Essentials of Computational Chemistry provides a balanced introduction to this dynamic subject. Suitable for both experimentalists and theorists, a wide range of samples and applications are included drawn from all key areas. The book carefully leads the reader thorough the necessary equations providing information explanations and reasoning where necessary and firmly placing each equation in context.
Table of Contents:
Preface to the First Edition xv
Preface to the Second Edition xix
Acknowledgments xxi
1 What are Theory, Computation, and Modeling? 1
1.1 Definition of Terms 1
1.2 Quantum Mechanics 4
1.3 Computable Quantities 5
1.3.1 Structure 5
1.3.2 Potential Energy Surfaces 6
1.3.3 Chemical Properties 10
1.4 Cost and Efficiency 11
1.4.1 Intrinsic Value 11
1.4.2 Hardware and Software 12
1.4.3 Algorithms 14
1.5 Note on Units 15
Bibliography and Suggested Additional Reading 15
References 16
2 Molecular Mechanics 17
2.1 History and Fundamental Assumptions 17
2.2 Potential Energy Functional Forms 19
2.2.1 Bond Stretching 19
2.2.2 Valence Angle Bending 21
2.2.3 Torsions 22
2.2.4 van der Waals Interactions 27
2.2.5 Electrostatic Interactions 30
2.2.6 Cross Terms and Additional Non-bonded Terms 34
2.2.7 Parameterization Strategies 36
2.3 Force-field Energies and Thermodynamics 39
2.4 Geometry Optimization 40
2.4.1 Optimization Algorithms 41
2.4.2 Optimization Aspects Specific to Force Fields 46
2.5 Menagerie of Modern Force Fields 50
2.5.1 Available Force Fields 50
2.5.2 Validation 59
2.6 Force Fields and Docking 62
2.7 Case Study: (2R∗,4S∗)-1-Hydroxy-2,4-dimethylhex-5-ene 64
Bibliography and Suggested Additional Reading 66
References 67
3 Simulations of Molecular Ensembles 69
3.1 Relationship Between MM Optima and Real Systems 69
3.2 Phase Space and Trajectories 70
3.2.1 Properties as Ensemble Averages 70
3.2.2 Properties as Time Averages of Trajectories 71
3.3 Molecular Dynamics 72
3.3.1 Harmonic Oscillator Trajectories 72
3.3.2 Non-analytical Systems 74
3.3.3 Practical Issues in Propagation 77
3.3.4 Stochastic Dynamics 79
3.4 Monte Carlo 80
3.4.1 Manipulation of Phase-space Integrals 80
3.4.2 Metropolis Sampling 81
3.5 Ensemble and Dynamical Property Examples 82
3.6 Key Details in Formalism 88
3.6.1 Cutoffs and Boundary Conditions 88
3.6.2 Polarization 90
3.6.3 Control of System Variables 91
3.6.4 Simulation Convergence 93
3.6.5 The Multiple Minima Problem 96
3.7 Force Field Performance in Simulations 98
3.8 Case Study: Silica Sodalite 99
Bibliography and Suggested Additional Reading 101
References 102
4 Foundations of Molecular Orbital Theory 105
4.1 Quantum Mechanics and the Wave Function 105
4.2 The Hamiltonian Operator 106
4.2.1 General Features 106
4.2.2 The Variational Principle 108
4.2.3 The Born–Oppenheimer Approximation 110
4.3 Construction of Trial Wave Functions 111
4.3.1 The LCAO Basis Set Approach 111
4.3.2 The Secular Equation 113
4.4 H¨uckel Theory 115
4.4.1 Fundamental Principles 115
4.4.2 Application to the Allyl System 116
4.5 Many-electron Wave Functions 119
4.5.1 Hartree-product Wave Functions 120
4.5.2 The Hartree Hamiltonian 121
4.5.3 Electron Spin and Antisymmetry 122
4.5.4 Slater Determinants 124
4.5.5 The Hartree-Fock Self-consistent Field Method 126
Bibliography and Suggested Additional Reading 129
References 130
5 Semiempirical Implementations of Molecular Orbital Theory 131
5.1 Semiempirical Philosophy 131
5.1.1 Chemically Virtuous Approximations 131
5.1.2 Analytic Derivatives 133
5.2 Extended H¨uckel Theory 134
5.3 CNDO Formalism 136
5.4 INDO Formalism 139
5.4.1 INDO and INDO/S 139
5.4.2 MINDO/3 and SINDO1 141
5.5 Basic NDDO Formalism 143
5.5.1 MNDO 143
5.5.2 AM1 145
5.5.3 PM3 146
5.6 General Performance Overview of Basic NDDO Models 147
5.6.1 Energetics 147
5.6.2 Geometries 150
5.6.3 Charge Distributions 151
5.7 Ongoing Developments in Semiempirical MO Theory 152
5.7.1 Use of Semiempirical Properties in SAR 152
5.7.2 d Orbitals in NDDO Models 153
5.7.3 SRP Models 155
5.7.4 Linear Scaling 157
5.7.5 Other Changes in Functional Form 157
5.8 Case Study: Asymmetric Alkylation of Benzaldehyde 159
Bibliography and Suggested Additional Reading 162
References 163
6 Ab Initio Implementations of Hartree–Fock Molecular Orbital Theory 165
6.1 Ab Initio Philosophy 165
6.2 Basis Sets 166
6.2.1 Functional Forms 167
6.2.2 Contracted Gaussian Functions 168
6.2.3 Single-ζ , Multiple-ζ , and Split-Valence 170
6.2.4 Polarization Functions 173
6.2.5 Diffuse Functions 176
6.2.6 The HF Limit 176
6.2.7 Effective Core Potentials 178
6.2.8 Sources 180
6.3 Key Technical and Practical Points of Hartree–Fock Theory 180
6.3.1 SCF Convergence 181
6.3.2 Symmetry 182
6.3.3 Open-shell Systems 188
6.3.4 Efficiency of Implementation and Use 190
6.4 General Performance Overview of Ab Initio HF Theory 192
6.4.1 Energetics 192
6.4.2 Geometries 196
6.4.3 Charge Distributions 198
6.5 Case Study: Polymerization of 4-Substituted Aromatic Enynes 199
Bibliography and Suggested Additional Reading 201
References 201
7 Including Electron Correlation in Molecular Orbital Theory 203
7.1 Dynamical vs. Non-dynamical Electron Correlation 203
7.2 Multiconfiguration Self-Consistent Field Theory 205
7.2.1 Conceptual Basis 205
7.2.2 Active Space Specification 207
7.2.3 Full Configuration Interaction 211
7.3 Configuration Interaction 211
7.3.1 Single-determinant Reference 211
7.3.2 Multireference 216
7.4 Perturbation Theory 216
7.4.1 General Principles 216
7.4.2 Single-reference 219
7.4.3 Multireference 223
7.4.4 First-order Perturbation Theory for Some Relativistic Effects 223
7.5 Coupled-cluster Theory 224
7.6 Practical Issues in Application 227
7.6.1 Basis Set Convergence 227
7.6.2 Sensitivity to Reference Wave Function 230
7.6.3 Price/Performance Summary 235
7.7 Parameterized Methods 237
7.7.1 Scaling Correlation Energies 238
7.7.2 Extrapolation 239
7.7.3 Multilevel Methods 239
7.8 Case Study: Ethylenedione Radical Anion 244
Bibliography and Suggested Additional Reading 246
References 247
8 Density Functional Theory 249
8.1 Theoretical Motivation 249
8.1.1 Philosophy 249
8.1.2 Early Approximations 250
8.2 Rigorous Foundation 252
8.2.1 The Hohenberg–Kohn Existence Theorem 252
8.2.2 The Hohenberg–Kohn Variational Theorem 254
8.3 Kohn–Sham Self-consistent Field Methodology 255
8.4 Exchange-correlation Functionals 257
8.4.1 Local Density Approximation 258
8.4.2 Density Gradient and Kinetic Energy Density Corrections 263
8.4.3 Adiabatic Connection Methods 264
8.4.4 Semiempirical DFT 268
8.5 Advantages and Disadvantages of DFT Compared to MO Theory 271
8.5.1 Densities vs. Wave Functions 271
8.5.2 Computational Efficiency 273
8.5.3 Limitations of the KS Formalism 274
8.5.4 Systematic Improvability 278
8.5.5 Worst-case Scenarios 278
8.6 General Performance Overview of DFT 280
8.6.1 Energetics 280
8.6.2 Geometries 291
8.6.3 Charge Distributions 294
8.7 Case Study: Transition-Metal Catalyzed Carbonylation of Methanol 299
Bibliography and Suggested Additional Reading 300
References 301
9 Charge Distribution and Spectroscopic Properties 305
9.1 Properties Related to Charge Distribution 305
9.1.1 Electric Multipole Moments 305
9.1.2 Molecular Electrostatic Potential 308
9.1.3 Partial Atomic Charges 309
9.1.4 Total Spin 324
9.1.5 Polarizability and Hyperpolarizability 325
9.1.6 ESR Hyperfine Coupling Constants 327
9.2 Ionization Potentials and Electron Affinities 330
9.3 Spectroscopy of Nuclear Motion 331
9.3.1 Rotational 332
9.3.2 Vibrational 334
9.4 NMR Spectral Properties 344
9.4.1 Technical Issues 344
9.4.2 Chemical Shifts and Spin–spin Coupling Constants 345
9.5 Case Study: Matrix Isolation of Perfluorinated p-Benzyne 349
Bibliography and Suggested Additional Reading 351
References 351
10 Thermodynamic Properties 355
10.1 Microscopic–macroscopic Connection 355
10.2 Zero-point Vibrational Energy 356
10.3 Ensemble Properties and Basic Statistical Mechanics 357
10.3.1 Ideal Gas Assumption 358
10.3.2 Separability of Energy Components 359
10.3.3 Molecular Electronic Partition Function 360
10.3.4 Molecular Translational Partition Function 361
10.3.5 Molecular Rotational Partition Function 362
10.3.6 Molecular Vibrational Partition Function 364
10.4 Standard-state Heats and Free Energies of Formation and Reaction 366
10.4.1 Direct Computation 367
10.4.2 Parametric Improvement 370
10.4.3 Isodesmic Equations 372
10.5 Technical Caveats 375
10.5.1 Semiempirical Heats of Formation 375
10.5.2 Low-frequency Motions 375
10.5.3 Equilibrium Populations over Multiple Minima 377
10.5.4 Standard-state Conversions 378
10.5.5 Standard-state Free Energies, Equilibrium Constants, and Concentrations 379
10.6 Case Study: Heat of Formation of H2NOH 381
Bibliography and Suggested Additional Reading 383
References 383
11 Implicit Models for Condensed Phases 385
11.1 Condensed-phase Effects on Structure and Reactivity 385
11.1.1 Free Energy of Transfer and Its Physical Components 386
11.1.2 Solvation as It Affects Potential Energy Surfaces 389
11.2 Electrostatic Interactions with a Continuum 393
11.2.1 The Poisson Equation 394
11.2.2 Generalized Born 402
11.2.3 Conductor-like Screening Model 404
11.3 Continuum Models for Non-electrostatic Interactions 406
11.3.1 Specific Component Models 406
11.3.2 Atomic Surface Tensions 407
11.4 Strengths and Weaknesses of Continuum Solvation Models 410
11.4.1 General Performance for Solvation Free Energies 410
11.4.2 Partitioning 416
11.4.3 Non-isotropic Media 416
11.4.4 Potentials of Mean Force and Solvent Structure 419
11.4.5 Molecular Dynamics with Implicit Solvent 420
11.4.6 Equilibrium vs. Non-equilibrium Solvation 421
11.5 Case Study: Aqueous Reductive Dechlorination of Hexachloroethane 422
Bibliography and Suggested Additional Reading 424
References 425
12 Explicit Models for Condensed Phases 429
12.1 Motivation 429
12.2 Computing Free-energy Differences 429
12.2.1 Raw Differences 430
12.2.2 Free-energy Perturbation 432
12.2.3 Slow Growth and Thermodynamic Integration 435
12.2.4 Free-energy Cycles 437
12.2.5 Potentials of Mean Force 439
12.2.6 Technical Issues and Error Analysis 443
12.3 Other Thermodynamic Properties 444
12.4 Solvent Models 445
12.4.1 Classical Models 445
12.4.2 Quantal Models 447
12.5 Relative Merits of Explicit and Implicit Solvent Models 448
12.5.1 Analysis of Solvation Shell Structure and Energetics 448
12.5.2 Speed/Efficiency 450
12.5.3 Non-equilibrium Solvation 450
12.5.4 Mixed Explicit/Implicit Models 451
12.6 Case Study: Binding of Biotin Analogs to Avidin 452
Bibliography and Suggested Additional Reading 454
References 455
13 Hybrid Quantal/Classical Models 457
13.1 Motivation 457
13.2 Boundaries Through Space 458
13.2.1 Unpolarized Interactions 459
13.2.2 Polarized QM/Unpolarized MM 461
13.2.3 Fully Polarized Interactions 466
13.3 Boundaries Through Bonds 467
13.3.1 Linear Combinations of Model Compounds 467
13.3.2 Link Atoms 473
13.3.3 Frozen Orbitals 475
13.4 Empirical Valence Bond Methods 477
13.4.1 Potential Energy Surfaces 478
13.4.2 Following Reaction Paths 480
13.4.3 Generalization to QM/MM 481
13.5 Case Study: Catalytic Mechanism of Yeast Enolase 482
Bibliography and Suggested Additional Reading 484
References 485
14 Excited Electronic States 487
14.1 Determinantal/Configurational Representation of Excited States 487
14.2 Singly Excited States 492
14.2.1 SCF Applicability 493
14.2.2 CI Singles 496
14.2.3 Rydberg States 498
14.3 General Excited State Methods 499
14.3.1 Higher Roots in MCSCF and CI Calculations 499
14.3.2 Propagator Methods and Time-dependent DFT 501
14.4 Sum and Projection Methods 504
14.5 Transition Probabilities 507
14.6 Solvatochromism 511
14.7 Case Study: Organic Light Emitting Diode Alq3 513
Bibliography and Suggested Additional Reading 515
References 516
15 Adiabatic Reaction Dynamics 519
15.1 Reaction Kinetics and Rate Constants 519
15.1.1 Unimolecular Reactions 520
15.1.2 Bimolecular Reactions 521
15.2 Reaction Paths and Transition States 522
15.3 Transition-state Theory 524
15.3.1 Canonical Equation 524
15.3.2 Variational Transition-state Theory 531
15.3.3 Quantum Effects on the Rate Constant 533
15.4 Condensed-phase Dynamics 538
15.5 Non-adiabatic Dynamics 539
15.5.1 General Surface Crossings 539
15.5.2 Marcus Theory 541
15.6 Case Study: Isomerization of Propylene Oxide 544
Bibliography and Suggested Additional Reading 546
References 546
Appendix A Acronym Glossary 549
Appendix B Symmetry and Group Theory 557
B.1 Symmetry Elements 557
B.2 Molecular Point Groups and Irreducible Representations 559
B.3 Assigning Electronic State Symmetries 561
B.4 Symmetry in the Evaluation of Integrals and Partition Functions 562
Appendix C Spin Algebra 565
C.1 Spin Operators 565
C.2 Pure- and Mixed-spin Wave Functions 566
C.3 UHF Wave Functions 571
C.4 Spin Projection/Annihilation 571
Reference 574
Appendix D Orbital Localization 575
D.1 Orbitals as Empirical Constructs 575
D.2 Natural Bond Orbital Analysis 578
References 579
Index 581
About the Author :
Christopher Cramer, Professor of Computational Chemistry Department of Chemistry, University of Minnesota,Minneapolis, USA
