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Electronic structure and reactivities of the perfect, defected, and doped single-walled carbon nanotubes Liu, Lei 2006

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Electronic Structure and Reactivities of the Perfect, Defected, and Doped Single-Walled Carbon Nanotubes by Lei Liu B.Sc. Beijing Normal University, 2003 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T OF T H E R E Q U I R E M E N T S F O R T H E D E G R E E OF M A S T E R OF SCIENCE in T H E F A C U L T Y OF G R A D U A T E STUDIES (Chemistry) THE UNIVERSITY OF BRITISH COLUMBIA April, 2006 © Lei Liu, 2006 Abstract In this thesis, the electronic structure and reactivities of the perfect, defected, and doped single-walled carbon nanotubes (SWCNTs) have been studied by various theoretical methods, including density functional theory, semiempirical methods, and force fields. Among different defects of the SWCNTs, we have concentrated our studies on the vacancy defect and substitutional^  doped defect. Of the vacancy defected SWCNTS, we first studied their geometries, energetics, and electronic structures. After comparing the vacancy defected SWCNTs with the perfect SWCNTs, we found that the vacancy defect introduces localized electronic states near the Fermi level, thus enhancing the chemical reactivity of the SWCNTs. We then studied the reaction mechanisms of the vacancy defect on the (5,5) SWNCT with NO and O3. We have discovered that the reaction between NO and the vacancy defect provides a possible way to fabricate the substitutionally N-doped SWCNTs. We also obtained a microscopic understanding of the ozonization at the vacancy defect site of the SWCNT. To further understand the doping effects, we have studied the precious metal Pt-doped SWCNTs at different positions of the (5,5) SWCNT rod. We found that the doping of Pt in the SWCNT rod results in localized states at Pt, thus rendering Pt as the active center in chemical reactions. We found that the doping of Pt in the middle of the sidewall of the nanorod has a stronger interaction with adsorbates (e.g., H2 and C2H4) than the doping of Pt at the hemispheric caps of the nanorod. ii Table of Contents Abstract i i Table of Contents i i i List of Tables v i List of Figures v i i List of Abbreviations and Acronyms ix Acknowledgements x i Chapter 1. Introduction 1.1. Nanoscience, Fullerenes, and Carbon Nanotubes 1 1.2. Defects on the Single-Walled Carbon Nanotube 3 1.3. This Work 4 1.4. References 5 Chapter 2. Brief Introduction to the Theoretical Methods 2.1. First-Principles Methods 7 2.1.1. Ffartree-Fock and Post-Hartree-Fock Methods 8 2.1.2. Density Functional Theory 10 2.2. Semiempirical Quantum Mechanical Methods 12 2.3 O N I O M Model 13 2.4. References 14 Chapter 3. Ab Initio Studies of Vacancy Defected Fullerenes and Single-Walled Carbon Nanotubes 3.1. Introduction 17 3.2. Computational Details 20 3.3. Results and Discussions 21 iii 3.3.1. Vacancy Defected Fullerenes 21 3.3.2. Vacancy Defected S W C N T s 34 3.4. Conclusion 41 3.5. References 47 Chapter 4. Chemical Reaction of Nitric Oxides with the 5-1DB Defect of the Single-Walled Carbon Nanotube 4.1. Introduction 50 4.2. Computational Methods and O N I O M Model Selection 51 4.3. Results and Discussion 57 4.3.1. Attacking o f the First N O 57 4.3.2. Attacking of the Second N O 61 4.4. Conclusions 63 4.5. References 63 Chapter 5. Ozonization at the Vacancy Defect Site of the Single-Walled Carbon Nanotube 5.1. Introduction 66 5.2. Computational Methods 68 5.3. Results and Discussion 69 5.3.1. Static Quantum Mechanical Studies 69 5.3.1.1. Reaction of O 3 on the Active Carbon Atom 70 5.3.1.2. 1,3-DC of 0 3 on the C 8 - C 9 Bond (Position 1) 71 5.3.1.3. 1,3-DC o f 0 3 on the C 6 - C 7 Bond (Position 2) 74 5.3.1.4. 1,3-DC of 0 3 on the C 4 - C 5 Bond (Position 3) 75 5.3.1.5. 1,3-DC of 0 3 on the C 2 - C 3 Bond (Position 4) 79 5.3.2. Ab Initio Molecular Dynamics Studies 80 5.4. Conclusion 82 5.5. References 82 iv Chapter 6. Electronic Properties and Reactivity of the Pt-Doped Carbon Nanotubes 6.1. Introduction 85 6.2. Models and Computational Details 86 6.3. Results and Discussions 87 6.3.1. Perfect SWCNT Rods 87 6.3.2. Pt-doped SWCNT Rods 92 6.3.2.1. Cap-end-doped C]69Pt(ce) 93 6.3.2.2. Cap-doped Ci69Pt(c) 95 6.3.2.3. Wall-doped Ci69Pt(w) 96 6.3.3. Adsorptions of C2H4 and H2 on Ci69Pt 98 6.4. Conclusions 103 6.5. References 104 Chapter 7. Conclusions and Recommendations for Future Work 7.1 Conclusions 110 7.2 Recommendations for Future Work 111 List of Tables 3.1 Bond lengths of the single vacancy defected C6o and C70. 22 3.2 Energies of C 6 0 , C59(4-9), C59(5-8), C 7 0 , C69(4-9), and C69(5-8). 24 3.3 Vertical electron affinity, adiabatic electron affinity, vertical ionization potential, adiabatic ionization potential, and chemical hardness of Cs9(4-9), Cs9 (5-8), C69(4-9), and C69(5-8). 33 3.4 Energies calculated at the BPW91/6-31G level of theory of all the related defects of the single and double defected (5,5) and (10,0) SWCNTs and the perfect (5,5) and (10,0) SWCNTs. 37 3.5 Bond lengths of the single- and double-vacancy defects of the (5,5) SWCNT. 38 3.6 Bond lengths of the single- and double-vacancy defects of the (10,0) SWCNT. 39 5.1 Bond lengths, bond orders, and partial charges of the 9-membered ring of the 5-1DB defect. 70 6.1 Relative stabilities of the Pt-doped nanorods and adsorption energies of C2H4 and H 2 on the Pt-doped nanorods. 100 vi List of Figures 1.1 Structure of Ceo- 1 1.2 Illustration of possible wrapping of graphite sheet to the SWCNT. 2 1.3 Illustration of different defects on the SWCNT. 3 3.1 Structures of the single-vacancy defected C6o and C70 with partial charges of important carbon atoms. 20 3.2 Isomerization pathways of the single vacancy defected Ceo and structures of the transition states. 25 3.3 Frontier molecular orbitals of the singlet C59(4-9). 26 3.4 Alpha-spin frontier molecular orbitals of the triplet C59(5-8). 28 3.5 Frontier molecular orbitals of the singlet C69(4-9). 30 3.6 Alpha-spin frontier molecular orbitals of the triplet C69(5-8). 33 3.7 Structures of the ideal single- and double-vacancy and related defects on the (5,5) SWCNT. 35 3.8 Structures of the ideal single- and double-vacancy and related defects on the (10,0) SWCNT. 36 3.9 The change of the density of states after introducing vacancy defects on the (5,5) SWCNT and the (10,0) SWCNT. 42 3.10 Frontier molecular orbitals of the (5,5) SWCNT 1 asym. cluster. 43 3.11 Frontier molecular orbitals of the (5,5) SWCNT 2 asym. cluster. 44 3.12 Frontier molecular orbitals of the (10,0) SWCNT 1 sym. cluster. 45 3.13 Frontier molecular orbitals of the (10,0) SWCNT 2 sym. cluster. 46 4.1 Structure of the single vacancy on (5,5) SWCNT and the partial charges on the 9-membered ring of the 5-1DB defect. 52 4.2 Total and local density of states for the open-ended (5,5) SWCNT segment. 54 4.3 Total and local density of states of the open-ended (5,5) SWNCT with a 5-1DB defect. 55 4.4 Frontier molecular orbitals of Ci9 9 H2o and C9H8. 56 4.5 Reaction profiles and geometries of the transition states, intermediates, and final product of the reaction of NOs with Ci99Ff2o- 59 vii 4.6 Structure, partial charges, and frontier molecular orbitals of the substitutionally N-doped (5,5) SWCNT. 62 5.1 Single-vacancy defect on the sidewall of the (5,5) SWCNT. 68 5.2 Geometries of the transition states, intermediates, and final product of the reaction of O 3 with the active carbon atom. 72 5.3 Geometries of the transition states, intermediates, and final product of the 1,3-DC of 0 3 on the C8-C9 bond (position 1). 74 5.4 Geometries of the transition states, intermediates, and final product of the 1,3-DC of 0 3 on the C6-C7 bond (position 2). 77 5.5 Geometries of the transition states, intermediates, and final product of the 1,3-DC of 0 3 on the C4-C5 bond (position 3). 79 5.6 Geometries of the transition states, intermediates, and final product of the 1,3-DC of 0 3 on the C2-C3 bond (position 4). 80 5.7 Relative potential energy for the system during the ADMP simulation of lpsat300K. 81 6.1 Total and local density of states for nanorod Cno- 88 6.2 Total and local density of states for nanorod Ci8o- 89 6.3 Frontier molecular orbitals of nanorod Cno with the D5h symmetry. 90 6.4 Frontier molecular orbitals of nanorod C180 with the D 5 d symmetry. 91 6.5 Total and local density of states for the Pt cap-end-doped nanorod, Ci69Pt(ce). 94 6.6 Relevant frontier molecular orbitals of the Pt cap-end-doped nanorod Ci69Pt(ce). 95 6.7 Total and local density of states for the Pt cap-doped nanorod, Ci69Pt(c). 96 6.8 Frontier molecular orbitals of the Pt cap-doped nanorod, Ci69Pt(c). 97 6.9 Total and local density of states for the Pt wall-doped Nanorod, Ci69Pt(w). 98 6.10 Relevant frontier molecular orbitals of the Pt wall-doped nanorod, Ci69Pt(w). 99 6.11 Relevant bond distances of the adsorptions of C2H4 and H2 on the Pt atom in the Pt-doped nanorod, (C169Pt). 101 6.12 The molecular orbitals relevant to the interaction of the adsorbents (C2H4 or H2) with the Pt-doped nanorod (CngPt). 102 viii List of Abbreviations and Acronyms MWCNT Multi-Walled Carbon Nanotube SWCNT Single-Walled Carbon Nanotube CNTs Carbon Nanotubes DFT Density Functional Theory HF Hartree-Fock LCAOs Linear Combination of the Atomic Orbitals MO Molecular Orbital MCSCF Multiconfiguration Self-Consistent Field MRCI Multireference Configuration Interaction MP Moller-Plesset perturbation theory CC Coupled-Cluster KS Kohn-Sham TF Thomas-Fermi HK Hohenberg-Kohn LDA Local-Density Approximation GGA Generalized Gradient Approximation ZDO Zero Differential Overlap CNDO Complete Neglect of Differential Overlap INDO Intermediate Neglect of Differential Overlap NDDO Neglect of Diatomic Differential Overlap ONIOM Our own N-layered Integrated molecular Orbital and molecular Mechanics 5-1DB one pentagon and one dangling bond NBO Natural Bond Orbital PES Potential Energy Surface BPW91 Becke' s (B) exchange functional and Perdew' s (PW91) correlation functional PBC Periodic Boundary Condition HOMO Highest Occupied Molecular Orbital ix LUMO Lowest Unoccupied Molecular Orbital VEA Vertical Electron Affinity VDA Vertical Detachment Affinity AEA Adiabatic Electron Affinity vrp Vertical Ionization Potential AIP Adiabatic Ionization Potential FMOs Frontier Molecular Orbitals LDOS Local Density of States UFF Universal Force Field SLDB Same Level Different Basis Set ADMP Atom-Centered Density Matrix Propagation X Acknowledgements I would like to express my sincere gratitude to my supervisor, Dr. Yan Alexander Wang, for his guidance throughout my graduate study. I also want to thank my lab-mates, Dr. Wei Quan Tian, Dr. Baojin Zhou, Mr. Y u Zhang, Mr. Ya-Kun Chen, and Mr. Steven Hepperle for their kind help. Especially, I would like to express my appreciation to Dr. Wei Quan Tian, who has never shirked from answering my naive questions and always helped me solve all the technical problems. I also want to acknowledge the Gladys Estella Laird and the Charles A . McDowell fellowships from the Department of Chemistry at the University of British Columbia. Finally, I would like to thank my parents and parents-in-law for their love and support. I reserve my special gratitude to my wife, Xirui. Without her love and encouragement, I would not have been able to overcome the most difficult times and finish this work. Lei Liu Vancouver April, 2006 xi Chapter 1 Introduction 1.1 . Nanoscience, Fullerenes, and Carbon Nanotubes Nanoscience has been an emerging area of science since the middle of the 1980's, and it deals with objects with dimensions ranging from a few nanometers to one hundred nanometers.1 Nanosized objects are quite fascinating for several reasons. Their ultra-small size may render interesting quantum phenomena, and the nanostructures are believed to be the basis of nanoelectronics.1 During the last twenty years, fullerenes, carbon nanotubes, and quantum dots have emerged as interesting classes of nanostructures. Fullerene was discovered by Kroto, Smalley and coworkers in 1985. It was actually discovered by serendipity in their experiment which was aimed at understanding the mechanism of forming long-chain carbon atoms in interstellar space. The most common fullerene is Ceo, which consists of 60 carbon atoms. Ceo is a truncated icosahedron, with 20 hexagons and 12 pentagons (see Fig. 1.1). Each pentagon is surrounded by five hexagons, i.e., there is no direct connection between the pentagons. Since the discovery, fullerenes have attracted the attention of thousands of chemists and physicists due to their unique properties and broad potential applications, such as superconductors,3 molecular containers,4 etc. Figure 1.1. Structure o f C 6 0 . 1 The m u l t i - w a l l e d carbon nanotube ( M W C N T ) was first d iscovered b y I i j ima i n 1991 i n carbon-soot made b y an arc-discharge method . 5 A b o u t two years later, I i j ima then observed the s ing le -wal led carbon nanotube ( S W C N T ) . 6 S ince then, thousands o f scientists have j o i n e d the research field o f carbon nanotubes ( C N T s ) o w i n g to their fascinating mechanica l , thermal, and electr ical properties and var ious p romis ing applicat ions, i nc lud ing hydrogen storage, chemica l sensors, nanobioelectronics, etc. W i t h i n the last fifteen years, more than ten thousand papers about C N T s have been publ i shed w o r l d w i d e . > X Figure 1.2. Illustration of possible wrapping of graphite sheet to the S W C N T . Structure of the (5,5) S W C N T is shown on the left. Axis x is the wrapping direction and axis y is the elongation direction. A B is the chiral vector, a and b are the basis vectors. The S W C N T can be v i sua l i zed as a r o l l o f a s ingle graphite sheet, as shown i n F i g . 1.2. It is characterized b y the ch i ra l vector A B = na + nb, w h i c h is the wrapp ing direct ion o f the graphite sheet. B y convent ion, a specific S W C N T is labeled as (n,m). In the (n,m) notation, the (n,n) vectors denote armchair type S W C N T s , the (« ,0 ) vectors denote z igzag type S W C N T s , and other k inds o f (n,m) vectors denote ch i ra l type S W C N T s . Theorists also showed that the (n,m) vectors can be used to define the electr ical properties o f the 2 CNTs. The general "n - m rule" can be described as the following: (n,ri) tubes are metallic; tubes with n - m = 3N (an integral N) are narrow-gap semiconductive; and all other tubes are wide-gap semiconductive.10'11 These theoretical predictions were confirmed by experimentalists, who successfully utilized scanning tunneling microscopy * 12 13 to relate the electronic structures and the physical structures of the SWCNTs. ' 1.2. Defects on the Single-Walled Carbon Nanotube Defects exist natively or can be introduced artificially on the SWCNTs. The defects on the SWCNT are classified into topological (containing rings other than hexagons), rehybridization (hybridization of the carbon atoms between sp2 and sp3), incomplete bonding defects (vacancies, dislocations, etc.), and doping with other elements (nitrogen, boron, etc.).u Similar classification of the defects is applicable for the fullerenes. Examples of the defects are given in Fig. 1.3. The defects on the SWCNTs can induce changes to the electronic properties and the reactivity of the SWCNTs and lead to additional interesting properties and potential applications. vvb Figure 1.3. (a) Perfect S W C N T ; (b) Stone-Wales defect; (c) Rehybridization defect; (d) Vacancy defect; (e) Substitutionally B-doped defect. 3 Substitutionally N- and B-doped SWCNTs have received significant attention from both theoretical and experimental scientists. Peng et al. pointed out that the substitutionally B- and N-doped CNTs can be used as sensitive and selective chemical sensors.15 Choi et al. showed that acceptor and donor states will occur near the Fermi level after the substitutional doping of B and N into the CNTs, which leads to /?-type and n-type CNTs and broadens their application in nanoelectronics.16 Blase et al. suggested that the substitutionally B- and N-doped CNTs are possible candidates for nanosize * 17 electronic and photonic devices with various electronic properties. Vacancy defects on the SWCNTs have also drawn people's attention recently. Vacancy defects can either occur as native defects or be induced by ion or electron irradiation on the SWCNTs.1 8'1 9 It has been shown that the vacancy will introduce localized electronic states near the Fermi level and significantly change the electronic state and conducting properties of the SWCNTs. 2 0 , 2 1 Thus, the vacancy defects can lead to additional chemical reactivity for the SWCNTs and act as functionalization sites on the SWNCTs. Such reactivity of the vacancy defects was utilized to cut the SWCNTs in a 22 well-controlled oxidative way by Smalley and coworkers recently. 1.3. This Work The main focus of this thesis is applying quantum chemistry methods to understand the electronic properties and chemical relativities of the substitutionally doped and vacancy defected SWCNTs. Chapter 2 gives a brief introduction to the theoretical methods we have used. Chapter 3 focuses on the theoretical studies of the single- and double-vacancy defects on the (10,0) and (5,5) SWCNTs from the perspectives of geometry, energetics, and electronic structure. Studies of the single vacancy on fullerenes Ceo and C70 will also be performed as comparisons to the single vacancy on the SWCNTs. Chapter 4 presents the chemical reaction of nitric oxides (NOs) with the single-vacancy defect of the SWCNT. We will present the detailed reaction pathway and demonstrate this reaction to be a possible way to fabricate position controllable substitutionally doped SWCNTs with a low doping concentration under mild conditions. 4 Chapter 5 discusses the ozonization at the vacancy defect site of the SWCNTs, in which we have applied both static quantum mechanical and atom-centered density matrix propagation (ADMP) based ab initio molecular dynamical simulations. The ADMP simulations show there is a very fast dissociation pathway. This investigation will offer a microscopic understanding of the ozonization at the vacancy defect site. Chapter 6 highlights our studies of the substitutionally doped SWCNTs. Most of the work conducted in other labs concentrate on the study of the substitutionally B- and N-doped SWCNTs, while we proposed to study the precious metal Pt-doped SWCNTs. There have been a lot of experimental and theoretical studies on the precious metal doped fullerenes,23 but our study on the SWCNT system is the first of its kind. We will show that the doped Pt atom serves as the enhanced and localized active center on the SWCNT. The final chapter, Chapter 7, draws the conclusions about these projects and gives suggestions for the future work. 1.4. References (1) (a) Whitesides, G. M. Small 2005,1, 172. (b) Balzani, Z. Small 2005,1, 278. (2) Kroto, H. W.; Heath, J. R.; O'Brien, S. C ; Curl, R. F.; Smalley, R. E. Nature 1985, 318, 162. (3) Hebard, A. F.; Rosseinsky, M. J.; Haddon, R. C ; Murphy, D. W.; Glarum, S. H.; Palstra, T. T. M.; Ramirez, A. P.; Kortan, A. R. Nature 1991, 350, 600. (4) Peres, T; Cao, B. P.; Cui, W. D.; Khong, A; Cross, R. J.; Saunders, M; Lifshitz, C. Int. J. Mass Sprectrom. 2001, 210, 410. (5) Iijima,S.A/atore 1991, 55 ,^56. (6) Iijima, S.; Ichihashi, T. Nature 1993, 363, 603. (7) Liu, C ; Fan Y. Y.; Liu, M.; Cong H. T.; Cheng, H. M.; Dresselhaus, M. S. Science 1999, 286, 1127. (8) Kong, J.; Franklin, N. R.; Zhou C. W.; Chapline, M. G.; Peng, S.; Cho, K. J.; Dai, H. J. Science 2000, 287, 622. (9) Katz, E.; Willner, I.; ChemPhysChem 2004, 5, 1085. (10) N. Hamada, S. -I. Sawada, A. Oshiyama, Phys. Rev. Lett. 1992, 68, 1579. 5 (11) Dresselhaus, M. S.; Dresselhaus, G.; Eklund, P. C. Science of Fullerenes and Carbon Nanotubes; Academic Press, Inc.: San Diego, 1995; Chapter 19. (12) Wildoer, J. W. G.; Venema, L. C ; Rinzler, A. G.; Smalley, R. E.; Dekker, C. Nature 1998, 391, 59. (13) Odom, T. W.; Huang, J.-L.; Kim, P.; Lieber, C. M. Nature 1998, 391, 62. (14) Charlier, J-C. Acc. Chem. Res. 2002, 35, 1063. (15) Peng, S.; Cho, K. J. Nano Lett. 2003, 3, 513. (16) Choi, H. J.; Ihm, J.; Louie, S. G.; Cohen, M. L. Phys. ReW. Lett. 1999, 307, 158. (17) Blase, X.; Charlier, J.-C; De Vita, A.; Car, R. Appl. Phys. Lett. 1997, 70, 197. (18) (a) Kiang, C.-H.; Goddard, W. A. Ill; Beyers, R; Bethune, D. S. J. Phys. Chem. 1996, 100, 3749. (b) Zhu, Y.; Yi, T.; Zheng, B.; Cao, L. Appl. Surf. Sci. 1999, 137, 83. (19) Ajayan, P. M.; Ravikumar, V.; Charlier, J.-C. Phys. Rev. Lett. 1998, 81, 1437. (20) Zhao, J. J.; Park, H; Han, J.; Lu, J. P. J. Phys. Chem. B 2004,108, 4227. (21) Liu, L. V.; Tian, W. Q.; Wang Y. A. J. Phys. Chem. B 2006,110, 1999. (22) Ziegler, K. J.; Gu, Z.; Peng, H.; Flor, E. L.; Hauge, R. H.; Smalley, R. E. J. Am. Chem. Soc. 2005,127, 1541. (23) (a) Clemmer, D. E.; Hunter, J. M.; Shelimov, K. B.; Jarrold, M. F. Nature 1994, 372, 248. (b) Branz, W.; Billas, I. M. L.; Malinowski, N.; Tast, F.; Heinebrodt, M.; Martin, T. P.; J. Chem. Phys. 1998, 109, 3425. (c) Kong, Q.; Shen, Y.; Zhao, L.; Zhuang, J.; Qian, S.; Li, Y.; Lin, Y.; Cai, R. J. Chem. Phys. 2002, 116, 128. (d) Hayashi, A.; Xie, Y.; Poblet, J. M.; Campanera, J. M.; Lebrilla, C. B.; Balch, A. L. J. Phys. Chem. A 2004,108, 2192. 6 Chapter 2 Brief Introduction to the Theoretical Methods This chapter is intended to give a brief outline about the theoretical methods used nowadays in nanoscience. For detailed description, readers are referred to standard text books.1-5 2.1. First-Principles Methods The fundamental objective of quantum mechanical methods is to solve the time-independent Schrodinger equation, HW = E*¥, (2.1) where E is the total energy. The Hamiltonian operator, H, is defined as 77 = 7^ + 7 + V. +V +VK„, (2.2) N e Ne ee N N ' v ' where the first two terms, 7N and T , are the kinetic energy operators of the nuclei and the electrons, and the last three terms are the Coulomb interaction operators between the nuclei and the electrons, between the electrons, and between the nuclei, respectively. Expanding all the terms into their definitions, we write Eq. (2.2) as M , JV , M N 7 N N M M 7 7 H = -Y V2A- I - v , 2 - I S ^ + S I ±A±JL ( 2 3 ) A=\ 2 M A i=l 2 A=l i=l riA i=\ j>l rij A=l B>A tAB where MA is the ratio of the mass of nucleus A to the mass of an electron, ZA is the atomic number of nucleus A, riA is the distance between electron i and nucleus A, ry is the distance between electron i and electron j, rAB is the distance between nucleus A and B, N is the total number of the electrons, and M is the total number of the nuclei. The wave function, *F, solution of Eq. (2.1), contains all the information about a system. However, the exact solution is only possible for very simple systems like H2 + . Fortunately, two approximations can be utilized to greatly simplify this problem, namely the adiabatic approximation that restricts electronic wave function on a single electronic 7 surface, and the Born-Oppenheimer approximation that separates the motions of the nuclei from the electrons because the nuclei move much slower than the electrons do. So within the Born-Oppenheimer approximation, for a fixed nuclear framework, the first term in Eq. (2.3), the kinetic energy of the nuclei, can be neglected, and the last term in Eq. (2.3), the electrostatic potential between the nuclei, can be treated as a constant. The electronic Hamiltonian is then defined by the remaining terms in Eq. (2.3): N N N 1 M N 7 i\ J\ i H =-E - V. 2-Z S ^ + I I -A=\ /=1 HA I=1 j>\ rij and the electronic Schrddinger equation is (2.4) (2.5) where is the electronic wave function, which explicitly depends on the electron coordinates {?.} but parametrically depends on the nuclear coordinates{&A}. Hence, the total energy of a fixed nuclear structure is M M 7 y E =E + 1 £ t 0 t a l 6 A-l B>A rAB (2.6) Eqs. (2.4)-(2.6) constitute the problem of electronic structure theory. If only fundamental physical constants are used in solving the electronic Schrodinger equation, first-principles methods emerge. Based on the choice of the basic variational variables, first-principles methods have two flavors: wave-function-based ab initio methods and electron-density-based density functional theory (DFT).6"9 2.1.1. Hartree-Fock and Post-Hartree-Fock Methods The Hartree-Fock (HF) method is fundamental to the wave-function-based ab initio methods. It is the starting point for more advanced electronic structure methods. In the HF method, the wave function is approximated by a single Slater determinant: A-i (1) *2(1) ••• XNO) Xl(2) *2(2) . . . A'.v(2) \\r — 1 A ' 2 ( A 0 (2.7) 8 for an ./V-electron system, where%t is the z'th spin orbital and 1 / V/V! is the normalization constant. The way to find the approximation to the ground-state energy is to use the variational principle, which states that energy from the best trial wave function will give an upper limit of the exact non-relativistic ground-state energy of the system. Following the variational principle, the HF equation can be derived, /(1)*,(1) = *,*,(!), (2.8) where /(l) is the Fock operator. The Fock operator is an effective one-electron operator, 1 My / ( D — ^ - E ^ + v"^) , (2.9) 2 A=\ riA where vHF(i)is the HF potential, which depends on all the occupied spin orbitals. The HF potential can be considered as the mean potential field experienced by the ith electron, v^iD^iJj-Kj), (2.10) j where J. is the Coulomb operator and K. is the exchange operator for two-electron interactions. Most of the CPU time is spent in calculating the two-electron integrals due to these two operators. It is quite clear that the Fock operator depends on its eigenfunctions, so solving the HF equations must be an iterative process, often called the self-consistent field. The first two terms of Eq. (2.9) can be defined as the core Hamiltonian operator h(i). So, Eq. (2.8) can be rewritten as m^hw+f^'j.-K.). (2.ii) j The linear combination of the atomic orbitals (LCAOs) can be then introduced as the molecular orbitals (MOs), Zi=YiCai<Pa> ( 2 - 1 2 ) a and the HF equation is recasted as the Roothaan-Hall equations in the atomic orbital basis set, FC = SCe, (2.13) 9 where F is the Fock matrix, S is the overlap matrix, C is the MO coefficient matrix, and e is the diagonal matrix of the orbital energies. Now, solving of the HF equations becomes solving the Roothaan-Hall matrix equations.10 Although the HF method is a mean-field theory, it can often give a good approximation to the ground-state wave functions and show qualitatively correct information about many materials and compounds. However, the HF method is not capable of describing highly correlated systems, because of neglecting the electron correlation effects by assuming the single determinant form of the wave function. High-level theories, such as multiconfiguration self-consistent field (MCSCF), 1 1 multireference configuration interaction (MRCI),1 2 Moller-Plesset (MP) pertubation theory,13 or coupled-cluster (CC) methods,14 are then necessary to incorporate electron correlation effects. Such advanced methods are developed to make improvement over the HF method, so they are also called the post-Hartree-Fock theories. Reader are referred to the references for detailed descriptions.1-5 2.1.2. Density Functional Theory The conventional ab initio methods discussed in section 2.1.1 use the wave function as the central variational quantity. The computational cost scales formally higher than the fourth power of the number of basis functions to incorporate the electron correlation effects into the HF approximation. However, the modern DFT, which uses the electron density p(f) as the central variational quantity, scales as the third power of the number of basis functions within the Kohn-Sham (KS) scheme.7 Most importantly, electron correlation effects are incorporated in DFT. The first idea of DFT can be dated back to the Thomas-Fermi (TF) model proposed by Thomas15 and Fermi16 in the 1920's, 10 J . J\R-r | 2 JJ rn where the first term is the TF kinetic energy functional, which is based on the results of quantum statistical mechanics of the uniform electron gas, and the second term and the last term are the classical nuclear-electron Coulomb attraction and classical electron-electron Coulomb repulsion, respectively. Clearly, there is no dependence on the wave 10 function in Eq. (2.14). But the TF model is only of historical interest, due to its inability to treat chemical systems. The starting point of the modern DFT is the publication of the landmark paper by Hohenberg and Kohn in 1964.6 Within this paper, the first Hohenberg-Kohn (HK) theorem states that there is a one-to-one mapping between the ground-state electron density, the external potential Vext(r), and the ground-state wave function. So, it implies that all the properties of a system are functionals of the electron density. The second HK theorem states that the true ground-state electron density is the density that minimizes the ground-state energy as a functional of the electron density. The second HK theorem provides a variational principle to identify the ground-state electron density. The kinetic energy has a large contribution to the total energy. So, it is very important to calculate the kinetic energy accurately. Actually, the failure of quantitatively treating the kinetic energy in the TF model is the main reason for the ignorance of this model in the chemistry community. In 1965,7 Kohn and Sham introduced the celebrated Kohn-Sham (KS) approach to treat the kinetic energy almost exactly, which is the second milestone in the development of the modern DFT. The basic idea of the KS approach is to build a fictitious reference system of non-interacting electrons, which has the same ground-state total electron density as the real interacting system. Kohn and Sham suggested calculating the kinetic energy of the reference system by T.=-\t,{z,\Vi\z,)> (2-15> £ 1=1 where %. is the spin orbital of the non-interacting reference system. These orbitals are normally called the KS orbitals. The total energy is then expressed as E [ p ( r ) ] = T t [ p i r ) ] + E N ^ p i r ) ] + J [ p ( r ) ] + E„lp(f)]. (2.16) Within the orbital expression, Eq. (2.16) can be rewritten as N ( 1 M y N E[p(r)] = £ (Xl\-Ly\Xl)-(Xl\Z^-\zl)  (2.17) 1=1 V Z A=\ riA Z 1=1 y=l rn where the first term is the kinetic energy of the reference system, the second term is the nuclei electron Coulomb attraction energy, the third term is the classical electron-electron 11 interaction energy, and the last term is the exchange-correlation energy, which includes the non-classical self-interaction energy correction, non-classical electron-electron interaction energy and the correlation part of the true kinetic energy. By applying the variational principle to find the optimal KS orbitals that minimize E[p(f)], we can derive the pseudoeigenvalue KS equation: r-^,-t—+i£S^2 + yx]z^slzlt (2.18) where Vxc is the exchange-correlation potential. Normally, the form of the exchange-correlation energy and the explicit expression of the exchange-correlation potential are unknown. Vxc is formally defined as the functional derivative of the exchange-correlation energy, SF dp Because the exact forms of the exchange-correlation functionals are unknown, approximations have to be made. The exchange-correlation functionals are mainly modeled in three ways: the local-density approximation (LDA), the generalized gradient approximation (GGA), and the hybrid approach. In the LDA, the energy of a system depends on the local value of the electron density. In the GGA, the energy of a system depends not only on the local value of the electron density but also on the gradients of the electron density of different orders. While in the hybrid DFT, the exact exchange defined in terms of the KS orbitals (just like the one used in the HF approximation defined in terms of the HF orbitals) is admixed. Such a hybrid approach of mixing the exact exchange further improves the prediction accuracy of DFT method in physical and chemical applications. 2.2. Semiempirical Quantum Mechanical Methods As mentioned in section 2.1.1, the most time consuming procedure in the HF method is calculating the two-electron integrals. Semiempirical quantum mechanical methods, which adopt the framework of the HF approximation, were developed to address this problem. 12 In all modern semiempirical methods, only the valence electrons are considered explicitly; the core electrons are assumed to be sufficiently invariant to different chemical environmental changes and are treated implicitly by reducing the nuclear charges. Each valence electron is described by only one Slater-type atomic orbital to further reduce the computational cost. The evaluation of two electron integrals is simplified by parameters fitted to experimental date, such as ionization energies of atoms or dipole moments of molecules. The basic approximation in semiempirical methods is the zero differential overlap (ZDO) approximation, in which all the products of basis functions of the same electron on different atoms are neglected. The remaining integrals are parameterized and fitted through benchmarking with available experimental data. Different semiempirical methods emerged depending on how the approximations in the neglect of two-electron integrals and in the fitting of parameters are made. Among all variants of the ZDO approximation, the complete neglect of differential overlap (CNDO) method is the crudest approximation. In the CNDO method, only Coulomb one-center and two-center two-electron integrals remain. With some more refined ZDO approximations, the intermediate neglect of differential overlap (INDO) method and the neglect of diatomic differential overlap (NDDO) methods {e.g., MNDO, 1 7 AMI, 1 8 and P M 3 1 9 ) emerged with much-improved accuracy. In this thesis, we have used AMI and P M 3 in conjugation with DFT methods in the ONIOM scheme. 2.3. O N I O M Model The large size of nano-systems and the scaling factor of the computational cost limit the application of quantum mechanical methods. One option is using parallel plane wave 20 21 quantum mechanical packages, such as the widely used CPMD or VASP packages. But this demands a lot of computational resources. Another way is using the ONIOM model,22'23 which is widely used in studying the CNTs 2 4 - 2 6 The essential idea of the ONIOM model is as follows. In most cases, chemical reactions are localized in the proximity of the active site. Such a localized nature of chemical reactions legitimizes an accurate treatment of the active site with a high-level theory, while the surroundings (the rest of the chemical system) can be treated with a low-level theory. This embedding approach requires relatively few computing resources but still keeps the essential 13 environmental effects exerted on the active site by the surroundings. The basic formula of ONIOM can be written as E(ONIOM, real) = E(high, M) + E(low, real) - E(low, M), (2.20) where E(ONIOM, real) is the total energy of the system, E(low, real) is the energy of the real system at the low-level theory, E(low,M) is the energy of the model system (the active site) at the low-level theory, and E(high,M) is the energy of the model system at the high-level theory. The link atom is a buffer atom in the model system replacing the actual atom in the real system connected to the model system. For very large systems, the low-level theory for the overall real system is usually semiempirical quantum mechanical methods or molecular mechanics based on force fields. In molecular mechanics, the electronic structure of the system is not explicitly considered. The interatomic interactions are divided into bond, angle, torsion angle, and weak interactions, including the van der Waals interaction. Such interactions are parameterized through fitting to the available experimental data or any high-level quantum mechanical calculation results. Depending on the fitting procedure, different parameterizations give rise to various force 27 fields for the interatomic interactions. The most popular force fields are Amber, Charmm,28 MM3, 2 9 U F F , 3 0 etc. 2.4. References (1) Szabo, A; Ostlund, N. S. "Modern Quantum Chemistry." Dover, New York, 1996. (2) McWeeny, R. "Methods of Molecular Quantum Mechanics," 2nd Ed., Academic, New York, 1992. (3) Jensen, F. "Introduction to Computational Chemistry." Wiley, New York, 1998. (4) Young, D. C. "Computational Chemistry: A Practical Guide for Applying Techniques to Real World Problems." Wiley, New York, 2001. (5) Cramer, C. J. "Essentials of Computational Chemistry: Theories and Models." Wiley, New York, 2002. (6) Hohenberg, P.; Kohn, W. Phys. Rev. 1964,136, B864. (7) Kohn, W.; Sham, L. J. Phys. Rev. 1965, 40, 1133. 14 (8) Parr, R. G.; Yang, W. "Density-Functional Theory of Atoms and Molecules." Oxford University Press, New York, 1989. (9) Wang, Y. A.; Carter, E. A. in "Theoretical Methods in Condensed Phase Chemistry" (Schwartz, S. D. Ed.), p. 117. Kluwer, Dordrecht, 2000. (10) Roothaan, C. C. J. Rev. Mod. Phys. 1951, 23, 69. (11) Roos, B. O. in "Advances in Chemical Physics: Ab Initio Methods in Quantum Chemistry Part II" (K. P. Lawley, Ed.), Vol. 69, p. 1. Wiley, New York, 1987. (12) Shavitt, I. in "Modern Theoretical Chemistry" (Schaefer, H. F. Ed.), Vol. 3, p. 189. Plenum, New York, 1977. 5) Moller, C ; Plesset, M. S., Phys. Rev. 1934, 4(5,618. 1) Cizek, J., J. Chem. Phys. 1966, 45, 4256. 5) Thomas, L. PL, Proc. Camb. PhU. Soc. 1927, 23, 542. 5) Fermi, E., Rend. Accad. Lincei 1927, 6, 602. 7) Dewar, M. J. S.; Thiel, W., J. Am. Chem. Soc. 1977, 99, 4899. I) Dewar, M. J. S; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P., J. Am. Chem. Soc. 1985, 107, 3902. )) Stewart, J. J. P., J. Comput. Chem. 1989, 10, 209; (b) Stewart, J. J. P., J. Comput. Chem. 1989,10, 221. )) CPMD, Copyright IBM Corp 1990-2001, Copyright MPIfiir Festkorperforschung Stuttgart 1997-2004. I) Kresse G.; Hafner, J. Phys. Rev. B 1993, 47, 558. I) Maseras F.; Morokuma, K. J. Comp. Chem. 1995,16, 1170. 3) Morokuma, K. Bull. Korean Chem. Soc. 2003, 24, 797. X) Walch, S. P. Chem. Phys. Lett. 2003, 374, 501. 5) Ricca, A.; Bauschlicher, C. W.; Maiti, A. Phys. Rev. B 2003, 68, 035433. 5) Lu, X.; Tian, F.; Xu, X.; Wang, N.; Zhang, Q. J. Am. Chem. Soc. 2003,125, 10459. 7) Cornell, W. D.; Cieplak, P.l; Bayly, C. I.; Gould, I. R.; Merz K. M. Jr., Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollman, P. A. J. Am. Chem. Soc. 1995, i i 7 , 5179. (28) Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.; Swaminathan, S.; Karplus, M. J. Comp. Chem. 1983, 4, 187. 15 (29) Allinger, N. L.; Yuh, Y. H.; Lii, J.-H. J. Am. Chem. Soc. 1989, 111, 8551. (30) Rappe, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard III, W. A.; Skiff, W. M. J. Am. Chem. Soc. 1992,114, 10024. 16 Chapter 3 Ab Initio Studies of Vacancy Defected Fullerenes and Single-Walled Carbon Nanotubes 3.1. Introduction Since the discoveries of fullerenes by Smalley and co-workers in 19851 and carbon nanotubes by Iijima in the early 1990s,2 thousands of scientists all over the world have been attracted to the research field of fullerenes and carbon nanotubes due to their interesting properties and promising applications, for example, fullerenes as superconductors3 and HIV protease inhibitors,4 and carbon nanotubes as chemical sensors, nano-scale electronics, hydrogen storage materials, etc. Defects can exist natively or can be introduced on the carbon nanotubes and fullerenes. Defects on the single-walled carbon nanotubes (SWCNTs) are classified into topological (containing rings other than hexagons), rehybridization (hybridization of the carbon atoms between sp2 and sp3), incomplete bonding defects (vacancies, dislocations, etc.), and doping with other elements (nitrogen, boron, etc.).s Defects on fullerenes can also be categorized similarly. For example, the most common native defects on fullerenes, the Stone-Wales defect,9 formed by rotating the central bond of a pyracylene patch 90° on the surface, are the topological defects. Even-number vacancy defected C6o, such as C58, C56, and C54, can be made through laser irradiation.10 Odd-number vacancy defected C60, such as C 5 9 , C57, C55, and C53, have been produced from the laser desorption ionization of C 6 0 O . 1 1 All such clusters have incomplete bonding defects. Among all these kinds of defects on the fullerenes and the SWCNTs, vacancy defects have been shown to have very interesting properties and applications. The vacancies on the defected fullerenes were proposed to serve as the windows for atoms or small molecules to enter the cage in the endohedral fullerene chemistry.12 Vacancies on the carbon nanotubes can be created by ion or electron irradiation.13'14 The vacancies on the 17 SWCNTs introduce localized electronic states on the SWCNTs for chemical reactions,15 can play the role of chemical connectors between two defected nanotubes16 and the 17 18 mediating role in the substitutional doping of N on the sidewall of the SWCNTs. ' Several theoretical studies have been devoted to investigate the properties of the vacancy defected fullerene Ceo-19-24 The structures and stabilities of all the isomers of C59, C58, and C57 have been systematically studied with ab initio methods.22,24 It was reported that triplet Cs9(5-8) is the more stable cluster of the two possible isomers of C59: Cs9(5-8) and C59(4-9) (Figs. 3.1b and 3.1c). The initial singlet Cs9(4-9) isomer transforms into the singlet C59(5-8) structure during unrestricted DFT optimization.24 It is worthwhile to re-exam the electronic properties of Cs9(5-8) and Cs9(4-9) and explore the isomerization pathways between these two isomers. For comparison, we also study the single-vacancy defected C70, which is the second abundant fullerene after C6o-The vacancies on the carbon nanotubes have also been studied recently,14-18'25-32 including the effect of vacancies on the conductance,25-27 on the mechanical 29 30 15 28 * properties, ' and on the electronic properties of carbon nanotubes. ' During the process of vacancy creation, energetic electrons produce mostly single vacancies, while heavy ion irradiation produces mostly multi-vacancies.33 Removing one or more carbon atoms from the carbon nanotube first produces ideal vacancies (see Figs. 3.1a and 3.Id), which are unstable. Ajayan et al. have shown that the carbon nanotubes will respond to the loss of carbon atoms by surface reconstruction, which will create vacancy related point defects.14 The nature of single vacancy and their related point defects has been studied systematically by Lu et al. with the tight-binding method.32 Double and triple vacancies and related defects have been studied by Mielke et al. and Sammalkorpi et al.30 In these studies, however, the ground states of the defected nanotubes are not mentioned and the structural information has some contradictions. For example, it was reported in Lu's paper that the symmetric 5-1DB (one pentagon and one dangling bond) defects (Fig. 3.7c) do not exist for the armchair type SWCNT: even with the symmetric 5-1DB defect geometry as the initial guess, the asymmetric 5-1DB defect (Fig. 3.7b) was obtained easily. However, the symmetric 5-1DB defect on the (5,5) SWCNT was shown to be stable in Mielke's paper.29 To resolve such conflict, we will investigate the 18 electronic properties of the single and double vacancies on the SWCNTs with ab initio methods. (a) Ideal single vacancy on C 6 0 (b) C 5 9(4-9) (c) C59(5-8) (d) Ideal single vacancy on C 7 0 (e) C 6 9(4-9) (f) C69(5-8) 0.025 ^ -0051 -0.098 0.083 0.056 0.056 0.015 ^ -0.049 -0.130_ i 0.25 -0.098 0.025^ -0.051 0.037 0.037 -0.130 0.015""' -0.049 (g) Partial charges o f the carbon atoms in the nonagon o f the singlet (left) and triplet (right) C 5 9(4-9) (h) Partial charges o f the carbon atoms in the octagon o f the singlet (left) and triplet (right) C59(5-8) 19 0.025 »„. "0066 -0.093 0.114 0.063 0.063 -0.093 0 . 0 2 5 ^ -0.066 0.029 ^ -0065 -0.129 c 0.260 0.047 0.047 -0.129 0.029'" ' -0.065 (i) Partial charges o f the carbon atoms in the nonagon o f the singlet (left) and triplet (right) C6c>(4-9) 0.022 -0.071 -0.027 -0.009 0.166 %J! 7^0.235 - 0 . 0 2 3 \ - £fk -0.080 Tm^yteM -0.08 "0.019 0.033 (j) Partial charges o f the carbon atoms in the octagon o f the singlet (left) and triplet (right) C69(5-8) F i g u r e 3.1. Structures o f the single-vacancy defected C 6 0 and C 7 0 with partial charges o f important carbon atoms. 3.2. Computational Details Due to the icosahedral symmetry, all the carbon atoms are equivalent in C6o- While in C70, there are five different kinds of symmetrically distinct carbon atoms, thus resulting in many possibilities for vacancy. For simplicity, we will only consider the situation that the missing carbon atom located in the pentagon at the pole of C70. Geometry optimizations are performed with the hybrid density functional method, B3LYP, 3 4' 3 5 with the standard 6-31G(d) basis set. Single-point calculations at the B3LYP/6-311G(d) level of theory are performed with the B3LYP/6-31G(d) optimized geometries. Natural bond orbital (NBO)36 analysis has been performed to determine the partial charge distribution and the bonding characters of these systems. B3LYP/6-31G is employed to study the isomerization between Cs9(5-8) and Cs9(4-9) on the singlet and triplet potential energy surfaces (PESs). The (5,5) and (10,0) SWCNTs are chosen to represent the typical armchair and zigzag 20 SWCNTs, respectively. Becke's (B) exchange functional and Perdew's (PW91) correlation functional based on the generalized gradient approximation (GGA) combined with the 6-31G basis set are employed in geometry optimization and property prediction. The SWCNTs are modeled by imposing periodic boundary conditions (PBCs). The unit cells contains about 100 and 120 carbon atoms for the (5,5) and (10,0) SWCNTs, respectively. The integrations of k space are achieved by using the default numbers of k points, 27 and 26 for the (5,5) and (10,0) SWCNTs, respectively. Spin-unrestricted calculations are carried out for the singlet and triplet electronic states, and spin-restricted calculations are also done for the singlet electronic states. All 30 calculations are performed with the Gaussian 03 package. 3.3. Results and Discussions 3.3.1. Vacancy Defected Fullerenes There are two types of bonds in Ceo, the shorter double bonds and the longer single bonds, which are predicted to be 1.395 A and 1.453 A at the B3LYP/6-31G (d) level of theory, respectively, in good agreement with the experiments (1.390 A and 1.453 A, respectively).40 The good performance of the B3LYP/6-31G(d) method in treating C6o gives us confidence in its application. The structure of the ideal single vacancy C6o and C70 and the related point defects are shown in Fig. 3.1, with important carbon atoms labelled numerically. In C59, CI forms a bond with C5 or C8 leading to the C59(5-8) isomer (5 and 8 denoting the newly forming pentagon and octagon), and C5 forms a bond with C8 leading to the C59(4-9) isomer (4 and 9 denoting the newly forming rectangle and nonagon). In C69, CI forms a bond with C5 or C8 leading to the C69(5-8) isomer, and C5 forms a bond with C8 leading to the C69(4-9) isomer. There is one unsaturated carbon atom in each isomer. The unsaturated carbon atom locates on the pentagon for the 4-9 type defects or on the hexagon for the 5-8 type defects. Important bond lengths are tabulated in Table 3.1. Comparing with the HF/3-21G and B3LYP/3-21G results22 for the Cs9(4-9) isomer, we find that most bonds are shorter in our B3LYP/6-31G(d) results due to the larger basis set we used. Table 3.2 lists the total energies and cohesive energies of the isomers computed at the B3LYP/6-311G(d)//B3LYP/6-31G(d) level of theory. For the C59(4-9) isomer, the singlet state is 21 Table 3.1. Bond lengths (in A) of the single vacancy defected C 6 0 and C 7 0 . C 5 9(4-9) C 5 9(5-8) C 6 9(4-9) C 6 9(5-8) HF/3-21G a B 3 L Y P / 3 - 2 1 G 3 B3LYP/6-31G(d) B3LYP/6-31G(d) B3LYP/6-31G(d) B3LYP/6-31G(d) Bonds S(R) b S(R) T ( U ) b S(R) S(U) T(U) S(R) S(U) T(U) S(R) S(U) T(U) S(R) S(U) T(U) C 1 - C 2 1.478 1.450 1.415 1.441 1.440 1.407 1.526 1.526 1.526 1.434 1.434 1.407 1.483 1.483 1.463 C 1 - C 5 1.530 1.530 1.528 C 1 - C 8 1.451 1.451 1.494 C l - C l l 1.478 1.450 1.415 1.441 1.440 1.407 1.495 1.495 1.421 1.434 1.434 1.407 1.446 1.446 1.488 C 2 - C 3 1.353 1.401 1.391 1.389 1.389 1.398 1.462 1.462 1.477 1.382 1.382 1.391 1.370 1.370 1.372 C 3 - C 4 1.494 1.485 1.483 1.479 1.479 1.479 1.448 1.448 1.458 1.469 1.469 1.470 1.448 1.448 1.452 C 4 - C 5 1.362 1.400 1.390 1.396 1.396 1.401 1.420 1.420 1.399 1.397 1.397 1.403 1.410 1.410 1.419 C 5 - C 6 1.458 1.479 1.467 1.453 1.453 1.454 1.378 1.378 1.357 1.454 1.454 1.453 1.457 1.457 1.472 C 6 - C 7 1.427 1.455 1.439 1.431 1.431 1.428 1.435 1.435 1.466 1.430 1.430 1.426 1.442 1.442 1.452 C 7 - C 8 1.458 1.479 1.467 1.453 1.453 1.454 1.426 1.426 1.411 1.454 1.454 1.453 1.418 1.418 1.397 C 5 - C 8 1.636 1.646 1.644 1.599 1.597 1.608 1.582 1.582 1.591 C 8 - C 9 1.362 1.400 1.390 1.396 1.396 1.401 1.488 1.488 1.468 1.397 1.397 1.403 1.375 1.375 1.358 C9-C10 1.494 1.485 1.483 1.479 1.479 1.479 1.440 1.440 1.378 1.469 1.469 1.470 1.431 1.431 1.459 C10-C11 1.353 1.401 1.391 1.389 1.389 1.398 1.427 1.427 1.456 1.382 1.382 1.391 1.416 1.416 1.401 'ref. 22. b R : Spin-restricted; U : Spin-unrestricted; S: Singlet; T: Triplet 0.82 kcal/mol more stable than the triplet state; for the Cs9(5-8) isomer, the triplet state is 3.39 kcal/mol more stable than the singlet state; for the C69(4-9) isomer, the singlet state is 2.32 kcal/mol lower in energy than the triplet state; and for the C69(5-8) isomer, the triplet state is 2.57 kcal/mol lower in energy than the singlet state. Thus, the triplet Cs9(5-8) and C69(5-8) isomers are the most stable isomer for C59 and C69, respectively. Single-vacancy defected C70 is more stable than single-vacancy defected C60 according to the cohesive energies. Most of our results for C59 are consistent with Ref. 24, except that Ref. 24 reported a higher spin-contamination in the spin-unrestricted singlet calculation of C59(5-8) and the transformation of the open-shell singlet Cs9(4-9) structure into the singlet open-shell C59(5-8) structure. One has to bear in mind that such a small energy difference within the present DFT methods can only reach a conclusion that these electronic states have very similar stability. For the singlet Cs9(4-9), the dangling carbon atom CI forms single bonds with C2 and C l l . The bond lengths of C1-C2 and C l - C l l are both 1.441 A because of the C s symmetry. Based on the NBO analysis, there are two 2-center a NBOs involving CI: ff(Cl-C2) = 0.668 CI (sp233) + 0.745 C2 (sp209) and a(Cl-Cll) with the same bonding character due to the C s symmetry of Cs9(4-9). There are two lone-pair-type NBOs for CI: one is an sp150 hybridized orbital with 1.79 electrons and the other one is a pure p orbital with 0.36 electrons. The partial charges of the carbon atoms on the nonagon are shown in Fig. 3.1g for singlet and triplet Cs9(4-9). CI has +0.083 charge and its two neighbours have -0.098 charges in the singlet case, while in the triplet case, CI has a much larger positive charge (+0.251) and its two neighbours also have larger negative charges (-0.130). The relevant frontier molecular orbitals (FMOs) of the singlet C59(4-9) are shown in Fig. 3.2. The H0M0-1 (Fig. 3.2e) is mainly the lone-pair sp150 hybridized orbital and the LUMO (Fig. 3.2g) is mainly the lone-pair p unhybridized orbital. There is nearly no electron population on CI in the HOMO (Fig. 3.2f). The HOMO energy of the singlet C59(4-9) is -6.15 eV, higher than that of the perfect C 6 0 (-6.40 eV); the LUMO energy of the singlet C59(4-9) is -4.22 eV, lower than that of the perfect C6o (-3.68 eV). Thus, the HOMO-LUMO gap is only 1.93 eV, smaller than that of the perfect C6o (2.72 eV). For the triplet C5g(5-8), the dangling carbon atom C5 forms a single bond with C4 and a double bond with C6. The bond lengths of C5-C4 and C5=C6 are 1.399 A and 1.357 A, 23 Table 3.2. Energies of C 6 0 , C S 9(4-9), C 5 9(5-8), C 7 0 , C 6 9(4-9), and C 6 9(5-8) at the B3LYP/6-31 lG(d)//B3LYP/6-31G(d) level of theory. Etotai (Hartree) E s a e (kcal/mol) A E 1 (kcal/mol) Model S ( R a ) S ( U b ) T ( U C ) S (R) S (U) T ( U ) S(R) S ( U ) T ( U ) C60 -2286.5888 159.27 C 5 9(4-9) -2248.2431 -2248.2431 (0) d -2248.2418 (2.05) 156.76 156.76 156.75 2.51 2.51 2.52 C 5 9(5-8) -2248.2690 -2248.2690 (0) -2248.2744 (2.05) 157.04 157.04 157.09 2.23 2.23 2.18 C70 -2667.7857 160.16 C 6 9(4-9) -2629.4433 -2629.4433 (0) -2629.4396 (2.04) 158.05 158.05 158.02 2.11 2.11 2.14 C 6 9(5-8) -2629.4629 -2629.4629 (0) -2629.4670 (2.05) 158.23 158.23 158.27 1.93 1.93 1.89 aSpin-restricted singlet results. bSpin-unrestricted singlet results. cSpin-unrestricted triplet results. dThe values in the parentheses are the <S2> values. eThe stability energy per atom, defined as EJn, where E B is the energy difference between the isolated carbon atoms and the cluster and n is the total number of carbon atoms in the cluster. f A E = E s a (perfect fullerene) - E s a (defected fullerene). (a) Backbone (side view) (b) H O M C M (-6.60) (c) H O M O - 3 (-6.51) (d) H O M O - 2 (-6.45) (e) H O M O - 1 (-6.28) (f) H O M O (-6.15) (g) L U M O (-4.22) (h) L U M O + 1 (-3.79) (i) L U M O + 2 (-3.56) (j) L U M O + 3 (-3.42) (k) L U M O + 4 (-2.52) F i g u r e 3.2. Frontier molecular orbitals o f singlet C 5 9 ( 4 - 9 ) . H O M O - n (p e V ) is the nth molecular orbital below the H O M O with orbital energy p e V . L U M O + m (q e V ) is the with molecular orbital above the L U M O with orbital energy q e V . respectively. The point group of the triplet C 5 9 ( 5 - 8 ) is Ci. Based on the NBO analysis, there are three 2-center NBOs involving C 5 . Two NBOs represent the double bond of C 5 = C 6 : ff(C5-C6) = 0 . 6 8 4 C 5 (sp1 5 1 ) + 0 . 7 2 9 C 6 (sphS2) and T T ( C 5 - C 6 ) = 0 . 7 2 0 C 5 (sp99") + 0 . 7 2 9 C 6 (sp99") and the other a NBO represents the single bond of C 5 - C 4 : CT(C5-C4) = 0 . 6 8 5 C 5 (sph62) + 0 . 7 2 9 C 4 (sp211). There are also two lone-pair-type 25 NBOs for C5: one is a sp hybridized orbital with 0.947 electrons in alpha spin and the other one is an almost pure p orbital with 0.062 electrons in beta spin. The alpha-spin FMOs are shown in Fig. 3.3. The HOMO-4 and the HOMO contain the lone-pair p unhybridized orbitals (Figs. 3.3b and 3.3f). The orbital energy of the alpha-spin HOMO of triplet C 5 9(5-8) is -5.78 eV, higher than that of perfect C 6 0 (-6.40 eV); the orbital energy of alpha-spin LUMO of triplet Cs9(5-8) is -3.77 eV, just a little bit (a) Backbone (side view) (b) H O M O - 4 (-6.58) (c) H O M O - 3 (-6.44) (d) H O M O - 2 (-6.40) (e) H O M O - 1 (-6.17) (f) H O M O (-5.78) (g) L U M O (-3.77) (h) L U M O + 1 (-3.66) (i) L U M O + 2 (-3.37) (j) L U M O + 3 (-2.69) (k) L U M O + 4 (-2.56) F i g u r e 3.3. A lpha- sp in frontier molecular orbitals o f triplet C 5 9 ( 5 - 8 ) . H O M O - w (p e V ) is the nth molecular orbital below the H O M O with orbital energy p e V . L U M O + / n (q e V ) is the mth molecular orbital above the L U M O with orbital energy q e V . 26 lower than that of perfect C6o (-3.68 eV). The orbital energy of the beta-spin HOMO of triplet C59(5-8) is -6.10 eV, higher than that of the perfect C6o (-6.40 eV); the orbital energy of the beta-spin LUMO of the triplet C59(5-8) is -4.41 eV, lower than that of perfect C6o (-3.68 eV). Thus, the alpha-spin HOMO-LUMO gap (2.01 eV) and the beta-spin HOMO-LUMO gap (1.69 eV) are both smaller than that of the perfect C 6 0 (2.72 eV). For singlet C69(4-9), the dangling carbon atom CI forms single bonds with C2 and C l l . The bond lengths of C1-C2 and C l - C l l are both 1.434 A because of the C s symmetry. Based on the NBO analysis, there are two 2-center a NBOs involving CI: a(Cl-C2) = 0.668 CI (sp232) + 0.744 C2 (sp2U) and a(Cl-Cll) with the same bonding properties due to the C s symmetry of C69(4-9). There are two lone-pair-type NBOs for CI: one is an sp152 hybridized orbital with 1.76 electrons and the other one is a pure p orbital with 0.35 electrons. The partial charges of the carbon atoms on the nonagon are shown in Fig. 3.1i for singlet and triplet C69(4-9). CI has +0.144 charge and its two neighbours have -0.093 charges in the singlet case, while in the triplet case, CI has +0.260 charge, and its two neighbours have -0.129 charges. The relevant FMOs in the singlet C69(4-9) are shown in Fig. 3.4. The HOMO-4 (Fig. 3.4b) is the lone-pair sp1'52 hybridized orbital and the LUMO (Fig. 3.4g) contains the lone-pair unhybridized p orbital. The HOMO energy of singlet C69(4-9) is -6.22 eV, just a little bit higher than that of perfect C70 ( -6.34 eV); the LUMO energy of singlet C69(4-9) is -4.36 eV, lower than that of perfect C 7 0 (-3.67 eV). Thus, the HOMO-LUMO gap is only 2.15 eV, smaller than that of perfect C 7 0 (2.67 eV). For triplet C69(5-8), the dangling carbon atom C8 forms single bond with C7 and double bond with C9. The bond lengths of C8-C7 and C8=C9 are 1.397 A and 1.358 A , respectively. The point group of the triplet C69(5-8) is Ci. Based on the NBO analysis, there are three 2-center NBOs involving C8. Two NBOs represents the C8=C9 double bond: a(C8-C9) = 0.684 C8 (sp1-53) + 0.729 C9 (sp1'81) and 7i(C8-C9) = 0.713 C8 (sp99") + 0.701 C9 (sp9999); and the other o NBO represents the C8-C7 single bond: a(C8-C7) = 0.729 C7 (sp2A1) + 0.685C8 (sp161). There are also two lone-pair-type NBOs for CI: one is a sp3'53 hybridized orbital with 0.947 electrons in alpha spin and the other 27 (a) Backbone (side view) (b) H O M O - 4 (-6.58) (c) H O M O - 3 (-6.44) (d) H O M O - 2 (-6.40) (e) H O M O - 1 (-6.17) (f) H O M O (-5.78) (g) L U M O (-4.37) (h) L U M O + 1 (-3.60) (i) L U M O + 2 (-3.53) (j) L U M O + 3 (-3.36) (k) L U M O + 4 (-3.21) F i g u r e 3.4. Frontier molecular orbitals o f singlet C 6 9 ( 4 - 9 ) . H O M O - n (p e V ) is the nth molecular orbital below the H O M O with orbital energy p e V . L U M O + n z (q e V ) is the /nth molecular orbital above the L U M O with orbital energy q e V . one is an almost pure p orbital with 0.395 electrons in beta spin. The HOMO contains the lone-pair p unhybridized orbital (Fig. 3.5f)- The HOMO-LUMO gap is 1.33 eV, much smaller than that of perfect C70 (2.67 eV). The orbital energy of the alpha-spin HOMO of triplet 0-69(5-8) is -5.95 eV, higher than that of perfect C-60 (-6.34 eV); the orbital energy of the alpha-spin LUMO of triplet C69(5-8) is -3.77 eV, a little bit lower than that of perfect C 7 0 (-3.67 eV). The orbital energy of the beta-spin HOMO of triplet C69(5-8) is 28 -6.04 eV, higher than that of perfect C6o (-6.34 eV); the beta-spin LUMO energy of the triplet C69(5-8) is -4.60 eV, lower than that of the perfect C 7 0 (-3.67 eV). Thus, the alpha-spin HOMO-LUMO gap (2.18 eV) and the beta-spin HOMO-LUMO gap (1.44 eV) are both smaller than that of the perfect C70 (2.67 eV). It is interesting to recognize that these clusters can be actually treated as carbenes. A carbene carbon is a divalent carbon atom with six valence electrons, and it possesses two nonbonding electrons, which can lead to either the singlet (opposite spin) state or the triplet (parallel spin) state. The simplest carbene is methylene. If the methylene is linear, it will have two degenerate p orbitals, and each of the two nonbonding electrons will occupy one of these two p orbitals with the same spin, thus yielding a triplet ground state. If the methylene is bent, the degeneracy of these two p orbitals will be broken. The orbital perpendicular to the bent methylene is called "p", while the other orbital is called "a" that hybrids with the s orbital and becomes stabilized. The more 5 character a has, the bigger the energy gap between a and p will be. If the a-p energy gap is big, the two nonbonding electrons will prefer to stay in the p orbital with opposite spins, thus becoming a singlet carbene. If the a-p energy gap is small, the two nonbonding electrons will prefer to stay in different orbitals with the same spin, thus producing a triplet carbene. Our results indicate that the singlet carbene carbon atom prefers to stay on the pentagon and the triplet carbene carbon atom prefers to stay on the hexagon in the isomers of C59 and C69. One reason for this scenario is that the triplet carbene carbon atom prefers bigger bond angle in the hexagon of the defect site, whereas the singlet carbene carbon prefers the smaller angle in the pentagon of the defect site. Another reason is due to electronic effects. Let us take Cs9(4-9) and 059(5-8) as examples. From their NBO analysis, we know that the a orbitals for the carbene carbon atoms of Cs9(4-9) and C59(5-8) are sp] 5 0 and sp3'57 hybridized, respectively. This means that the a-p energy gap of the carbene carbon atom of C59(4-9) is larger than that of Cs9(5-8). On the other hand, we find that the p orbital of the carbene carbon atom of Cs9(5-8) forms a 7r bond with one of its neighbour carbon atoms, while this is not true for the carbene carbon atom of C59(4-9). This effect can lower the energy of the p orbital of the carbene carbon atom of 059(5-8), thus leading to a smaller a-p energy gap. 29 (a) Backbone (side view) (b) H O M O - 4 (-6.11) (c) H O M O - 3 (-6.47) (d) H O M O - 2 (-6.38) (e) H O M O - 1 (-6.17) (f) H O M O (-5.95) (g) L U M O (-3.80) (h) LUMO+1 (-3.63) (i) LUMO+2 (-3.40) (j) L U M O + 3 (-3.08) (k) LUMO+4 (-2.87) Figure 3.5. Alpha-spin frontier molecular orbitals of triplet C 69(5-8). H O M O - n (p eV) is the nth molecular orbital below the H O M O with orbital energy p eV. L U M O + w (q eV) is the /nth molecular orbital above the L U M O with orbital energy q eV. The isomerization pathways of the Cs9(4-9) and Cs9(5-8) isomers on the singlet and triplet PESs are explored with B3LYP/6-31G. The relative energies, the transition-state structures, and the imaginary vibrational modes are shown in Fig. 3.6. The energy of the triplet C59(5-8) is set to be the reference zero-point 0.00 kcal/mol. On the singlet PES, the barrier of the singlet Cs9(4-9) transforming into the singlet Cs9(5-8) is 35.69 kcal/mol and 30 the reverse barrier is 54.50 kcal/mol; the barrier between the singlet Cs9(5-8)L and the singlet C59(5-8)R (L means C1-C3 bond-forming, and R means C1-C2 bond-forming) is 49.45 kcal/mol. On the triplet PES, the barrier of the triplet Cs9(4-9) transforming into the triplet C59(5-8) is 17.49 kcal/mol and the reverse barrier is 41.69 kcal/mol; the barrier between the triplet C59(5-8)L and triplet C59(5-8)R is 38.87 kcal/mol. Clearly, the isomerization takes place more readily on the triplet PES. Both vertical and adiabatic values of the electron ionization and affinity energies without zero-point correction for ground-state Cs9(4-9), C5g(5-8), C69(4-9), and C69(5-8) are calculated at the B3LYP/6-311G(d)//B3LYP/6-31G(d) level of theory and shown in Table 3.3. The vertical electron affinity (VEA) or vertical detachment affinity (VDA) is defined as the energy difference between the neutral cluster and its anion both at the equilibrium geometry of the anion; the adiabatic electron affinity (AEA) or simple electron affinity (EA) is defined as the energy difference between the neutral cluster and its anion at their own equilibrium geometries.41 The vertical ionization potential (VIP) is defined as the energy difference between the cation and its neutral cluster both at the equilibrium geometry of the neutral cluster; the adiabatic ionization potential (AIP) is defined as the energy difference between the cation and its neutral cluster at their own equilibrium geometries. The VEA and AEA of the Cs9(4-9) and C69(4-9) clusters are' smaller than those of the C59(5-8) and C69(5-8) clusters. While the VIP and AIP of the C59(4-9) and C69(4-9) clusters are larger than those of the C59(5-8) and C69(5-8) clusters. This suggests that the C59(4-9) and C69(4-9) clusters are harder (i.e., more chemically inert) than the C59(5-8) and C69(5-8) clusters, respectively, according to the concept of chemical hardness 4 2 The values of the chemical hardness, 7? «(VIP - VEAV2, are also tabulated in Table 3.3. The differences between the VEA and the AEA and between the VIP and the AIP for all of these clusters are very small, indicating that the optimized geometries of the neutral clusters and their corresponding anionic and cationic clusters are close to one another. 31 T S 5 8 - 4 9 L (41.69) JC59(4-9) (24.20) 3 t S 5 8 - 4 9 R 3C39(5-8)L (41.69) \ (000) 3C59(5-8)R (0.00) (b) Triplet P E S pathway profile (c) Ideal single vacancy on C 6 o (d) T S 5 8 . 5 8 (e) T S 4 9 - 5 8 R 32 (i) 3 T S 4 9 . 5 8 L F i g u r e 3 . 6 . (a) and (b) are the isomerization pathway profiles o f the single-vacancy defected C 6 0 on the singlet and triplet potential energy surfaces, respectively (energies are in kcal /mol) . (c) Ideal single vacancy on C 6 0 ; (d)-(i) are structures o f the transition states (numbers are the atom distances in A and the blue arrows represent the imaginary vibrational modes). In (f) and (i), L denotes the bond formation between C I and C 3 , thus leading to a pentagon on the left. In (e) and (h), R denotes the bond formation between C I and C 2 , thus leading to a pentagon on the right. T a b l e 3 . 3 . T h e vertical electron affinity ( V E A ) , the adiabatic electron affinity ( A E A ) , the vertical ionization potential (VIP) , the adiabatic ionization potential (AIP) , and the chemical hardness (77) o f C 5 9 ( 4 - 9 ) , C 5 9 ( 5 - 8 ) , C 6 9 ( 4 - 9 ) , and C 6 9 ( 5 - 8 ) . A l l numbers are in e V . Cluster V E A A E A V I P A I P V C 5 9 ( 4 - 9 ) 3.42 3.32 7.36 7.29 1.98 C 5 9 ( 5 - 8 ) 3.68 3.34 6.92 6.79 1.72 C 6 9 ( 4 - 9 ) 3.66 3.55 7.35 7.30 1.88 C 6 9 ( 5 - 8 ) 3.91 3.61 7.06 6.95 1.67 33 3.3.2. Vacancy Defected SWCNTs Perfect (5,5) and (10,0) SWCNTs are studied for comparison with defect SWCNTs. Removal of a single atom gives a 12-membered ring on both of the (5,5) and (10,0) SWCNTs, as shown in Figs. 3.7a and 3.8a. After the surface reconstruction, a pentagon and a nonagon (contains an unsaturated carbon atom) appear in two different ways for both of the (5,5) and (10,0) SWCNTs. One is symmetric (Fig. 3.7c and 3.8c), and the other is asymmetric (Figs. 3.7b and 3.8b).30 Additionally, there are two ways to lose two adjacent carbon atoms on both of the (5,5) and (10,0) SWCNTs, and 14-membered rings appear upon the loss of two adjacent carbon atoms, as shown in Figs. 3.7d, 3.7f, 3.8d, and 3.8f. After the surface reconstruction, two pentagon rings and one octagon ring appear in the symmetric (Figs. 3.7e and 3.8e) and asymmetric (Figs. 3.7g and 3.8g) ways. No dangling bonds present for the double-vacancy defects. The energies and important bond lengths of these isomers are shown in Tables 3.4—3.6. The (5,5) SWCNT 1 asym. isomer (Fig. 3.7b) is more stable than the (5,5) SWCNT 1 sym. isomer (Fig. 3.7c). The ground state of the (5,5) SWCNT 1 asym. isomer is singlet, whose total energy is 2.26 kcal/mol lower than that of the triplet state. While the ground state of the (5,5) SWCNT 1 sym. isomer is triplet, whose energy is 9.66 kcal/mol lower than that of the singlet state. One should notice that the bridging bonds of the pentagon and the nonagon in the (5,5) SWCNT 1 sym. isomers are very weak, and are 1.846 A and 1.871 A in length for the singlet and the triplet cases, respectively. While for the asymmetric isomers, the bridges are typical C-C single bonds, with bond distances 1.579 A and 1.565 A for the singlet and the triplet cases. Our results agree well with the predictions of Mielke et al.29 It supports the existence of the symmetric type 5-1DB defect on the (5,5) SWCNT, which was shown to be nonexistent by Lu et al. with the tight-binding method.32 We also calculated the (5,5) SWCNT 1 sym. isomer of a finite model, which has the same number of carbon atoms as in the PBC model and its two open ends are capped by hydrogen atoms. In this model, the bridging bonds of the pentagon and the nonagon are 1.639 A and 1.649 A in length for the singlet and triplet cases, respectively, which are shorter than their counterparts in the PBC model. This is simply due to the releasing of the constraint at the two open ends of the finite model. The energy of the triplet isomer is 34 (c) (5,5) 1 sym. (d) Ideal symmetric double vacancy (e) (5,5) 2 sym. (f) Ideal asymmetric double vacancy (g) (5,5) 2 asym. F i g u r e 3.7. Structures o f the ideal single and double vacancies and related defects on the (5,5) S W C N T . 35 (a) Ideal single vacancy (b) (10,0) 1 asym. (c) (10,0) 1 sym. (d) Ideal symmetric double vacancy (e) (10,0) 2 sym. (f) Ideal asymmetric double vacancy (g) (10,0) 2 asym. F i g u r e 3.8. Structures o f the ideal single and double vacancies and related defects on the (10,0) S W C N T . 36 Table 3.4. Energies calculated at the BPW91/6-31G level of theory for all the related defects of the single- and double-vacancy defected (5,5) and (10,0) SWCNTs and the perfect (5,5) and (10,0) SWCNTs . Etotai(Hartree) E s a " (kcal/mol) A E e (kcal/mol) Model S ( R a ) S ( U C ) T ( U C ) S(R) S (U) T ( U ) S(R) S(U) T ( U ) (5,5) S W C N T -3810.0481 169.20 (5,5) S W C N T 1 asym. -3771.7310 -3771.7310 (0) f -3771.7274(2.02) 167.85 167.85 167.83 1.35 1.35 1.37 (5,5) S W C N T 1 sym. -3771.6790 -3771.6790(0) -3771.6944(2.02) 167.52 167.52 167.62 1.68 1.68 1.58 (5,5) S W C N T 2 asym. -3733.6917 -3733.6917(0) -3733.6744 (2.02) 168.23 168.23 168.12 0.97 0.97 1.08 (5,5) S W C N T 2 sym. -3733.5905 -3733.5905 (0) -3733.5735 (2.01) 167.58 167.58 167.48 1.62 1.62 1.72 (10,0) S W C N T ^1572.2690 170.31 (10,0) S W C N T 1 asym. -4533.9033 -4533.9033 (0) -4533.9102 (2.02) 168.94 168.94 168.98 1.37 1.37 1.33 (10,0) S W C N T 1 sym. -4533.9535 -4533.9535 (0) -4533.9402 (2.02) 169.21 169.21 169.14 1.10 1.10 1.17 (10,0) S W C N T 2 asym. -4495.8388 -4533.8388 (0) ^495.8144(2.00) 169.13 169.13 169.00 1.18 1.18 1.31 (10,0) S W C N T 2 sym. ^1495.9168 -4495.9171 (0) -4495.9041 (2.00) 169.55 169.55 169.48 0.76 0.76 0.83 "Spin-restricted singlet results. bSpin-unrestricted singlet results. cSpin-unrestricted triplet results. dThe stability energy per atom, defined as E t e /n , where E t e is the energy difference between the isolated carbon atoms and the cluster and n is the total number of carbon atoms in the cluster. e A E f = E s a (perfect S W C N T ) - E s a (defected SWCNT) . f 2 The values in the parentheses are the <S > values. Table 3.5. Bond lengths (in A ) of the single- and double-vacancy defects of the (5,5) SWCNT. (5,5) S W C N T 1 asym. (5,5) S W C N T 1 sym. (5,5) S W C N T 2 asym. (5,5) S W C N T 2 sym. Bond S(R) S(U) T(U) S(R) S(U) T(U) S(R) S(U) T(U) S(R) S(U) T(U) C 1 - C 2 1.463 1.463 1.466 1.435 1.435 1.431 1.426 1.426 1.436 1.442 1.442 1.441 C 1 - C 5 1.846 1.846 1.871 1.687 1.687 1.664 C 1 - C 9 1.579 1.580 1.565 C l - C l l 1.534 1.534 1.517 C1-C12 1.475 1.475 1.462 1.541 1.541 1.528 C1-C14 1.447 1.447 1.451 1.498 1.498 1.511 C 2 - C 3 1.435 1.434 1.462 1.541 1.541 1.528 C 3 - C 4 1.430 1.430 1.442 1.421 1.421 1.422 1.451 1.451 1.457 1.414 1.414 1.414 C 4 - C 5 1.402 1.402 1.394 1.435 1.435 1.431 1.435 1.435 1.444 1.442 1.442 1.441 C 4 - C 8 1.534 1.534 1.517 C 5 - C 6 1.399 1.399 1.388 1.541 1.541 1.528 1.430 1.430 1.427 1.498 1.498 1.511 C 6 - C 7 1.441 1.441 1.446 1.458 1.458 1.458 1.430 1.430 1.431 1.476 1.476 1.461 C 7 - C 8 1.459 1.458 1.458 1.444 1.444 1.443 1.447 1.447 1.451 1.498 1.498 1.511 C 8 - C 9 1.480 1.480 1.492 1.374 1.374 1.377 1.426 1.426 1.436 1.441 1.441 1.441 C8-C12 1.687 1.687 1.664 C9-C10 1.439 1.439 1.448 1.374 1.374 1.377 1.464 1.464 1.456 1.414 1.414 1.414 C10-C11 1.424 1.424 1.421 1.444 1.444 1.443 1.451 1.451 1.457 1.414 1.414 1.414 C11-C12 1.427 1.427 1.427 1.458 1.458 1.458 1.435 1.435 1.444 1.442 1.442 1.441 C12-C13 1.430 1.430 1.427 1.498 1.498 1.511 C13-C14 1.430 1.430 1.431 1.476 1.476 1.461 Table 3.6. Bond lengths (in A ) of the single- and double-vacancy defects of the (10,0) S W C N T . (10,0) S W C N T 1 asym. (10,0) S W C N T 1 sym. (10,0) S W C N T 2 asym. (10,0) S W C N T 2 sym. Bonds S(R) a S(U) T(U) S(R) S(U) T(U) S(R) S(U) T(U) S(R) S(U) T(U) C 1 - C 2 1.432 1.432 1.438 1.456 1.456 1.473 1.447 1.447 1.470 1.432 1.432 1.444 C 1 - C 5 1.761 1.761 1.751 C 1 - C 9 1.560 1.560 1.530 C l - C l l 1.641 1.641 1.604 1.511 1.511 1.477 C1-C12 1.520 1.520 1.528 1.447 1.447 1.446 C1-C14 1.456 1.456 1.457 1.429 1.429 1.440 C 2 - C 3 1.419 1.419 1.416 1.437 1.437 1.437 1.483 1.483 1.469 1.452 1.452 1.435 C 3 - C 4 1.421 1.421 1.421 1.432 1.432 1.439 1.478 1.478 1.494 1.432 1.432 1.444 C 4 - C 5 1.460 1.460 1.452 1.404 1.404 1.393 1.434 1.434 1.445 1.429 1.429 1.440 C 4 - C 8 1.640 1.640 1.604 1.512 1.512 1.477 C 5 - C 6 1.485 1.485 1.493 1.404 1.404 1.393 1.413 1.413 1.408 1.431 1.431 1.428 C 6 - C 7 1.452 1.452 1.458 1.432 1.432 1.439 1.422 1.422 1.425 1.431 1.431 1.428 C 7 - C 8 1.423 1.423 1.422 1.437 1.437 1.437 1.456 1.456 1.457 1.429 1.429 1.440 C 8 - C 9 1.400 1.400 1.385 1.456 1.456 1.473 1.447 1.447 1.471 1.432 1.432 1.444 C9-C10 1.384 1.384 1.372 1.447 1.447 1.446 1.483 1.483 1.469 1.453 1.453 1.435 C10-C11 1.444 1.444 1.448 1.424 1.424 1.423 1.478 1.478 1.494 1.432 1.432 1.444 C11-C12 1.470 1.470 1.472 1.424 1.424 1.423 1.434 1.434 1.445 1.429 1.429 1.440 C12-C13 1.413 1.413 1.408 1.431 1.431 1.428 C13-C14 1.422 1.422 1.424 1.431 1.431 1.428 a R : Spin-restricted; U : Spin-unrestricted; S: Singlet; T: Triplet. 14.1 kcal/mol lower than that of the singlet isomer, which agrees with the results of the PBC model. Thus, we have confirmed the existence of the symmetric type 5-1DB defect on the (5,5) SWCNT. The (5,5) SWCNT 2 asym. isomer (Fig. 3.7g) is more stable than its symmetric counterpart. The energy of the singlet state is 10.86 kcal/mol lower than that of the triplet state. The ground state of the (5,5) SWCNT 2 sym. isomers is also singlet, whose energy is 10.67 kcal/mol lower than that of the triplet state. The bond length of the bridging bonds in the (5,5) SWCNT 2 sym. are 1.67 A, longer than that in the (5,5) SWCNT sym. isomer (1.53 A). The removal of one or two carbon atoms from the perfect (5,5) SWCNT decreases, the cohesive energy per carbon atom by 1.35, 1.58, 0.97, and 1.62 kcal/mol for the (5,5) SWCNT 1 asym., (5,5) SWCNT 1 sym., (5,5) SWCNT 2 asym., and (5,5) SWCNT 2 sym. clusters, respectively. Apparently, the (5,5) SWCNT 2 asym. isomer is the most stable one. In our model, the band gap for the perfect (5,5) SWCNT is 2.59 eV, the band gap for the singlet (5,5) SWCNT 1 asym. isomer is 0.80 eV, and the band gap for the singlet (5,5) SWCNT 2 asym. isomer is 1.03 eV. According to the density of states (DOS) plot (Fig. 3.9a), one can see that the single and double vacancies introduce electronic states across the Fermi level; hence, the introduction of vacancy defects will increase the conductance of the (5,5) SWCNT. This conclusion is consistent with the band-gap data mentioned above. According to the FMO analysis (Figs. 3.10 and 3.11) of the singlet (5,5) SWCNT 1 asym. and the singlet (5,5) SWCNT 2 asym. clusters, we can see that the vacancy defects severely destruct the 7T conjugated system of the (5,5) SWCNTs. The vacancy defects also create localized electronic states, which are clearly shown by the HOMO and the LUMO of the (5,5) SWCNT 1 asym. cluster around the nonagon. However, the localization is not that obvious for the (5,5) SWCNT 2 asym. cluster. The HOMO and the LUMO of the (5,5) SWCNT 2 asym. cluster are 7r bonds around the octagon. Now, let us turn to the (10,0) SWCNT. The (10,0) SWCNT 1 sym. isomers (Fig. 3.8c) are more stable than their asymmetric counterparts (Fig. 3.8). The ground state of the (10,0) SWCNT 1 sym. isomer is singlet, which is 8.34 kcal/mol lower than the triplet state. The ground state of the (10,0) SWCNT 1 sym. isomer is triplet, which is 4.44 40 kcal/mol lower than that of the symmetric counterpart. The bridging bonds of the symmetric isomers are 1.560 A and 1.530 A for the singlet and triplet states, respectively. While the bridging bonds for the asymmetric isomers are much longer with bond distances 1.761 A and 1.751 A for the singlet and triplet states, respectively. The (10,0) SWCNT 2 sym. isomers are more stable than their asymmetric counterparts. The energies of the singlet states are 8.16 kcal/mol and 15.31 kcal/mol lower than those of the triplet states for the symmetric and asymmetric isomers, respectively. The bridging bonds for symmetric and asymmetric isomers are around 1.500 A and 1.620 A, respectively. The removal of one or two carbon atoms from the perfect (10,0) SWCNT also decreases the cohesive energy per carbon atom by 1.33, 1.10, 1.18, and 0.76 kcal/mol for the (10,0) SWCNT 1 asym., (10,0) SWCNT 1 sym., (10,0) SWCNT 2 asym., and (10,0) SWCNT 2 sym. isomers, respectively. Among them, the (10,0) SWCNT 2 sym. isomer is the most stable one. In our model, the band gap for the perfect (10,0) SWCNT is 0.74 eV, the band gap for the singlet (10,0) SWCNT 1 sym. isomer is 0.27 eV, and the band gap for singlet (10,0) SWCNT 2 sym. isomer is very small, only 0.03 eV. From the DOS plot in Fig. 3.9b, one can also conclude that the single and double vacancies will introduce electronic states across the Fermi level, again enhancing the conductance of the (10,0) SWCNT. According to the FMO analysis (Figs. 3.12 and 3.13) of these two clusters, we can see that the vacancy defects also severely destruct the 7T conjugated system of the (10,0) SWCNT. However, it is quite interesting to notice that the localization of the electronic state is not as obvious as that on the (5,5) SWCNT. Nonetheless, the LUMO of the (10,0) SWCNT 1 sym. cluster obviously has some major contribution from the defect site. 3.4. Conclusion By applying DFT methods, the structure, stability, and electronic properties of single-vacancy defected Ceo and C70 and single- and double-vacancy defected SWCNTs are studied in detail. It is found that the presence of the vacancy defects decreases the HOMO-LUMO gaps of C60 and C70. The isomerization of the single-vacancy defected C60 takes place readily on the triplet PES. Based on the concept of chemical hardness, the C59(4-9) and C69(4-9) clusters are harder (i.e., more chemically inert) than the Cs9(5-8) and C69(5-8) clusters. The ground state of the single- and double-vacancy defected (5,5) 41 and (10,0) SWCNTs are singlet. The symmetric single-vacancy defected (5,5) SWCNT does exist, albeit not very stable. The symmetric singlet double-vacancy defected (10,0) SWCNT is the most stable cluster among the models we have studied. The vacancies on the SWCNTs will also decrease the HOMO- LUMO gaps, destruct the 7T conjugated system of the frontier molecular orbitals, thus enhance their conductivity and chemical activity. -5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0 Energy (eV) F i g u r e 3.9. T h e change o f the density o f states after introducing vacancy defects on the (5,5) S W C N T (above) and the (10,0) S W C N T (below). 42 (a) Backbone (b) H O M O ^ (-5.60) (c) H O M O - 3 (-5.44) (d) H O M O - 2 (-5.41) (e) H O M O - 1 (-5.30) (f) H O M O (-4.99) (g) L U M O (-4.19) (h) LUMO+1 (-3.10) (i) LUMO+2 (-3.07) (j) L U M O + 3 (-3.02) (k) LUMO+4 (-2.96) Figure 3.10. Frontier molecular orbitals of the (5,5) S W C N T 1 asym. cluster. H O M O - n (p eV) is the nth molecular orbital below the H O M O with orbital energy p eV. LUMO+nz (q eV) is the mth molecular orbital above the L U M O with orbital energy q eV. (a) Backbone (b) H O M O ^ (-5.59) (c) H O M O - 3 (-5.58) (d) H O M O - 2 (-5.30) (e) H O M O - 1 (-5.20) (f) H O M O (-5.14) (g) L U M O (-4.11) (h) LUMO+1 (-3.10) (i) LUMO+2 (-3.07) (j) LUMO+3 (-2.99) (k) LUMO+4 (-2.94) Figure 3.11. Frontier molecular orbitals of the (5,5) S W C N T 2 asym. cluster. H O M O - n (p eV) is the «th molecular orbital below the H O M O with orbital energy p eV. LUMO+m (q eV) is the wth molecular orbital above the L U M O with orbital energy q eV. (a) B a c k bone (b) H O M O ^ l (-5.66 (c) H O M O - 3 (-5.09) (d) H O M O - 2 (-5.01) (e) H O M O - 1 (-4.65) (f) H O M O (-4.54) (g) L U M O (-4.27) (h) L U M O + 1 (-3.81) (i) L U M O + 2 (-3.73) (j) L U M O + 3 (-3.29) (k) L U M O + 4 (-3.29) F i g u r e 3.12. Frontier molecular orbitals o f the (10,0) S W C N T 1 sym. cluster. H O M O - n (p e V ) is the nth molecular orbital below the H O M O with orbital energy p e V . L U M O + m (q e V ) is the mth molecular orbital above the L U M O with orbital energy q e V . (a) Backbone (b) H O M O - 4 (-5.52) (c) H O M O - 3 (-5.47) (d) H O M O - 2 (-5.01) (i) L U M O + 2 (-3.70) (j) L U M O + 3 (-3.48) (k) L U M O + 4 (-3.32) F i g u r e 3.13. Frontier molecular orbitals o f the (10,0) S W C N T 2 sym. cluster. H O M O - n (p e V ) is the nth molecular orbital below the H O M O with orbital energy p e V . L U M O + n ? (q e V ) is the /nth molecular orbital above the L U M O with orbital energy q e V . 3.6. References (1) Kroto, H. W.; Health, J. R.; O'Brien, S. C ; Curl, R. F.; Smalley, R. E. Nature 1985, 318, 162. (2) (a) S. Iijima, Nature 1991, 354, 56. (b) Iijima S.; Ichihashi, T. Nature 1993, 363, 603. (3) Schmalz, T. G.; Seitz, W. A.; Klein, D. J.; Hite, G. E. J. Am. Chem. Soc. 1988,110, 1113. (4) a) Sijbesma, R.; Srdanov, G.; Wudl, F.; Castoro, J. A.; Wilkins, C ; Friedman, S. H.; DeCamp, D. L.; Kenyon, G. L. J. Am. Chem. Soc. 1993,115, 6510; b) Friedman, S. H.; DeCamp, D. L.; Sijbesma, R. P.; Srdanov, G.; Wudl, F.; Kenyon, G. L. J. Am. Chem. Soc. 1993,115, 6506. (5) Kong, J.; Franklin, N. R.; Zhou, C. W.; Chapline, M. G.; Peng, S.; Cho, K. J.;. Dai, H. J. Science 2000, 287, 622. (6) Avouris, P. Acc. Chem. Res. 2002, 35, 1026. (7) Liu, C ; Fan, Y. Y.; Liu, M.; Cong, H. T.; Cheng, H. M.; Dresselhaus, M. S. Science, 1999, 286, 1127. (8) Charlier, J.-C. Acc. Chem. Res. 2002, 35, 1063. (9) Stone A. J.; Wales, D. J. Chem. Phys. Lett. 1986,128, 501. (10) O'Brien, S. C ; Heath, J. R.; Curl, R. F.; Smalley, R. E. J. Chem. Phys. 1988, 88, 220. (11) Deng, J.-P.; Ju, D.-D.; Her, G.-R.; Mou, C.-Y.; Chen, C.-J.; Lin, Y.-Y.; Han, C.-C. J. Phys. Chem. 1993, 97, 11575. (12) Saunders, M.; Jimenezazquez, H. A.; Cross, R. J.; Poreda, R. J. Science 1993, 259, 1428. (13) a) Kiang, C.-H.; Goddard III, W. A.; Beyers, R.; Bethune, D. S. J. Phys. Chem. 1996, 100, 3749; b) Zhu, Y.; Yi, T.; Zheng, B.; Cao, L. Appl. Surf. Sci. 1999, 137, 83. (14) Ajayan, P. M.; Ravikumar, V.; Charlier, J.-C. Phys. Rev. Lett. 1998, 81, 1437. (15) Tian, W. Q.; Liu, L. V.; Wang Y. A. (in preparation). (16) Terrones, M.; Terrones, H.; Banhart, F.; Charlier, J.-C; Ajayan, P. M. Science 2000, 255, 1226. 47 (17) Srivastava, D.; Menon, M.; Daraio, C ; Jin, S.; Sadanadan, B.; Rao, A. M. Phys. Rev. B 2004, 69,153414. (18) Liu, L. V.; Tian, W. Q.; Wang Y. A. J. Phys. Chem. B 2006,110, 1999. (19) Murry, R. L.; Strout, D. L.; Odom, G. K.; Scuseria, G. E. Nature 1993, 366, 655. (20) Sun, M.-L.; Slanina, Z.; Lee, S.-L. Fullerene Sci. Technol. 1995, 3, 627. (21) Turker, L. J. Mol. Struct.: THEOCHEM2001, 571, 99. (22) Hu Y. H.; Ruckenstein, E. J. Chem. Phys. 2003, 77P, 10073. (23) Hu Y. H.; Ruckenstein, E. J. Chem. Phys. 2004,120, 7971. (24) Lee S. U.; Han, Y.-K. J. Chem. Phys. 2004,121, 3941. (25) Igami, M.; Nakanishi, T.; Ando, T. J. Phys. Soc. Jpn. 1999, 68, 716. (26) Hansson, A.; Paulsson, M.; Stafstrom, S. Phys. Rev. B 2000, 62, 7639. (27) Igami, M.; Nakanishi, T.; Ando, T. Physica B 2000, 284-288, 1746. (28) Fagan, S. B.; da Silva, L. B.; Mota, R. Nano Lett. 2003, 3, 289. (29) Mielke, S. L.; Troya, D.; Zhang, S.; Li, J. L.; Xiao, S. P.; Car, R.; Ruoff, R. S.; Schatz, G. C ; Belytschko, T. Chem. Phys. Lett. 2004, 390, 413. (30) Sammalkorpi, M.; Krasheninnikov, A.; Kuronen, A.; Nordlund, K.; Kaski, K. Phys. Rev. B 2004, 70, 245416. (31) Rossato, J.; Baierle, R. J.; Fazzio, A.; Mota, R. Nano Lett. 2005, 5, 197. (32) Lu A. J.; Pan, B. C. Phys. Rev. Lett. 2004, 92, 105504. (33) Banhart, F. Rep. Prog. Phys. 1999, 62,-1181. (34) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (35) Lee, C ; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785. (36) NBO Version 3.1, Glendening, E. D.; Carpenter, A. E.; Weinhold F. (1995); Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. Rev. 1988, 88, 899. (37) Becke, A. D. Phys. Rev. A 1988, 38, 3098. (38) (a) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais C. Phys. Rev. B 1992, 46, 6671; (b) Perdew, J. P.; Burke, K.; Wang Y. Phys. Rev. B 1999, 54, 16533. (39) Gaussian 03, Revision B.05, Frisch M. J. et al. Gaussian, Inc., Pittsburgh PA, 2003. (40) Leclercq, F.; Damay, P.; Foukani, M.; Chieux, P.; Bellissent-Funel, M. C.; Rassat, A.; Fabre, C. Phys. Rev. B 1993, 48, 2748. 48 (41) Rienstra-Kiracofe, J. C ; Tschumper, G. S.; Schaefer III, H. F. Chem. Rev. 2002, 102, 231. (42) Pearson, R. G. Chemical Hardness, Wiley-VCH Verlag: Weinheim, Germany, 1997. 49 Chapter 4 Chemical Reaction of Nitric Oxides with the 5-1DB Defect of the Single-Walled Carbon Nanotube 4.1. Introduction Since the discovery of carbon nanotubes (CNTs) by Iijima,1 thousands of scientists have joined the research field of CNTs owing to their fascinating mechanical, thermal, and electrical properties, and various promising applications, including hydrogen storage,2 chemical sensors,3 and nanobioelectronics,4 etc. Substitutionally B- and N-doped CNTs have received significant attention from theoretical and experimental scientists.5-14 Peng et al. pointed out that the substitutionally B- and N-doped CNTs can be used as sensitive and selective chemical sensors;5 Choi et al. showed that acceptor and donor states will occur near the Fermi level after substitutional doping of B and N into the CNTs, which leads to .p-type and n-type CNTs and broadens their application in nanoelectronics;6 Blase et al. indicated that substitutionally B- and N-doped CNTs are possible candidates for nanosize electronic and photonic devices with various electronic properties.7 By using the generalized tight-binding molecular dynamics method, Srivastava et al. showed that the nitrogen atom (if produced as free gas-phase neutral atoms) can be substitutionally doped into the SWCNTs mediating the vacancy.9 Nowadays, there are several successful synthesis methods for substitutionally B- and N-doped CNTs, including substitution reactions by thermal treatment,10 chemical vapor deposition,11 arc method,12 and laser ablation,13. But all these methods require critical conditions of very high temperatures of hundreds to thousands degrees and cannot control the doping positions and concentration of heteroatoms on the sidewall of the f A version o f this chapter has been published as L i u , L . V . ; Tian, W . Q. ; Wang, Y . A . "Chemical Reaction o f Nitric Oxides with the 5 -1DB Defect o f the Single-Walled Carbon Nanotube", J. Phys. Chem. B 2 0 0 6 , 110, 1999. Reproduced with permission. Copyright[2006] American Chemical Society. 50 SWNCT. 1 0 - 1 4 It has been recently recognized that low doping concentration may enhance the electric conductance and leave the mechanical properties of the CNTs almost unchanged.14 However, reported experimental and theoretical studies on substitutionally B- and N-doped SWNCTs are scarce.14 It is our hope that our work will provide some theoretical guidance in this important, emerging new field. A single vacancy that has three two-coordinated carbon atoms may be artificially introduced by ion and electron irradiation15'16 or exist as native defects.17 For SWCNTs with small diameters, a single vacancy (Fig. 4.1a) with three dangling bonds (DBs) is only metastable: two of these three two-coordinated carbon atoms will recombine to form a much more stable pentagon carbon ring, leaving the third two-coordinated carbon atom with one dangling bond and forming the so-called 5-1DB defect,16'18 as shown in Figs. 4.1b and 4.1c. The vacancies and dangling bonds on the SWCNTs may play the role of chemical connectors of two defected nanotubes,19 chemisorption site for acetone203 and hydrogen gas,20b and chemical reaction site for nitrogen dioxide.200 The existence of the 5-1DB defects may provide us a possible new way to functionalize the sidewall of the SWCNT. In this paper, we will first assess the chemical reactivity of the 5-1DB defects from the analyses of the frontier molecular orbitals (FMOs) and local density of states (LDOS). And then, we will study the reaction of nitric oxides (NOs) with the 5-1DB defect on the SWCNT. We will show that it is highly possible to fabricate position-controllable substitutionally N-doped SWCNTs with low doping concentration under mild conditions. To our best knowledge, nobody has reported any theoretical studies about how to use some simple chemical reactions of the 5-1DB defects on the SWCNT to fabricate position-controllable substitutionally N-doped SWCNTs with low doping concentration under mild conditions. 4.2. Computational Methods and ONIOM Model Selection We first prepared a fragment of the (5,5) SWCNT (C200H20), which has 200 carbon atoms and 20 capping hydrogen atoms at the two ends. We then removed a carbon atom from the center of the (5,5) SWCNT segment to create a single vacancy, as shown in Fig. 4.1a. We initially applied the semi empirical MNDO-PM3 method to optimize the 51 (a) Single vacancy (b) Top view of the 5-1 DB defect 0.028 A j - O . 1 1 8 0 ^ f - ° - 0 0 3 0.1490 #0.016 J J - 0 . 0 1 4 ^ , ^ - 0 . 0 1 7 J i j Active Carbon (c) Side view of the 5-1 DB defect (d) 9-membered ring with partial charges Figure 4.1. (a) The single vacancy on the (5,5) S W C N T ; (b) The top view of the 5-1DB defect on the (5,5) S W C N T , where the 9-membered ring is chosen as the high layer and the other carbon atoms are chosen as the low layer in a two-layered O N I O M model; (c) The side view of the 5-1 DB defect on the (5,5) S W C N T , where the active carbon atom sticks out of the sidewall surface of the S W C N T ; (d) The 9-membered ring (with partial charges) of the 5-1DB defect capped by hydrogen atoms. The double lines in (d) denote C=C double bonds. geometries of C200H20 and the SWCNT with a single vacancy (C199H20), and then fully optimized the geometries within the hybrid density functional method B3LYP 2 2' 2 3 with the 6-31G basis set. We have carried out both of the spin-restricted and the spin-unrestricted DFT calculations and found that for both C200H20 and C199H20, the spin-unrestricted DFT calculations always converge to the spin-restricted DFT wave functions. This clearly indicates that the SWCNT with a single vacancy is a closed-shell singlet carbene. For the optimized structure of the SWCNT with a single vacancy, we got the 5-1DB defected SWCNT as shown in Figs. 4.1b and 4.1c. One can see that there is a carbon atom (called the active carbon atom hereafter) that stays out of the sidewall surface of the SWCNT. This out-of-surface geometry will facilitate the active carbon atom to react with incoming molecular or atomic species, due to the smaller steric hindrance when • 20 compared with other carbon atoms near the 5-1DB defect site. ONIOM is a method pioneered by Morokuma24 and is widely used for studies of SWCNTs. 2 5 - 2 7 In an ONIOM model, up to three layers can be treated in the calculation of 52 a large molecular system, and different theoretical methods can be applied for different layers. In general, the dangling bonds of each layer at the boundary should be capped by atoms so that the resulting bonds at the boundary closely resemble the original chemical environment and bond characters. In this study, hydrogen atoms are appropriate to be used as the capping atoms. When using ONIOM, one has to choose an appropriate partition of the system into the high- and low-level layers and assign suitable methods for different layers. The most important rule is including the major players (chemically active atoms) of the system in the high-level layer and the minor players in the low-level layer.28 In order to choose a suitable ONIOM model, we did the following calculations. Single-point calculations for C200H-20 and the (5,5) SWCNT with a 5-1DB defect were performed at the B3LYP/6-31G level of theory. We found that the HOMO-LUMO gap of the (5,5) SWCNT with a 5-1DB defect is 0.84 eV, which is smaller than the gap of C200H20 (1.38 eV). This is due to the relaxation of the geometric constraint of the SWCNT after the removal of one carbon atom, which also stabilizes the HOMO and the LUMO. The LDOS of different regions in C200H20 corresponding to the (5,5) SWCNT with a 5-1DB defect are plotted in Figs. 4.2 and 4.3 to illustrate how the 5-1DB defect affects the electronic structure of the (5,5) SWCNT. We found that for C2ooH20, the LDOS of each layer are very similar and contribute equally to the FMOs and there is no localized electronic state on C2ooH2o- For C199H20, we found that the contribution to the HOMO and the LUMO from the 9-membered ring (LI in Fig. 4.3) of the (5,5) SWCNT with a 5-1DB defect is much bigger than that of the corresponding region (LI in Fig. 4.2) in C2ooH2o-The FMOs of C199H20 are shown in Fig. 4.4. One finds that the 5-1DB defect strongly destructs the conjugated 7T system of C200H20. The HOMO of Ci 9 9H 2o mainly consists of lone-pair electrons of the active carbon atom and the it bonds of the other carbon atoms of the 9-membered ring. For the LUMO of C199H20, the 9-membered ring, especially the active carbon atom, has the dominant contribution, while only half of the sidewall of the SWCNT contributes to the LUMO. Clearly, the 5-1DB defect leads to the existence of localized electronic states and hosts the regioselective reactive region on the sidewall of the SWCNT. Furthermore, according to natural bond orbital (NBO) analysis, there are four C=C double bonds in the 9-membered ring of the 5-1DB defect (see Fig. 4. Id), 53 1000 -10 -8 -6 -4 -2 0 2 4 6 Energy (eV) Figure 4.2. The total and local densities of states for the open-end (5,5) S W C N T segment C2ooH2o with the D 5 d symmetry. HOMO (-4.35 eV) is the highest occupied molecular orbital and LUMO (-2.97 eV) is the lowest unoccupied molecular orbital. L I , L2, L3, and L4 are local density of states for each specified layer of C200H20 as outlined on the structure. and the 9-membered ring connects to its neighboring carbon atoms via C-C single bonds, which are ideal to be replaced by the buffering C - H single bonds in the ONIOM model. So, we treated the 9-membered ring as the major player of the 5-1DB defected SWCNT system. To verify this assessment, we performed a single-point calculation of the 9-membered ring of the 5-1DB, defect capped by the hydrogen atoms (CgHg shown in Fig. 4. Id) also at the B3LYP/6-31G level of theory. After comparing the FMOs of C199H20 and CgHg, we 54 i 1 1 1 1 1 r -10 -8 -6 -4 -2 0 2 4 6 Energy (eV) Figure 4.3. The total and local density of states of the open-end (5,5) S W N C T with a 5-1DB defect, C199H20. H O M O (-4.19 eV) is the highest occupied molecular orbital and L U M O (-3.35 eV) is the lowest unoccupied molecular orbital. L I , L2 , L 3 , and L4 are local density of states for each specified layer of C 1 9 9 H 2 o as outlined on the structure. found that the H O M O and the L U M O of C199H20 are very close to those of CgHg, as shown in Fig. 4.4. According to Fukui's frontier orbital theory, 2 9 the H O M O and the L O M O are the most important molecular orbitals in chemical reactions. We hence concluded that the 9-membered ring of the 5-1DB defect, especially the active carbon atom, is the chemically active center, and the C 9 Hg model can be used to represent most of the chemical properties of the 5-1DB defect on the S W C N T . Based on the above discussion, we decided to use a two-layered O N I O M model for the system. We included the 9-membered ring of the 5-1DB defect and N O in the high layer, which was treated at the B3LYP/6-31G(d) level of theory. A l l the other carbon atoms were set in the low layer, treated by the universal force field (UFF). In fact, this 55 (a) LUMO of C,99H2o (-3.37 eV) (b) LUMO of C 9 H 8 (-2.78 eV) (c) HOMO of C I 9 9 H 2 0 (-4.21 eV) (d) HOMO of C 9 H 8 (-4.79 eV) Figure 4.4. Frontier molecular orbitals of C | 9 9 H 2 0 and C 9 H 8 . The numbers in parentheses are the orbital energies in eV. is the only logical way to define the high layer of the ONIOM model because the 9-membered ring connects to its neighboring carbon atoms in the SWCNT via C - C single bonds, which are ideally replaced by the buffering C - H single bonds in the ONIOM model. To incorporate more neighboring carbon atoms around the 9-membered ring into the expanded high layer of the ONIOM model will inevitably cut many aromatic C=C double bonds, hence drastically changing the electronic structure of the SWCNT. Although the "same level different basis set" (SLDB) method is highly recommended for the treatment of the SWCNTs by Kar et al., it can introduce artificial charge polarization and transfer due to the fact that electrons like to stay near the atoms with more basis functions. Hence, we did not use the SLDB method in our studies. The Hessian was calculated to verify the nature of all the stationary points (transition states or local minima). The partial charges and NBOs were studied by using the NBO 3.1 3 2 module in the Gaussian 03 package.33 The spin-unrestricted DFT method was applied to all open-shell species. To get the energetics, single-point calculations of all the reactant, the transition states, the intermediates, and the final product were performed at the B3LYP/6-31G level of theory for the optimized geometries obtained from the ONIOM model. We term this 56 scheme the ONIOM/DFT scheme, in which single-point DFT calculations, based on the optimized structures within the ONIOM model, are used to obtain the total energies. This ONIOM/DFT scheme has been benchmarked against fully converged DFT optimizations of several intermediate states of the system we studied here, and we also showed that the ONIOM/DFT scheme can reproduce the structures and the energy differences of the full DFT results quite well. 33 Al l calculations were done by using the Gaussian 03 package. 4.3. Results and Discussion 4.3.1. Attacking of the First NO The active carbon atom CI forms bonds with its two neighboring carbon atoms, C4 and C5, as shown in Fig. 4.5a. Based on the NBO analysis, there are two 2-center a NBOs involving the active carbon atom: a(Cl -C4) = 0.678 CI (spl95) + 0.735 C4 (sp2-00) and a(Cl -C5) = 0.676 CI (sp2-06) + 0.73 6 C5 (sp2M). There are two lone-pair-type NBOs for the active carbon atom: one is an sp2'01 hybridized orbital with 1.51 electrons and the other is a pure p orbital with 0.51 electrons. Hence, the active carbon atom is clearly sp hybridized. The NBO partial charges for carbon atoms of the nine-membered ring are shown in Fig. 4.Id. Only the active carbon atom and its two immediate neighbors, C4 and C5, have relatively large partial charges, and the active carbon atom has the biggest partial charge, which means that the active carbon atom will have the largest electrostatic effects. As discussed above, the active carbon atom CI has the smallest steric hindrance and is the most chemically reactive center. We consequently considered two initial attacking modes of NO toward C I , O-end attacking and N-end attacking, and we only found a transition state for the O-end attacking mode. This can be rationalized from the electrostatic effect. When NO is far away from CI , the orbital interaction effect is very small, and the electrostatic effect should be the dominant factor controlling the initial reaction. The NBO partial charges of NO are distributed as N(+0.181)=O(-0.181), whereas the active carbon atom has a +0.149 partial charge. This explains why we only found the O-end attacking transition state. The geometry of this transition state (TS1) is shown in Fig. 4.5a. The C2-C3 bond length is 1.55 A, a typical C - C single bond. The 57 distance between O and CI is 1.70 A. The energy barrier is only 8.6 kcal/mol, which means the initial attacking is very feasible, mainly due to the strong electrostatic attraction and molecular orbital overlap between O and CI. At this stage, the pentagon of the 5-1DB defect still exists, and there are 0.052 electrons transferred from the SWCNT to NO. From the shapes and energies of the FMOs of TS1, NO and the SWCNT with the 5-1DB defect, the orbital interaction for TS1 can be viewed as the single occupied molecular orbital (SOMO) of NO interacting with the HOMO of the SWCNT with the 5-1DB defect. After overcoming the initial reaction barrier, the system reaches the first intermediate, LM1 (shown in Fig. 4.5b), with a bridge configuration. The oxygen atom is still chemically bounded to C1, and the nitrogen atom begins to form a chemical bond with C2. When O approaches CI, N also approaches C2, with an in-phase orbital overlap. The energy of LM1 is 19.1 kcal/mol lower than that of the reactants, i.e., the initial reaction is exothermic. 1.20 (a) T S 1 ( A E = 8.6) (b) L M 1 ( A E = -19 .1) (c) T S 2 ( A E = -6 .9 ) (d) L M 2 ( A E = -92.4) (e) T S 3 ( A E = -51 .3) (f) L M 3 ( A E = -90 .0) 58 (g) TS4 ( A E = 3.7) (h) F i n a l p r o d u c t ( A E = -78.3) T S l AE - 8.6 (i) React ion profile o f N O with the 5 - 1 D B defect (j) React ion profile o f N O with L M 3 F i g u r e 4.5. React ion profiles and geometries o f the transition states, intermediates, and final product o f the reaction o f N O with C i 9 9 H 2 o . T h e units o f energy and b o n d length are in kca l /mol and A, respectively. T h e active carbon atom is labeled as C a r b o n 1, and the other two important carbon atoms are labeled as Carbons 2 and 3. T h e nitrogen atoms are in blue, and the oxygen atoms are in red. 59 In L M 1 , the pentagon begins to open, the C2-C3 bond is slightly broken with an elongated bond length 1.69 A (quite close to 1.55 A in TS1) , and the double bond characters of C2=C6 and C3=C7 are still preserved (see Fig. 4.Id). Clearly, even when the C2-C3 bond is partially broken, C2 and C3 still connect to their neighboring carbon atoms in the low layer via C-C single bonds. This fact offers strong support for our partitioning scheme of the two-layered ONIOM model. Due to the partial breaking of the C2-C3 bond, C3 in L M 1 becomes a new active center because it has one potential dangling bond upon a complete breaking of the C2-C3 bond. The geometry of T S 2 is shown in Fig. 4.5c. The distance between N and C3 is 1.94 A , indicating the bond forming and breaking motions at T S 2 . The system can easily overcome this energy barrier of 12.2 kcal/mol from L M 1 to T S 2 , which is smaller than the energy released from the initial reaction (19.1 kcal/mol). After crossing T S 2 , the system reaches L M 2 (shown in Fig. 4.5d). In L M 2 , C2 and C3 separate further away with a distance of 2.39 A. N forms bonds with C2 and C3 with bond lengths of 1.39 A and 1.40 A , respectively, resulting in a 6-membered ring of five carbon atoms and one nitrogen atom. The formation of L M 2 is highly exothermic: the system releases 85.5 kcal/mol. Such a large amount of energy release will assist the system to move further and even break some strong bonds. The geometries of T S 3 and L M 3 are shown in Figs. 4.5e and 5f. In T S 3 , the nitrogen atom attacks CI and the oxygen atom breaks away from CI, which is a pseudo SN2 reaction. The structure of T S 3 clearly indicates that it connects to the two intermediates that have either O or N bounded to CI. Although the energy barrier for T S 3 is as high as 41.1 kcal/mol, the previous steps already have released enough energy to help the system overcome this barrier. For L M 3 , one can see that N forms single bonds with CI, C2, and C3, and also with O. The oxygen atom sticks out of the sidewall of the nanotube. The energy of L M 3 is 90.0 kcal/mol lower than that of the reactants, and it is only 2.4 kcal/mol higher than L M 2 , indicating that L M 3 is quite stable. In conclusion, the net reaction of NO with C199H20 is that NO inserts its N into the defect site with the initial attack of O toward the active carbon atom. This reaction is highly thermally feasible (Fig. 4.5i). 60 4.3.2. Attacking of the Second NO Based o n the N B O analysis , there are three 2-center N B O s i n v o l v i n g N and its three ne ighbor ing carbon atoms i n L M 3 : a ( N - C l ) = 0.800 N O / ? 2 7 8 ) + 0.600 C l ( s p 3 0 5 ) , a ( N - C 2 ) = 0.801 N ( ^ 2 - 7 2 ) + 0.599 C 2 ( s p 2 9 1 ) , and a ( N - C 3 ) = 0.800 N(sp2n) + 0.600 C 3 ( s p 2 ' 9 5 ) . It is obvious that the N B O s o f these three carbon atoms have h igh p characters. N also forms a a bond w i t h O , <r(N-0) = 0.751 N ( s p 3 " ) + 0.660 0(sp1A\ w i t h a bond length o f 1.41 A. The N B O orbi ta l coefficients o f N and O i n a ( N - O ) c lear ly indicate that it is m a i n l y the head-to-head overlap o f sp3 hybr id i zed orbitals o f N and one p orbital o f O . The unpaired electron is mos t ly loca l i zed o n O , w h i c h has a - 0 . 5 7 4 part ial charge. The re la t ive ly l ong b o n d distance between N and O (1.41 A) indicates that O is not s trongly bounded to N , so this N - 0 bond m a y be easi ly b roken upon proper attack f rom another N O molecu le i n the N O excess environment. Therefore, w e considered the attack o f a second N O toward L M 3 (C199H20NO). The transit ion state TS4 is shown i n F i g . 4.5g. In TS4, the N end o f the second N O attacks C I and O l (the oxygen atom o f the first N O ) . The distance between C I and N 2 (the ni trogen atom o f the second N O ) is 1.61 A ; the C l - N l (the ni trogen atom o f the first N O ) bond elongates to 1.58 A ; and the distance between N 2 and O l is 2.55 A. The electrostatic attraction between N 2 and O l stabil izes TS4 , whereas the electrostatic repuls ion between C I and N 2 counterbalances this attraction. The overa l l interaction o f these two reactants renders the react ion barrier for TS4 to be o n l y 3.7 k c a l / m o l : this react ion is ve ry facile. F o l l o w i n g the v ibra t ional mode o f the imaginary frequency, w e found the final product, a complex o f NO2 w i t h Ci9 9 Pi2oNO, w h i c h is shown i n F i g . 4 .5h. In the final product, NO2 bonds to C i 9 9 H 2 o N O through a long ion ic N 2 - C 1 bond w i t h a b o n d length o f 1.64 A , and the interaction between the oxygen atom ( O l ) o f N 0 2 and the ni trogen atom ( N I ) o f C199H20NO is ve ry weak w i t h a bond distance o f 2.64 A . In an experiment setting, N 0 2 can be r emoved f rom the surface o f the S W C N T b y a flow o f A r gas. The formation o f the final product releases 78.3 k c a l / m o l o f energy from the react ion o f the second N O w i t h C199H20NO. The forward react ion barrier is o n l y 3.7 k c a l / m o l , but the reverse react ion barrier is as h igh as 82.0 k c a l / m o l , w h i c h means that the reverse react ion is k ine t i ca l ly v i r tua l ly imposs ib le under normal condi t ions. 61 In summary, the second NO extracts the oxygen atom from C199H20NO, forming NO2 and the N-substitutionally doped SWCNT through a one-step reaction (Fig. 4.5j). This reaction can be explained by the FMO analysis. When N2 attacks C I , the positive lobe of the SOMO on N2 of the second NO has an in-phase overlap with the H O M O on CI of L M 3 . At the same time, the negative lobe of the SOMO on N2 also has an in-phase overlap with the HOMO on O of L M 3 . These effective molecular orbital overlaps make the one-step reaction possible. Structure optimization and N B O analysis were also performed for the N -substitutionally doped (5,5) SWCNT (Ci99NH2o). The doped N stays a little bit above the sidewall surface of the SWCNT (Fig. 4.6a), because of the longer CT(C-N) bonds and the asymmetric sp3 hybridization of N . The partial charges are shown in Fig. 4.6b. The band gap is only 0.74 eV, which is smaller than those of C2ooH2oand C199H20 (1.38 eV and 0.84 eV, respectively). This means that the substitutional doping of N wil l decrease the band gap of the (5,5) SWCNT, i.e., increasing its conductivity. Substitutional doping of N can also destruct the conjugated 7T system of C200H20 and introduce localized electronic states (Figs. 4.6c and 4.6d) like what the 5-1DB defect does to the pure SWCNT, but to a lesser degree. (c) H O M O (-3.81 e V ) (d) L U M O (-3.07 e V ) F i g u r e 4.6. Structure, partial charges, and F M O s o f the substitutionally N - d o p e d (5,5) S W C N T . T h e numbers in parentheses are the orbital energies in e V . 62 4.4. Conclusions In conclusion, we have performed theoretical studies of the chemical reactivity of the 5-1DB defect on the SWCNT by a two-layered ONIOM model. The LDOS, FMO, and NBO analyses indicate that our ONIOM model successfully captures the essence of the chemical reactivity of the system. This work clearly indicates that the 5-1DB defect on the SWCNT is chemically reactive. Thus, it can be used as the active site for the functionalization of the SWCNT. We have presented a possible way to fabricate the substitutionally N-doped (5,5) SWCNT mediating the 5-1DB defect. A rational reaction pathway has been explored in details (Figs. 4.5i and 4.5j). First, an NO attacks the active carbon atom of the 5-1DB defect, yielding C199H20NO, which has the nitrogen atom inserted into the sidewall of the SWCNT and the oxygen atom sticking out of the surface. Second, another NO attacks C199H20NO, forming the final product, which has the nitrogen atom completely heals the defect site. These reactions are thermally self-catalyzed, which reveals the possibility to fabricate the substitutionally heteroatom-doped SWCNT under mild conditions. We believe that our theoretical investigation shall provide guidance for experimentalists in their future work in this area. 4.5. References (1) (a) Iijima, S. Nature 1991, 354, 56. (b) Iijima S.; Ichihashi, T. Nature 1993, 363, 603. (2) Liu C ; Fan Y. Y.; Liu M.; Cong H. T.; Cheng H. M.; Dresselhaus, M. S. Science 1999, 286, 1127. (3) Kong, J.; Franklin, N. R.; Zhou C. W.; Chapline, M. G.; Peng, S.; Cho, K. J.; Dai, H. J. Science 2000, 287, 622. (4) Katz E.; Willner, I.; ChemPhysChem 2004, 5, 1085. (5) Peng S.; Cho, K. J. Nano Lett 2003, 3, 513. (6) Choi, H. J.; Ihm, J.; Louie, S. G.; Cohen, M. L. Phys. Rev. Lett. 1999, 307, 158. (7) Blase, X.; Charlier, J.-C; De Vita, A.; Car, R. Appl. Phys. Lett. 1997, 70, 197. (8) Nikulkina, A. V.; D'yachkov, P. N. Russ. J. Inorg. Chem. 2004, 49, 430. (9) Srivastava, D.; Menon, M.; Daraio, C ; Jin, S.; Sadanadan, B.; Rao A. M. Phys. Rev. B 2004, 69, 153414. 63 (10) (a) Golberg, D.; Bando, Y.; Han, W.; Kurashima, K.; Sato, T. Chem. Phys. Lett. 1999, 308, 337. (b) Golberg, D.; Bando, Y.; Bourgeois, L.; Kurashima, K.; Sato, T. Carbon 2000, 38, 2017. (11) Sung, S. L.; Tsai, S. H.; Tseng, C. H.; Chiang, F. K.; Liu, X. W.; Shih, H. C. Appl. Phys. Lett. 1999, 74, 197. (12) (a) Stephan, O.; Ajayan, P. M.; Colliex, C ; Redlich, Ph.; Lambert, J. M.; Bernier, P.; Lefin, P. Science 1994, 266, 1683. (b) Glerup, M.; Steinmetz, J.; Samaille, D.; Stephan, O.; Enouz. S.; Loiseau, A.; Roth, S.; Bernier, P. Chem. Phys. Lett. 2004, 387, 193. (13) (a) Zhang, Y.; Gu, H.; Suenaga, K.; Iijima, S. Chem. Phys. Lett. 1997, 279, 264. (b) Gai, P. L.; Stephan, O.; McGuire, K.; Rao, A. M.; Dresselhaus, M. S.; Dresselhaus, G. ; Colliex, C. J. Mater. Chem. 2004, 14, 669. (14) Terrones, M.; Jorio, A.; Endo, M.; Rao, A. M.; Kim, Y. A.; Hayashi, T.; Terrones, H. ; Charlier, J.-C; Dresselhaus, G.; Dresselhaus, M. S. Material Today 2004, 7, 30. (15) Krasheninnikov A. V.; Nordlund, K. J. Vac. Sci. Technol. B 2002, 20, 728. (16) Ajayan, P. M.; Ravikumar, V.; Charlier, J.-C. Phys. Rev. Lett. 1998, 81, 1437. (17) Charlier, J.-C. Acc. Chem. Res. 2002, 35, 1063. (18) Krasheninnikov, A. V.; Nordlund, K.; Sirvio, M.; Salonen, E.; Keinonen, J. Phys. Rev. B 2001, 63, 245405. (19) Terrones, M.; Terrones, H.; Banhart, F.; Charlier, J.-C; Ajayan, P. M. Scicence 2000, 288, 1226. (20) (a) Chakrapani, N ; Zhang, Y. M.; Nayak, S. K.; Moore, J. A.; Carroll, D. L.; Choi, Y. Y.; Ajayan, P. M. J. Phys. Chem. B 2003, 107, 9308. (b) Lu, A. J.; Pan B. C. Phys. Rev. B 2005, 71, 165416. (c) Mercuri, F.; Sgamellotti, A.; Valentini, L.; Armentano, I.; Kenny, J. M. J. Phys. Chem. B 2005,109, 13175. (21) Stewart, J. J. P. J. Comp. Chem. 1989,10, 209. (22) Becke, A. D.J. Chem. Phys. 1993, 98, 5648. (23) Lee, C. T.; Yang, W.; Parr, R. G. Phys. Rev. A 1988, 37, 785. (24) Maseras F.; Morokuma, K. J. Comp. Chem. 1995, 16, 1170. (25) Walch, S. P. Chem. Phys. Lett. 2003, 374, 501. (26) Ricca, A.; Bauschlicher, C. W.; Maiti, A. Phys. Rev. B 2003, 68, 035433. 64 (27) Lu, X.; Tian, F.; Xu, X.; Wang, N ; Zhang, Q. J. Am. Chem. Soc. 2003,125, 10459. (28) Morokuma, K. Bull. Korean Chem. Soc. 2003, 24, 797. (29) Fukui, K. Science 1987, 218, 747. (30) Rappe, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard III, W. A.; Skiff, W. M. J. Am. Chem. Soc. 2004,114, 10024. (31) Kar, T.; Akdimb, B.; Duan, X.; Pachter, R. Chem. Phys. Lett. 2004, 392, 176. (32) (a) NBO Version 3.1, Glendening, E. D.; Carpenter, A. E.; Weinhold F., 1995. (b) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. Rev. 1988, 88, 899. (33) Gaussian 03, Revision B.05, M. J. Frisch et al., Gaussian, Inc., Pittsburgh PA, 2003. 65 Chapter 5 Ozonization at the Vacancy Defect Site of the Single-Walled Carbon Nanotube 5.1. Introduction Single-Walled Carbon Nanotubes (SWCNTs) have been intensively studied during the last decade since the discoveries of Iijima in the early 1990s.1 A lot of potential applications of the SWCNTs have been proposed due to their unique properties: high Young's modulus, high thermal conductivity, and high aspect ratio structure, etc. Over the years, applications of SWCNTs have been successfully realized as chemical sensors,2 hydrogen storage materials,3 and vacuum electronic devices.4 Access to the interior of the SWCNTs is essential for most of these applications. Unfortunately, most of the SWCNTs are synthesized with closed hemispherical fullerene-like end-caps, which prevent internal adsorption of chemical reagents.5 It is thus often necessary to open the capped ends via chemical means.6-14 All these end-opening methods take advantage of the higher reactivity of the end caps, because the pyramidalization angles of any hemispherical fullerene-like end-cap are bigger than those of the sidewalls of the nanotubes. Gas-phase ozone oxidation is one of the well-developed end-opening methods.9-13 The oxidation process removes the caps and introduces or enlarges vacancy defects on the sidewall, producing two kinds of functional groups, esters and quinones, at the ends or at the defective sites of the sidewall. After high-temperature thermal treatment, these two functional groups will decompose and emit a large amount of CO and C O 2 . 1 1 - 1 3 Olefin ozonolysis can be understood through the standard Criegee's mechanism15 (Scheme 5.1). As an 18-valence-electron 1,3-dipolar molecule, ozone reacts with an * A version o f this chapter has been submitted for publication in J . Phys. Chem. B (2006) L i u , L . V . ; Tian , W . Q . ; Wang, Y . A . "Ozonization at the Vacancy Defect Site o f the Single-Walled Carbon Nanotube". 66 olefin via 1,3-dipolar cycloaddition (1,3-DC) to the Trbond of the olefin and forms the primary ozonide (3), which has an unstable five-member ring. Then, one of the 0-0 bonds and the C-C single bond of the primary ozonide then break to produce a carbonyl compound (5) and a carbonyl oxide (6) in a zwitterion form. These two compounds will recombine to form an ozonide (7). Recently, a similar Criegee's mechanism has been proposed in the reactions of ozone with Ceo and the SWCNTs. 1 6 - 1 8 © O \ / u r O V \ / \ \ / \ \ \ (=) c=c + o 3 - / C - c x - xVj-°ci 1 c=o + c=o *• c c Scheme 5.1. The Criegee's mechanism of olefin ozonolysis. Several theoretical studies have been carried out to understand the ozonization of perfect SWCNTs 1 7' 1 8 and SWCNTs with Stone-Wales defects.19-21 To the best of our knowledge, there has been no reported theoretical studies on the chemical reaction of ozone with the vacancy defect sites of SWCNTs. Vacancy defects can either occur as native defects or be induced by ion or electron irradiation of SWCNTs.2 2'2 3 The structures, mechanical and electronic properties, and potential applications of the SWCNTs with vacancy defects have been recently predicted theoretically.23-29 The chirality of the SWCNT should have a more important effect on the reactivity of the vacancy defect than the diameter of the SWCNT, since the chirality of the SWCNT could modify the structure of the vacancy defect24 Direct observations of the vacancy defects on graphite and on double-walled carbon nanotubes have been reported recently by Iijima and 30 31 coworkers using in situ high-resolution transmission electron microscopy technique. ' In our previous studies, we have shown that the vacancy defect introduces localized electronic states at the defect site, which leads to regioselectivity on the sidewall of the SWCNTs and further facilitates the selective functionalization of the SWCNTs.2 5'2 6 Such 67 reactivity of the vacancy defect was utilized to cut the SWCNTs in a well-controlled oxidative way by Smalley and coworkers. In this work, we present our theoretical studies of the ozonization at the single vacancy defect site on the sidewall of the (5,5) SWCNT to further understand the chemical properties of the vacancy defect site. 5.2. Computational Methods We first built a fragment of the (5,5) SWCNT of 120 carbon atoms with 20 end-capping hydrogen atoms, C120H20. The hydrogen atoms are used to saturate the carbon atoms with dangling bonds at the two ends. We removed one carbon atom from the middle of the sidewall of C120H-20, producing an ideal single vacancy, which contains three carbon atoms with dangling bonds (Fig. 5.1a). Due to the large system size, we first employed the semiempirical AMI method33 to optimize the geometry. We further refined the AMI optimized geometry with DFT method at the B3LYP/6-31G(d) level of theory.34'35 In the optimized structure, two of the three carbon atoms with dangling bonds combine to form an asymmetric 5-1DB defect23, which has one newly formed 5-membered ring and one carbon atom with dangling bond (Fig. 5.1b). We have carried out systematic theoretical calculations to examine the structure and the stability of the 5-1DB defect on the SWCNT and found that the ground state of the 5-1DB defect on the (5,5) SWCNT is singlet.36 We employed the ONIOM 3 7 method to explore the reaction pathways. In the ONIOM (a) ideal single vacancy (b) the 5 - 1 D B defect F i g u r e 5.1. Single vacancy defect on the sidewall o f the (5,5) S W C N T (carbon atoms within the nonagon o f the 5-1 D B defect are numbered). 68 model, the AMI method and the B3LYP/6-31G(d) method have been used for the lower-level and higher-level treatments, respectively. The 9-membered ring of the 5-1DB defect was chosen to be the higher layer (Fig. 5.1b). This 2-layered ONIOM model is capable of capturing the essential chemical reactivity of the 5-1DB defect. All the structures of the transition states, the intermediates, and the products were located by this 2-layered ONIOM model. The Hessian was calculated to verify the nature of the stationary points on the potential energy surface: one and only one imaginary frequency for the transition state, and no imaginary frequency for the minima. Local minima connected by a transition state were found from the optimization of the disturbed structures of the transition state. To verify the results of the 2-layered ONIOM model, single-point calculations were performed at the B3LYP/6-31G(d) level of theory whenever necessary. Partial charges and bonding properties were studied by using the NBO 3.138 module in the Gaussian 03 package.39 To confirm the assessment of the static quantum mechanical calculations, we also carried out the atom-centered density matrix propagation (ADMP)40"42 based ab initio molecular dynamics (AIMD) to study the reaction of ozone with the vacancy defect site at 300 K with time step 0.25 fs and fictitious electronic mass 0.1 au. A 2-layered ONIOM/ADMP scheme was applied for the AIMD simulation.43 The partition of the ONIOM model in the ADMP calculations is the same as that of the static quantum mechanical calculations, except that we used the universal force field (UFF)44 for the lower layer to save computational time. All the above calculations were carried out by using the Gaussian 03 package.39 5.3. Results and Discussion 5.3.1. Static Quantum Mechanical Studies The bond lengths, bond orders, and partial charges of the 9-membered ring of the 5-1DB vacancy defect are shown in Table 5.1. Among these nine C-C bonds, the C5-C6 bond on the pentagon is the longest (with bond length 1.55 A) and the weakest (with bond order 1.09). The C9-C1 bond is the shortest bond with bond length 1.39 A and bond order 1.31. The carbon atom with the dangling bond, CI, has the largest positive charge +0.10, whereas its two neighboring carbon atoms have the two largest negative 69 charges, -0.12 for C2 and -0.05 for C9. These large partial charges significantly make the two bonds connecting CI to its two neighboring carbon atoms C2 and C9 shorter and stronger. Previously, we have found that CI is the major contributor to the HOMO and the LUMO of the vacancy-defected SWCNT. 2 5 The out-of-plane geometry and the large positive charge of CI make it more reactive toward the attacking reagents. Hereafter, we will call CI the active carbon atom. The bond lengths and the bond orders indicate that around the 5-1DB defect site, the C2-C3, C4-C5, C6-C7, and C8-C9 bonds have some significant 7T bond character. In fact, these four bonds have similar bond lengths to the other aromatic C=C double bonds on the sidewall of the SWCNT. We thus studied the attacking of ozone on CI and these four bonds in the 9-membered ring as prototype reactions of O 3 with the 5-1DB defect site, whose results are presented as the following: the reaction on CI, on the C8-C9 bond (position 1), on the C6-C7 bond (position 2), on the C4-C5 bond (position 3), and on the C2-C3 bond (position 4). At the end, we present our ADMP results. Table 5.1. Bond lengths (in A), bond orders, and partial charges of the 9-membered ring of the 5-1DB defect. Bond Bond length Bond order Atom Charge C 1 - C 2 1.40 1.31 C I 0.10 C 2 - C 3 1.41 1.23 C2 -0.12 C 3 - C 4 1.44 1.18 C3 0.03 C 4 - C 5 1.46 1.27 C4 0.00 C 5 - C 6 1.55 1.09 C5 0.01 C 6 - C 7 1.44 1.35 C6 0.00 C 7 - C 8 1.47 1.16 C7 0.00 C 8 - C 9 1.42 1.28 C8 -0.03 C 9 - C 1 1.39 1.31 C9 -0.05 5.3.1.1. Reaction of 0 3 on the Active Carbon Atom The structures of the initial intermediate ("Complex) and the initial attacking transition state on CI (aTSl) are shown in Figs. 5.2a and 5.2b. In "Complex, O 3 and CI form a 4-membered ring. Based on the NBO analysis of "Complex, the partial charges of 70 CI, 01, 02, and 03 are 0.13, -0.20, 0.23, and -0.21, respectively, which means that 0.19 electrons are transferred from the SWCNT to O 3 . In terms of electrostatic effects, the electrostatic attractions between CI and Ol and between CI and 03 stabilize "Complex, whereas the electrostatic repulsion between CI and 02 counteracts with this attractive stabilization. In a TSl , O 3 and CI form a more compact 4-membered ring than the one in "Complex. The bond lengths of the Cl-01 and Cl-03 bonds shorten to 2.24 A and 2.85 A, respectively. The imaginary vibrational mode shows the shortening of the Cl-01 bond and elongating of the 01-02 bond, indicating the attacking of 01 to CI and the breaking of the 01-02 bond, i.e., the dissociation of O 3 . Based on the NBO analysis of a TSl , the partial charges of 01, 02, 03, and CI are -0.21, 0.22, -0.21, and 0.14, respectively. So, there are 0.20 electrons transferred from the SWCNT to O 3 , and the electrostatic interaction scheme in a TSl is qualitatively the same as that in "Complex. Following the imaginary vibrational mode forward, we found that CI indeed captures 01 and the outgoing singlet O2 ( Ag) can be immediately quenched into the triplet O2 ( £ g ) through thermal collisions. The Cl-01 bond is very strong with a bond length of 1.21 A , close to a typical carbonylic C=0 double bond. The structure of the product ("Product) is shown in Fig. 5.2c. The energies of "Complex and "TS1 are 5.9 kcal/mol and 0.3 kcal/mol lower than the reactants, respectively. The forward reaction barrier is only 5.6 kcal/mol for "Complex, and the effective forward reaction barrier of the overall reaction is very close to zero, only -0.3 kcal/mol. The overall energy released from the reaction is -128.0 kcal/mol. Based on the energy profile, the reaction of O 3 with CI is highly exothermic and facile. 5.3.1.2.1,3-DC of 0 3 on the C8-C9 Bond (Position 1) The structures of the initial intermediate (P1Complex) and transition state (P1TS1) are shown in Figs. 5.3a and 5.3b. plComplex was reported as a 7T-complex in previous matrix spectroscopic and theoretical studies of ozonization of certain alkenes.45 The complex is stabilized by the interaction of the 7T-type HOMO and LUMO on alkenes and O 3 . "Complex is 4.3 kcal/mol more stable than the reactants, whereas P ,TS1 lays 2.4 kcal/mol above the reactants. In P 1TS1, the lengths of the C8-01 and C9-03 bonds are 71 (d) Energy profile F i g u r e 5.2. Geometries o f the transition states, the intermediates, and the final product o f the reaction o f 0 3 with the active carbon atom o f C119H20. T h e units o f energy and bond length are in kca l /mol and A, respectively. T h e oxygen atoms are in red. 2.45 A and 1.87 A, respectively. This indicates that the 1,3-DC of 0 3 on C8-C9 follows an asynchronous way. In the first intermediate P 1 L M 1 (Fig. 5.3c), the C8-C9 bond length is 1.66 A, longer than those of "Complex (1.44 A) and P 1 T S 1 (1.483 A), due to the rehybridization of C8 and C9 from sp2 to sp3. The binding energy of P 1 L M 1 is -27.2 kcal/mol (relative to the reactants), which means the 1,3-DC of O 3 on C8-C9 is exothermic. We also explored the forward decomposition of P 1 L M 1 . Two different pathways were found. In the first pathway, the system climbs through the transition state P I T S 2 (Fig. 5.3d), by breaking the 02-03 bond (2.16 A) and forming the Cl-03 bond (1.781 A), with an activation barrier 35.3 kcal/mol. After overcoming P 1 T S 2 , 01 and 02 dissociate 72 as a singlet O2, the C9-03 bond breaks, and 03 forms a carbonylic C=0 double bond with CI, and yields the same product "Product as in the reaction of O 3 on CI. The second decomposition pathway goes through another transition state P 1 T S 2 ' (Fig. 5.3e) and forms an epoxy adduct p,epo89 (Fig. 5.3f). The imaginary vibrational mode clearly shows the breaking of the 01-02 and C9-03 bonds. The activation barrier from P , L M 1 to P 1 T S 2 ' is 42.9 kcal/mol, which is 7.6 kcal/mol higher than that of the first decomposition pathway. In contrast to the high exothermicity of the first decomposition pathway (—61.5 kcal/mol relative to P I L M 1 ) , the second decomposition pathway is endo thermic (17.5 kcal/mol with respect to P 1 L M 1 ) . Therefore, the first decomposition pathway is kinetically and thermodynamically much more favourable than the second decomposition pathway. However, the high reaction barrier (35.3 kcal/mol) from P 1 L M 1 ( d ) P 1 T S 2 ( e ) p , T S 2 ' (f) P , epo89 + 0 2 (%~) 73 "Product + 0 2 ( \ ) -128.0 (g) Energy profile Figure 5.3. Geometries of the transition states, the intermediates, and the final product of the 1,3-DC of 0 3 on the C 8 - C 9 bond (position 1) on the 9-membered ring of C i i 9 H 2 o . The units of energy and bond length are in kcal/mol and A , respectively. The oxygen atoms are in red. to the products makes this reaction pathway uncompetitive to the dissociation pathway on the active atom. 5.3.1.3.1,3-DC of 0 3 on the C6-C7 Bond (Position 2) The structures of P2Complex, P 2TS1, and P 2LM1 are shown in Figs. 5.4a, 5.4b, and 5.4c. P2Complex is also a 7r-complex according to its structure. The imaginary frequency mode of P 2TS1 mainly shows the attacking of 01 on C6 and the stretching of the C5-C6 bond. In the primary ozonide P 2 LM1, the C5-C6 bond (1.72 A) is nearly broken. With respect to the energy of the reactants, p2Complex lays 4.5 kcal/mol lower, whereas P2TS1 stays 6.4 kcal/mol higher. Thus, the forward reaction barrier from P2Complex is 10.9 74 kcal/mol, which is 5.3 kcal/mol higher than that of the reaction on CI. The binding energy of P 2LM1 is -24.2 kcal/mol, which means the 1,3-DC of O 3 on C6-C7 is also exothermic. Two different decomposition or isomerization pathways of P 2LM1 were explored. The first pathway needs to overcome a 28.5 kcal/mol activation barrier and reaches the transition state P 2TS2 (Fig. 5.4d), in which 03 attacks C8 and breaks the 02-03 bond. After passing P 2TS2, the system relaxes to P 2LM2 (Fig. 5.4e) by releasing nearly 5 kcal/mol energy. In P 2LM2, 03 forms an epoxy adduct with C7 and C8 and C6—01 elongates slightly. P 2 LM2 is 23.6 kcal/mol less stable than P 2 LM1. P 2 LM2 can isomerize to P2Product (Fig. 5.4g) through another transition state, P 2TS3 (Fig. 5.4f), by overcoming a small barrier of 2.5 kcal/mol. In P 2TS3, 01 begins to migrate from C6 to CI. In p2Product, Ol forms a bond with CI and 02 forms a bond with C6: Ol and 02 thus coalesce into a bridge between C6 and CI. P2Product is 79.2 kcal/mol more stable than the reactants. Another isomerization pathway of P 2LM1 goes through the transition state P 2TS2' (Fig. 5.4h), in which 01, 02, 03, C6, and C7 are almost in the same plane. The imaginary vibrational mode of P 2TS2' clearly shows the swinging motion of 02 about the 01-03-C6-C7 plane. There is virtually no energy cost in going from P 2LM1 to P 2TS2'. After passing P 2TS2', the system goes to the endo-primary ozonide P 2 LM2' (Fig. 5.4i), whose energy is only 0.5 kcal/mol lower than that of the exo-primary pzonide P 2 LM1. The isomerization continues moving forward to overcome a 24.8 kcal/mol barrier and reaches P 2TS3' (Fig. 5.4j), in which C5-C6 is almost broken (1.86 A). Here, the imaginary vibrational mode shows the breaking of the 03-C7 and 01-02 bonds and the attacking of 01 to C5. Once overcoming this barrier, the system yields the final product P2Product' (Fig. 5.4k), which is 159.8 kcal/mol more stable than the reactants. However, the 24.6 kcal/mol reaction barrier from P 2 LM2' to the final products renders this pathway unfavorable compared to the dissociation on the active atom. 5.3.1.4.1,3-DC of 0 3 on the C4 -C5 Bond (Position 3) The structures of P3Complex, P 3TS1, and P 3LM1 are shown in Figs. 5.5a, 5.5b, and 5.5c. P3Complex is also a 7T-complex according to its structure. The imaginary vibrational mode of P 3TS1 clearly indicates the concerted attacking of 01 to C4 and 03 to C5 and 75 shows the stretching of the C4-C5 bond. The reaction barrier for the 1,3-DC on C4-C5 is 19.3 kcal/mol. After overcoming this barrier, the system goes to P 3 LM1, which is not a primary ozonide. In P 3 LM1, the C4-C5 bond (2.98 A) is totally broken, and 01, 02, and 03 form a bridge between C4 and C5. P 3 LM1 is 46.8 kcal/mol below the energy of the reactants. It is thermodynamically more stable than the primary ozonides P 1 LM1 and (g) "P roduc t (h) TS2' 76 (i) P 2LM2' 0) TS3' (k) " P r o d u c t ' P 2 T S j ^Product' -159.8 (1) Energy profile F i g u r e 5.4. Geometries o f the transition states, the intermediates, and the final product o f the the 1,3-D C o f 0 3 on the C 6 - C 7 bond (position 2) on the 9-membered ring o f C i i 9 H 2 o . T h e units o f energy and bond length are in kcal /mol and A, respectively. T h e oxygen atoms are in red. Two isomerization pathways of P 3 LM1 were found. The first one goes through P 3TS2 (Fig. 5.5d), by breaking of the 01-02 bond with a barrier of only 7.7 kcal/mol. After crossing P 3TS2, the system goes to P3Product (Fig. 5.5e), which is 51.5 kcal/mol more stable than the reactants. Another pathway goes through P 3TS2' (Fig. 5.5f), in which 03 77 attacks CI and simultaneously breaks the bond with 02 with a barrier of only 8.9 kcal/mol. The product, P3Product', is shown in Fig. 5.5g, in which 03 bridges CI and C5, and it is 100.5 kcal/mol more stable than the reactants. In spite of the exothermicity of this reaction pathway, the first reaction barrier from P3Complex to P 3 LM1 is much higher than the corresponding reaction barrier from "Complex to a T S l . (g) "Product' 78 -100.5 (h) Energy profile F i g u r e 5.5. Geometries o f the transition states, the intermediates, and the final product o f the the 1,3-D C o f 0 3 on the C 4 - C 5 bond Oposition 3) on the 9-membered ring o f C i 1 9 H 2 o . T h e units o f energy and bond length are in kca l /mol and A, respectively. T h e oxygen atoms are in red. 5.3.1.5. Reaction of 0 3 on the C 2 - C 3 Bond (Position 4) The structures of P 4TS1 and P 4 LM1 are shown in Figs. 5.6a and 5.6b. We did not find a 7r-complex for the reaction on the C2-C3 bond. In P 4TS1, the 01-C2 bond is 1.50 A, which is much shorter than those in the previous initial-reaction transition states. The reaction barrier is 17.3 kcal/mol. The primary ozonide P 4 LM1 is only 6.2 kcal/mol more stable than the reactants and is the least stable primary ozonide we have found. We also found a dissociation pathway for P 4 LM1 with an activation barrier 23.5 kcal/mol. The system goes through P 4TS2 (Fig. 5.6c), in which 01 begins to break the bond with 0 2 and attack CI at the same time and 02-03 tends to leave as the singlet O 2 . After overcoming P 4TS2, 02-03 indeed dissociate from the system and 01 migrates from C2 to CI, yielding the same final product (aProduct) as that in the reaction on CI. The initial reaction barrier is too high for the system to reach P 4 LM1 in comparison with the initial reaction barrier of the dissociation at the active carbon atom. 79 (a) P 4 T S 1 (b) P 4 L M 1 (c) P 4 T S 2 "Product + 02(%~) -128.0 (d) Energy profile F i g u r e 5.6. Geometries o f the transition states, the intermediates, and the final product o f the 1 ,3-DC o f 0 3 on the C 2 - C 3 bond (position 4) on the 9-membered ring o f C119H20. T h e units o f energy and bond length are in kcal /mol and A, respectively. T h e oxygen atoms are in red. 5.3.2. Ab Initio Molecular Dynamics Studies Static quantum mechanical studies have investigated for five different reaction positions of O 3 on the 9-membered ring of the 5-1DB defect site. After comparing all the 80 reaction pathways, we can conclude that the reaction of O 3 on the active carbon atom CI is most probable, because it is a one-step reaction with the lowest initial attacking barrier. This reaction pathway is kinetically much more favorable than the other ones. 0 100 200 300 400 500 600 700 800 900 1000 Simulation Time (fs) Figure 5.7. Relative potential energy (in kcal/mol) for the system during the A D M P simulation of 1 ps at 300 K . The insert is the relative potential energy for the first 100 fs. To confirm our assessment from the static quantum mechanical studies of the reactions of O 3 around the 5-1DB defect, we have carried out ADMP-based AIMD simulations at 300 K. Initially, we placed an O 3 molecule above the center of 9-membered ring so that all the reactive sites around the 5-1DB defect have equal chance to interact with the incoming O 3 molecule. Our dynamical simulation results confirm the spontaneous dissociation of O 3 on CI to be the most probable reaction process, whose animated reaction trajectory is available in the Supporting Information. The change of potential energy of the system during the simulations is shown in Fig. 5.7. In less than 50 fs, the system quickly overcomes a ca. 20 kcal/mol barrier and releases a large amount of heat (about 160 kcal/mol), during which one oxygen atom is captured by the active carbon atom CI, forming a carbonylic C=0 bond, and the other two oxygen atoms leave as O2. This mechanism is consistent with the scenario from the 81 static quantum mechanical study discussed above, despite the differences in the energies due to the different methods used for the lower layer of the 2-layered ONIOM model. 5.4. Conclusion In conclusion, we have investigated the reactions of O 3 with the 5-1DB defect on the (5,5) SWCNT by static quantum mechanical and ADMP-based AIMD methods within a 2-layered ONIOM model. Different pathways on the five possible reactive positions of the 9-membered ring of the 5-1DB defect were explored. The most favored reaction takes place on the active carbon atom, through a one-step process, in which the active carbon atom captures an oxygen atom from O 3 and the remaining two oxygen atoms dissociate away as singlet O2. The other four reaction pathways follow the standard 1,3-dipolar cycloaddition mechanism. Our AIMD dynamical simulation at 300 K indicates the fast spontaneous dissociation of O 3 on the 5-1DB defect. The high exothermicity and the low reaction barrier of this dissociation reaction suggests that it is thermally and kinetically very favourable. 5.5. References (1) Iijima S.; Ichihashi, T. Nature 1993, 363, 603. (2) Kong, J.; Franklin, N. R.; Zhou, C. W.; Chapline, M. G.; Peng, S.; Cho, K. J.; Dai, H. J. Science 2000, 287, 622. (3) Liu C ; Fan, Y. Y.; Liu, M.; Cong, H. T.; Cheng, H. M.; Dresselhaus, M. S. Science 1999, 286, 1127. (4) Zhou, O.; Shimoda, FL; Gao, B.; Oh, S.; Fleming, L.; Yue, G. Acc. Chem. Res. 2002, 35, 1045. (5) Ebbsen, T. W., Carbon Nanotubes: Preparation and Properties, CRC Press: Boca Raton, FL (1997). (6) Tsang, S. C ; Harris, P. J. F.; Green, M. L. H. Nature 1993, 362, 520. (7) Ajayan, P. M.; Ebbesen, T. W.; Ichihashi, T.; Iijima, S.; Tanigaki, K.; Hiura, H. Nature 1993, 362, 522. (8) Liu, J.; Rinzler, A. G.; Dai, H.; Hamer, J. H.; Bradley, R. K.; Boul, P.J.; Lu, A.; 82 Iverson, T.; Shelimov, K.; Huffman, C. B.; Rodriguez-Macias, F.; Shon, Y.-S.; Lee, T. R.; Colbert, D. T.; Smalley, R. E. Science 1998, 280, 1253. (9) Mawhinney, D. B.; Naumenko, V.; Kuznetsova, A.; Yates, J. T.; Liu, J.; Smalley, R. E. J. Am. Chem. Soc. 2000,122, 2383. (10) Byl, O.; Kondratyuk, P.; Forth, S. T.; FitzGerald, S. A.; Chen L.; Johnson, J. K.; Yates, J. T. J. Am. Chem. Soc. 2003,125, 5889. (11) Mawhinney, D. B.; Naumenko, V.; Kuznetsova, A.; Yates, J. T.; Liu, J.; Smalley, R. E. Chem. Phys. Lett. 2000, 324, 213. (12) Kuznetsova, A.; Popova, I.; Yates, J. T.; Bronikowski, M. J.; Huffman, C. B.; Liu, J.; Smalley, R. E.; Hwu, H. H.; Chen, J. G. G. J. Am. Chem. Soc. 2001,123, 10699. (13) Kuznetsova, A.; Mawhinney, D. B.; Naumenko, V.; Yates, J. T.; Liu, J.; Smalley, R. E. Chem. Phys. Lett. 2000, 321, 292. (14) Niyogi, S.; Hamon, M. A.; Hu, H.; Zhao, B.; Bhowmik, P.; Sen, R.; Itkis, M. E.; Haddon, R. C. Acc. Chem. Res. 2002, 35, 1105. (15) Criegee, R. Angew. Chem. Int. Ed. 1975,14,745. (16) Shang, Z.; Pan, Y.; Cai, Z.; Zhao, X.; Tang, A. J. Phys. Chem. A 2000,104, 1915. (17) Lu, X.; Zhang, L.; Xu, X.; Wang, N.; Zhang, Q. J. Phys. Chem. B 2002, 705,2136. (18) Yim W. L.; Liu, Z. F. Chem. Phys. Lett. 2004, 398, 297. (19) Picozzi, S.; Santucci, S.; Lozzi, L.; Cantalini, C.; Baratto, C.; Sberveglieri, G.; Armentan, I.; Kenny, J. M.; Valentini, L.; Delley, B. J. Vac. Sci. Technol. A 2004, 22, 1466. (20) Picozzi, S.; Santucci, S.; Lozzi, L.; Valentini, L.; Delley, B. J. Chem. Phys. 2004, 120, 7147. (21) Lu, X.; Chen, Z.; Schleyer, P. V. R. J. Am. Chem. Soc. 2005,127, 20. (22) a) Kiang, C.-H.; Goddard, W. A. Ill; Beyers, R; Bethune, D. S. J. Phys. Chem. 1996, 100, 3749. b) Zhu, Y.; Yi, T.; Zheng, B.; Cao, L. Appl. Surf. Sci. 1999,137, 83. (23) Ajayan, P. M.; Ravikumar, V.; Charlier, J.-C. Phys. Rev. Lett. 1998, 81, 1437. (24) Lu A. J.; Pan, B. C. Phys. Rev. Lett. 2004, 92, 105504. (25) Tian, W. Q.; Liu, L. V.; Wang Y. A. (in preparation). (26) Liu, L. V.; Tian, W. Q.; Wang Y. A. J. Phys. Chem. B 2006,110, 1999. (27) Fagan, S. B.; da Silva, L. B.; Mota, R. Nano Lett. 2003, 3, 289. 83 (28) Mielke, S. L.; Troya, D.; Zhang, S.; Li, J. L.; Xiao, S. P.; Car, R.; Ruoff, R. S.; Schatz, G. C ; Belytschko, T. Chem. Phys. Lett. 2004, 390, 413. (29) Srivastava, D.; Menon, M.; Daraio, C ; Jin, S.; Sadanadan, B.; Rao A. M. Phys. Rev. 5 2004, 69, 153414. (30) Hashimoto, A.; Suenaga, K.; Gloter, A.; Urita, K.; Iijima, S. Nature 2004, 430, 870. (31) Urita, K.; Suenaga, K.; Sugai, T.; Shinohara, H; Iijima, S. Phys. Rev. Lett. 2005, 94, 155502. (32) Ziegler, K. J.; Gu, Z.; Peng, H.; Flor, E. L.; Hauge, R. H.; Smalley, R. E. J. Am. Chem. Soc. 2005,127, 1541. (33) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. P. P. J. Am. Chem. Soc. 1986,108, 5771. (34) Becke, A. D. Chem. Phys. 1993, 98, 5648. (35) Lee, C ; Yang, W.; Parr, R. G. Phys. Rev. A 1988, 37, 785. (36.) Liu, L. V.; Tian, W. Q.; Wang Y. A. (in preparation). (37) Maseras F.; Morokuma. K. J. Comput. Chem. 1995,16, 1170. (38) NBO Version 3.1, Glendening, E. D.; Carpenter, A. E.; Weinhold F. (1995); Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. Rev. 1988, 88, 899. (39) Gaussian 03, Revision B.05, M. J. Frisch et al., Gaussian, Inc., Pittsburgh PA, 2003. (40) Schlegel, H. B.; Millam, J. M.; Iyengar, S. S.; Voth, G. A.; Daniels, A. D.; Scuseria, G. E.; Frisch, M. J. J. Chem. Phys. 2001,114, 9758. (41) Iyengar, S. S.; Schlegel, H. B.; Millam, J. M.; Voth, G. A.; Scuseria, G. E.; Frisch, M. J. J. Chem. Phys. 2001,115, 10291. (42) Schlegel, H. B.; Iyengar, S. S.; Li, X.; Millam, J. M.; Voth, G. A.; Scuseria, G. E.; Frisch, M. J. J. Chem. Phys. 2002,117, 8694. (43) Rega, N.; Iyengar, S. S.; Voth, G. A.; Schlegel, H. B.; Vreven, T.; Frisch, M. J. J. Phys. Chem. B 2004,108, 4210. (44) Rappe, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A. Ill; Skiff, W. M. J. Am. Chem. Soc. 1992,114, 10024. (45) a) Kohlmiller, C. K.; Andrews, L. J. Am. Chem. Soc. 1981, 103, 2578. b) McKee, M. L.; Rohlfing, C. M. J. Am. Chem. Soc. 1989, 111, 2497. 84 Chapter 6 Electronic Properties and Reactivity of the Pt-Doped Carbon Nanotubes 6.1. Introduction Since the discovery of the single-walled carbon nanotube (SWCNT),1 experimental and theoretical investigations on the chemical2,3 and physical4,5 properties of the SWCNT have been growing rapidly due to its potential applications6 in molecular electronics,7 chemical sensor,8 vacuum electronic devices,9 field emission flat panel display,10 catalysis,11 and optics.12 The SWCNT can be visualized as a roll of the graphite sheet and can be classified as metallic, narrow-gap and moderate-gap semiconducting nanotubes according to the wrapping vectors (m,n).13 As shown in Fig. 1.2, nanotubes are characterized with a chiral vector (AB - ma+nb) in which nanotubes are wrapped and a translation vector in which nanotubes elongate. If n - m = 3q (with integral m, n, and q), the nanotube is metallic. Otherwise, it is semiconducting with a band gap.13b There are further detailed classifications of nanotubes with respect to the conductance according to the "n - m rules".13 As one-dimensional rolled graphite sheets, nanotubes display different electronic properties from those of planar graphite sheets and fullerenes: the electronic properties of nanotubes can be controlled by their diameters with different hybridization effects.53 For example, the pyramidalization of nanotubes is different from fullerenes and there exists 7x-orbital misalignment between adjacent pairs of conjugated carbon atoms,2a which renders different reactivity of nanotubes from fullerenes and among nanotubes of various diameters.2a,5e'14 Chemical reactions can take place on the sidewall of the nanotubes15 or § A version of this chapter has been submitted for publication as an invited article in Phys. Chem. Chem. Phys. (2006). Tian, W . Q . ; L i u , L . V . ; Wang, Y . A . "Electronic Properties and Reactivity o f the Pt-Doped Carbon Nanotubes". 85 at the ends of the nano tubes. 1 5 j ' 1 5 k ' 1 6 In spite of numerous studies, the reactivity of the SWCNT is still not clear and deserves further investigtion. Partial changes in the nanotube structure through vacancy,18 doping with other elements (replacement of the carbon atoms on the SWCNT to produce the hetero SWCNT),1 9 and distortion20 can modify the electronics and reactivity of the nanotubes to some degree. 1 8 g ' 1 9 c It has been found that substituting a carbon atom by a metal atom in fullerenes21 renders the metal atom as an active center in chemical reactions.216'22 As a pseudo one-dimensional system with tube structure, the SWCNTs with defects and doping can serve as catalysts for gas-phase and liquid-phase reactions: the reactants enter from one end of an open SWCNT, the reaction is catalyzed at the defect or doping sites of the SWCNT, and the products exit from the other end of the open SWCNT. A good understanding of the electronic structure of the perfect, defected, and doped SWCNTs helps to comprehend the reactivity of such SWCNTs and to utilize such SWCNTs in chemical reactions. In this work, we will study the structures and reactivity of the hetero SWCNTs (HSWCNTs) to shed some light on the reactivity of and possible applications of such HSWCNTs. Unlike most main group element doped HSWCNTs,1 9 the HSWCNTs we study here a the transition-metal doped (more specifically, precious-metal Pt doped) HSWCNTs. 6.2. Models and Computational Details The model for the SWCNT is chosen to be the (5,5) armchair metallic SWCNT with two hemispheric caps, which are the half spheres of the fullerene. The open ends of the SWCNT were found to be active centers in many reactions, e.g., oxidation of the SWCNT, 1 6 b and the structure of the open ends go through bond-distance reconstruction.3' No end-localized state has been found at energies near the Fermi surface for the open-end SWCNT.3' On the contrary, the caps in the capped nanorod were predicted to be important to the electronic property of the nanorod3d and there exist electronic states localized on the caps43'23 because of the less stable pentagons,24 despite that there is no significant contributions to the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the nanorod from the caps.30 However, 86 the differences in curvature and % bonding distinguish the chemical properties of fullerenes and the SWCNTs2a and thus divide the nanorod into at least two regions: the caps and the sidewall. The structures of the (5,5) SWCNT rod and the Pt-doped (5,5) SWCNT rod with substitutions at the middle of the sidewall and at one of the end caps are studied with density functional theory (DFT). Becke's exchange functional (B) and Perdew's correlation functional (PW91)27 based the generalized gradient approximations are 28 • employed in structure optimization and property prediction. Pople's 6-31G Gaussian basis set is used for carbon atoms and the relativistic 18-electron Los Alamos National Laboratory (LANL2DZ) effective core pseudopotential29 with the basis set (3s3p2d) is used for the Pt atom. Because of its better predictive ability of relative energies, the hybrid DFT method B3LYP 3 1 with the smaller LANL2MB 2 9 basis set is used for the geometry optimizations of the adsorptions of C2H4 and H2 on the Pt-doped SWCNTs and the absorption energies are further refined by single-point energy calculations with the bigger LANL2DZ basis set. Partial charge analysis is performed with the natural bond orbitals (NBOs).32 The geometries of all the Pt-doped nanorods are reoptimized with B3LYP/LNL2MB. The Gaussian 0333 quantum chemical package is employed for all calculations in the present work. 6.3. Results and Discussions 6.3.1. Perfect S W C N T Rods Figs. 6.1 and 6.2 display the geometries of the two (5,5) SWCNT rods, C ) 7o and Cigo, with D5h and D 5 d symmetries, and their density of states (DOS) and local density of states (LDOS), respectively. The DOS displays the overall electronic structure of a system, while the LDOS shows the electronic structure of a particular region and indicates the contribution of the atoms in that particular region to the overall DOS. The plots of the DOS and the LDOS above zero are for the discussion of the chemistry of the systems hereafter. The similarity of the DOS and the LDOS of these two SWCNT rods is expected, since only one additional circular cz's-polyene chain does not significantly change the 87 -10 -8 -6 -4 -2 0 2 4 6 Energy (eV) F i g u r e 6.1. Density o f states and local density o f states for nanorod C 1 7 0 with the D 5 h symmetry. H O M O is the highest occupied molecular orbital with orbital energy -4.61 e V , and L U M O is the lowest unoccupied molecular orbital with orbital energy - 4 . 2 6 e V . L I , L 2 , L 3 , and L 4 are the local density o f states for each specified layer o f atoms o f C i 7 0 as marked on the structure. electronic structure from C 1 7 0 to Ci8o- Previous studies also found similarity in the HOMO-LUMO gaps of the (5,5) SWCNT rods, C170 and C , 8 0 . 3 d Figs. 6.1 and 6.2 also exhibit the LDOS of the cw-polyene chains in Cm and Ciso along the SWCNT axis and the LDOS of the cap (a hemisphere of Ceo). The shapes of the LDOS of different layers are similar at the frontier MO region, which indicates derealization of the frontier MOs of the SWCNT rods. The contributions to the HOMO, the LUMO, and other occupied frontier MOs from the caps are not significant; the contributions to the HOMO and the LUMO of Cno and C^o are mainly from the sidewalls of the SWCNTs. The conspicuous contributions to the DOS from the LDOS of the cap lie about 1.0 eV below 88 1400 -10 -8 -6 -4 -2 0 2 4 6 Energy (eV) Figure 6.2. Density of states and local density of states for nanorod Ci 8 o with the D 5 d symmetry. H O M O is the highest occupied molecular orbital with orbital energy -4.60 eV, and L U M O is the lowest unoccupied molecular orbital with orbital energy -4.23 eV. L I , L 2 , L 3 , and L4 are the local density of states for each specified layer of atoms of Ci 8 o as marked on the structure. the HOMO and 0.5 eV above the LUMO, as indicated in Figs. 6.1 and 6.2. The MOs give detailed information about the contributions of the LDOS from each layer to the DOS of the SWCNT rod. The occupied and unoccupied frontier MOs for the SWCNT rods Cno and C i 8 0 are plotted in Figs. 6.3 and 6.4, respectively. The highest four occupied MOs of Cno and Cigo are n orbitals with contributions from the sidewalls of the SWCNT rods and are delocalized on the sidewalls. The occupied MOs with major contribution from the caps lie about 1 eV below the HOMO, similar to the picture manifested by the LDOS of the cap in Figs. 6.1 and 6.2. The HOMO and the LUMO have sole contributions from the sidewall of the SWCNT. The lowest two unoccupied MOs of 89 Cno and Ci8o are delocalized n orbitals of the sidewalls of the SWCNTs and are followed by four (two two-fold degenerate) localized MOs on the caps. The patterns of the HOMO and the LUMO in Cno are different from their counterparts in Cigo. Such a pattern change was observed for shorter SWCNT rods before.3c H O M O - 7 (-5.83 e V ) H O M O - 6 (-5.83 e V ) H O M O - 5 (-5.68 e V ) H O M O - 4 (-5.68 e V ) H O M O - 3 (-5.66 e V ) H O M O - 2 (-5.59 e V ) H O M O - 1 (-5.07 e V ) H O M O (-4.61 e V ) L U M O (-4.26 e V ) L U M O + 1 (-3.73 e V ) L U M O + 2 (-3.63 e V ) L U M O + 3 (-3.63 e V ) L U M O + 4 (-3.53 e V ) L U M O + 5 (-3.53 e V ) F i g u r e 6.3. Frontier molecular orbitals o f nanorod C i 7 0 with the D 5 h symmetry. H O M O - n (p e V ) is the nth orbital below the H O M O with orbital energy p e V . L U M O + m (q e V ) is the rath orbital above the L U M O with orbital energy q e V . 90 H O M O - 7 (-5.81 e V ) H O M O - 6 (-5.81 e V ) H O M O - 5 (-5.78 e V ) H O M O - 4 (-5.67 e V ) H O M O - 3 (-5.67 e V ) H O M O - 2 (-5.26 e V ) H O M O - 1 (-5.16 e V ) H O M O (-4.60 e V ) L U M O (-4.23 e V ) L U M O + 1 (-3.76 e V ) L U M O + 2 (-3.59 e V ) L U M O + 3 (-3.59 e V ) L U M O + 4 (-3.56 e V ) L U M O + 5 (-3.56 e V ) Figure 6.4. Frontier molecular orbitals o f nanorod C i 8 o with the D 5 d symmetry. H O M O - n (p e V ) is the nth orbital below the H O M O with orbital energy p e V . L U M O + w (q eV) is the with orbital above the L U M O with orbital energy q e V . From the MOs, one can infer that, when reacting with strong electron acceptors, the SWCNT rods Cno and dgo will donate electrons from the sidewalls of the SWCNTs to the electron acceptors. When Cno and Cigo accept electrons, the first four electrons will go to the middle of the sidewalls of the SWCNTs, and any extra (up to eight) electrons 91 will go to the caps. From the frontier occupied MOs of Cno and Ciso, one cannot see clearly the separation of the electronic structure of the caps from the sidewall of the SWCNT, though there exists some gradual geometric change from the caps to the sidewall.34 The delocalized MOs on the sidewall of the SWCNT rods extend to the ridge of the pentagons of the caps. The pentagon regions have 6-6 (between two hexagons) and 6-5 (between a hexagon and a pentagon) CC bond alternation, similar to that in C6o-From the MOs of Cno and Ciso, one can infer that the electronic structure on the caps is localized and the geometric (topological) role of the caps can be the dominant factor to determine the electronic properties of the SWCNT rods.34 The atoms on the last layer of L4 (II in Figs. 6.1 and 6.2) have the largest negative charge in Ciso and large negative charge in Cno. hi chemical reactions, this layer is reactive toward electron acceptors and can be treated as a bridge between the sidewall and the cap of a SWCNT rod. The middle layers of the sidewall of the SWCNT rod have positive charge. For Cno, the vertical ionization potential (IP) and electron affinity (EA) are 5.86 and 2.89 eV, respectively. Due to the similarity of the electronic and geometric structures of Cno and Ciso, we will focus on Cno and its doping derivatives for the rest of the investigation. 6.3.2. Pt-doped SWCNT Rods For Cno, NBO partial charge analysis indicates that the five atoms connecting to the top pentagon of the cap have the largest negative charges and the atoms of the next layer (I in Fig. 6.1) have the largest positive charge. Thus, the caps can be chemical reaction centers. Substitution of the carbon atoms in the cap by other elements will change the chemical selectivity and sensitivity of the SWCNT rod in catalytic reactions. Replacing one carbon atom with a Pt atom in the end pentagon, in the next layer, or on the sidewall of Cno results in three Pt-doped SWCNT rods: the cap-end-doped Ci69Pt(ce), the cap-doped Ci69Pt(c), and the wall-doped Ci69Pt(w), as shown in Figs. 6.5, 6.7, and 6.9. Single-point calculations at the BPW91/6-31G level of theory predict Ci69Pt(ce) is the most stable nanorod: the total energies of Ci69Pt(c) and Ci69Pt(w) are 0.8 and 17.9 kcal/mol higher, respectively. Evidently, the cap-doped SWCNTs are more stable than 92 the wall-doped SWCNT, because of the relaxation of the constraint on the cap through doping. The total energy of the triplet electronic state of the Pt-doped nanorod is found to be higher than that of the singlet, i.e., the ground state of the Pt-doped nanorod is singlet. 6.3.2.1. Cap-end-doped Ci69Pt(ce) Figs. 6.5 and 6.6 display the structure, the DOS, the LDOS, and the frontier MOs of Ci69Pt(ce). The Pt-C bond distances at the cap end are 2.01 A and the other Pt-C bond distances are 1.96 A. Clearly, the Pt atom points outwards along the translation direction of the SWCNT. The distortion of the SWCNT rod due to the Pt-doping is localized on the pentagons and hexagons around Pt. The overall DOS of Ci69Pt(ce) is similar to that of Cno with the D5h symmetry. The doping of Pt produces more peaks in the DOS in the frontier MO region due to the introduction of the Pt 5d orbitals and the induced electronic structure change in the doped cap. The LDOS of LI and L2 in Fig. 6.5 clearly indicates such changes. LI (the LDOS of Pt) in Fig. 6.5 manifests the contribution of Pt to the DOS of Ci69Pt(ce). The LDOS of the remaining layers in Fig. 6.5 are similar to one another. The frontier MOs in Fig. 6.6 reveal details of the electronic structure of Ci69Pt(ce). The HOMO of Ci69Pt(ce) is similar to that of Cno, except for the significant contributions from Pt and its neighboring carbon atoms in Ci69Pt(ce). The effect of Pt on the electronic structure of Ci69Pt(ce) is also reflected in several other occupied MOs: the HOMO-1, the HOMO-5, the HOMO-6, and the HOMO-7. The HOMO-1 has some major contributions from the Pt 5d orbitals, which form d-p 7i bonds with the carbon atoms in the next layer. The geometric distortion in Ci69Pt(ce) induces single and double CC bond alteration around Pt, which is reflected in the strong n bonding around the doped cap in the HOMO-5. The symmetry of the it bonds in the HOMO-7, the HOMO-6, and the HOMO-5 (corresponding to the HOMO-7, the HOMO-6, and the HOMO-5 in Cno) is destroyed in Ci69Pt(ce), resulting in concentrated n bonding on one end cap as clearly shown in Fig. 6.6. The LUMO of Ci69Pt(ce) is very similar to that of Cno- The next two unoccupied MOs, the LUMO+1 and the LUMO+2, of Ci69Pt(ce) are mainly from the 5d orbitals of Pt, and the contribution to these two unoccupied MOs from the un-doped cap 93 diminishes. According to the MOs of Ci69Pt(ce), it is quite clear that the reactive center in Ci69Pt(ce) is around the location of Pt. 1000 -10 -8 -6 -4 -2 0 2 4 6 Energy (eV) Figure 6.5. Density of states and local density of states for the Pt cap-end-doped nanorod Ci 69Pt(ce) with the C s symmetry. H O M O is the highest occupied molecular orbital with orbital energy -4.51 eV, and L U M O is the lowest unoccupied molecular orbital with orbital energy -4.21 eV. L I , L 2 , L3 , L4, L5 , L6 , L7 , L8 , and L9 are the local density of states for each specified layer of atoms of Ci 6 9 Pt(ce) as marked on the structure. The Pt atom can donate electrons to electron acceptors and its empty 5d orbitals can accept electrons from electron donors, e.g., in reaction with gases like H2, C2H4, CO, NH3, NO, etc. NBO partial charge analysis indicates that Pt transfers about 0.80 electrons (0.40 electrons from 6s and 0.40 electrons from 5d) to nearby carbons: the electronic 94 configuration of Pt is essentially [core]5<i8 6 06s 0 6 0. The carbon atom connecting to Pt in the second layer from the doped cap end has the largest negative charge, -0.22. The vertical IP and EA of Ci69Pt(ce) are 5.45 and 3.40 eV, respectively. H O M O - 7 (-5.78 e V ) H O M O - 6 (-5.71 e V ) H O M O - 5 (-5.63 e V ) H O M O - 1 (-4.79 e V ) H O M O (-4.51 e V ) L U M O + 1 (-4.00 e V ) L U M O + 2 (-3.82 e V ) L U M O + 4 (-3.57 e V ) L U M O + 5 (-3.57 e V ) F i g u r e 6 . 6 . Relevant frontier molecular orbitals o f the Pt cap-end-doped nanorod Ci 6 9Pt(ce) with C s symmetry. H O M O - n (p e V ) is the nth orbital below the H O M O with orbital energy p e V . L U M O + w (q e V ) is the /nth orbital above the L U M O with orbital energy q e V . 6.3.2.2. Cap-doped Ci69Pt(c) Fig. 6.7 shows that the DOS and the LDOS of each layer of atoms of Ci69Pt(c) are very similar to those of Ci69Pt(ce). The structure of Ci69Pt(c) is also similar to that of Ci69Pt(ce), except for the region around Pt. The Pt-C bond distance between Pt and the carbon atom in the top pentagon is 1.97 A; the other two equivalent Pt-C bond distances are 2.00 A. The long Pt-C bonds make the carbon atom of the top pentagon connected to Pt slightly point out of the pentagon, as shown in Fig. 6.7. The frontier MOs of Ci69Pt(c), as shown in Fig. 6.8, are very similar to those of Ci69Pt(ce) in Fig. 6.6. The noticeable difference is that Pt contributes to the HOMO of Ci69Pt(c) more than it does in C]69Pt(ce), 95 which will enhance the reactivity of Pt in Ci69Pt(c). The electronic configuration of Pt is essentially [core]5J8 6 36s 0 6 0. The partial charge of Pt is 0.77 and the carbon atom connecting to Pt in the top pentagon has the largest negative partial charge, -0.25. The vertical UP and E A of Ci69Pt(c) are 5.49 and 3.21 eV, respectively. -10 -8 -6 -4 -2 0 2 4 6 Energy (eV) F i g u r e 6.7. Density o f states and local density o f states for the Pt cap-doped nanorod C ^ P t C c ) with the C s symmetry. H O M O is the highest occupied molecular orbital with orbital energy -4 .48 e V , and L U M O is the lowest unoccupied molecular orbital with orbital energy -4 .25 e V . L I , L 2 , L 3 , L 4 , L 5 , L 6 , L 7 , L 8 , and L 9 are the local density o f states for each specified layer o f atoms o f Ci 6 9Pt(c) as marked on the structure. 6.3.2.3. Wall-doped C 1 6 9Pt(w) Figs. 6.9 and 6.10 display the DOS, the LDOS of each layer, and the frontier MOs of Ci69Pt(w). The DOS of Ci69Pt(w) around the frontier MO region is different from those 96 of Ci69Pt(ce) and Ci69Pt(c): the contribution to the DOS at the frontier MO region from Pt has noticeably increased in Ci6gPt(w). The LDOS of Pt indicates that Pt contributes significantly to the DOS at the frontier MO region in Ci69Pt(w). The introduction of Pt on the sidewall of the SWCNT also drastically changes the LDOS of its neighboring carbon layers, which can be vividly demonstrated by the comparison of the LDOS of L2 and L3 in Fig. 6.9 with LI and L2 of Cno in Fig. 6.1. The LDOS contribution from each layer is also depicted by the frontier MOs, as shown in Fig. 6.10. From the HOMO-1 to the LUMO+3, Pt has significant contributions to each MO. The HOMO-LUMO gap (0.35 eV) of Cno is larger than those of, Ci69Pt(ce) (0.30 eV), Ci69Pt(c) (0.23 eV), and Ci69Pt(w) (0.20 eV). In chemical reactions, Pt will serve as various catalytic centers with flexible oxidation states capable of accepting and donating electrons. The electronic configuration of Pt is essentially [core]5d8636s054. The partial charge of Pt is 0.83. The partial charge of the carbon atom connecting to Pt in the symmetric plane is -0.18, where the Pt-C bond H O M O - 7 (-5.79 e V ) H O M O - 5 (-5.64 e V ) H O M O - 4 (-5.62 e V ) H O M O - 1 (-4.82 e V ) H O M O (-4.48 e V ) L U M O + 1 (-4.06 e V ) L U M O + 2 (-3.75 e V ) L U M O + 4 (-3.56 e V ) L U M O + 5 (-3.39 e V ) F i g u r e 6 .8 . Frontier molecular orbitals o f the Pt cap-doped nanorod C, 6 9Pt(c) with the C s symmetry. H O M O - n (p e V ) is the nth orbital below the H O M O with orbital energy p e V . L U M O + w (q e V ) is the /nth orbital above the L U M O with orbital energy q e V . 97 800 -10 -8 -6 -4 -2 0 2 4 6 Energy (eV) Figure 6.9. Density of states and local density of states for the Pt wall-doped nanorod Ci 69Pt(w) with the C s symmetry. H O M O is the highest occupied molecular orbital with orbital energy -4.46 eV, and L U M O is the lowest unoccupied molecular orbital with orbital energy -4.26 eV. L I , L 2 , L3 , L4, and L5 are the local density of states for each specified layer of atoms of Ci 6 9 Pt(w) as marked on the structure. distance is 2.01 A. The partial charges of the other two equivalent carbon atoms connecting to Pt are -0.10, and the two equivalent Pt-C bond distances are 1.95 A. The vertical IP and EA of Ci69Pt(w) are 5.44 and 3.28 eV, respectively. 6.3.3. Adsorptions of C 2 H 4 and H 2 on C i 6 9 P t From the EAs and IPs of Cno and the three Pt-doped nanorods, one can see that the doping of Pt enhances both the electron accepting and donating capacities of the doped nanorod. Thus, the doping of Pt certainly changes the chemical reactivity and 98 regioselectivity of the SWCNT and broadens the field of application of the SWCNT rods in such areas as gas sensors.35 Present studies have found that the change of structure and reactivity through the doping of Pt in the SWCNT is localized at the doping site. H O M O - 1 (-5.06 e V ) H O M O (-4.46 e V ) L U M O (-4.26 e V ) L U M O + 1 (-4.00 e V ) L U M O + 2 (-3.88 e V ) L U M O + 3 (-3.63 e V ) L U M O + 5 (-3.52 e V ) F i g u r e 6.10. Relevant frontier molecular orbitals o f the Pt wal l -doped nanorod C i 6 9 P t ( w ) with the C s symmetry. H O M O - n (p e V ) is the nth orbital below the H O M O with orbital energy p e V . L U M O + z n (q e V ) is the with orbital above the L U M O with orbital energy q e V . To reveal the different reactivity of the Pt-doped SWCNTs, we are now studying adsorptions of C2H4 and H 2 on the Pt atom of the three Pt-doped SWCNTs. The relative stability of the Pt-doped SWCNTs and the adsorption energies of C2H4 and Ff2 on the Pt-doped SWCNTs are collected in Table 6.1. As can be seen from the bond distances at the adsorption site in Fig. 6.11, there is no significant structural change at the Pt-doped region for the adsorption of H2 on the two cap-doped SWCNTs, as exemplified by the Pt-C bond distances. These two cases are physisorptions according to the H - H bond distance and the distances between H2 and the SWCNT shown in Fig. 6.11 and the adsorption energies in Table 6.1. On the other hand, 99 the adsorption o f H2 on the Pt atom in the middle o f the nanorod Ci69Pt(w) is a chemical one. Obviously, the H - H bond is broken and the two hydrogen atoms form chemical bonds with Pt with bond lengths o f ca 1.70A. The distance between the two hydrogen atoms is 2.29A. This chemisorption releases about 10.0 kcal/mol energy, which is nearly five times the energy (about 2.0~3.0 kcal/mol) released by the adsorption o f H2 on the Pt atom at the end cape o f the SWCNT rods. The interaction between H2 and Pt in the two physisorptions is mainly the electron transfer from the bonding orbital o f H2 to the empty 5d orbital o f Pt, as indicated by the MOs in Fig. 6.12. Though the two hydrogen atoms in the adsorption on Ci6gPt(w) are separated, the interaction between these two hydrogen atoms remains strong, as revealed by the MO overlaps between them (Fig. 6.12). Table 6.1. Relative stabilities of the Pt-doped nanorods and adsorption energies of C 2 H 4 and H 2 on the Pt-doped nanorods. The minus sign indicates the release of the heat of formation upon the adsorption. A l l energies are in kcal/mol. Adsorbate Level of theory C 1 6 9 Pt(ce) C I 6 9 Pt(c) C I 6 9 Pt (w) none BPW/6-31G 0.0 0.8 17.9 B3LYP/Lanl2mb 0.0 2.4 28.6 B3LYP/Lanl2dz 0.0 3.3 26.3 C 2 H 4 B3LYP/Lanl2mb -22.4 -23.5 -19.2 B3LYP/Lanl2dz -20.6 -22.2 -14.7 H 2 B3LYP/Lanl2mb -2.1 -2.3 -10.7 B3LYP/Lanl2dz -2.8 -3.0 ' -10.9 The adsorption of C2H4 on the Pt atom in the three Pt-doped nanorods is physisorption with C-Pt distances ca 2.30 A. As the adsorption site changes from the end-caps of Ci69Pt(ce) and Ci69Pt(c) to the middle of the sidewall of Ci69Pt(w), the CC bond distance in C2FI4 gets longer, and Pt-C bond distances between C2H4 and Pt get shorter, perhaps indicating the strength of the interaction between C2H4 and the Pt-doped SWCNTs in this ascending order: C]69Pt(ce) < Ci69Pt(c) < Ci69Pt(w). However, this conclusion based on structure analysis alone does not agree with the data in Table 6.1: the adsorption energy of C2H4 is the smallest on Ci69Pt(w) and the largest on Ci69Pt(c). The 100 C 2 H 4 Adsorption H 2 Adsorption Ci69Pt(ce) C1 6 9Pt(c) (1.33) 1.40 2.37 \ : 2.39 2.1 (0.73) 0.75 *-* 2.72-: 2.61 (2.06) V: 2mQ7jtt(2m) 1.01 (2.02) oi 2:^-\o. 2.68 (2.05) .06 • 2 12 (i.OOyi (2.06) C169Pt(w) F i g u r e 6.11. Relevant bond distances (in A) o f the adsorptions o f C 2 H 4 and H 2 on the Pt atom in the Pt-doped nanorods ( C ^ P t ) . T h e Pt atom is in purple. T h e C = C bond distances in the C 2 H 4 adsorption and the H H bond distances in the H 2 adsorption are in black. T h e P t C bond distances between Pt and the carbon atoms o f C 2 H 4 in the C 2 H 4 adsorption and the P t H bond distances in the H 2 adsorption are in blue. T h e P t C bond distances between Pt and its nearest carbon atoms o f the S W C N T are in red. The numbers in parentheses are the P t C bond distances o f the isolated C i 6 9 P t without adsorption, the C = C bond distance in the isolated free C 2 H 4 , and the H - H bond distance o f the isolated free H 2 . 101 491 fm 340 - 501 522 I :2 350 ^ 523jg/Df> 353 ^ 524 * ' 3 5 5 ^ ^ 524 .„ 367 ^5 ^ v 1 C 2 H 4 + H 2+ C 2 H 4 + H2+ C 2 H 4 + H2+ C 1 6 9 Pt(ce) C 1 6 9 Pt(ce) C 1 6 9 Pt(c) C 1 6 9 Pt(c) C 1 6 9 Pt(w) C 1 6 9 Pt(w) F i g u r e 6.12. Portions o f the molecular orbitals relevant to the interaction o f the adsorbates, C 2 H 4 and H 2 , with the three kinds o f the Pt-doped nanorods, C i 6 9 P t ( c e ) , C i 6 9 P t ( c ) , and C i 6 9 P t ( w ) . T h e numbers beside the molecular orbitals are the orbital indexes. T h e critical geometries o f these structures are shown in F i g . 6.11. trend of the adsorption strengths of C2H4 on the Pt-doped SWCNTs is the compromise of the weakening of the C=C double bond in C2H4, the electrostatic attraction between the 102 two carbon atoms of C2H4 and Pt, and the repulsion between the C2H4 and the SWCNT. It is also interesting to note that the geometries of the adsorptions of C2H4 on the Pt atom at the end-cap of the Pt-doped SWCNTs are very similar to those on the Pt-doped fullerene, Cs9Pt,2 1 e which should possess similar adsorption strengths. Overall, the adsorptions of H2 and C2H4 get stronger as the adsorption site changes from the hemispheric cap to the sidewall of the SWCNT, as manifested by the relevant MOs in Fig. 6.12 and the adsorption energies in Table 6.1. 6.4. Conclusions Within DFT, the electronic structures and chemical reactivity of the SWCNT rods Cno and C i 8 0 , the Pt-doped SWCNT rods Ci69Pt(ce), C]69Pt(c), and Ci69Pt(w) have been studied in detail. According to the analyses, we have reached the following conclusions: 1. There indeed exist localized electronic states on the caps of the SWCNT rods as confirmed by the DOS, the LDOS, and the frontier MOs. The circular cw-polyene chain between the cap and the sidewall of the SWCNT is chemically active. 2. The ground state of the Pt-doped SWCNT rod is singlet. 3. The doping of Pt in the SWCNT rod results in localized electronic states at Pt, thus rendering Pt as the active center in chemical reactions, particularly for the wall-doped Ci69Pt(w). The Pt-doped SWCNT rod with Pt at the end of the cap, CiegPtCce), can be used as chemical sensor, since the doping of Pt enhances the sensitivity of the cap in interaction with the substrate due to the Pt 5d orbitals and the charge transfer from Pt to the carbon atoms. In Pt-doped SWCNT rods, Pt is essentially acting as Pt+, because of the electron transfer of about one electron from Pt to the carbon atoms. 4. The doping of Pt in the middle of the sidewall of the nanorod has stronger interaction with the adsorbates (e.g., H2 and C2H4) than the nanorods with the doping of Pt at the hemispheric caps. This further suggests that the Pt-doped SWCNT has stronger adsorbing capacity than the Pt-doped fullerene. However, this phenomenon has to be investigated for systems involving other metals. In summary, present DFT studies reveal that doping produces localized active centers, thus enhancing the chemical reactivity of the SWCNTs (with hemispherically capped 103 ends). Our studies point to new directions for future applications of the SWCNTs in catalysis, chemic sensor, surface science, and nanotube chemistry. 6.5. References (1) (a) Iijima S.; Ichihashi, T. Nature 1993, 363, 603. (b) Bethune, D. S.; Kiang, C.-H.; de Vries, M. S.; Gorman, G.; Savoy, R.; Vazquez J.; Beyers, R. Nature 1993, 363, 605. (2) (a) Niyogi, S.; Hamon, M. A.; Hu, H.; Zhao, B.; Bhowmik, P.; Sen, R.; Itkis M. E.; Haddon, R. C ; Acc. Chem. Res. 2002, 35, 1105. (b) Hermraj-Benny, T.; Banerjee S.; Wong, S. S. Chem. Mater. 2004, 16, 1855. (c) Nhut, J.-M., Nguyen, P.; Pham-Huu, C ; Keller N.; Ledoux, M.-J. Catal. Today 2004, 91, 91. (d) Zhang, J.; Zou, H.; Qing, Q.; Yang, Y.; Li, Q.; Liu, Z.; Guo X.; Du, Z. J. Phys. Chem. B 2003, 107, 3712. (3) (a) Yamabe, T.; Imade, M.; Tanaka, M.; Sato, T. Synth. Metals 2001, 117, 61. (b) Lu, X.; Tian, F.; Feng, Y.; Xu, X.; Wang, N ; Zhang, Q. Nano Lett. 2002, 2, 1325. (c) Li, J.; Zhang, Y.; Zhang, M. Chem. Phys. Lett. 2002, 364, 328. (d) Cioslowski, J.; Rao, N.; Moncrieff, D. J. Am. Chem. Soc. 2002, 124, 8485. (e) Kar, T.; Akdim, B.; Duan, X.; Pachter, R. Chem. Phys. Lett. 2004, 392, 176. (f) Zhao, M.; Xia, Y.; Lewis, J. P.; Mei, L. J. Phys. Chem. B 2004, 108, 9599. (g) Gustavsson, S.; Rosen, A.; Grennberg, H.; Bolton, K. Chem. Eur. J. 2004, 10, 2223. (h) Joselevich, E. ChemPhysChem 2004, 5, 619. (i) Zhou, Z.; Steigerwald, M.; Hybertsen, M.; Brus, L.; Friesner, R. J. Am. Chem. Soc. 2004, 126, 3597. 0) Yumura, T.; Hirahara, K.; Bandow, S.; Yoshizawa, K.; Iijima, S. Chem. Phys. Lett. 2004, 386, 38. (4) (a) Carroll, D. L.; Redlich, P.; Ajayan, P. M.; Charlier, J. C ; Blase, X.; De Vita, A.; Car, R. Phys. Rev. Lett. 1997, 78, 2811. (b) Klusek, Z.; Kowalczyk, P.; Byszewski, P. Vacuum 2001, 63, 145. (c) Shiraishi,, M.; Ata, M. Synth. Metal 2002, 128, 235. (d) Dean, K. A.; Chalamala, B. R. J. Vac. Sci. Technol. B 2003, 21, 868. (e) Kim, H.; Lee, J.; Kahng, S. -J.; Son, Y. -W.; Lee, S. B.; Lee, C. -K.; Ihm, J.; Kuk, Y. Phys. Rev. Lett. 2003, 90, 216107. (5) (a) Blase, X.; Bbenedict, L. X.; Shirley, E. L.; Louie, S. G. Phys. Rev. Lett. 1994, 72, 1878. (b) Lee, Y. H.; Kim, S. G.; Tomanek, D. Phys. Rev. Lett. 1997, 78, 2393. (c) 104 Yaguchi, T.; Ando, T. Phys. Soc. Jpn. 2001, 70, 1327. (d) Yaguchi, T.; Ando, T. J. Phys. Soc. Jpn. 2002, 71, 2224. (e) Jiang, J.; Dong, J.; Xing, D. Y. Phys. Rev. B 2002, 65, 245418. (f) Compernolle, S.; Chibotaru, L.; Ceulemans, A. J. Chem. Phys. 2003, 119, 2854. (g) Chico, L.; Jaskolski, W. Phys. Rev. B 2004, 69, 085406. (h) Guo, G. Y.; Chu, K. C ; Wang, D. -S.; Duan, C. -G. Phys. Rev. B 2004, 69, 205416. (6) Ajayan, P. M.; Zhou, O. Z. in Carbon Nanotubes Synthesis, Structure, Properties, and Applications, Dresselhaus, M. S.; Dresselhaus, G.; Avoutis, Ph. (Eds.) Springer, Berlin, 2001. (7) (a) Avouris, P. Acc. Chem. Res. 2002, 35, 1026. (b) Antonov, R. D.; Johnson, A. T. Phys. Rev. Lett. 1999, 83, 3274. (c) Fuhrer, M. S.; Nygard, J.; Shih, L.; Forero, M.; Yoon, Y. -G.; Mazzoni, M. S. C ; Choi, H. J.; Ihm, J.; Louie, S. G.; Zettl, A.; McEuen, P. L. Science 2000, 288, 494. (8) (a) Kong, J.; Franklin, N. R.; Zhou, C ; Chapline, M. G.; Peng, S.; Cho, K.; Dai, H. Science 2000, 287, 622. (b) Collins, P. G.; Bradley, K.; Ishigami, M.; Zettl, A. Science 2000, 287, 1801. (c) Goldoni, A.; Larciprete, R.; Petaccia, L.; Lizzit, S. J. Am. Soc. Chem. 2003,125, 11329. (9) Zhou, O.; Shimoda, FL; Gao, B.; Oh, S.; Fleming, L.; Yue, G. Acc. Chem. Res. 2002, 35, 1045. (10) Choi, W. B.; Chung, D. S.; Kang, J. H.; Kim, H. Y.; Jin, Y. W.; Han, I. T.; Lee, Y. H.; Jung, J. E.; Lee, N. S.; Park, G. S.; Kim, J. M. Appl. Phys. Lett. 1999, 75, 3129. (11) Serp, P.; Corrias, M.; Kalck, P. Appl. Catal. A 2003, 253, 337. (12) (a) Botti, S.; Ciardi, R.; De Dominicis, L.; Asilyan, L. S.; Fantoni, R.; Marolo, T. Chem. Phys. Lett. 2003, 378, 117. (b) Tatsuura, S.; Furuki, M.; Sato, Y.; Iwasa, I.; Tian, M.; Mitsu, H. Adv. Mater. 2003, 15, 534. (c) Set, S. Y.; Yaguchi, H.; Tanaka, Y.; Jablonski, M. J. Lightwave Technol. 2004, 22, 51. (d) Rozhin, A. G.; Sakakibara, Y.; Tokumoto, M.; Kataura, H.; Achiba, Y. Thin Solid Films 2004, 464-465, 368. (13) (a) Hamada, N.; Sawada, S. -I.; Oshiyama, A. Phys. Rev. Lett. 1992, 68, 1579. (b) Dresselhaus, M. S.; Dresselhaus, G.; Eklund, P. C. Science of Fullerenes and Carbon Nanotubes; Academic Press, Inc.: San Diego, 1995; Chapter 19. (14) Chiang, I. W.; Brinson, B. E.; Huang, A. Y.; Willis, P. A.; Bronikowski, M. J.; Margrave, J. L.; Smalley, R. E.; Hauge, R. H. Phys. Chem. B 2001,105, 8297. 105 (15) (a) Mickelson, E. T.; Huffman, C. B.; Rinzler, A. G.; Smalley, R. E.; Hauge, R. H.; Margrave, J. L. Chem. Phys. Lett. 1998, 296, 188. (b) Boul, P. J.; Liu, J.; Mickelson, E. T.; Huffman, C. B.; Ericson, L. M.; Chiang, I. W.; Smith, K. A.; Colbert, D. T.; Hauge, R. H.; Margrave, J. L.; Smalley, R. E. Chem. Phys. Lett. 1999, 310, 367. (c)Holzinger, M.; Vostrowsky, O.; Hirsch, F. H.; Kappes, M.; Weiss, R.; Jellen, F. Angew. Chem. Lnt. Ed. 2001, 40, 4002. (d) Bahr, J. L.; Tour, J. L. Chem. Mater. 2001, 13, 3823. (e) Bahr, J. L.; Yang, J.; Kosynkin, D. V.; Bronikowski, M. J.; Smalley, R. E.; Tour, J. M. J. Am. Chem. Soc. 2001,123, 6536. (f) Georgakilas, V.; Kordatos, K.; Prato, M.; Guldi, D. M.; Holzinger, M.; Hirsch, A. J. Am. Chem. Soc. 2002, 124, 760. (g) Umek, P.; Seo, J. W.; Hernadi, K.; Mrzel, A.; Pechy, P.; Mihailovic, D. D.; Forro, L. Chem. Mater. 2003,15, 4751. (h) Stevens, J. L.; Huang, A. Y.; Peng, H.; Chiang, I. W.; Khabashesku, V. N.; Margrave, J. L. Nano Lett. 2003, 3, 331. (i) Peng, H.; Alemany, L. B.; Margrave, J. L.; Khabashesku, V. N. J. Am. Chem. Soc. 2003, 125, 15174. (j) Hu, H.; Zhao, B.; Hamon, M. A.; Kamaras, K.; Itkis, M. E.; Haddon, R. C. J. Am. Chem. Soc. 2003, 125, 14893. (k) Banerjee, S.; Kahn, M. G. C ; Wong, S. S. Chem. Eur. J. 2003, 9, 1898. (1) Zhao, B.; Hu, H.; Haddon, R. C. Adv. Funct. Mater. 2004, 14, 71. (m) Zhang, L.; Kiny, V. U.; Pesng, H.; Zhu, J.; Lobo, R. F. M.; Margrave, J. L.; Khabashesku, V. N. Chem. Mater. 2004,16, 2055. (16) (a) Hamon, M. A.; Chen, J.; Hu, H.; Chen, Y.; Itkis, M. E.; Rao, A. M.; Eklund, P. C ; Haddon, R. C. Adv. Mater. 1999, 11, 834. (b) Zhang, J.; Zou, H.; Qing, Q.; Yang, Y.; Li, Q.; Liu, Z.; Guo, X.; Du, Z. J. Phys. Chem. B 2003,107, 3712. (17) Bahr, J. L.; Tour, J. M. J. Mater. Chem. 2002,12, 1952. (18) Ajayan, P. M.; Ravikumar, V.; Charlier, J. -C. Phys. Rev. Lett. 1998, 81, 1437. (b) Igami, M.; Nakanishi, T.; Ando, T. J. Phys. Soc. Jpn. 1999, 68, 716. (c) Igami, M.; Nakanishi, T.; Ando, T. Physica B 2000, 284, 1746. (d) Krasheninnikov, A. V.; Nordlund, K. Phys. Solid State 2002, 44, 470. (e) Charlier, J. -C. Acc. Chem. Res. 2002, 35, 1063. (f) Krasheninnikov, A. V.; Nordlund, K. J. Vac. Sci. Technol. B 2002, 20, 728. (g) Lu, A. J.; Pan, B. C. Phys. Rev. Lett. 2004, 92, 105504. (f) Belavin V. V.; Bulusheva, L. G.; Okotrub, A. V. Int. J. Quant. Chem. 2004, 96, 239. (g) Valentini, L.; Mercuri, F.; Armentano, I.; Cantalini, C ; Picozzi, S.; Lozzi, L.; 106 Santucci, S.; Sgamellotti, A.; Kenny, J. M. Chem. Phys. Lett. 2004, 387, 356. (h) Liu, L. V.; Tian W. Q.; Wang, Y. A. J. Phys. Chem. B 2006,110, 1999. (19) (a) Carroll, D. L.; Redlich, Ph.; Blase, X.; Charlier, J. - C ; Curran, S.; Ajayan, P. M.; Roth, S.; Ruhle, M. Phys. Rev. Lett. 1998, 81, 2332 (B,exp). (b) Han, W.; Bando, Y.; Kurashima, K.; Sato, T. Chem. Phys. Lett. 1999, 299, 368. (c) Peng, S.; Cho, K. Nano Lett. 2003, 3, 513. (d) Zhao, M.; Xia, Y.; Lewis, J.; Zhang, R. J. Appl. Phys. 2003, 94, 2398. (e) Nikulkina, A. V.; D'yachkov, P. N. Russ. J. Inorg. Chem. 2004, 49, 430. (20) (a) Lambin, Ph.; Lucas, A. A.; Charlier, J. C. J. Phys. Chem. Solids 1997, 58, 1833. (b) choi, H. J.; Dim, J.; Louie, S. G.; Cohen, M. L. Phys. Rev. Lett. 2000, 84, 2917. (c) Nardelli, M. B.; Fattebert, J. -L.; Orlikowski, D.; Roland, C.; Zhao, Q.; Bernholc, J. Carbon 2000, 38, 1703. (d) Hu, H. -F.; Li, Y. -B.; He, H. -B. Diamond Related Mater. 2001, 10, 1818. (e) Zhou, L. G.; Shi, S. Q. Carbon 2003, 41, 579. (f) Miyamoto, Y.; Rubio, A.; Berber, S.; Yoon, M.; Tomanek, D. Phys. Rev. B 2004, 69, 121413. (21) (a) Clemmer, D. E.; Hunter, J. M.; Shelimov, K. B.; Jarrold, M. F. Nature 1994, 372, 248. (b) Branz, W.; Billas, I. M. L.; Malinowski, N.; Tast, F.; Heinebrodt, M.; Martin, T. P. J. Chem. Phys. 1998,109, 3425. (c) Poblet, J. M.; Munoz, J.; Winkler, K.; Cancilla, M.; Hayashi, A.; Lebrilla, C. B.; Balch, A. L. Chem. Commun. 1999, 493. (d) Kong, Q.; Shen, Y.; Zhao, L.; Zhuang, J.; Qian, S.; Li, Y.; Lin, Y.; Cai, R. J. Chem. Phys. 2002, 116, 128. (e) Hayashi, A.; Xie, Y.; Poblet, J. M.; Campanera, J. M.; Lebrilla, C. B.; Balch, A. L. J. Phys. Chem. A 2004,108, 2192. (22) (a) Ding, C ; Yang, J.; Cui, X.; Chan, C. T. J. Chem. Phys. 1999, 111, 8481. (b) Billas, I. M. L.; Massobrio, C.; Boero, M.; Parrinello, M.; Branz, W.; Tast, F.; Malinowski, N.; Heinebrodt, M.; Martin, T. P. Comput. Mater. Sci. 2000, 77, 191. (23) De Vita, A.; Charlier, J. -Ch.; Blase, X.; Car, R. Appl. Phys. A 1999, 68, 283. (24) Tamura, R.; Tsukada, M. Phys. Rev. B 1995, 52, 6015. (25) (a) Hohenberg, P.; Kohn, W. Phys. Rev. 1964, 136, B864. (b) Kohn, W.; Sham, L. J. Phys. Rev. 1965, 40, A l 133. (c) Parr, R. G.; Yang, W. Density-functional theory of atoms and molecules, Oxford University Press: New York, 1989. (26) Becke, A. D. Phys. Rev. A 1988, 38, 3098. 107 (27) (a) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys. Rev. B 1992, 46, 6671. (b) Perdew, J. P.; Burke, K.; Wang, Y. Phys. Rev. B 1996, 54, 16533. (28) (a) Ditchfield, R.; Hehre, W. J.; Pople, J. A. J. Chem. Phys. 1971, 54, 724. (b) Hehre, W. J.; Ditchfield, R.; Pople, J. A. J. Chem. Phys. 1972, 56, 2257. (c) Hariharan, P. C ; Pople, J. A. Mol. Phys. 1974, 27, 209. (d) Gordon, M. S. Chem. Phys. Lett. 1980, 76, 163. (29) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 299. (30) (a) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (b) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785. (c) Miehlich, B.; Savin, A.; Stoll, H.; Preuss, H. Chem. Phys. Lett. 1989, 157, 200. (31) (a) Sheng, Y.; Musaev, D. G.; Reddy, K. S.; McDonald F. E.; Morokuma, K. J. Am. Chem. Soc. 2002, 124, 4149. (b) Tian W. Q.; Wang, Y. A. J. Org. Chem. 2004, 69, 4299. (32) (a) Reed, A. E.; Weinhold, F. J. Chem. Phys. 1983, 78, 4066. (b) J. E. Carpenter, PhD thesis, University of Wisconsin, Madison, Wl, 1987. (c) Carpenter, J. E.; Weinhold, F. J. Mol. Struct. (Theochem) 1988, 169, 41. (d) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. Rev. 1988, 88, 899. (33) Gaussian 03, Revision B.05, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr., J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C ; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Cossi; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C ; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C ; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C ; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; 108 Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C ; Pople, J. A. Gaussian, Inc., Pittsburgh PA, 2003. (34) Yumura, T.; Bandow, S.; Yoshizawa, K.; Iijima, S. J. Phys. Chem. B 2004, 108, 11426. (35) Mpourmpakis, G.; Froudakis, G. E.; Andriotis A. N.; Menon, M. Appl. Phys. Lett. 2005,57, 193105. 109 C h a p t e r 7 C o n c l u s i o n s a n d R e c o m m e n d a t i o n s f o r F u t u r e W o r k 7.1. Conclusions In this thesis, the electronic structures and reactivities of the perfect, defected, and doped SWCNTs have been studied by various theoretical methods, including density functional theory, semiempirical methods, and force field molecular mechanics. Especially, we concentrated on the studies of the vacancy defect and the precious metal substitutionally doped defect. According to the studies, we have reached the following conclusions: 1. We found that introducing the single- and double-vacancy defects will decrease the HOMO-LUMO gaps, destruct the 7r conjugated system of the frontier molecular orbitals, and thus enhance the conductivity and chemical activity of the SWCNTs. 2. The reactions between NO and the 5-1DB defect on the (5,5) SWCNT have been studied by a two-layered ONIOM model. The partition pattern applied in the ONIOM model has been proven to be suitable by the LDOS, FMO, and NBO analyses. This study has clearly proven the chemical activity of the 5-1DB defect. Detailed reaction pathways were also explored. We found that NO attacks the active carbon atom of the 5-1DB defect, forming an intermediate, which has the nitrogen atom inserted into the sidewall of the SWCNT and the oxygen atom sticking out of the surface. The intermediate reacts with another NO, forming the final product, with the nitrogen atom healing the defect site completely. This suggests a possible way to fabricate the substitutionally N-doped (5,5) SWCNT by means of some simple chemical reactions mediating the 5-1DB defect. 3. The reaction between O 3 and the 5-1DB defect on the (5,5) SWCNT has been studied by both static quantum mechanical and ADMP-based AIMD methods within a two-layered ONIOM model. Different pathways on the five possible reactive positions of the 9-membered ring of the 5-1DB defect were explored. We found that the most 110 favored reaction takes place on the active carbon atom through a one-step process, in which the active carbon atom captures an oxygen atom from O 3 and the remaining two oxygen atoms dissociate away as singlet O2. The other four reaction pathways follow the standard 1,3-dipolar cycloaddition mechanism. Our AIMD dynamical simulation at 300 K indicates the fast spontaneous dissociation of O 3 on the 5-1DB defect, i.e., one oxygen atom is captured by the active carbon atom. The high exothermicity and the low reaction barrier of this dissociation reaction suggest that it is thermally and kinetically very favourable. 4. For the study of the substitutionally Pt-doped SWCNT, we found the ground state of the Pt-doped SWCNT rod is singlet. The doping of Pt in the SWCNT rod results in localized electronic states at Pt, thus rendering Pt a active center in chemical reactions, particularly for the wall-doped SWCNT. The Pt-doped SWCNT rod with Pt on the end of the cap, can be used as an AFM tip or chemical gas sensor, since the doping of Pt enhances the sensitivity of the cap in interaction with a substrate due to the Pt 5d orbitals and the charge transfer from Pt to the carbon atoms. In the Pt-doped SWCNT rod, Pt is essentially acting as Pt+, because of the charge transfer (about 1 electron) from Pt to the carbon atoms. The vacancy in the defected SWCNT with open ends creates a localized active center at the defect site and enhances the chemical reactivity and regioselectivity of the open-ended SWCNT. 7.2. Recommendations for Future Work There are several recommendations for the future work. 1. Due to the limitation of computation resources, we have made some compromises in our studies in Chapter 3. We only studied the (5,5) and (10,0) SWCNTs as representative examples to the armchair and zigzag type SWCNTs. If possible, we should perform a systematic investigation, to include many more SWCNTs with a large range of varied diameters. The bigger the diameter is, the less strain the SWCNT sidewall has. It is expected that there will be some major geometrical changes for the vacancy defect as the diameter increases. Another possible direction is extending the study to chiral type SWCNTs, which are rarely studied in the literature. 2. In Chapters 4 and 5, we applied a two-layed ONIOM model to study the reactions of NO and O 3 with the vacancy defect. For the higher layer, we only included nine carbon atoms. Although we have performed the LDOS, FMO, NBO analyses and very expensive benchmark calculations to verify the partition pattern of this model, full DFT calculations are still needed to confirm the reaction pathways for these two reactions, if possible. 3. Most studies of the SWCNTs in this thesis are performed on finite models, hi Chapter 3, we have observed some subtle differences between the results of the PBC and finite models. Therefore, it is highly desirable to benchmark the results of the finite models against the PBC data in the future. 112 

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