as CCSD(T) method, where the parentheses indicate that the triple excitations are estimated perturbatively. This method is widely implemented in most of the modern quantum chemistry packages, and CCSD(T)/CBS is referred to as the “gold standard” for systems that do not have multi-reference wavefunction character. 25 Even with perturbative triples, CCSD(T) has N7 scaling, where N is the system size. CCSD(T) is still restricted to chemical systems containing about 15 or fewer atoms. One attractive and relatively recently developed variant of CCSD(T) is the “domain-based local pair natural orbital CCSD(T) approach”, abbreviated DLPNO-CCSD(T).60 The DLPNO-CCSD(T) method is linear scaling (N scaling) with respect to the system size and gives results that are comparable to CCSD(T). 2.4 Multi-Configurational Self-Consistent Field Theory The HF described in Sections 2.1 is a single reference method (i.e. the wavefunction description is based on just one electronic configuration). In most cases, the single-reference approach is suitable. However, there are some important chemical systems for which single-reference methods fail dramatically. The difference between single-reference and multi-reference systems is illustrated by the example of O2 in the closed-shell singlet electronic state, see Figure 2.1. O2 has eight 2p electrons that doubly occupy three bonding orbitals, with the remaining two electrons occupying one of two energetically degenerate π antibonding orbitals. The singlet state electronic configuration is σ2π2π2(π*a2π*b0)σ*0. Since π*a and π*b are energetically degenerate, the configuration can also be expressed as σ2π2π2(π*a0π*b2)σ*0. 26 Figure 2.1. Molecular orbital diagram of 1O2 based on only O 2p orbitals. One σ and two π orbitals are filled first, while the remaining electron pair (red color) can either occupy the degenerated π*a or π*b orbitals. Both configurations have the same possibility, so the real wave function must be represented by a combination of two aforementioned electronic configurations with equal weights (Eq. 2.11). This illustrates that the wavefunction for 1O2 is multi-reference because more than one electronic configuration is required to describe the (unnormalized) wavefunction. Ψ 𝑂1 2 =12Ψ(⋅⋅⋅ 𝜋𝑎∗ 2𝜋𝑏∗ 0𝜎∗ 0) +12Ψ(⋅⋅⋅ 𝜋𝑎∗ 0𝜋𝑏∗ 2𝜎∗ 0) (2.11) The additional energy that arises from using a multi-reference wavefunction is called the static correlation, which is often differentiated from dynamic correlation (although they are related). One common method used to solve for the wavefunctions and energies of multi-reference systems is multi-configurational self-consistent field theory (MCSCF). The complete active space self-consistent field (CASSCF) is a practical algorithm for MCSCF. The CASSCF approach will simultaneously optimize the orbitals used to construct particular configuration 27 functions and the expansion coefficients for each of the configurations used to build the wavefunction (as shown in Eq. 2.11). CASSCF requires the specification of an active space of orbitals and electrons that will be used to generate the configurations. Figure 2.2 demonstrates the concept in two different cases. In only the active space (box in Figure 2.2) is allowed all excitations and possible occupations, while orbitals outside of the box are kept either doubly filled if they are occupied or empty if they are unoccupied. In the case of singlet O2, the simplest CASSCF approach to generate a reasonable wavefunction is to distribute the two red electrons into two π* orbitals; this is referred to as a CASSCF(2,2) calculation. A better description of the wavefunction could be obtained with a CASSCF(6,4) calculation, where references are generated by permuting all of the π electrons amongst all of the π and π* orbitals. Figure 2.2. Schematic illustrations of CASSCF(2,2) (left) and CASSCF(6,4) (right). The blue box with a dash-line defines the active space in which all possible electrons configurations are generated. Ideally, the active space in a CASSCF calculation would be as large as possible to include as much dynamic correlation as possible. However, the computational costs of 28 CASSCF calculations grow very quickly with active space size, so there are practical limitations to the size of the active space considered. The general relationship of the number of configurations N with respect to the number of electrons m and orbitals n in the complete active space is summarized by Eq. 2.12. N grows factorially as the size of active space and the number of electrons involved. Calculations beyond CASSCF(16,16) represent the practical limit of what is achievable using current computing hardware. Compared with the HF based methods, the CASSCF method is not a “black-box” method. The user must carefully select appropriate active space and orbitals before running the calculation, and poor choices will lead to misleading outcomes. 𝑁 =𝑛! (𝑛 + 1)!(𝑚2 )! (𝑚2 + 1)! (𝑛 −𝑚2 )! (𝑛 −𝑚2 + 1)! (2.12) MCSCF and CASSCF do not thoroughly account for dynamical correlation. Adding perturbation is one of the most popular techniques for incorporating dynamical correlation into CASSCF calculations, and one common method is CASPT2.61 2.5 Density Functional Theory All of the computational methods described so far are based on molecular wavefunctions. Although the wavefunctions can be systematically improved by including more electronic configurations or by using larger basis sets, the associated computational costs grow rapidly. An alternative approach is to use density functional theory (DFT), which constructs the three-dimensional electron density of a system. The main advantage of DFT is 29 that the three-dimensional electron density problem is computationally much easier to solve than the N! (or Nn) problem associated with the correlated wavefunction approach. The cornerstones of DFT are two theorems proposed by Hohenberg and Kohn in 1964.62 Briefly, the first Hohenberg-Kohn (HK) theorem states that the non-degenerate ground-state electron density 𝜌 determines the Hamiltonian, wave function, energy, and other important properties of a chemical system. The HK theorem suggests the existence of an exact energy functional 𝐸[𝜌] (Eq. 2.13), but it does not describe the form of the exact functional. 𝐸[𝜌] = 𝑇[𝜌] − ∑ ∫𝑍𝑘𝜌(𝑟)|𝑟 − 𝑅𝑘|𝑑𝑟𝑘+ ∬𝜌(𝑟1)𝜌(𝑟2)𝑟12𝑑𝑟1𝑑𝑟2 + 𝐸𝑋𝐶[𝜌] (2.13) The four terms that constitute 𝐸[𝜌] in Eq. 2.13 (in the sequence) correspond to functionals for the kinetic, classic Coulombic electron-nuclei and electron-electron interactions, and exchange-correlation functional 𝐸𝑋𝐶[𝜌] . 𝑇[𝜌] is the kinetic energy and the sum of − ∑ ∫𝑍𝑘𝜌(𝑟)|𝑟−𝑅𝑘|𝑑𝑟𝑘 + ∬𝜌(𝑟1)𝜌(𝑟2)𝑟12𝑑𝑟1𝑑𝑟2 is the classic Columbic interaction. For this sum, the first integration is for electron-nuclei interactions and the second is for electron-electron interactions. While exact expressions for the first three terms can be constructed, the form of 𝐸𝑋𝐶[𝜌] is unknown. However, many approximate forms of 𝐸𝑋𝐶[𝜌] are able to provide satisfying results. An illustration of the increasing quality of DFT-based approaches is provided in Figure 2.3: the so-called Jacob’s Ladder for DFT.63 The second Hohenberg-Kohn theorem is similar to the Variational Principle discussed in Section 2.1: a trial density can be varied until it results in the minimum energy of the chemical system. Evaluation of the electron density of a chemical system is much less 30 complicated than calculating correlated wavefunctions, because of the three-dimensional nature of 𝜌. However, the exact functional form of 𝐸[𝜌] is not known, so approximations must be used. Figure 2.3. Jacob’s ladder for DFT exchange-correlation functionals. The lowest rung is the LDA and the second highest is the double-hybrid functionals. The cost increases going up the ladder, while the accuracy ideally (but does not necessarily) follows the same trend. The simplest model for 𝐸𝑋𝐶[𝜌] is the local density approximation (LDA), which evaluates electron exchange based on a simple expression related to the electron density in a localized region of space. The LDA approach uses a correlation functional based on Monte Carlo simulations of fully interacting electron gases of different densities. LDA generally does a poor job at predicting chemical properties, and so it is rarely used today except for some solid-state systems.64 31 In order to account for the spatial change of the electron density in a chemical system, electron density gradients can be included in the expression for 𝐸𝑋𝐶[𝜌]. Such DFT-based methods are referred to as generalized-gradient approximation (GGA) methods. Following this direction, additional quantities such as the second derivative of electron density and orbital kinetic energy can be introduced into the 𝐸𝑋𝐶[𝜌] expression: these methods are called meta-GGAs. One popular meta-GAA is M06-L,65 it is widely used for inorganic catalysts and can even handle the multi-reference systems.66 In 1988, Becke took a different approach to improve DFT based methods.67 Recognizing that HF theory evaluates exchange exactly, Becke proposed a functional form for 𝐸𝑋𝐶[𝜌] in which an optimal admixture of exchange from HF and LDA is used in combination with an expression for the correlation functional based on the local electron density. This “hybrid functional” approach resulted in a method that is able to predict many chemical properties with much higher accuracy than GGA functionals. Becke’s approach was popularized as B3LYP,68,69 and the large number of annual citations of the functional reflect its versatility in computational chemistry. Several hybrid GGA functionals have since been developed and are in active use. Truhlar used a hybrid approach with a meta-GGA functional to develop the M06-2X method,70 which shows excellent performance on organic thermochemistry calculations. A well-known drawback of DFT methods, including B3LYP, is that they do not contain dispersion physics and there many of them are not able to model non-covalent interactions. However, this deficiency can be alleviated by the incorporation of empirical dispersion correction methods such as D3 or D3BJ.71–73 Also, including the empirical dispersion 32 correlation generally improve the accuracy of thermochemistry properties determined by the calculation. 2.6 Geometry and Frequency Geometry optimizations and frequency calculations are the two most common simulations performed in computational chemistry. The purpose of geometry optimizations is to locate a minimum on the potential energy surface (PES) (Eq. 2.14). The expression indicates that the partial derivative of the energy (E) of the system with respect to the atomic coordinates Ri needs to be zero (i.e. the force (Fi) acting on the atoms to be zero). When Eq. 2.14 is obeyed, the molecular structure is at a minimum point on a multidimensional energy surface, which may be a local or a global minimum. Eq. 2.14 is also obeyed at saddle points on a PES. Generally, geometry optimizations are less sensitive to the level of theory compared to energy calculations, so a very computationally expensive approach is not required for obtaining reasonably good molecular structures. 𝐹𝑖 = −𝜕𝐸(𝑅1, 𝑅2,⋅⋅⋅, 𝑅𝑁)𝜕𝑅𝑖= 0 (2.14) Frequency calculations usually accompany geometry optimizations. A minima point is confirmed when all of the vibrations associated with a molecule’s normal modes of vibration are positive. A transition state (TS) structure is characterized by the presence of only one imaginary frequency (i.e. a first-order saddle point) that connects reactants to products. Frequency calculations are associated with a second-order partial derivative of atomic 33 coordinate with respect to energy, which is called the Hessian (Eq. 2.15). Frequency calculations are also necessary for obtaining thermodynamic quantities, as discussed in the next section. 𝐻𝑖,𝑗 =𝜕2𝐸𝜕𝑅𝑖𝜕𝑅𝑗 (2.15) 2.7 Thermochemistry Frequency calculations produce partition functions Q, which can be used to calculate various thermodynamic quantities such as enthalpy (H) and entropy (S). For instance, the physical relationship between Q and S is described in Eq. 2.16, where k is the Boltzmann constant and T is temperature. We will skip the detailed mathematical expressions for calculating various thermal quantities here, and the interested reader is referred elsewhere.74,75 𝑆 = 𝑘 𝑙𝑛 𝑄 + 𝑘𝑇(𝜕 𝑙𝑛 𝑄𝜕𝑇)𝑣 (2.16) Here, we briefly describe notations for common energetic and thermal quantities. From solving the Schrödinger equation, the electronic energy Eel is provided. However, even at 0 K, molecules still vibrate, and the corresponding energy of the vibrations is called zero-point energy (ZPE). The ZPE corrected electronic energy is denoted as E0. 𝐸0 = 𝐸𝑒𝑙 + 𝑍𝑃𝐸 (2.17) 34 QM calculations by default use the harmonic oscillator approximation, from which ZPE can be calculated as follows: 𝐸0 = 𝐸𝑒𝑙 + 𝑍𝑃𝐸 = 𝐸𝑒𝑙 + ∑12ℎ𝑣𝑖𝑖 (2.18) where h is the Planck’s constant and vi is the harmonic vibrational frequency. The relationship between Eel and enthalpy H(T) is: 𝐻(𝑇) = 𝑈(𝑇) + 𝑃𝑉 = 𝐸𝑒𝑙 + ∑12ℎ𝑣𝑖𝑖+ 𝑈0→𝑇 + 𝑃𝑉 (2.19) where P is pressure, V is volume, and U(T) is the internal energy. There is an additional thermal correction called U0→T, which accounts for thermal contribution beyond 0 K. U0→T can be calculated using: 𝑈0→𝑇 = ∫ 𝐶𝑣𝑑𝑇𝑇0 (2.20) where Cv is the constant volume heat capacity, and this integration is over the temperature from 0 K to T K. Therefore, Eq. 2.19 can be rewritten as: 𝐻(𝑇) = 𝑈(𝑇) + 𝑃𝑉 = 𝐸𝑒𝑙 + ∑12ℎ𝑣𝑖𝑖+ ∫ 𝐶𝑣𝑑𝑇𝑇0+ 𝑃𝑉 (2.21) Similar to entropy (S) (Eq. 2.16), U(T) can be expressed by partition function Q, which is as follows: 𝐻(𝑇) = 𝑈(𝑇) + 𝑃𝑉 = 𝑘𝑇2 (𝜕 𝑙𝑛 𝑄𝜕𝑇)𝑣+ 𝑃𝑉 (2.22) 35 Then, the Gibbs free energy G(T) can then be calculated using: 𝐺(𝑇) = 𝐻(𝑇) − 𝑇 × 𝑆(𝑇) = 𝑘𝑇2 (𝜕 𝑙𝑛 𝑄𝜕𝑇)𝑣+ 𝑃𝑉 − 𝑇 × [𝑘 𝑙𝑛 𝑄 + 𝑘𝑇(𝜕 𝑙𝑛 𝑄𝜕𝑇)𝑣] (2.23) All the QM thermochemistry calculations are based on the ideal gas-phase model that is defined by the ideal gas law as follows: 𝑃𝑉 = 𝑛𝑅𝑇 (2.24) where P is pressure, V is volume, n is the moles of gas, and R is the ideal gas constant. 36 Chapter 3: Methodology This chapter gives a short description of the computational methods used in this thesis. It aims to provide readers the necessary information to reproduce the computational results presented in Chapters 4-6. Three DFT methods, some with empirical dispersion corrections, were used in this thesis: M06-2X71-D3,72 M06-L65, and B3LYP68,69-D3BJ71,73 with 6-31G** or def2-TZVP basis sets. CCSD(T)76 were performed with cc-pVTZ or aug-cc-pV(T-Q)Z CBS. These calculations were performed with Gaussian16 package.77 CASPT261 with 6-31G**, and DLPNO-CCSD(T)60-TightPNO with cc-pV(D-T)Z CBS or cc-pV(T-Q)Z CBS were performed using the ORCA 4.2 package.78 All minimum energy structures were confirmed by the absence of imaginary frequency, and TS structures were characterized by the presence of only one imaginary frequency. For nomenclature, M06-2X-D3 using 6-31G** basis set can be written as M06-2X-D3/6-31G**. For multi-reference calculations, the M06-L/6-31G** was used to obtain the geometry and frequency, and CASPT2/6-31G** was used to obtain the final electronic energy. This combined approach can be abbreviated as CASPT2/6-31G**//M06-L/6-31G**. The CBS extrapolation used a two-points scheme with cc-pVnZ (n is the cardinal number) basis sets suggested by ORCA manual.79,80 It extrapolates HF (EHF) and correlation (Ecorr) parts separately, using the following formulas: 𝐸𝐻𝐹(𝑋)= 𝐸𝐻𝐹𝐶𝐵𝑆 + 𝐴𝑒−𝛼√𝑋 (3.1) 37 𝐸𝑐𝑜𝑟𝑟𝐶𝐵𝑆 =𝑋𝛽𝐸𝑐𝑜𝑟𝑟(𝑋)− 𝑌𝛽𝐸𝑐𝑜𝑟𝑟(𝑌)𝑋𝛽 − 𝑌𝛽 (3.2) where X and Y are cardinal numbers (e.g. X=2 for double-zeta basis sets, 3 for triple-zeta, etc.), α is 4.42 and β is 2.46 when extrapolating cc-pVDZ with cc-pVTZ basis sets (abbreviated as cc-pV(D-T)Z). These values for α and β are 5.46 and 3.05, respectively when using cc-pV(T-Q)Z extrapolation. 38 Chapter 4: Mechanistic Profile 4.1 Methylene Insertion into Methane Methylene insertion into methane is a prototypical system for studying carbene insertion barrier heights. The small system size allows us to perform “gold standard” CCSD(T)/CBS calculations, and the results can be used to benchmark the DFT methods used in this work. To our best knowledge, all previous studies on the methylene/methane insertion reaction do not consider the thermal contributions to reaction barrier heights. In this section, the ability of the M06-2X method with 6-31G** basis sets to predict the singlet-triplet splittings and the barriers associated with methylene and its insertion into methane is also explored, along with thermal effects on these properties. The reason for choosing the M06-2X functional is its accuracy for organic thermochemistry calculations. These data are summarized in Table 4.1. 39 Table 4.1. Summary of the calculated singlet-triplet (S-T) gaps of methylene and its insertion barrier heights to methane by M06-2X-D3 and CCSD(T)/CBS. Energetic terms including Eel, E0, H, S, and G are reported. All geometries and thermal corrections were obtained from M06-2X-D3/6-31G** in gas phase. The temperatures used are 50K, 298K, and 400K, and the pressure is 1 atm. The units are kJ/mol. Reaction Barrier S-T Gapa Singlet Insertion Triplet Abstraction M06-2X-D3/6-31G** ∆Eel 65.6 -12.9 51.1 CCSD(T)/aug-cc-pV(T-Q)Z CBS ∆Eel 38.8 -8.8 52.3 M06-2X-D3/6-31G** ∆E0 63.4 -0.2 43.6 M06-2X-D3/6-31G** ∆G 50K 63.4 3.3 46.3 M06-2X-D3/6-31G** ∆G 298K 63.5 35.5 71.6 M06-2X-D3/6-31G** ∆H 298K 63.3 -6.1 39.7 M06-2X-D3/6-31G** -T∆S 298K 0.1 41.6 31.9 M06-2X-D3/6-31G** ∆G 298K (pre-complex)b N/A 9.9 56.8 M06-2X-D3/6-31G** ∆G 400K 63.5 49.8 82.4 a The positive gap indicates the triplet state is more stable than the singlet state. b The barrier is relative to the pre-reaction complex. The calculated singlet-triplet (S-T) gaps by electronic energy, enthalpy, and free energy shown in Table 4.1 are all within 2.3 kJ/mol of each other, which is negligible compared to the ~60 kJ/mol calculated S-T splitting. This indicates that the S-T splitting is dominated by electronic energy in the methylene system. The calculated free energies of the singlet-triplet gaps at 50K, 298K, and 400K are the same to within 0.1 kJ/mol, indicating that temperature has no significant effect on the relative stability of methylene electronic states. These results imply that in the carbene reactions we study in this thesis, S-T gaps will likewise be insensitive to experimental thermal conditions. On the other hand, singlet insertion and triplet abstraction barriers exhibit a strong temperature dependence. For singlet insertion, the reaction is barrier-less at low temperature (50K), but has a 35.5 kJ/mol free energy barrier at 298K, and increases to 49.8 kJ/mol at 400K. For the triplet abstraction, the barrier height follows a similar trend to that of the singlet barrier 40 with respect to temperature change, but the corresponding changes are relatively smaller. Also, the singlet methylene insertion into methane is nearly barrier-less at a very low temperature, but the triplet abstraction has a calculated barrier of 43.6 kJ/mol at 0 K. By decomposing free energy into enthalpic and entropic contributions, it can be concluded that the major contribution to the barrier change is from entropy. Therefore, carbene insertion, whether by direct singlet insertion or triplet abstraction/radical recombination, may be highly sensitive to experimental thermal conditions. Experimental conditions will therefore affect the cross-linking efficacy of carbenes. It must be pointed out that in the experimental system, reactants and the cross-linkers will have limited mobility, since the carbene precursors are adsorbed to the targeted polymeric substrate before activation.1 Therefore, the entropic costs associated with the insertion reaction will be mitigated. In Table 4.1, the results of the calculations of free energy barrier heights relative to the pre-reaction complex (i.e. 9.9 kJ/mol for the singlet insertion and 56.8 kJ/mol for the triplet abstraction) show how the entropic costs of the reaction are reduced when mobility is eliminated. In the methylene/methane example, M06-2X-D3/6-31G** reproduces the energy barriers for both singlet and triplet reactions to within 4.1 kJ/mol of the “gold standard”. We expect M06-2X to perform reasonably well for the reaction barriers we calculated in larger cross-linker systems we study in this thesis, as this functional has demonstrated good performance for thermochemistry and reaction barriers in a wide range of organic reactions. However, M06-2X-D3/6-31G** predicts the methylene S-T splitting to be 26.8 kJ/mol too high. Hybrid functionals (e.g. B3LYP or M06-2X) in general have been shown to overestimate the relative stability of triplet states.81 Such errors will not affect the prediction when a carbene 41 has a triplet ground state. However, DFT calculations may provide misleading conclusions when the singlet state is slightly more stable than the triplet. For the systems studied in this thesis, a ~25 kJ/mol error is suggested at the M06-2X/6-31G** level on calculating S-T splittings. Therefore, caution needs to be taken for such a circumstance, and a high-level wavefunction calculation is required for confirmation (see Chapter 6). To summarize, we showed that S-T splitting is less sensitive to temperature effects compared with the singlet or triplet free energy barriers associated with the methylene/methane reaction. M06-2X-D3/6-31G** predicts calculated barrier heights in good agreement with the high-level wavefunction method, but the same is not true for the S-T splitting. For the methylene/methane insertion reaction, the singlet barrier is lower than the triplet abstraction-recombination barrier, but it will be shown that this is not the case for insertions of all carbenes. 4.2 Cross-Linking Reaction Energy Profile In this section, we will explore the mechanism for carbene formation and cross-linking by computing the energetics associated with each step of the process using M06-2X/6-31G**. A simplified model of methane is used as the substrate subjected to insertion by the carbene (1 in Scheme 4.1, and it was also shown in Figure 1.2 (c)). 42 Scheme 4.1. Free energy profile (298K, 1 atm) of the bis-diazirine to carbene formation. All geometries and thermal corrections were obtained from M06-2X-D3/6-31G** except for purple italic values, which were from CASPT2(12,12)/6-31G**//M06L/6-31G**. The red and purple values are reaction barriers, and green values are the S-T gap, where S is singlet and T is triplet. The units are kJ/mol. Scheme 4.1 shows the formation of carbenes from a bis-diazirine cross-linker precursor. Step 1→2A is the concerted formation of a single carbene center, which has a calculated free energy barrier of 153.5 kJ/mol. The pathway 1→2B→2A is a two-step process to carbene formation that goes through a diazo intermediate. The TS associated with 1→2B possesses significant multi-reference character,33 which cannot be described by M06-2X. Therefore, we used CASPT2(12,12) to determine the energy of the TS structure, for which the geometry and thermal corrections were obtained from M06L/6-31G**. The active space consists of 4 C-N sigma bonding MOs, 2 N-N pi bonding MOs and their corresponding antibonding orbitals. This selection reasonably represents the bonding changes that occur during diazo formation. The calculated barriers by CASPT2 suggest that diazo formation requires 6.2 kJ/mol more free energy than the concerted carbene formation process. This finding aligns well with the fact that only a negligible amount of the diazo species is detected in the experiments.1 43 Step 2B→2A shows the formation of carbene from the diazo intermediate and has a calculated free energy barrier as 138.5 kJ/mol. This calculated barrier is lower than the concerted carbene formation step (153.5 kJ/mol). Therefore, if experimental conditions are such that diazo intermediates form, these will likely convert to the carbene. The calculated S-T splitting of 2A is 40.1 kJ/mol, suggesting the carbene has a triplet ground state. Consequently, the carbene will be firstly formed in the closed-shell singlet state, and then relax to the triplet state through the inter-system crossing. The formation of the bis-carbene center is shown as 2A→3B. The calculated barrier (when 2A is in the triplet state after the ISC) is only 2.1 kJ/mol higher than (or 0.8 kJ/mol when 2A is a singlet carbene) that of the formation of the monocarbene. This indicates that the presence of a carbene center does not significantly alter the barrier associated with 2A→3B. This finding is expected because the two carbene units are meta to each other on the ring and therefore have limited electronic communication between each other. We may conclude that carbene centers that are not electronically coupled behave as independent carbenes. This finding justifies the use of a single carbene model to study insertion reactions (see Chapter 6). In summary, Scheme 4.1 shows that the concerted formation of the carbene is the lowest free energy pathway, and carbene formation most likely occurs in a stepwise fashion. Under thermal conditions, it is not likely that two carbene centers will be formed simultaneously. 44 Scheme 4.2. Free energy profile for singlet carbene insertion and triplet carbene abstraction pathways. All geometries and thermal corrections were obtained from M06-2X-D3/6-31G**. The green value is the S-T gap, and red values are free energy barriers associated with each step. The units are kJ/mol. Scheme 4.2 shows that carbene 2A can react with methane through two distinct pathways. Step 2A→3A via 2AS-3A-TS is the concerted singlet insertion, which has a calculated free energy barrier of 82.9 kJ/mol. The triplet pathway 2A→3A through 2AT-3A-TS has a calculated free energy barrier to abstraction that is 11.7 kJ/mol lower than that associated with the singlet insertion. We assume that the radical recombination step via 2AT-3A-INT is barrier-less. Therefore, the abstraction-recombination pathway is preferred and is ca. 70 kJ/mol, which is less than half the barrier associated with carbene formation. The large difference in the barriers suggests that carbene will readily undergo the abstraction reaction upon formation, so it is unlikely that 1 will form a bis-carbene prior to reaction with the substrate. Step 3A→4 is the second carbene formation step and has a calculated free energy barrier of 153.4 kJ/mol. This barrier is nearly identical to the first concerted carbene formation barrier (Scheme 4.1). Again, the effect of meta-substituents on the barrier is minor and confirms that bis-carbenes of the type investigated here have carbene centers that behave independently of each other. 45 4.3 Different Ring Structure and Tether Unit In this section, we investigate how the use of pyridine, rather than benzene in 2A will affect the concentration of detected diazo intermediates, and explain why this change does not alter the cross-linking efficacy (as observed in the experiments). We also explore how the changes in the ring structure influence the calculated reaction barriers. Figure 4.1. The carbon center A on the ring can be replaced by a nitrogen atom. Under thermal activation, the nitrogen substituted ring produces more diazo intermediates than the carbon ring as observed by experiments.1 We investigated the effects of a nitrogen substitution into the aromatic ring on the behavior of the carbene (see Figure 4.1). It has been observed experimentally that the pyridine-based carbene precursor produces more diazo intermediates compared with substituted benzene carbene precursor upon thermal activation.1 However, both rings show similar cross-linking efficacy, which indicates a similar barrier height for insertion. 46 Table 4.2. Summary of the calculated free energy (298K, 1 atm) carbene S-T gaps and reaction barriers for concerted carbene formation, diazo formation from a diazirine, carbene formation from a diazo intermediate, singlet insertion to methane, and triplet carbene hydrogen abstraction from methane in kJ/mol. All geometries and thermal corrections were obtained from M06-2X-D3/6-31G** except for the bold italic values were from CASPT2(12,12)/6-31G**//M06L/6-31G**. Reaction Barrier Carbene Formationa S-T gap Diazo Formation Diazo to Carbeneb Singlet Insertion Triplet Abstraction A=C 153.5 (140.6) 40.1 146.8 138.5 82.9 70.2 A=N 154.9 (146.1) 40.3 149.9 139.3 81.5 69.1 a This is the concerted carbene formation barrier from the diazirine precursor. b This is the carbene formation barrier from the diazo intermediate (see Scheme 4.1). According to Table 4.2, both rings prefer the concerted carbene formation rather than diazo formation. For A=C (benzene ring), the calculated free energy barrier for diazo formation is 6.2 kJ/mol higher than the concerted carbene formation step. However, for A=N (pyridine ring), the calculated diazo formation barrier is only 3.8 kJ/mol higher than the carbene formation barrier. For the relative difference between the calculated diazo and concerted carbene formation barriers, the A=C is 2.4 kJ/mol higher than the A=N case. This suggests that more diazo intermediates will be formed for A=N than A=C, which agrees with experiments.1 Since the calculated barriers of carbene formation from a diazo is about 25 kJ/mol lower than from a diazirine percussor in both cases, all diazo intermediates will readily convert to carbenes. The rest of the tabulated barriers and the S-T gap are nearly identical for both species, and this suggests that both rings will perform similarly as cross-linkers. The results suggest that the introduction of heteroatoms into carbene precursor 1 will not improve cross-linker performance. 47 Figure 4.2. Illustration of the first generation (Gen 1) and the second generation (Gen 2) cross-linkers. The joint that connects two rings is defined as a tether unit. Gen 2b has a double-length tether unit than Gen 2a. One weakness of a single-ring bis-diazirine cross-linker is its low molecular weight, which will result in higher volatility (which may also be associated with potential explosiveness) than heavier species. This will be problematic for the thermal activation of the carbene, which will lead to cross-linker loss. Such a deficiency can be addressed by introducing another phenyl ring into cross-linkers to increase the molecular weight (Figure 4.2). The first generation cross-linker (Gen 1) used one carbon center with two trifluoromethyl groups as a tether unit, and the second generation cross-linkers (Gen 2a & Gen 2b) use longer chain, fluorinated tethers. The longer tether units not only makes the cross-linker more flexible, but also enhances the adhesion strength and mechanical strength of the materials as cross-linkers by increasing the strength of 48 the C-C bonds.82,83 The reason is that deformation allowed by longer tether units can absorb more force, so it results in “tough bonds”. We explored the relevant energetics associated with the Gen 1, Gen 2a, and Gen 2b cross-linkers, and the results are presented in Table 4.3. Table 4.3. Summary of the calculated free energy (298K, 1 atm) S-T gaps and reaction barriers of singlet insertion to and triplet carbene hydrogen abstraction from methane (CH4) or the central CH2 of propane (C3H8) in kJ/mol. All geometries and thermal corrections were obtained from M06-2X-D3/6-31G**. Reaction Barrier S-T gap Singlet Insertion Triplet Abstraction Gen 1 (CH4) 40.6 83.4 69.5 Gen 1 (C3H8) 40.6 58.9 45.1 Gen 2a (C3H8) 41.1 55.5 41.9 Gen 2b (C3H8) 41.7 56.8 42.2 Using the carbon chains as the tether unit changes the S-T gap negligibly compared with 2A, indicating that the para (-CF2-)x substituents do not impact the S-T gap despite the fact that the substituent is a strong inductive electron-withdrawing group. Additionally, the insertion (or abstraction) of Gen 1 into methane also shows very similar calculated barriers to 2A, and this suggests that the electronic nature of the carbene does not significantly alter by introducing the longer tether unit. According to the calculations, Gen 1 insertion into (or abstraction of hydrogen from) methane requires about 24 kJ/mol more free energy than reactions with the secondary carbon in propane (which is a better mimic of polyethylene). The cause of this difference is that the C-H bond is stronger in methane than central -CH2- of propane, so we will expect cross-linkers are more likely to attack the secondary carbon than the primary carbon center. For the insertion into propane, both Gen 1 and Gen 2 cross-linkers show similar free energy barriers for singlet insertion and triplet abstraction with the largest difference in barriers being only 3.4 kJ/mol. It is therefore expected that both species will display similar cross-49 linking efficacy. Both species are predicted to have triplet ground states, and the triplet abstraction routes have lower calculated barriers than singlet insertion. In conclusion, the tether units on the carbene precursors of the form shown in Fig. 4.2 do not modify the calculated free energy barrier height and carbene splitting significantly, and each diazirine center behaves independently. Therefore, the use of fluorinated hydrocarbon chains to increase the molecular weight for enhanced thermal stability and/or enhance mechanical strength is a good design strategy.83 50 Chapter 5: Bis-Carbenes 5.1 Substituent Effect on Single Carbene Singlet-Triplet Gap This section gives a short but representative study on the electronic states of selected single carbenes. This study offers guidance for the design of carbene cross-linkers with a desired ground electronic state and provides insights for the bis-carbene study in Section 5.2. A total of eight single carbenes were selected (Figure 5.1), starting with the prototypical methylene (1) to the halogen or phenyl substituted carbenes (2)-(7). Chlorine and fluorine are chosen as halogens for this study because of their prominence in the literature. Since the proposed novel cross-linkers all have an aromatic ring framework, it is necessary to explore how the phenyl group influences the singlet-triplet splittings. The last carbene (8) is a simplified model for the cross-linker 2A. The calculated S-T splittings, obtained using various methods, are presented in Table 5.1. Figure 5.1. Selected singlet carbene systems for S-T splitting studies. (8) is the simplified system for the cross-linker 2A. 51 Table 5.1. Calculated electronic energy S-T splitting with available experimental data. All geometries and free energy contributions (298K, 1atm) were from M06-2X-D3/def2-TZVP, except for B3LYP data that were optimized separately at B3LYP-D3BJ/def2-TZVP. The energetic calculations of CASSCF used cc-pVTZ basis set, and DLPNO-CCSD(T) used cc-pV(D-T)Z CBS. The units are kJ/mol. # carbene experimental values B3LYP-D3BJ M06-2X-D3 CASSCF(2,2) DLPNO-CCSD(T) thermal contribution (∆G) (1) 37.784 49.0 56.9 34.7 38.9 0.4 (2) -18.029 -14.6 -11.7 -14.2 -26.4 2.1 (3) -62.329 -49.4 -48.1 -46.9 -63.6 2.1 (4) -87.085 -72.0 -71.5 -54.4 -84.5 1.7 (5) -225.930 -219.7 -220.5 -205.0 -241.8 2.9 (6) - -21.3 -19.2 -32.6 -32.6 2.5 (7) - -59.0 -58.2 -72.8 -73.2 3.8 (8) - 17.6 25.1 22.6 5.4 5.4 Table 5.1 shows that substituting a halogen on the methylene will significantly stabilize the singlet state relative to the triplet. The singlet state is 37.7 kJ/mol higher than the triplet state in the methylene system (1) by experiments. Replacing a hydrogen atom with a chlorine atom (2) changes the ground state to a singlet with an S-T splitting of -18.0 kJ/mol. The influence of fluorine substitution is more substantial than chlorine, and (3) has an experimental S-T gap of -62.3 kJ/mol. This 44.3 kJ/mol difference of the experimental S-T gap between (2) and (3) may be attributed to the fact that the smaller size of fluorine allows for better orbital overlap of the F 2p orbital with the empty 2p-π orbital of the carbene (see Section 1.3.2), making the fluorine atoms better electron donors than chlorine. Replacing all hydrogen atoms of methylene (1) with halogens further increases the S-T splitting by further stabilizing the singlet ground state of carbenes. For instance, CCl2 (4) has an experimental S-T gap of -87.0 kJ/mol and CF2 (5) has a gap of -225.9 kJ/mol, and both are larger than their mono-halogen substituted counterparts ((2) and (3)). The gap of CF2 is more than twice the gap of CHF ((3), -62.3 kJ/mol). A similar trend is also observed among chorine carbenes ((2) and (4)). This suggests that the influence of halogen substitutions is not simply 52 additive in selected carbene systems, but also has an additional synergetic effect-perhaps involving the inductive withdrawing effects of the halogen atoms. To our best knowledge, phenyl carbenes (6), (7), and (8) have no experimentally reported S-T splittings. As mentioned in Chapter 1, the splittings of carbenes are difficult to obtain through experimental measurements, and computational methods can be used to provide some useful insights. In Table 5.1, comparisons of the calculated electronic energy S-T splittings with the available experimental data show that all of the computational methods are able to provide qualitatively correct gaps, but DLPNO-CCSD(T)/CBS shows the best overall agreement with the limited experimental values. The calculated electronic S-T gaps between B3LYP and M06-2X are within 8 kJ/mol, but both tend to overestimate the stability of the triplet state relative to the singlet state as discussed in Section 4.1. The CASSCF(2,2) calculations comprise the sp2-σ and 2p-π orbitals of carbenes, and provides a better estimation of the splitting of methylene (1) than B3LYP and M06-2X. However, it has comparatively large errors when predicting gaps for halogen and phenyl carbenes. The errors are likely due to the small active space used, which fails to include the contribution of lone pairs donation from halogens. Since the DLPNO-CCSD(T) results are more accurate compared with other computational methods used, we use the results from DLPNO-CCSD(T) to understand the influence of phenyl group on S-T splittings, and to give us some sense for the errors associated with the DFT methods which are used in subsequent barrier height calculations. CPhCl (6) has a calculated electronic energy splitting of -32.6 kJ/mol, which is 6.2 kJ/mol lower than the gap of CHCl (2). Similarly, CPhF (7) has a calculated gap that is 9.6 kJ/mol lower than CHF (5). 53 These suggest that the phenyl group with halogen can slightly increase the relative stability of the singlet state. A possible reason is that the Ph group further increases the splitting by stabilizing the partially occupied 2p-π orbital in which the halides have donated some electron density. Since F donates more electrons than Cl, the Ph stabilizes Ph-C-F more than Ph-C-Cl by about 3.4 kJ/mol. On the other hand, our simplified cross-linker (8) has a calculated electronic gap of 5.4 kJ/mol, indicating that it has a triplet ground state. This shows that the phenyl group cannot reverse the ground state significantly to a singlet state as does chlorine or fluorine. Moreover, the CF3 group can only act via induction and therefore cannot stabilize the singlet state as much as in the case of F or Cl (i.e. no direct π-type bonding). The right-most column in Table 5.1 is the calculated free energy contributions to the splitting (298K, 1atm), and all these thermal contributions are positive. This suggests thermal effects, which need to be considered for cross-linkers activated thermally, slightly favors triplet ground states over singlets. However, its overall influence is minor, and most thermal corrections are within 4 kJ/mol except for (8), for which it is 5.4 kJ/mol. Therefore, thermal contributions generally are not expected to flip the ground state, except in circumstances where singlet states are essentially energetically degenerate with their triplet states. In summary, the results from the S-T studies demonstrate how halogen substituents can be used to stabilize singlet states of carbenes and show phenyl groups can promote the stabilization of singlet states further in halogen carbenes (but the phenyl group itself cannot change the ground state from a triplet to a singlet). Additionally, DLPNO-CCSD(T) can provide good predictions to S-T splittings of carbenes, and the calculated free energy contributions slightly favor (e.g. less than 5.4 kJ/mol in these single carbenes) triplet states 54 over singlets. This information will be important for the design of carbenes having particular insertion mechanisms – see Section 6.3. 5.2 para and meta Bis-Carbene Ground States This section will discuss the influence of aromatic ring delocalization on the ground electronic states of bis-carbenes. We have demonstrated in Section 4.2 that the bis-diazirine cross-linker follows a stepwise carbene formation pathway under thermal activation, so the formation of a bis-carbene intermediate under thermal activation conditions is not likely. However, this is not the case under photoactivation, under which it is possible to form the two carbene centers simultaneously. Two carbene centers on a bis-diazirine precursor can be arranged around the benzene ring in ortho (o), meta (m), or para (p) relative positions. When the bis-carbene has an ortho arrangement (i.e. o-phenylenebis(carbene)), the two carbene centers tend to couple together to form a cyclobutane ring, which deactivates the species as a cross-linker. Therefore, only meta and para phenylenebis(carbene) systems are studied (Figure 5.2). For m-phenylenebis(carbene), each carbene center has little electronic communication, as the aromatic ring delocalization is minor. Consequently, we expect that a bis-carbene arrangement of this type will adopt an electronic structure that is analogous to that of a single carbene (see Section 4.2). The two carbene centers in the p-phenylenebis(carbene) have more electronic interaction than the meta counterpart, and there is the possibility of significant electronic rearrangement through delocalization. 55 Each carbene center may adopt either a singlet or triplet ground state, as illustrated in Figure 5.2. Therefore, the bis-carbene can have a closed-shell singlet (cs, two carbene centers both adopt singlet states) or an open-shell quintet (oq, two carbene centers both adopt triplet states) ground state. Alternatively, the diradical electronic structure, in which there is one unpaired electron localized on each center, with the electrons that adopt the same or opposite spin states will result in an open-shell triplet (ot, for the same spin) or an open-shell singlet (os, for the opposite spin). A zwitterionic electronic arrangement is possible, in principle, however this is unlikely in the systems under investigation owing to the symmetry in the cross-linker (i.e. both R groups are the same). Figure 5.2. Illustration of possible resonance forms in meta- or para-phenylenebis(carbene) compounds. Three R substituents are considered (R=F (9), Cl (10), or CF3 (11)) in this study (Table 5.2). The p-phenylenebis(carbene) with two halogens ((9) or (10)) have been reported experimentally86,87 and studied computationally.88–91 We firstly compared our results with previous computational results to verify our approach, which used dispersion corrections and the M06-2X functional. Then, we applied our approach to study the electronic state of the proposed cross-linker (11). In order to facilitate the discussion, the closed-shell singlet state (cs) is set as the zero point for calculating the relative energies. 56 Table 5.2. Summary of calculated electronic energies of various electronic states relative to the closed-shell singlet state (define as zero) in selected p-phenylenebis(carbene)s. All geometries were from M06-2X-D3/def2-TZVP, except for B3LYP data were optimized separately at B3LYP-D3BJ/def2-TZVP. CCSD(T) calculations used cc-pVTZ basis set. The units are in kJ/mol. B3LYP-D3(BJ) M06-2X-D3 CCSD(T) cs oq ot os cs oq ot os cs oq ot R=Cl (9) 0.0 58.2 -43.5 -48.5 0.0 47.3 -46.0 -53.1 0.0 71.5 -34.3 R=F (10) 0.0 136.0 26.4 20.9 0.0 130.5 29.3 21.8 0.0 156.5 41.0 R=CF3 (11) 0.0 -22.2 -128.4 -133.1 0.0 -56.9 -143.9 -152.7 0.0 -25.1 -134.3 It has been reported that p-phenylenebis(chloromethylene) (9) adopts an open-shell singlet (os) diradical structre,86,88–91 while p-phenylenebis(fluoromethylene) (10) is a closed-shell singlet (cs) bis-carbene.87 In Table 5.2, B3LYP and M06-2X calculations provide the same conclusion as these previous works. The CCSD(T) results also indicate that (9) is a diradical while (10) is a cs bis-carbene. For the p-phenylenebis(trifluoromethylmethylene) (11), our computational results indicate that it behaves similarly to p-phenylenebis(chloromethylene) (9), which adopts an open-shell singlet (os) ground state. Therefore, (11) is likely to cross-link through the abstraction/recombination pathway upon photoactivation. Recall from Table 5.1 for the simple single carbenes related to these bis-carbenes, both CPhCl (6) and CPhF (7) have a singlet ground state, but CPhCF3 (8) has a triplet ground state. The calculated electronic energy S-T splittings by M06-2X are -19.2 kJ/mol (6), -58.2 kJ/mol (7), and 25.1 kJ/mol (8), respectively. Although CPhCl (6) and CPhF (7) both have a singlet ground state, the calculated electronic energy S-T gap of CPhCl is 39.0 kJ/mol smaller than CPhF. Since the singlet state is strongly stabilized in CPhF (7), it is reasonable that p-phenylenebis(fluoromethylene) (10) keeps each end as cs as in its single carbene counterpart, and the resonance stabilization mediated by the aromatic ring is not stabilizing enough to change this. Conversely, CPhCl (6) has a much smaller calculated electronic S-T gap than CPhF (7), hence the aromatic ring 57 delocalization in (9) results in relatively more stabilization of the diradical electronic structure. This ring stabilization is about 44 kJ/mol as determined by M06-2X according to the electronic energy difference between cs and ot, and about 34 kJ/mol by CCSD(T). This suggests that any single carbene with a singlet ground state that is equal to or less than ~22kJ/mol (half of 44 kJ/mol discussed above and based on M06-2X) lower than the triplet state, its corresponding p-phenylenebis(carbene) species will adopt a diradical electronic structure due to the overall stability from the aromatic ring delocalization. On the other hand, the calculations suggest that when a carbene has a triplet ground state (e.g. CPhCF3 (8)), its bis-carbene counterpart (e.g. p-phenylenebis(trifluoromethylmethylene) (11)) will adopt a diradical electronic structure. For the diradical electronic structure in (9)-(11) shown in Table 5.2, both B3LYP and M06-2X show that os is more stable than ot by about 4-9 kJ/mol. An explanation for this finding is that the electrons in os have a spin arrangement that allows for delocalization into the ring. In Figure 5.2, it can be seen that the diradical will have electrons on each end having the opposite spin. Therefore, electrons in ot require a spin-flip of one electron to achieve the same degree of delocalization, and this is less favored than os state. Table 5.3. Summary of calculated electronic energies of various electronic states relative to the closed-shell singlet state (define as zero) in selected m-phenylenebis(carbene)s. All geometries were from M06-2X-D3/def2-TZVP, except for B3LYP data was optimized separately at B3LYP-D3BJ/def2-TZVP. CCSD(T) calculations used cc-pVTZ basis set. The units are in kJ/mol. B3LYP-D3BJ M06-2X-D3 CCSD(T) cs oq ot os# cs oq ot os# cs oq ot R=Cl (12) 0.0 23.8 13.8 a 0.0 22.2 13.4 a 0.0 51.0 32.2 R=F (13) 0.0 98.3 128.0 a 0.0 99.6 197.1 a 0.0 129.3 141.8 R=CF3 (14) 0.0 -60.2 28.5 -33.9 0.0 -72.0 55.6 -51.9 0.0 -43.5 56.5 # This os is a special form of oq in which electrons on the two carbene centers have opposite spins. a It has a cs ground state,90,92 so os# is not calculated. 58 The m-phenylenebis(carbene) systems, as listed in Table 5.3, are not likely to form a diradical structure, so each center tends to maintain its independent carbene character. This was confirmed by our calculations on m-phenylenebis(carbene) (12)-(14) using the DFT and CCSD(T) methods. All three computational methods indicate that the ot states of the m-phenylenebis(carbene)s have one carbene center in a closed singlet state and the other in a triplet state. The oq state is when the two carbene centers are both in triplet states. We also explore how the same or opposite spins between two triplet carbene centers may play a role in the m-phenylenebis(carbene)s. The “#” is used to indicate that the open-shell singlet in the meta species is different from those described in the para case. In the former, the singlet is formed when two unpaired electrons on each center are parallel, while in os# one center has two spin-up electrons, and the other center has two spin-down electrons. In Table 5.3, all B3LYP, M06-2X, and CCSD(T) results confirm that m-phenylenebis(chloromethylene) (12) and m-phenylenebis(fluoromethylene) (13) have a cs ground state. This suggests that both carbene centers have weak electronic connections by meta-arrangement and the aromatic ring delocalization is minor, so each center retains the ground state of the corresponding single carbene model (i.e. (2) vs. (12) and (3) vs. (13)). By this logic, m-phenylenebis(trifluoromethylmethylene) (14) should have an oq ground state since CPhCF3 (8) is in a triplet state. The oq state of (14) is 43.5 kJ/mol more stable than the cs state and 100 kJ/mol more stable than the ot state by CCSD(T) calculations, and is ~20-25 kJ/mol more stable than os#. 59 In conclusion, phenylenebis(carbene) with meta or para arrangement has more diversity in electronic states than single carbenes because of a combination of two single carbene centers. p-phenylenebis(carbene)s are highly affected by the aromatic ring delocalization, which may result in a diradical structure. However, this is not the case for m-phenylenebis(carbene)s, in which case the delocalization is minor. Overall, both B3LYP and M06-2X provide qualitatively the same results on these relative electronic energetic gaps and are aligned with CCSD(T) data in these bis-carbene systems. It should be reiterated that the bis-carbene intermediate may only be expected to present under photoactivation, and it is not likely to present under thermal activation as discussed in Section 4.2. Despite the fact that we expect no formation of bis-carbene under thermal conditions, this study is still of interest because it suggests that the para arrangement of carbenes will result in very different ground-state species under photoactivation and therefore provides a control mechanism for cross-linker development and application. The influence of para-substitution will be explored in more detail in Chapter 6. The meta arrangement is recommended when there is a preference for the cross-linker to have the same ground state on each center as their corresponding single carbenes. The bis-carbene ground state studies provide insights into how to use para-substitutions to alter the carbene ground state through aromatic ring resonances, and demonstrate extra complexities from the photoactivation compared with the thermal activation. 60 Chapter 6: Exploring Cross-Linking Efficacy of Cross-Linkers This chapter explores the Hammett relationships in the carbene formation and insertion steps, which can provide insights into the design of next-generation cross-linkers. The Hammett relationship is an empirical one that connects molecular structures to free energies. The relationship is mostly used to understand the chemical behavior of substituted benzene systems,93 such as cross-linker 2A, and to allow for easy predictions of molecular behavior. In this section, the simple aryl diazirines (or carbenes) are used since we have shown in Section 4.2 that the bis-diazirine adopts a stepwise pathway to form the carbene center upon thermal activation. 6.1 Carbene Formation Barrier Wulff and co-workers found that there exists a linear relationship between the onset temperature (Tonset) and σp+ constants for the carbene formation step of selected single diazirine systems (right corner in Figure 6.1) in experiments.94 The Tonset is the minimum temperature to activate diazirine precursor to form the corresponding carbene. In order to further confirm whether Tonset can be viewed as a reflection of the reaction barrier of the carbene formation, the free energy barriers of the carbene formation are calculated using DFT. The results are presented in Figure 6.1. 61 Figure 6.1. The plot of experimental Tonset versus the calculated reaction free energy barrier (298K, 1atm) using M06-2X-D3/6-31G** for the carbene formation step. The model carbene precursor is inset. The plot is modified based on unpublished data from Wulff and co-workers with permissions.94 The units are in °C and kJ/mol. Figure 6.1 demonstrates an excellent linear relationship between the calculated reaction free energy barriers and Tonset of the carbene formation with only very small deviations from the line (R2 = 0.9785). This suggests that Tonset is a reflection of the reaction barrier. The 4-MeO (a strong EDG) substituted diazirine has the lowest calculated reaction free energy barrier, while the 4-NO2 (a strong EWG) counterpart has the highest barrier. The calculated free energy barriers of other substituents (4-t-Bu, 4-H, and 4-CF3) also show a similar relation with respect to their strength as an EDG or EWG. This suggests that the calculated barrier heights will display the Hammett relationship, which in turn may provide some insights into the control of the activation temperature of a diazirine through para-substitutions. 62 Figure 6.2. Selected R groups and para-substituents X used in this chapter (see Table 6.1 for their corresponding σp+ values). The carbene formation shown is under thermal activation. Table 6.1. Summary of the selected para-substituents X shown in Figure. 6.2, and their corresponding σp+ constants.95 X= NMe2 NH2 OH OMe CH3 t-Bu H Cl CF3 CN NO2 σp+ -1.7 -1.3 -0.92 -0.78 -0.31 -0.26 0 0.11 0.61 0.66 0.79 To explore the Hammett relationship in carbene formation, we selected single diazirines with four R groups and eleven para-substituents X (see Figure 6.2). For the R groups, we studied the CF3 group used in the proposed cross-linkers (e.g. 2A) and the two halogens discussed in the previous chapter (F, Cl). OMe was also included out of interest in learning how strong conjugative effects at the carbene center would alter reactivity. We saw in Section 5.1 that when R=halogens, singlet carbenes are preferred over triplet carbenes. OMe is expected to stabilize the singlet state of carbenes even more than halogens through direct conjugation of an oxygen lone-pair and the empty 2p-π orbital of the carbene. The selected eleven para-substituents were ranked based on their σp+constants,95 from the most electron-donating (NMe2) to the most electron-withdrawing (NO2) – see Table 6.1. 63 Figure 6.3. Plot of the calculated reaction free energy barrier (298K, 1atm) versus σp+ of the para-substituents using M06-2X-D3/6-31G** for the concerted carbene formation. The units are in kJ/mol. Figure 6.3 shows that how para-substituents affect the calculated free energy barrier of the concerted carbene formation (which has no diazo intermediate, see Section 4.2) for selected model diazirines. For CF3 diazirines, there is clear linearity between σp+ and the calculated free energy barrier and therefore a clear Hammett relation. An electron-donating para-substituent (e.g. NMe2) results in a lower carbene formation barrier than an electron-withdrawing substituent (e.g. NO2). The magnitude of the calculated free energy barrier varies from ~138 kJ/mol to ~156 kJ/mol due to the change of para-substituents, and this corresponds well to the 40 °C variation on the Tonset in experiments (Figure 6.1). This provides some insights into how we may use different para-substituents to tune the activation temperature of the cross-linker, making it more versatile to cross-link polymeric substrates with different meting points. 64 For Cl diazirines (slope: 2.4), a Hammett relationship still holds (R2=0.71) but the para-substituents induce smaller changes in barriers than in the CF3 diazirines (slope: 7.2). The difference between the strongest EDG and the strongest EWG for the calculated free energy barrier heights is about 7 kJ/mol for Cl diazirines compared with 18 kJ/mol for CF3 diazirines. For F diazirines (slope: 0.3), there does not seem to be a Hammett relationship (R2=0.05): that is, altering the nature of the para-substituent does not significantly change the barrier height of the reaction. This implies that para-substituents cannot be used to tune the activation temperature of cross-linkers derived from F diazirines. For diazirines with R=OMe (slope: -2.0), the Hammett relationship is similar to that of Cl diazirines, but with an opposite sign. That is, for OMe diazirines, an electron-withdrawing para-substituent tends to lower the reaction barrier. Since the carbene formation barrier is the free energy difference between the diazirines and their corresponding TS, we use the isodesmic schemes below (Figure 6.4) to analyze the effects of substituents on the relative stabilities of the parent diazirine and their corresponding TS separately. 65 Figure 6.4. Illustration of the isodesmic schemes for studying the influence of X substituents for the parent reaction (top) and the TS reaction (bottom). In Figure 6.4, the parent isodesmic reaction scheme is used to study the relative (de)stabilization of the diazirine afforded by para-substituents X, and the TS isodesmic reaction scheme is used to study the contribution of the relative (de)stabilization of the TS afforded by para-substituents X, to the overall barrier for carbene formation. In both schemes, reactants are para-substituted (X) diazirines (or TSs) and benzene, and products are the unsubstituted diazirines (or TSs) and the corresponding X-substituted benzenes. Positive calculated free energies of reactions indicate that reactants are more thermally stable than products and there is a stabilizing interaction between the X and the diazirine (or TS) moieties CN2R (or CN2R‡). Conversely, a negative free energy of reaction indicates a destabilizing interaction between the substituents and the diazirine (or TS) moieties. The plots of the isodesmic free energy versus σp+ for the X substituents are shown in Figure 6.5 for each of the R groups. The difference between the parent and the TS isodesmic schemes gives the 66 carbene formation reaction, and the corresponding free energy differences give the free energy barrier to carbene formation relative to X=H (i.e. unsubstituted aryl carbene, which is defined as the zero point in Figure 6.5). 67 Figure 6.5. Plots of the isodesmic free energy (298K, 1atm) versus σp+ of the para-substituents for the parent reaction (top) and the TS reaction (bottom) using M06-2X-D3/6-31G**. The units are in kJ/mol. For the parent isodesmic reaction (top, Figure. 6.5), the overall free energy for all R groups is positive when X is an EDG, and becomes negative when X is an EWG. This indicates that all of the diazirine moieties CN2R in this study are electron-withdrawing groups. The slopes of the regression lines are similar for all R=CF3, F, and Cl groups in parent reaction, 68 indicating the CN2R groups all have about the same electron-withdrawing ability. For R=OMe, the slope is about half of those of the R groups, suggesting that CN2OMe is the weakest EWG of the four. This is explained by the R group’s influence the overall electron-withdrawing character through induction effects, and the OMe group has the weakest induction effect. Also, one would expect N2 to be somewhat withdrawing since N is more electronegative than C, so one might expect any CN2R group to be an EWG. A similar trend on the overall free energy is observed in the TS isodesmic reaction (bottom, Figure 6.5), but only the TS moieties CN2R‡ with R=CF3, F, and Cl behave as EWGs. The slopes of these plots vary much more with R groups than do the parent isodesmic reaction, as indicated by the slopes of the best-fit lines: CF3 (slope: -12.5) > Cl (slope: -7.5) > F (slope: -5.3) > OMe (slope: -0.4) by magnitude. This suggests that the para-substituents have a greater impact on the (de)stabilization of the TS structure than on the parent structure. In the case of R=OMe, the isodesmic free energy of the TS reaction implies that this CN2R‡ group is neither electron-withdrawing nor donating. This may be associated with the conjugation that builds between the putative carbene center and the lone pairs of OMe in the TS. We found that the carbene formation process is a concerted asynchronous process, and that the TS structure is expected to have partially developed the orbital character of the carbene (i.e. one empty 2p-π and one doubly occupied σ). For R=CF3, F, and Cl, their π-donating ability through mesomeric effect is weaker than OMe, so their corresponding CN2R‡ moieties are EWGs. Since the isodesmic parent reaction and the TS reaction for R=F have a similar Hammett relationship (i.e. the slope is -4.9 for the parent reaction, and is -5.3 for the TS reaction with R=F, see Figure 6.5) and the barrier height is determined by the difference 69 between the parent and TS isodesmic schemes, the Hammett relationship for R=F shown in Figure 6.3 is almost flat. For R=OMe, the isodesmic TS Hammett relation is almost flat (slope: -0.4). The interactions between X and CN2R in the parent reaction (slope: -2.5) dominate the Hammett plot for the barrier to the formation of R=OMe carbenes and give the negative slope for R=OMe in Figure 6.3. The trends observed in Figure 6.3 for R=CF3 and R=Cl can be similarly understood. In these cases, the interactions between X and CN2R‡ in the TS dominate the Hammett relationships in Figure 6.3. Also, σp+ constants for R=CF3, Cl, F, and OMe are 0.61, 0.11, -0.07, and -0.78, respectively,95 and this trend correlates with the corresponding slopes (slopes: -12.5 (CF3), -7.5 (Cl), -5.3 (F), -0.4 (OMe)) in the isodesmic TS study by Figure 6.5. We can now understand the Hammett behavior associated with the TS isodesmic reactions by recognizing that two C-N covalent bonds are partially broken in the TS structure. Therefore, the empty 2p-π and the doubly occupied σ orbitals associated with the putative carbene have partially emerged in the TS structure. Interaction between the R groups and, in particular, the 2p-π orbital dictate the behavior observed in the bottom panel of Figure 6.5, and this behavior correlates well with their π-donating abilities. In summary, there is a positive Hammett relationship between the carbene formation barrier and σp+ for CF3 diazirines, suggesting that para-substituents can be used to tune the activation temperature. However, when CN2R becomes less electron-withdrawing, as is the case for R=Cl, F, or OMe, the slopes of the Hammett plots are reduced and there is less potential for controlling the activation temperature of diazirines carbene precursors through para-substitutions. 70 6.2 Reaction Free Energy of Carbene Formation The extrusion of N2 from a diazirine precursor leads to a carbene product, adopting either a singlet or a triplet state as its ground state. This section explores the ground state of para-substituted aryl carbenes and the presence of Hammett relationships in their overall formation free energies. 71 Figure 6.6. Plots of the calculated carbene formation reaction free energy (298K, 1atm) versus σp+ of the X substituents using M06-2X-D3/6-31G**. Dash line is when the triplet carbene is formed, and the solid line is when the singlet carbene is formed. The units are in kJ/mol. (a). R=CF3, (b). R=F, (c). R=Cl, and (d). R=OMe. Figure 6.6 describes the correlation between the carbene reaction free energy and σp+ of para-substituents. Although the reaction free energies are calculated for both singlet and 72 triplet carbenes, it should be noted that under thermal activation, the singlet carbene is always formed initially (Section 1.3.3). The singlet carbene may then convert to a triplet carbene through ISC when the triplet is lower in energy than the singlet (i.e. the ground state is a triplet). For all four systems shown in Figure 6.6, there is a clear Hammett relationship for the calculated singlet carbene formation free energy (all R2 are about 0.9, and all slopes are above 4.3). The singlet carbene has an empty 2p-π orbital, which is expected to conjugate strongly to the benzene ring and consequently with para-substituents. For example, the slope of the Hammett plot for the parent isodesmic scheme for CN2CF3 is -5.3 and the slope for R=CF3 carbenes (singlet) is +18.6, indicating that the singlet carbene center interacts more strongly with X than does the CN2R center, as expected. For R=OMe, the 2p-π orbital on the carbene will not be empty – rather it will more closely resemble a singly occupied orbital due to conjugation. The presence of a Hammett relationship is not obvious for the triplet carbene formation free energy (e.g. for R=CF3, R2 is 0.48 and the slope is 2.3). The triplet carbene formation free energy tends to decrease when there is an increase of σp+ for R=F, Cl, and OMe. However, it is almost unchanged for R=CF3. The triplet carbenes have a (nominally) singly occupied 2p-π orbital, which interacts only weakly with para-substituents through aromatic ring delocalization. For instance, the slope of the Hammett plot for the parent isodesmic scheme for CN2CF3 is -5.3 and the slope for R=CF3 carbenes (triplet) is +2.3, indicating comparatively weak interaction between the triplet carbene and X substituents (cf. slope of +18.6 for R=CF3 singlet carbenes). For R=OMe, the slope of -5.9 is for the analogous triplet carbene formation 73 can be understood on the basis that conjugation between the OMe and singly occupied 2p-π of the triplet carbene will make the triplet carbene center behave as an EDG. Weak or non-existent Hammett relations were also reported for the C-H BDE of para-substituent toluene.96,97 The benzyl radicals in this example are electronically analogous to triplet carbenes, which have a carbon-centered p-π conjugated with the aromatic ring. Wu and co-workers showed that para-X-toluene with both EDGs and EWGs reduce the BDE of the benzylic C-H bond in toluene relative to X=H. They concluded that the radical stabilities depend on the spin delocalization effects from para-substituents rather than their polar effects, so both a π-donor like NMe2 or a π-acceptor NO2 can stabilize the benzyl radical center and therefore lower the C-H BDE. It should be noted that a negative reaction free energy does not mean barrier-less reactions, but excess free energy can lead to improving the reaction outcomes associated with subsequent carbene insertion. For R=CF3 carbenes, the calculated free energies for both singlet and triplet carbene formation are positive, which indicates that the reaction is nonspontaneous. However, for R=OMe carbenes, the calculated free energy for the singlet carbene formation is negative by more than -60 kJ/mol, reflecting the stability of their singlet states. Most of the R= F and Cl singlet carbenes have negative free energies of formation, with the exception being those with very strong para-EWGs. Previous experiments concluded that the para-MeO R=CF3 carbene adopts a singlet ground state81 rather than the triplet state predicted by the M06-2X calculations. This is the situation discussed in Section 4.1 in which hybrid functionals tend to overestimate the relative 74 stability of the triplet carbene. For instance, M06-2X has a 26.8 kJ/mol error in the S-T gap of methylene. However, the large error in S-T gaps from M06-2X does not present in the reaction barriers of the methylene insertion or abstraction toward methane. For example, M06-2X predicts insertion and abstraction barriers for methylene that are within 4.1 kJ/mol of those predicted using CCSD(T)/CBS, and this agreement likely arises from error cancellation in the DFT calculations. We will explore in Section 6.3.1 whether such a good error cancellation still holds for the calculated barriers of aryl carbene insertions (larger systems compared to methylene). To resolve the ambiguity about the actual ground states of aryl carbenes, we used a high-level wavefunction approach proposed by Neese and co-workers on calculating the S-T gaps of aryl carbene.98 They suggested adopting DLPNO-CCSD(T)/cc-pV(T-Q)Z CBS for accurately predicting the S-T splittings of aryl carbenes. However, using DLPNO-CCSD(T)/cc-pVQZ is still computationally demanding and is limited in terms of the size of carbene systems to which it can be applied. Therefore, we use DLPNO-CCSD(T)/cc-pV(D-T)Z CBS for the studied aryl carbenes and expect that we can obtain reasonably accurate results. The calculated free energy gaps are summarized in Table 6.2. 75 Table 6.2. Summary of the calculated free energy (298K, 1atm) S-T splittings of R=CF3, F, Cl, and OMe carbenes using DLPNO-CCSD(T)/CBS//M06-2X-D3/6-31G**. (D-T)CBS stands for cc-pV(D-T)Z, and (T-Q) stands for cc-pV(T-Q)Z. The units are in kJ/mol. σp+ para-substituent CF3 F Cl OMe (D-T)CBS (T-Q)CBS (D-T)CBS (D-T)CBS (D-T)CBS -1.7 NMe2 -18.2 -19.5 -94.1 -56.3 -117.4 -1.3 NH2 -15.2 -16.8 -90.0 -51.9 -113.6 -0.92 OH -4.6 -5.2 -84.7 -45.6 -111.0 -0.78 OMe -5.9 -6.9 -84.4 -44.6 -110.7 -0.31 CH3 2.1 1.1 -74.4 -33.6 -100.5 -0.26 t-Bu 3.9 2.8 -74.7 -34.9 -103.4 0 H 10.5 9.7 -69.4 -30.0 -100.3 0.11 Cl 8.4 7.8 -70.4 -30.5 -100.8 0.61 CF3 20.2 19.7 -65.4 -23.5 -97.7 0.66 CN 24.1 22.9 -58.1 -18.3 -89.8 0.79 NO2 20.5 19.6 -60.4 -20.3 -94.0 To confirm that the cc-pV(D-T)Z CBS can predict equally accurate S-T splittings as the cc-pV(T-Q)Z CBS (proposed in literature) for aryl carbenes, we performed DLPNO-CCSD(T)/cc-pV(T-Q)Z calculations on the para-X R=CF3 carbenes. In Table 6.2, (D-T)CBS gives the same calculated free energy S-T gaps as (T-Q)CBS to within 1.5 kJ/mol. The DLPNO-CCSD(T) results predict that para-NMe2, NH2, OH, and OMe R=CF3 carbenes all have singlet ground states. Likewise, the para-X, R=F, Cl, and OMe carbenes all have singlet ground states. This aligns with the experimental observation discussed above. According to Figure 6.6, M06-2X generally predicts qualitatively correct gaps for R=Cl (Figure 6.6 (b)), F (Figure 6.6 (c)), and OMe (Figure 6.6 (d)), but it fails to predict the singlet ground states of para-NMe2, NH2, OH, and OMe for R=CF3 (Figure 6.6 (a)) carbenes. Therefore, although DFT is useful for qualitatively predicting S-T splittings of carbenes, caution is needed when interpreting the results for singlet states that are ca. 25 kJ/mol (by M06-2X) higher than the triplet states. In such cases, a high-level method is required to predict the true ground state. 76 In conclusion, very strong para-EDGs (e.g. NMe2 or OMe) can be used to maintain the singlet state in carbenes with R=CF3, where weaker EDGs and EWGs result in the triplet carbenes being the ground state. This has direct consequences in tuning the insertion reaction pathways for these carbenes, as discussed in the next section. Carbenes with R=F, Cl, and OMe all have singlet states regardless of the nature of their para-substituents. The free energies of formation of the singlet carbenes display stronger correlations with σp+ parameters than do the triplet carbenes, indicating that formation free energies of singlet carbenes can be modulated through para-substitution. 6.3 Carbene Insertion Barriers This section discusses the reaction barriers of carbene insertions. The study includes the stereotypical C-H insertion into propane and explores the possible insertion into C-F bonds using our model carbene systems. We also explore whether the fluorination of the ring can help reduce the self-reaction of the cross-linker. 6.3.1 C-H Insertion As discussed in Section 4.2, a carbene can react with the polymeric substrate to achieve cross-linking. A singlet carbene will undergo concerted insertion into a C-H bond while the triplet carbene will insert via an abstraction/recombination pathway. In this section, we use propane (middle CH2) as a simplified model for the polyethylene chain and explore the 77 insertion reaction of the aryl carbenes (R=CF3, F, Cl, or OMe) with various para-substituents (Figure 6.7). 78 Figure 6.7. Illustration of C-H insertion (or abstraction) from our model carbenes. The central C-H bond in propane is targeted for insertion reaction modeling. Figure 6.8. Plots of the calculated free energy barriers (298K, 1atm) versus σp+ of the X substituents using M06-2X-D3/6-31G** for singlet insertion (or triplet abstraction). The solid line represents the singlet insertion, and the dashed line represents the triplet abstraction. The units are in kJ/mol. Figure 6.8 shows that the calculated free energy barrier of the singlet insertion or triplet abstraction versus σp+. The calculated free energy barrier of the singlet insertion correlates far 79 better with σp+ than the triplet abstraction, and this observation is similar to the trends observed for the carbene formation free energy in Figure 6.6. Recall from Section 1.3.4 that the first phase of the singlet carbene insertion is the electrophilic attack from its empty 2p-π to the filled C-H bonding orbital, so the electrophilicity of the carbene center determines the reaction barrier. Therefore, an EDG at para-position makes the singlet carbene center less electrophilic than an EWG, resulting in a higher calculated free energy barrier of the singlet insertion when the para-substituents are EDGs. Similarly, based on the π electrons donating ability of R groups, OMe is the strongest EDG and CF3 is the weakest EDG. Consequently, R=OMe carbenes have ca. 130 kJ/mol higher insertion barrier than R=CF3 carbenes. The calculated free energy barriers of the triplet abstraction reactions are almost the same regardless of the R groups and X substituents, except for R=OMe carbenes which show a 10 kJ/mol higher abstraction barrier than the other three systems. A possible reason is that the strong π-donation of OMe results in more interaction with the singly occupied orbital of the carbene than the other three R groups. The conjugation between a lone-pair orbital on the oxygen atom in the OMe group and the singly occupied 2p-π orbital leads to the carbene centre adopting more carbanion character, therefore reducing the ease of hydrogen atom abstraction compared to carbene centres with more radical character. Overall, the triplet abstraction barrier is not very sensitive to either R groups or the para-X substituents, indicating that little control over the barrier heights can be achieved through the R groups and X substituents. According to the available experimental data for the para-X R=CF3 carbenes, the cross-linking efficacy for para-OMe, para-H, and para-CF3 are 91%, 15%, and 6%, respectively. 80 The cross-linking efficacy is defined as the percentage of the carbenes that insert into the substrates (e.g. polyethylene or cyclohexane) relative to the carbenes that were generated. The reason for different cross-linking efficacy may be two-fold. Firstly, para-OMe R=CF3 carbene has a singlet ground state and (as discussed in Section 1.3.4) singlet insertion is cleaner), but both the para-H and para-CF3 R=CF3 carbenes have triplet ground states. The major side products observed experimentally using triplet para-H and para-CF3 R=CF3 carbenes are ketones, which is possibly from the reaction between the triplet carbene and environmental O2. Experiments show that the triplet carbene traps the O2 rapidly even at low temperatures, but the singlet carbene does not react with O2.81 Our computational explorations also indicate that the reaction between the triplet carbene and O2 is barrier-less. Although the barrier for singlet insertion of para-OMe R=CF3 carbene is calculated to be around 34 kJ/mol higher than the triplet abstraction, the fact that it is not consumed through reaction with O2 may maintain its abundance in the reaction system. In principle, a lower free energy reaction pathway for the para-OMe R=CF3 carbene may be accessible by first exciting it to a triplet, which may then undergo hydrogen atom abstraction. However, the singlet-triplet excitation is formally forbidden, suggesting that the singlet insertion is the dominant process. Secondly, Section 6.2 shows that a stronger EDG at para-position results in a lower carbene formation barrier of R=CF3 carbenes. Therefore, the para-OMe carbene is expected to have the lowest formation barrier of X=OMe, H, and CF3 carbenes. This suggests that there may be a kinetic factor associated with the cross-linking efficacy in which the para-OMe carbene is more easily formed, so there are more para-OMe carbenes able to undergo insertion than the para-H or para-CF3 carbenes under the same thermal conditions. Moreover, a stronger 81 EDG at para-position tends to result in the release of more free energy upon carbene formation, and an exothermic reaction is likely to benefit the following insertion reaction of the carbene. We also performed the DLPNO-CCSD(T)/cc-pVTZ//M06-2X/6-31G** calculations to verify the accuracy of the M06-2X insertion barriers on para-OMe R=CF3 carbene, and DLPNO-CCSD(T) gives a 101.8 kJ/mol singlet insertion barrier (81.6 kJ/mol by M06-2X) and a 54.3 kJ/mol abstraction barrier (47.2 kJ/mol by M06-2X). This shows that for large systems (unlike the methylene), there is a discrepancy between the M06-2X and DLPNO-CCSD(T) results on insertions barriers. However, the errors for barrier height calculations are smaller than the predictions of the S-T splittings, and does not affect our conclusion here. 6.3.2 C-F Insertion The carbene-based cross-linkers are expected to be applicable to C-F bonds. This would allow for the cross-linking of Teflon, which is extremely difficult to do. Section 6.3.1 showed that R=CF3 carbenes have the lowest insertion barrier compared to R=F, Cl, OMe counterparts. Hence, we use the R=CF3 carbenes with NH2, H, or CF3 para-substituents to explore their reactions with C-F bonds. The model substrates are 2-fluoropropane, 2,2-difluoropropane, and perfluoropropane (Figure 6.9). 82 Figure 6.9. Illustration of C-F insertion (or abstraction) from our model R=CF3 carbenes. The targeted substrates used are 2-fluoropropane, 2,2-difluoropropane, and perfluoropropane. Table 6.3 below shows that the singlet insertion toward C-F bonds is highly influenced by para-substituents as is the case for C-H insertion. When X=NH2 (an EDG), the calculated free energy barrier of the singlet insertion into 2-fluoropropane is 62.4 kJ/mol higher than X=CF3 (an EWG). Additionally, the C-F insertion requires at least 40 kJ/mol more free energy than the C-H insertion. Changing from 2-fluoropropane to 2,2-difluoropropane increases the insertion barrier by about 6 kJ/mol, while insertion into perfluoropropane requires 50 kJ/mol more free energy. All of this indicates that it is harder to cross-link Teflon than polyethylene. Table 6.3. Summary of the calculated free energy barrier (298K, 1atm) for singlet C-F insertion shown in Fig. 6.9 using M06-2X-D3/6-31G**. The units are in kJ/mol. singlet insertion barrier 2-fluoropropane 2,2-difluoropropane perfluoropropane X=NH2 160.6 166.7 211.8 X=H 118.4 123.9 178.9 X=CF3 98.2 100.2 170.8 Such a big change in insertion barriers from 2-fluoropropane (or 2,2-difluoropropane) to perfluoropropane requires further explanation. Since the BDE of the middle C-F bond in perfluoropropane is not reported experimentally, we calculated the bond length and BDE of the middle C-F bond of the three substrates. The results at the M06-2X level of theory are 1.39 83 Å /485.4 kJ/mol for 2-fluoropropane, 1.36 Å/521.8 kJ/mol for 2,2-difluoropropane and 1.34 Å/508.7 kJ/mol for perfluoropropane. Consequently, such a large change in barrier heights is not associated with the strength of the middle C-F bond in perfluoropropane, which is weaker than the C-F of 2,2-difluoropropane. We hypothesize that the challenges associated with insertion into C-F bonds may be related to the changes that occur in C-F bonding orbitals as fluorination increases. In perfluoropropane, the central C-F bond is the shortest of the three fluorinated structures but, paradoxically, is not the strongest bond. Nevertheless, the short C-F bond in perfluoropropane suggests that the corresponding σ-bonding orbital will be very compact thus leading to the need for the attacking carbene to more closely approach the perfluorinated substrate in order to reach the insertion TS. Table 6.4 below shows the triplet abstraction barrier to C-F bonds is less sensitive to para-substituents than the singlet insertions. Going from 2-fluoropropane to 2,2-difluoropropane, the calculated free energy barrier of the triplet abstraction increases by about 14-17 kJ/mol and by about 4-12 kJ/mol in going from 2,2-difluoropropane to perfluoropropane. This aligns with the fact that the length of the C-F bond is decreasing gradually among the three substrates (so increasing C-F bonding orbital contraction). However, even the minimum calculated barrier is 183.7 kJ/mol, indicating such reaction is less likely to happen than C-H abstraction. Table 6.4. Summary of the calculated free energy barrier (298K, 1atm) for the triplet C-F abstraction shown in Fig. 6.9 using M06-2X-D3/6-31G**. The units are in kJ/mol. triplet abstraction barrier 2-fluoropropane 2,2-difluoropropane perfluoropropane X=NH2 188.4 204.7 208.6 X=H 184.1 201.3 208.8 X=CF3 183.7 197.4 209.1 84 In summary, both the singlet insertion and the triplet abstraction requires a free energy barrier of at least 170 kJ/mol in order to react with perfluoropropane (Teflon is polytetrafluoroethylene), which is not likely to happen under normal condition. It is possible to use very high temperatures to overcome such high barriers, but the cross-linkers may evaporate before the insertion reaction can proceed. Increasing the molecular weight of the cross-linkers will decrease volatility, and this could be an approach for cross-linking Teflon. 6.3.3 Fluorination of the Ring Cross-linkers may react with themselves before inserting into the substrates, and this will reduce their efficacy. Section 6.3.1 and 6.3.2 show that C-F insertions require much higher energy than C-H insertions, and this inspired us to fluorinate the ring to alleviate the self-reactions (e.g. insertion to the ring). We have described this study in ref[83]. 85 Figure 6.10. Possible reactions between carbene and benzene, and model carbene with benzene derivatives used for the study (in the square). Reproduced from ref[83] with permission from the Royal Society of Chemistry. Figure 6.10 shows carbenes may react with benzene derivative through various pathways. Besides the singlet insertion (Figure 6.10 (a)) or triplet abstraction (Figure 6.10 (d)) mechanisms described above, carbenes can react with the aromatic rings through cyclopropanation via addition reactions. The singlet addition (Figure 6.10 (b)) should be a concerted process, while the triplet addition (Figure 6.10 (c)) will go through a radical intermediate. Our recently published paper explores Gen 2a and Gen 2b cross-linkers (see Section 4.3), using X=CF3 and H cross-linker models (see the square in Figure 6.10). Both of these carbenes have triplet ground states (Section 6.2). 86 Table 6.5. Calculated enthalpy and free-energy (298K, 1atm) reaction barriers of model carbene to hexafluorobenzene or benzene using M06-2X-D3/6-31G**. The units are in kJ/mol. Reproduced from ref[83] with permission from the Royal Society of Chemistry. benzene derivative para-substituent reaction barrier Sins Sadd Tadd Tabs X=H ∆H298K N/A -32.8 10.5 167.1 ∆G298K N/A 27.8 66.4 211.6 X=CF3 ∆H298K N/A -34.9 11.2 168.3 ∆G298K N/A 25.2 68.0 213.1 X=H ∆H298K 6.0 -33.7 3.6 26.6 ∆G298K 59.9 22.7 55.9 73.1 X=CF3 ∆H298K -2.5 -41.2 0.2 25.2 ∆G298K 52.3 16.0 54.1 71.8 The calculated enthalpy and free energy barriers for the reactions of the cross-linker models with perfluorobenzene and benzene are summarized in Table 6.5. The TS of the singlet insertion to aromatic C-F bonds could not be found, but we suspect that they are much higher in barriers compared to aromatic C-H insertions because of the higher C-F strength in hexafluorobenzene. Table 6.5 shows that the addition reactions are much more facile than the insertions. Since our calculations indicate both model carbenes are in triplet states, the triplet addition (Figure 6.10 (c)) is the dominant pathway. For the triplet addition reaction to benzene, X=H carbene has a 55.9 kJ/mol calculated free energy barrier, and X=CF3 has a 54.1 kJ/mol calculated free energy barrier. Replacing benzene with hexafluorobenzene does not significantly increase (less than 14 kJ/mol) this free energy barrier, so this strategy cannot avoid cyclopropanation. Therefore, it is key that the concentration of the cross-linkers be controlled in order to avoid self-reaction (i.e. diffusion control). 87 Chapter 7: Conclusion This thesis uses quantum mechanical-based computational methods to explore how novel carbenes work as cross-linkers for soft materials and provides guidance for the developments of new cross-linkers. Firstly, we used methylene as a prototypical example of a carbene to illustrate that the singlet state engages in a concerted insertion, while the triplet state goes through an abstraction/recombination pathway to react with methane. In this system, the singlet insertion barrier is lower than the triplet abstraction, but this may not be true for other systems. It was shown that both the singlet insertion and triplet abstraction of methylene into methane are sensitive to temperature, and higher temperatures result in higher barriers but the change for the triplet abstraction is smaller than the singlet insertion. This temperature dependence of the barrier heights is caused by entropy rather than enthalpy, and experimental conditions are expected to affect the cross-linking efficacy (which is related to the insertion or abstraction barriers). On the other hand, the impact of temperature changes on the calculated S-T splittings of methylene is negligible, so S-T splittings are not expected to be sensitive to the thermal conditions in experiments. Our in silico study showed that the bis-diazirine based cross-linker 1 undergoes a concerted process to carbene formation. The resulting carbene adopts a triplet ground state, which will react with substrates via H-abstraction. The results indicate that the influence of meta-substitutions on the abstraction barrier is minor, and that each carbene center in bis-carbenes will behave independently. We also found that the single nitrogen atom substitution to the benzene ring results in more diazo intermediates, but it does not improve the cross-linker performance. Using a long (CF2)n tether unit can improve the mechanical strength of the bond 88 without affecting the cross-linking efficacy.83 Therefore, it is a useful strategy to alleviate the thermal volatility of the cross-linker and improve its performance at high temperatures. The introduction of halogens to carbenes significantly stabilizes the singlet state relative to the triplet, and using the phenyl group with halogens can slightly increase the tendency toward the singlet ground state even further. However, the phenyl group itself cannot alter the triplet ground state to the singlet ground state. For S-T splitting predictions, DLPNO-CCSD(T)/CBS shows the best agreement with the experimental data and therefore is recommended for accurate S-T splitting predictions. Both M06-2X (and B3LYP) tend to overestimate the stability of the triplet carbenes, and may provide false ground state predictions when the singlet state is only ~25 kJ/mol higher than the triplet state. Compared to meta-bis-carbenes, para-bis-carbenes exhibit stronger electronic communications at the carbene centers through ring delocalization. Although the formation of bis-carbene intermediates is not likely under thermal activation, they can be formed under photoactivation. When each carbene center has a triplet ground state, its para-bis-carbene counterpart is in an open-shell singlet diradical structure. When each carbene center has a singlet ground state, its para-bis-carbene counterpart may adopt an open-shell singlet diradical structure (e.g. p-phenylenebis(chloromethylene)) or a closed-shell singlet bis-carbene structure (e.g. p-phenylenebis(fluoromethylene)). This indicates that there are additional complexities when para-bis-carbenes are generated by photoactivation (compared with the thermal process). We used para-substituted aryl mono-diazirines to explore the general effect of para-substitution on S-T splittings, formation barriers, and insertion barriers. It was shown that the carbene formation barrier of para-substituted aryl mono-diazirine follows a positive Hammett 89 relationship, and the activation temperature can vary up to 40 °C between the strongest EDG and the strongest EWG in R=CF3 diazirines. However, when R groups are π-donors, Hammett correlations are diminished or even disappear (e.g. R=F), so we do not recommend the use of strong π-donors when there is interest in using substituents to control the activation temperature of carbene precursors. The overall reaction free energy of singlet carbene formation also follows positive Hammett relationships, much more so than their triplet carbene counterparts. Carbenes with R=Cl, F, and OMe have ground states that are singlets regardless of the nature of para-substituents. However, R=CF3 carbenes have singlet ground states when strong EDGs (e.g. NMe2 or OH) are used as para-substituents, and have triplet ground states for weak EDGs and all EWGs. Having an EDG para-substituent also increases the free energy released upon carbene formation, and this excess free energy may contribute to subsequent insertion reactions. The singlet carbene insertion barriers follow the Hammett relationship but with a negative correlation, and the triplet abstraction barriers have a much weaker correlation than the singlet insertion. Consequently, the para-substitution is not an effective strategy to moderate the triplet abstraction barriers. The stronger π-donors used for R groups increase the singlet insertion barrier, which reduces cross-linking efficacy. The C-F insertion (or abstraction) is also explored for the potential application on glue Teflon layers, but it requires a minimum of 70 kJ/mol higher free energy barriers (for both insertion and abstraction) than the C-H counterparts thereby it is less likely to happen under normal conditions. Higher temperatures may allow for Teflon cross-linking, however. Fluorination of the aromatic ring was explored as a means to minimize the self-reaction among cross-linkers. Our results indicate this approach is not effective in avoiding cyclopropanation, which is the major self-reaction that may occur with cross-linkers. 90 It was reported that triplet carbene traps environmental O2 in a barrier-less addition, and this will reduce the cross-linking efficacy of any triplet carbene used under ambient conditions. Singlet carbenes do not suffer such side reactions with O2 and will therefore have a higher insertion efficacy than triplet carbenes. Based on these findings above, Gen 3a (top, Figure 7.1) has been suggested as a more effective cross-linker and is currently under investigation with experimental collaborators. We also propose a type of cross-linker that can both incorporate para-substituent effects and flexibilities of the tether unit. (bottom in Figure 7.1). The benefits of the proposed Gen 4 cross-linker are as follows: 1. Carbenes with R=CF3 have lower insertion barriers than R=Cl, F, and OMe. 2. 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R=CF3 σp+ para-substituent S-T gap formation barrier insertion barrier abstraction barrier -1.7 NMe2 10.4 138.2 102.6 49.1 -1.3 NH2 7.3 140.0 103.0 49.3 -0.92 OH 19.7 145.4 87.6 48.3 -0.78 OMe 18.8 145.4 81.6 47.2 -0.31 CH3 27.1 147.6 77.1 49.0 -0.26 t-Bu 29.9 150.6 69.2 47.0 0 H 34.1 153.0 65.6 47.9 0.11 Cl 33.9 151.5 63.5 46.7 0.61 CF3 43.1 153.2 59.6 47.4 0.66 CN 45.6 155.3 53.0 45.6 0.79 NO2 46.7 156.5 49.8 44.4 R=F σp+ para-substituent S-T gap formation barrier insertion barrier abstraction barrier -1.7 NMe2 -75.1 153.4 185.2 52.0 -1.3 NH2 -73.7 154.8 183.8 50.1 -0.92 OH -66.6 155.8 174.2 51.8 -0.78 OMe -66.2 155.2 174.5 49.2 -0.31 CH3 -59.0 157.5 168.5 49.3 -0.26 t-Bu -57.8 156.4 166.7 49.1 0 H -54.7 156.6 163.0 48.4 0.11 Cl -54.4 155.8 161.0 46.3 0.61 CF3 -48.1 155.8 154.6 47.0 0.66 CN -42.4 154.6 149.0 44.8 0.79 NO2 -39.6 154.3 145.5 44.2 R=Cl σp+ para-substituent S-T gap formation barrier insertion barrier abstraction barrier -1.7 NMe2 -38.9 146.6 157.1 53.3 -1.3 NH2 -39.1 148.2 158.6 52.3 -0.92 OH -28.4 150.9 147.1 53.1 -0.78 OMe -28.1 151.5 146.6 51.7 -0.31 CH3 -18.8 153.2 139.2 52.6 -0.26 t-Bu -18.7 153.7 138.6 52.2 0 H -15.5 153.2 135.8 52.5 0.11 Cl -14.6 152.9 133.9 51.4 103 0.61 CF3 -6.3 153.7 126.4 50.5 0.66 CN -2.3 152.7 124.4 49.9 0.79 NO2 0.8 152.9 121.8 49.7 R=OMe σp+ para-substituent S-T gap formation barrier insertion barrier abstraction barrier -1.7 NMe2 -97.8 118.4 231.4 64.7 -1.3 NH2 -95.4 118.6 226.7 63.5 -0.92 OH -92.3 118.6 220.6 62.4 -0.78 OMe -91.3 118.0 220.4 62.5 -0.31 CH3 -83.8 117.5 213.2 64.7 -0.26 t-Bu -85.4 117.6 211.8 62.8 0 H -84.2 118.0 206.3 61.9 0.11 Cl -84.0 116.8 205.9 60.9 0.61 CF3 -79.4 115.5 201.2 59.2 0.66 CN -72.6 113.8 192.8 60.0 0.79 NO2 -70.7 112.8 188.8 58.6 Table A.2. Summary of the calculated (298K, 1atm) isodesmic fee energies (of the parent reaction or TS reaction) and reaction free energy (of the singlet carbene or triplet carbene) using M06-2X-D3/6-31G** for R=CF3, F, Cl, and OMe. The units are in kJ/mol. R=CF3 σp+ para-substituent isodesmic free energy (parent) isodesmic free energy (TS) reaction free energy (singlet) reaction free energy (triplet) -1.7 NMe2 6.6 21.4 25.2 14.8 -1.3 NH2 4.3 17.2 25.9 18.6 -0.92 OH 1.1 8.7 41.0 21.3 -0.78 OMe 1.7 9.3 41.3 22.5 -0.31 CH3 0.6 6.0 49.6 22.6 -0.26 t-Bu 1.6 4.0 53.7 23.8 0 H 0.0 0.0 58.8 24.6 0.11 Cl -3.6 -2.2 56.7 22.9 0.61 CF3 -5.8 -6.1 66.1 22.9 0.66 CN -6.5 -8.8 67.1 21.5 0.79 NO2 -7.7 -11.2 69.0 22.3 R=F σp+ para-substituent isodesmic free energy (parent) isodesmic free energy (TS) reaction free energy (singlet) reaction free energy (triplet) -1.7 NMe2 6.6 9.8 -21.1 54.1 -1.3 NH2 4.0 5.8 -20.9 52.8 -0.92 OH 0.9 1.6 -14.4 52.2 -0.78 OMe 1.3 2.6 -14.5 51.7 -0.31 CH3 1.1 0.2 -7.9 51.1 -0.26 t-Bu 1.7 1.9 -6.9 51.0 0 H 0.0 0.0 -4.7 50.0 0.11 Cl -3.4 -2.6 -6.4 48.0 0.61 CF3 -4.4 -3.7 -2.0 46.2 0.66 CN -6.0 -4.0 -0.6 41.8 104 0.79 NO2 -7.3 -5.1 0.9 40.5 R=Cl σp+ para-substituent isodesmic free energy (parent) isodesmic free energy (TS) reaction free energy (singlet) reaction free energy (triplet) -1.7 NMe2 7.8 14.3 -23.8 15.1 -1.3 NH2 4.7 9.7 -24.8 14.3 -0.92 OH 1.7 3.9 -13.9 14.5 -0.78 OMe 3.0 4.8 -12.9 15.3 -0.31 CH3 1.4 1.4 -5.4 13.4 -0.26 t-Bu 3.2 2.7 -3.7 15.0 0 H 0.0 0.0 -2.4 13.1 0.11 Cl -2.9 -2.7 -2.8 11.8 0.61 CF3 -2.9 -3.3 6.0 12.3 0.66 CN -5.6 -5.1 4.8 7.1 0.79 NO2 -6.8 -6.5 7.3 6.5 R=OMe σp+ para-substituent isodesmic free energy (parent) isodesmic free energy (TS) reaction free energy (singlet) reaction free energy (triplet) -1.7 NMe2 3.7 3.3 -72.2 25.5 -1.3 NH2 2.3 1.7 -69.8 25.6 -0.92 OH 0.6 0.1 -67.2 25.1 -0.78 OMe 0.9 0.9 -66.8 24.5 -0.31 CH3 0.8 1.3 -62.3 21.6 -0.26 t-Bu 0.7 1.2 -62.9 22.5 0 H 0.0 0.0 -61.6 22.6 0.11 Cl -1.6 -0.4 -63.9 20.0 0.61 CF3 -2.6 0.0 -61.9 17.5 0.66 CN -2.2 2.0 -61.3 11.3 0.79 NO2 -3.1 2.1 -61.1 9.6
Thesis/Dissertation
eng
Chemistry
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Ab initio studies of novel polymer cross-linkers
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