Theory and Applications of Computational The First Forty Years

Editors CLIFFORD E. DYKSTRA Department of Chemistry Indiana University-Purdue University Indianapolis (IUPUI) Indianapolis, IN, U.S.A. GERNOT FRENKING Fachbereich Chemie Phillips- Universität Marburg Marburg, Germany KWANG S. KIM Department of Chemistry Pohang University of Science and Technology Pohang, Republic of Korea GUSTAVO E. SCUSERIA Department of Chemistry Rice University Houston, TX, U.S.A.

Amsterdam - Boston - Heidelberg - London - New York - Oxford Paris - San Diego - San Francisco - Singapore - Sydney - Tokyo vii

Contents

Chapter 1. Computing technologies, theories, and algorithms. The making of 40 years and more of theoretical and Clifford E. Dykstra, Gernot Frenking, Kwang S. Kim and Gustavo E. Scuseria 1 1.1 Introduction 1 1.2 Technology and methodology 2 1.3 Outlook 6 1.4 Acknowledgements 7 1.5 References 7

Chapter 2. Dynamical, time-dependent view of molecular theory Yngve Öhrn and Erik Deumens 9 2.1 Introduction 9 2.2 Molecular Hamiltonian 12 2.3 The time-dependent variational principle in quantum mechanics 18 2.4 Coherent states 21 2.4.1 Gaussian wave packet as a coherent State 21 2.4.1.1 Gaussian wave packet with evolving width 25 2.4.2 The determinantal coherent State for N electrons 29 2.5 Minimal electron nuclear dynamics (END) 32 2.6 Rendering of dynamics 37 2.7 Acknowledgements 39 2.8 References 39

Chapter 3. Computation of non-covalent binding affinities J. Andrew McCammon 41 3.1 Introduction 41 3.2 Current methods 42 VIII Contents

3.3 Future prospects 43 3.4 Concluding perspective: molecular dynamics simulations and drug discovery 44 3.5 Acknowledgements 45 3.6 References 45

Chapter 4. Electrodynamics in computational chemistry Liniin Zhao, Shengli Zou, Encai Hao and George C. Schatz 47 4.1 Introduction 47 4.2 Electrodynamics of metal nanoparticles 49 4.2.1 Methods 49 4.2.2 Dielectric constants 50 4.2.3 Spherical particles 51 4.2.4 Effects of particle shape 51 4.2.5 Effects of solvent and of surrounding layers 52 4.2.6 Local electric fields and SERS 55 4.3 Electronic structure studies of surface enhanced Raman spectra 59 4.3.1 Surface modeis and electronic structure methods 59 4.3.2 Applications 60 4.4 Acknowledgements 63 4.5 References 64

Chapter 5. Variational transition State theory Bruce C. Garrett and Donald G. Truhlar 67 5.1 Introduction 67 5.2 Gas phase reactions 68 5.2.1 Classical mechanical theory 68 5.2.2 Inclusion of quantum mechanical effects 72 5.2.3 Improved prescriptions for the reaction coordinate and dividing surface 75 5.2.4 of the transition State 77 5.2.5 Applications 77 5.3 Reactions in Condensed phases 77 5.3.1 Reactions in rigid environments and application to reactions in crystals or at crystal-vapor interfaces 78 5.3.2 Reactions in fluid environments with a Single reaction coordinate 79 5.3.3 Reactions in fluid environments with an ensemble of reaction coordinates 82 5.4 Summary and conclusions 83 5.5 Acknowledgements 84 5.6 References 84 Contents ix

Chapter 6. Computational chemistry: attempting to simulate large molecular Systems Enrico Clementi 89 6.1 Introduction 89 6.2 The long preparation and the seeding time: 1930-1960 90 6.3 and the Laboratory of Molecular Structure and Spectra, Chicago, 1960 92 6.4 My Hartree-Fock, MC-SCF and density functional period: the 1960 decade 95 6.5 From Schrödinger to Newton; my second Simulation period 103 6.6 Statistical and fluid dynamic simulations, and also Computers hardware development in the Hudson Valley 105 6.7 Back to the beginning: a new approach to an old problem 108 6.8 Conclusions 111 6.9 Acknowledgements 111 6.10 References 111

Chapter 7. The beginnings of coupled-cluster theory: an eyewitness account Josef Paldus 115 7.1 'Prehistory' 116 7.2 Gestation 119 7.3 Birth 124 7.4 Growing pains 129 7.5 Maturation 132 7.6 Quovadis? 134 7.7 Acknowledgements 140 7.8 References 140

Chapter 8. Controlling quantum phenomena with photonic reagents Herschel Rabitz 149 8.1 How can control of quantum dynamics phenomena be achieved?. ... 149 8.2 Why does quantum control with photonic reagents appear to be so easy? 156 8.3 What is occurring during the process of Controlling quantum dynamics phenomena? 158 8.4 Conclusion 162 8.5 References 162

Chapter 9. First-principles calculations of anharmonic vibrational spectroscopy of large molecules R.B. Gerber, GM. Chaban, B. Brauer and Y. Miller 165 9.1 Introduction 165 x Contents

9.2 Anharmonic vibrational spectroscopy methods 167 9.2.1 Perturbation theory 168 9.2.2 The vibrational self-consistent field approach 169 9.2.3 Grid methods 172 9.2.4 Diffusion quantum Monte Carlo 172 9.2.5 Semiclassical methods 173 9.3 Ab initio vibrational spectroscopy 173 9.3.1 Fitting ab initio potentials versus direct ab initio spectroscopy calculations 173 9.3.2 Ab initio VSCF and CC-VSCF 174 9.3.2.1 VSCF equations 174 9.3.2.2 Representations of the potential 175 9.3.2.3 CC-VSCF equations 177 9.3.2.4 Anharmonic infrared intensities 178 9.3.2.5 Electronic structure methods used with VSCF 178 9.3.2.6 Improvements and extensions of VSCF and CC-VSCF 179 9.3.3 Ab initio anharmonic calculations using perturbation theory 180 9.4 Applications and Performance 180 9.4.1 Performance for large molecules 180 9.4.2 Spectroscopy calculations as a test of ab initio and DFT force fields 182 9.4.3 Vibrational spectroscopy of hydrogen-bonded Clusters 182 9.4.4 Ab initio spectroscopy and the identification of new molecular species 185 9.4.5 Ab initio spectroscopy and the elucidation of complex spectra 186 9.4.6 Overtones and combination mode transitions 186 9.4.7 Open-shell Systems 187 9.5 Future directions 188 9.5.1 Larger Systems 188 9.5.2 Quest for increased accuracy 189 9.5.3 Time-domain spectroscopy 189 9.6 Acknowledgements 189 9.7 References 190

Chapter 10. Finding minima, transition states, and following reaction pathways on ab initio potential energy surfaces Hrant P. Hratchian and H. Bernhard Schlegel 195 10.1 Introduction 195 10.2 Background 196 Contents xi

10.2.1 Potential energy surfaces 196 10.2.2 Analytic PES derivatives 198 10.2.3 Coordinate Systems 201 10.3 Minimization 202 10.3.1 Newton methods 203 10.3.2 GDIIS 207 10.3.3 QM/MM optimizations 209 10.3.4 Finding surface intersections and points of dosest approach 210 10.3.5 Practical considerations 212 10.3.5.1 Starting structure 212 10.3.5.2 Coordinate System 213 10.3.5.3 Minimization algorithm 215 10.3.5.4 Hessian quality 215 10.3.5.5 Tips for difficult minimizations 217 10.4 Transition State optimization 218 10.4.1 Local methods 219 10.4.2 Climbing, bracketing, and interpolation methods 220 10.4.3 Path optimization methods 224 10.4.4 Practical considerations 227 10.4.4.1 Building an initial structure 227 10.4.4.2 Coordinate System 228 10.4.4.3 Algorithm choice 229 10.4.4.4 Hessian quality 230 10.4.4.5 Verifying TSs 230 10.5 Reaction path following 230 10.5.1 First-order methods 232 10.5.2 Second-order methods 234 10.5.3 Higher order integrators 236 10.5.4 Dynamic reaction path 237 10.5.5 Practical considerations 238 10.5.5.1 Algorithm choice 238 10.5.5.2 Projected frequencies and coupling matrix elements 241 10.5.5.3 Bifurcation 242 10.5.5.4 Tips for difficult reaction path calculations 242 10.6 Summary and outlook 243 10.7 References 243

Chapter 11. Progress in the quantum description of vibrational motion of polyatomic molecules Joel M. Bowman, Stuart Carter and Nicholas C. Handy. ... 251 11.1 Introduction 251 11.2 Beyond the harmonic approximation 252 xii Contents

11.3 Vibrational CI theory 254 11.3.1 The n-mode representation of the potential 255 11.3.2 Results of selected calculations 257 11.3.3 The 'Reaction Path' Version of MULTIMODE 260 11.4 Current bottlenecks and future progress 263 11.5 Acknowledgements 265 11.6 References 265

Chapter 12. Toward accurate computations in photobiology Adalgisa Sinicropi and Massimo Olivucci 269 12.1 Introduction 269 12.2 Ab initio quantum chemical methods for excited states 272 12.3 Fate of light energy in photobiology 276 12.3.1 GFP spectroscopy 278 12.3.2 Rh spectroscopy 279 12.3.3 The photoisomerization path of Rh 282 12.3.4 Nature of the energy storage 284 12.4 From photobiology to biomimetic molecular switches 285 12.5 Conclusions 287 12.6 Acknowledgements 288 12.7 References 288

Chapter 13. The nature of the chemical boncl in the light of an energy decomposition analysis Matthias Lein and Gernot Frenking 291 13.1 Introduction 291 13.2 Energy decomposition analysis 295 13.3 Bonding in main-group Compounds 296 13.3.1 Diatomic molecules H2, N2, CO, BF 297 13.3.2 Dipnicogens N2-Bi2 302 13.3.3 Dihalogens F2-I2 303 13.3.4 Nonpolar Single bonds of the first octal row H„E-EH„ (E = Li-F; n = 0-3) 305 13.3.5 Nonpolar multiple bonds HB=BH, H2C=CH2, HN=NH andHC^CH 308 13.3.6 Nonpolar group-14 bonds H3E-EH3 (E = C-Pb) 310 13.3.7 Donor-acceptor bonds Y3B-NX3 and Y3B-PX3 (X, Y = H, Me, Cl) 311 13.3.8 Main group metallocenes ECp2 (E = Be-Ba, Zn, Si-Pb) and ECp (E = Li-Cs, B-Tl) 314 13.3.9 Bonding in SF6 and XeF6 and a comparison with WF6 .... 322 13.4 Bonding in transition metal Compounds 326 13.4.1 Carbonyl complexes TM(CO)g (TM9 = Hf2", Ta~, W, Re+, Os2+, lr3+) 326 Contents xiii

13.4.2 Group-13 heteroleptic diyl complexes (CO)4Fe-ER (E = B-Tl; R = Cp, Ph, Me) and homolytic diyl complexes Fe(EMe)5 (E = B-Tl) and TM(EMe)4 (TM = Ni, Pd, Pt; E = B-Tl) 332 13.4.3 Carbene and carbyne complexes and heavier homologues (CO)5W-CH2, (CO)5W-E(OH)2, C14W-EH2, Cl(CO)4W-EH and C13W-EH (E = C, Si, Ge, Sn, Pb) 342 13.4.4 Ethylene and acetylene complexes (CO)5TM-C2Hx and C14TM-C2HX (TM = Cr, Mo, W), (CO)4TM-C2Hx + (TM = Fe, Ru, Os) and TM -C2HA (TM = Cu, Ag, Au) 347 13.4.5 Phosphane complexes (CO)5TM-PX3 (TM = Cr, Mo, W; X = H, Me, F, Cl) 354 2 13.4.6 Dihydrogen complexes TM(CO)5(T) -H2) (TM = Cr, Mo, W) 2 and W(CO)3X2(T| -H2) (X = CO, PH3, PC13, PMe3) 357 5 5 13.4.7 Metallocene complexes Fe(r| -E5)2 and Ti(T| -E5)2~ (E = CH, N, P, As, Sb) and bis(benzene)chromium 360 13.5 Conclusion 366 13.6 Acknowledgements 367 13.7 References 367

Chapter 14. Superoperator many-body theory of molecular currents: non-equilibrium Green functions in real time Upendra Harbola and Shaul Mukamel 373 14.1 Introduction 373 14.2 Dyson equations for superoperator Green functions 375 14.3 The calculation of molecular currents 382 14.4 Discussion 384 14.5 Acknowledgements 384 Appendix 14A: Superoperator expressions for the Keldysh Green functions 385 Appendix 14B: Superoperator Green function expression for the current 387 Appendix 14C: Self-energies for superoperator Green functions. . . . 389 Appendix 14D: Dyson equations in the +/— representation 393 Appendix 14E: Wick's theorem for superoperators 394 14.6 References 395

Chapter 15. Role of computational chemistry in the theory of unimolecular reaction rates William L. Hase and Reinhard Schinke 397 15.1 Introduction 398 xiv Contents

15.2 Role of computational chemistry 400 15.2.1 The lifetime distribution 400 15.2.2 Intrinsic and apparent non-RRKM behavior 403 15.2.3 Phase space structures 405 15.2.4 Resonance states 409 15.2.5 Steps in unimolecular reaction rates 413 15.2.6 Impact of direct dynamics simulations 415 15.3 Thefuture 419 15.4 Acknowledgements 420 15.5 References 420

Chapter 16. Molecular dynamics: an account of its evolution Raymond Kapral and Giovanni Ciccotti 425 16.1 Introduction 425 16.2 Early days 426 16.3 Classical period of classical molecular dynamics 428 16.4 Quantum mechanics and molecular dynamics 432 16.5 Coarse grained and mesoscopic dynamics 435 16.6 Conclusion 437 16.7 Acknowledgements 437 16.8 References 438

Chapter 17. Equations of motion methods for Computing electron affinities and ionization potentials Jack Simons 443 17.1 Introduction 443 17.2 Basics of EOM theory as applied to EAs and IPs 445 17.2.1 The EA equations of motion 445 17.2.2 The analogous equations of motion for ionization potentials 447 17.2.3 The rank of the Operators 448 17.2.4 Equations of lower rank for both EAs and IPs 449 17.2.5 Summary 449 17.3 Practical implementations of EOM theories for EAs and IPs 450 17.3.1 The M0ller-Plesset based approximations 450 17.3.2 Relationship to Greens functions/propagators 453 17.3.3 The natural orbital or extended Koopmans' theorem approach 454 17.3.4 Multiconfiguration-based approximations 454 17.3.5 Coupled-cluster based EOM 455 17.4 Some special cases 457 17.4.1 Calculating EAs as IPs 457 17.4.2 Metastable anion states 457 Contents xv 17.5 Summary 461 17.6 Acknowledgements 461 17.7 References 461

Chapter 18. Multireference coupled Cluster method based on the Brillouin-Wigner perturbation theory Petr Cärsky, Jifi Pittner and Ivan Hubac 465 18.1 Introduction 465 18.2 Single-reference versus multireference methods 466 18.3 Overview of multireference CC methods 468 18.4 Multireference Brillouin-Wigner coupled Cluster method 470 18.5 Intruder states and size extensivity 472 18.6 Performance of the multireference Brillouin-Wigner CC method and applications 476 18.7 Summary 479 18.8 Acknowledgements 479 18.9 References 479

Chapter 19. Electronic structure: the momentum perspective Ajit J. Thakkar 483 19.1 Introduction 483 19.2 Momentum - space wave functions 484 19.3 Densities and density matrices 487 19.4 Properties of the momentum density 490 19.5 Experimental determination of momentum densities 491 19.6 Ab initio computations 494 19.7 Illustrative calculations 494 19.8 Concluding remarks 502 19.9 Acknowledgements 502 19.10 References 502

Chapter 20. Recent advances in ab initio, density functional theory, and relativistic electronic structure theory Haruyuki Nakano, Takahito Nakajima, Takao Tsuneda and Kimihiko Hirao 507 20.1 Introduction 507 20.2 Multireference perturbation theory and valence bond description of electronic structures of molecules 508 20.2.1 Multireference perturbation theory 508 20.2.1.1 Multireference M0ller-Plesset perturbation method 509 20.2.1.2 Multiconfigurational quasi-degenerate perturbation theory (MC-QDPT) 512 xvi Contents

20.2.1.3 Application of multireference perturbation theory

to singlet-triplet Splitting of CH2 and CF2 513 20.2.1.4 Extension of reference wavefunctions— quasi-degenerate perturbation theory with quasi-complete active space self-consistent field reference functions (QCAS-QDPT) 514 20.2.1.5 Further extension of reference wavefunctions— quasi-degenerate perturbation theory with general-multiconfiguration space self-consistent field reference functions (GMC-QDPT) 516 20.2.1.6 Application of QCAS-and GMC-QDPT 517 20.2.1.6.1 Transition State barrier height for the unimolecular dissociation reaction of formaldehyde

H2CO^H2 + CO 517 20.2.1.6.2 Valence excitation energies for formaldehyde 518 20.2.1.6.3 The most stable structure

ofSiC3 521 20.2.2 Valence bond description of complete active space self-consistent field function 523 20.2.2.1 The CASVB method 523 20.2.2.2 Description of electronic structure of benzene 525 20.2.2.3 Description of chemical reaction—hydrogen exchange reactions H2 + X —• H 4- HX (X = F, Cl, Br, and I) 526 20.3 Long-range and other corrections for density functionals 529 20.3.1 Conventional correction schemes in density functional theory 529 20.3.2 Long-range correction schemes for exchange functionals 532 20.3.3 Applicabilities of long-range correction scheme 533 20.3.3.1 Van der Waals calculations 534 20.3.3.2 Time-dependent density functional calculations 534 20.3.3.3 Transition metal dimer calculations 538 20.3.3.4 Other calculations 540 20.4 Relativistic molecular theory 540 20.4.1 Introduction 540 20.4.2 Four-component relativistic molecular theory 542 20.4.2.1 Dirac-Hartree-Fock and Dirac-Kohn-Sham methods 542 20.4.2.2 Generally contracted Gaussian-type spinors and kinetic balance 543 Contents xvii

20.4.2.3 Efficient evaluation of electron repulsion integrals 544 20.4.2.4 Relativistic pseudospectral approach 545 20.4.3 Two-component relativistic molecular theory 548 20.4.3.1 Approximate relativistic Hamiltonians 548 20.4.3.2 RESC method 548 20.4.3.3 Douglas-Kroll method 549 20.4.3.4 Extended Douglas-Kroll transformations applied to the relativistic many-electron Hamiltonian . . . 550 20.5 Summary 553 20.6 References 554

Chapter 21. Semiempirical quantum-chemical methods in computational chemistry Walter Thiel 559 21.1 Introduction 559 21.2 Historical overview 560 21.3 Established methods 563 21.3.1 Basic concepts 563 21.3.2 MNDO and related methods 564 21.4 Selected recent developments 566 21.4.1 Beyond the MNDO model: orthogonalization corrections 566 21.4.2 Implementation of d orbitals in MNDO-type methods .... 567 21.4.3 Modified general-purpose methods 568 21.4.4 Special-purpose parametrizations 569 21.4.5 Computational aspects 570 21.4.6 Linear scaling methods 571 21.4.7 Hybrid methods 572 21.5 Selected recent applications 573 21.6 Summary and outlook 576 21.7 Acknowledgements 577 21.8 References 577

Chapter 22. Size-consistent state-specific multi-reference methods: a survey of some recent developments Dola Pahari, Sudip Chattopadhyay, Sanghamitra Das, Debashis Mukherjee and Uttam Sinha Mahapatra 581 22.1 Introduction 582 22.2 The SS-MRCC formalism 589 22.2.1 General developments for the complete model space 589 22.2.2 The use of anonymous parentage for inactive excitations in SS-MRCC method: API-SSMRCC theory 593 xviii Contents

22.2.3 Proof of the Connectivity of the API-SSMRCC formalism 598 22.3 Emergence of state-specific multi-reference perturbation theory SS-MRPT from SS-MRCC theory 599 22.3.1 Choice of the zeroth order Hamiltonians 601 22.4 Emergence of the SS-MRCEPA(I) methods from SS-MRCC 602 22.5 The size-extensive state-specific MRCC formalism using an IMS 606 22.6 Results and discussion 611 22.6.1 H4 model 613 22.6.2 Insertion of Be into H2:BeH2 model 615 22.6.3 LiH molecule '. 619 22.6.4 BH molecule 624 22.6.5 First and second order electrical property: LiH molecule . . . 627 22.7 Summary and conclusions 629 22.8 Acknowledgements 630 22.9 References 631

Chapter 23. The valence bond diagram approach: a paradigm for chemical reactivity Sason Shaik and Philippe C. Hiberty 635 23.1 Introduction 635 23.2 VB diagrams for chemical reactivity 638 23.3 VBSCD—the origins of barriers in chemical reactions 638 23.3.1 Bridges, causes, and causality: a VBSCD perspective .... 640 23.3.2 Comments on quantitative applications of VBSCDs 642 23.3.3 Comments on and some qualitative applications of VBSCDs 643 23.3.3.1 Radical exchange reactions 644 23.3.3.2 Electrocyclic and transition metal catalyzed bond activation reactions 646 23.3.3.3 Reactions between nucleophiles and electrophiles 647 23.3.4 Making stereochemical predictions with the VBSCD model 650 23.4 Valence bond contiguration mixing diagrams 652 23.4.1 General features of the VBCMD 652 23.4.2 VBCMD with ionic intermediate curves 652 23.4.2.1 Proton transfer processes 653 23.4.2.2 Nucleophilic Substitution on Silicon—stable hypercoordinated species 654 23.4.3 VBCMD with intermediates nascent from 'foreign states' 656 C 23.4.3.1 The SRN2 and SRN2 mechanisms 656 Contents xix

23.5 Additional applications of VB diagrams 658 23.5.1 VBSCD: A general model for electronic delocalization. . . . 658 23.5.2 VBSCD: The twin-state concept and its link to photochemical reactivity 659 23.6 Prospective 663 23.7 Acknowledgements 664 Appendix 23A: Computing mono-determinant VB wave functions with Standard ab initio programs 664 23.8 References 665

Chapter 24. Progress in the development of exchange-correlation functionals Gustavo E. Scuseria and Viktor N. Staroverov 669 24.1 Introduction 669 24.2 Kohn-Sham density functional theory 671 24.2.1 Motivation for density functional theory 671 24.2.2 Kohn-Sham scheine 673 24.3 Exchange and correlation density functionals 675 24.3.1 Exchange-correlation energy 675 24.3.2 Ingredients of density functional approximations 677 24.3.3 Analytic properties of exchange-correlation functionals . . . 679 24.4 Strategies for designing density functionals 680 24.5 Local density approximations 682 24.5.1 Local density approximation for exchange 682 24.5.2 Local density approximation for correlation 684 24.6 Density-gradient expansion 686 24.7 Constraint satisfaction 688 24.7.1 Corrections on the asymptotic behavior 688 24.7.2 Normalization of the exchange-correlation hole 692 24.7.3 Systematic constraint satisfaction 695 24.8 Modeling the exchange-correlation hole 699 24.8.1 Exchange functionals based on a model hole 699 24.8.2 Functionals based on a correlated wave function 701 24.8.3 Functionals based on a model pair correlation function . . . 703 24.8.4 Functionals based on a density matrix expansion 704 24.9 Empirical fits 706 24.10 Mixing exact and approximate exchange 708 24.10.1 Global hybrids 708 24.10.2 Local hybrids ' 711 24.10.3 Screened hybrids 712 24.11 Implementation and Performance 714 24.12 Conclusion 716 24.13 Acknowledgements 717 24.14 References 717 XX Contents

Chapter 25. Multiconfigurational quantum chemistry Björn O. Roos 725 25.1 Introduction 725 25.2 The density matrix and the natural Orbitals 727 25.3 The hydrogen molecule 730 25.4 Degeneracy and near degeneracy 734 25.4.1 Static and dynamic electron correlation 736 25.5 Multiconfigurational wave functions 738 25.5.1 A brief historical expose 738 25.5.2 The MCSCF wave function 739 25.5.3 The complete active space SCF method 740 25.5.4 Choosing the active space 740 25.5.4.1 Atoms and atomic ions 741 25.5.4.2 Small molecules 741 25.5.4.3 Electronic spectroscopy for organic molecules 742 25.5.4.4 Transition metal Compounds 742 25.5.4.5 Lanthanide and actinide chemistry 743 25.6 Dynamic correlation and the CASPT2 method 744 25.7 The relativistic regime 747 25.8 Three examples 748 25.8.1 The ozone molecule 749 25.8.2 The allyl radical 751 25.8.2.1 The ground State 752 25.8.2.2 The electronic spectrum 754 25.8.3 The PbF molecule 756 25.9 Conclusions 760 25.10 Acknowledgements 761 25.11 References 761

Chapter 26. Concepts of perturbation, orbital interaction, orbital mixing and orbital occupation Myung-Hwan Whangbo 765 26.1 Introduction 765 26.2 Orbital interaction on the basis of effective one-electron Hamiltonian 766 26.2.1 Exact relationship between two sets of molecular Orbitals 766 26.2.2 Perturbation analysis and orbital interaction 767 26.2.2.1 Non-degenerate perturbation 768 26.2.2.2 Degenerate perturbation 769 26.2.3 Normal versus counterintuitive orbital interaction 770 26.3 Effect of electron-electron repulsion 772 Contents xxi

26.3.1 Configuration interaction 773 26.3.2 States with different orbital occupancy 774 26.3.3 Mapping between electronic and spin Hamiltonians 775 26.3.4 Spin polarization 777 26.3.5 Non-equivalent orbital interactions in an open-shell System 778 26.3.6 Orbital ordering in magnetic solids 780 26.4 Spin-orbit coupling and orbital mixing 782 26.5 Concluding remarks 783 26.6 Acknowledgements 783 26.7 References 783

Chapter 27. G2, G3 and associated quantum chemical modeis for accurate theoretical thermochemistry Krishnan Raghavachari and Larry A. Curtiss 785 27.1 Introduction 785 27.2 Thermochemical test sets 787 27.3 G2 theory 789 27.3.1 Assessment of G2 theory 793 27.4 G3 theory 794 27.4.1 Assessment of G3 theory 797 27.5 G3X theory 799 27.5.1 Assessment of G3X theory 801 27.6 G3S theory 803 27.7 G3 theory for third-row elements 807 27.8 Applications 808 27.9 Summary and concluding remarks 809 27.10 Acknowledgement 810 27.11 References 810

Chapter 28. Factors that affect conductance at the molecular level Charles W. Bauschlicher Jr. and Alessandra Ricca 813 28.1 Introduction 813 28.2 Molecular electronics 814 28.3 Carbon nanotubes as molecular sensors 820 28.4 Conclusions and outlook 827 28.5 Acknowledgements 829 28.6 References 829

Chapter 29. The CH- • -O hydrogen bond: a historical account Steve Scheiner 831 29.1 Introduction 831 xxii Contents

29.2 Early thinking 832 29.2.1 1970s: the beginning ofquantum chemical study 833 29.2.2 1980s: more accurate calculations 834 29.2.3 1990s: proliferation and diversification 835 29.3 A surprising Observation 837 29.3.1 Status at the end of the 20th Century 838 29.4 The 21st Century 839 29.4.1 H-bond: to be or not to be? 840 29.4.2 Underlying reasons for blue shift 843 29.4.3 Other approaches—similar Undings 846 29.4.4 Another Interpretation 847 29.5 Future perspectives 851 29.6 References 852

Chapter 30. Ab initio and DFT calculations on the Cope rearrangement, a reaction with a chameleonic transition State Weston Thatcher Borden 859 30.1 Introduction 859 30.2 Information from experiments about the Cope TS 861 30.3 MINDO/3, AMI, and CASSCF calculations on the Cope TS 862 30.4 Inclusion of dynamic electron correlation 863 30.5 Substituent effects on the Cope rearrangement 865 30.6 Summary 870 30.7 Acknowledgements 872 30.8 References 872

Chapter 31. High-temperature quantum chemical molecular dynamics simulations of carbon nanostructure self-assembly processes Stephan Irle, Guishan Zheng, Marcus Elstner and Keiji Morokuma 875 31.1 Introduction 876 31.2 Previous theoretical investigations toward fullerene formation mechanisms 877 31.3 Computational methodology 879 31.4 Self-assembly capping process of open-ended carbon nanotubes 880 31.5 Self-assembly offullerene molecules from ensembles ofrandomly oriented C2 molecules 883 31.6 Conclusions 887 31.7 Acknowledgements 887 31.8 References 887 Contents xxiii

Chapter 32. Computational chemistry of isomeric fullerenes and endofullerenes Zdenek Slanina and Shigeru Nagase 891 32.1 Introduction 891 32.2 Relative stabilities of isomers 892 32.3 Energetics and thermodynamics of carbon Clusters 893 32.4 Small carbon Clusters 896 32.5 Generation of cages 897 32.6 Smaller fullerenes 897 32.7 Higher fullerenes 898 32.8 Endohedral metallofullerenes 901 32.9 Concluding remarks 907 32.10 Acknowledgements 907 32.11 References 908

Chapter 33. On the importance of many-body forces in Clusters and Condensed phase Krzysztof Szalewicz, Robert Bukowski and Bogumil Jeziorski 919 33.1 Introduction 919 33.2 Defmitions 921 33.3 Historical perspective 923 33.4 Perturbation theory of intermolecular interactions 927 33.5 Overview of pair contributions 928 33.6 Perturbation theory of nonadditive forces 930 33.7 Comparison of nonadditive effects for selected Systems 933 33.8 Physical interpretation of nonadditive components 937 33.8.1 Third-order induction energy 939 33.9 Case studies of nonadditive effects in Clusters 942 33.9.1 Helium trimer 942 33.9.2 Argon trimer and Condensed phase 943 33.9.3 Ar-Ar-HF trimer 946 33.9.4 (H20)2 HCl trimer 947 33.10 Three-body effects in open-shell Clusters 948 3 33.10.1 Ar2NCT( 2~) trimer 948 33.10.2 High-spin sodium trimer 948 33.10.3 Ar20~ ionic trimer—the case of orbital degeneracy . . . . 949 33.11 Water Clusters and Condensed phase 951 33.11.1 Two-body potentials for water 951 33.11.2 Three-body potentials for water 953 33.11.3 Simulations of liquid water 954 13.12 Acknowledgements 958 13.13 References 958 xxiv Contents

Chapter 34. Clusters to functional molecules, nanomaterials, and molecular devices: theoretical exploration Kwang S. Kim, P. Tarakeshwar and Han Myoung Lee .... 963 34.1 Introduction 963 34.2 Theoretical background 966 34.3 Clusters 967 34.3.1 Aqueous Clusters 967 34.3.2 Metallic Clusters 974 34.3.3 Weakly bound Clusters 976 34.4 Ionophores, receptors, and chemical sensors 980 34.5 Nanomaterials 983 34.6 Molecular devices 987 34.7 Concluding remarks 989 34.8 Acknowledgements 989 34.9 References 989

Chapter 35. Monte Carlo simulations of the finite temperature properties of (H20)6 R.A. Christie and K.D. Jordan 995 35.1 Introduction 995 35.2 Methodology 998 35.3 Results 1001 35.3.1 Energetics of (H20)e; basis set and thermal effects 1001 35.3.2 Error analysis of the truncated n-body approximation for£ 1001 35.3.3 Inherent structures 1002 35.3.4 Radial distribution function 1002 35.3.5 Temperature dependence of the energy and heat capacity of (H20)6 1003 35.4 Conclusions 1005 35.5 Acknowledgements 1006 35.6 References 1006

Chapter 36. Computational quantum chemistry on polymer chains: aspects of the last half Century Jean-Marie Andre 1011 36.1 Introduction 1011 36.2 Electronic structure of polymers: methodology (1965-till date). . . . 1012 36.3 Band structure calculations and photoelectron spectra 1016 36.4 Band structure calculations and (semi)conducting properties (1978—tili date) 1020 36.5 Band structure calculations and non-linear optical properties 1025 36.6 Band structure calculations and electron transfer Marcus theory. . . . 1033 Contents xxv

36.7 Conclusions 1041 36.8 Acknowledgements 1042 36.9 References 1042

Chapter 37. Forty years of ab initio calculations on mtermolecular forces Paul E.S. Wormer and Ad van der Avoird 1047 37.1 Introduction 1047 37.2 Prehistory: before Computers 1048 37.3 Antiquity: the sixties 1049 37.3.1 Supermolecular methods 1049 37.3.2 Perturbation methods 1051 37.4 The middle ages: era of mainframes 1053 37.4.1 Unexpanded dispersion 1054 37.4.2 Multipole-expanded dispersion 1056 37.4.3 Applications 1058 37.5 Modern times: revolution and democracy 1059 37.5.1 The SAPT method 1060 37.5.2 The coupled Cluster method 1063 37.5.3 Latest developments 1064 Appendix 37A: Relationship between dispersion and £MP2 • • • 1069 37.6 References 1072

Chapter 38. Applied density functional theory and the deMon codes 1964-2004 D.R. Salahub, A. Goursot, J. Weber, A.M. Köster and A. Vela 1079 38.1 Introduction. From the 1920s to the 1960s 1079 38.2 The 1970s 1081 38.3 The 1980s 1083 38.4 The 1990s 1086 38.5 The 2000s 1089 38.6 Resume 1091 38.7 Acknowledgements 1091 38.8 References 1092

Chapter 39. SAC-CI method applied to molecular spectroscopy M. Ehara, J. Hasegawa and H. Nakatsuji 1099 39.1 Introduction 1099 39.2 SAC-CI method 1102 39.3 Excited and ionized states of Tr-conjugated organic Compounds 1106 Contents

39.3.1 Excitation and ionization spectra of furan and thiophene 1106 39.3.2 /?-Benzoquinone and its anion radical 1108 39.3.3 Aniline: Effect of the amino-group conformation to the excitation spectrum 1111 39.4 Collision-induced absorption spectra of CsXe SYSTEM 1112 39.5 Transition metal complexes 1115 39.5.1 Cr02Cl2 1115 39.5.2 Tetraoxo complexes: CrC^", M0O4", MnOi~, TcO^-, RuC>4~ andOsO^" 1116 39.5.3 Excited states and 95Mo NMR chemical shift _ of Mo04_nS^ (n = 0-4) and MoSe^" 1118 39.6 Photochemistry of transition metal complex, Ni(CO)4 1120 39.7 Porphyrins and related Compounds 1121 39.7.1 Excited states of free-base phthalocyanine 1122 39.7.2 Bacterial photosynthetic reaction center 1124 39.8 Inner-shell ionization spectroscopy 1125 39.8.1 Core-electron binding energy 1125 39.8.2 Inner-shell satellite spectrum 1126 39.8.3 Vibrational spectrum of inner-shell ionization 1127 39.9 Geometries of molecular excited states 1128 39.9.1 Malonaldehyde 1128 + 39.9.2 Multi-electron processes; C2 and CO 1129 39.9.3 Acetylene and CNC 1132 39.10 Hyperfme Splitting constants 1133 39.11 Summary 1136 39.12 Acknowledgements 1137 39.13 References 1137

Chapter 40. Forty years of Fenske-Hall molecular orbital theory Charles Edwin Webster and Michael B. Hall 1143 40.1 Introduction 1143 40.2 Illustrative example 1144 40.3 Theory 1146 40.4 Transition metal Clusters 1150 40.5 Conclusions 1163 40.6 Acknowledgements 1163 40.7 References 1163

Chapter 41. Advances in electronic structure theory: GAMESS a decade later Mark S. Gordon and Michael W. Schmidt 1167 41.1 Introduction 1 Contents xxvii

41.2 QM methods 1168 41.2.1 Variational methods 1168 41.2.2 Many-body methods 1172 41.2.3 Excited states, non-adiabatic and relativistic methods 1173 41.2.4 Properties related to nuclear energy derivatives 1175 41.2.5 Other properties 1176 41.3 Scalable electronic structure theory 1177 41.4 QM/MM Methods 1181 41.4.1 Discrete solvent approaches 1181 41.4.2 Surface chemistry 1183 41.4.3 Continuum solvent methods 1184 41.5 Summary and prognosis 1184 41.6 Acknowledgements 1185 41.7 References 1185

Chapter 42. How and why coupled-cluster theory became the pre-eminent method in an ab initio quantum chemistry Rodney J. Bartlett 1191 42.1 Introduction 1191 42.2 Origins: exp(72)l0> 1192 42.3 Higher excitations in CC theory: exp^ +T2 + T3-\ )l0) 1197 42.4 Analytical gradients and the CC functional: E = (Ol(l + A)//l0), Ek = <0l(l +A)Ä*l0> 1202 42.5 Excited states: HRk = Rkcok 1207 42.6 Developments for large molecules and polymers 1213 42.7 Acknowledgements 1216 42.8 References 1216

Biographical Sketches of contributors 1223

Subject Index 1267