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Introduction to Computational Chemistry, 3rd Edition

ISBN: 978-1-118-82599-0
660 pages
February 2017
Introduction to Computational Chemistry, 3rd Edition (1118825993) cover image

Description

Introduction to Computational Chemistry 3rd Edition provides a comprehensive account of the fundamental principles underlying different computational methods. Fully revised and updated throughout to reflect important method developments and improvements since publication of the previous edition, this timely update includes the following significant revisions and new topics:

* Polarizable force fields
* Tight-binding DFT
* More extensive DFT functionals, excited states and time dependent molecular properties
* Accelerated Molecular Dynamics methods
* Tensor decomposition methods
* Cluster analysis
* Reduced scaling and reduced prefactor methods

Additional information is available at: www.wiley.com/go/jensen/computationalchemistry3

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Table of Contents

Preface to the First Edition xv

Preface to the Second Edition xix

Preface to the Third Edition xxi

1 Introduction 1

1.1 Fundamental Issues 2

1.2 Describing the System 3

1.3 Fundamental Forces 3

1.4 The Dynamical Equation 5

1.5 Solving the Dynamical Equation 7

1.6 Separation of Variables 8

1.7 Classical Mechanics 11

1.8 Quantum Mechanics 13

1.9 Chemistry 18

References 19

2 Force Field Methods 20

2.1 Introduction 20

2.2 The Force Field Energy 21

2.3 Force Field Parameterization 53

2.4 Differences in Atomistic Force Fields 62

2.5 Water Models 66

2.6 Coarse Grained Force Fields 67

2.7 Computational Considerations 69

2.8 Validation of Force Fields 71

2.9 Practical Considerations 73

2.10 Advantages and Limitations of Force Field Methods 73

2.11 Transition Structure Modeling 74

2.12 Hybrid Force Field Electronic Structure Methods 78

References 82

3 Hartree–Fock Theory 88

3.1 The Adiabatic and Born–Oppenheimer Approximations 90

3.2 Hartree–FockTheory 94

3.3 The Energy of a Slater Determinant 95

3.4 Koopmans’ Theorem 100

3.5 The Basis Set Approximation 101

3.6 An Alternative Formulation of the Variational Problem 105

3.7 Restricted and Unrestricted Hartree–Fock 106

3.8 SCF Techniques 108

3.9 Periodic Systems 119

References 121

4 Electron Correlation Methods 124

4.1 Excited Slater Determinants 125

4.2 Configuration Interaction 128

4.3 Illustrating how CI Accounts for Electron Correlation, and the RHF Dissociation Problem 135

4.4 The UHF Dissociation and the Spin Contamination Problem 138

4.5 Size Consistency and Size Extensivity 142

4.6 Multiconfiguration Self-Consistent Field 143

4.7 Multireference Configuration Interaction 148

4.8 Many-Body Perturbation Theory 148

4.9 Coupled Cluster 157

4.10 Connections between Coupled Cluster, Configuration Interaction and Perturbation Theory 162

4.11 Methods Involving the Interelectronic Distance 166

4.12 Techniques for Improving the Computational Efficiency 169

4.13 Summary of Electron Correlation Methods 174

4.14 Excited States 176

4.15 Quantum Monte Carlo Methods 183

References 185

5 Basis Sets 188

5.1 Slater- and Gaussian-Type Orbitals 189

5.2 Classification of Basis Sets 190

5.3 Construction of Basis Sets 194

5.4 Examples of Standard Basis Sets 200

5.5 Plane Wave Basis Functions 208

5.6 Grid and Wavelet Basis Sets 210

5.7 Fitting Basis Sets 211

5.8 Computational Issues 211

5.9 Basis Set Extrapolation 212

5.10 Composite Extrapolation Procedures 215

5.11 Isogyric and Isodesmic Reactions 222

5.12 Effective Core Potentials 223

5.13 Basis Set Superposition and Incompleteness Errors 226

References 228

6 Density Functional Methods 233

6.1 Orbital-Free Density Functional Theory 234

6.2 Kohn–Sham Theory 235

6.3 Reduced Density Matrix and Density Cumulant Methods 237

6.4 Exchange and Correlation Holes 241

6.5 Exchange–Correlation Functionals 244

6.6 Performance of Density Functional Methods 258

6.7 Computational Considerations 260

6.8 Differences between Density Functional Theory and Hartree-Fock 262

6.9 Time-Dependent Density Functional Theory (TDDFT) 263

6.10 Ensemble Density Functional Theory 268

6.11 Density Functional Theory Problems 269

6.12 Final Considerations 269

References 270

7 Semi-empirical Methods 275

7.1 Neglect of Diatomic Differential Overlap (NDDO) Approximation 276

7.2 Intermediate Neglect of Differential Overlap (INDO) Approximation 277

7.3 Complete Neglect of Differential Overlap (CNDO) Approximation 277

7.4 Parameterization 278

7.5 Hückel Theory 283

7.6 Tight-Binding Density Functional Theory 285

7.7 Performance of Semi-empirical Methods 287

7.8 Advantages and Limitations of Semi-empirical Methods 289

References 290

8 Valence Bond Methods 291

8.1 Classical Valence Bond Theory 292

8.2 Spin-Coupled Valence Bond Theory 293

8.3 Generalized Valence Bond Theory 297

References 298

9 Relativistic Methods 299

9.1 The Dirac Equation 300

9.2 Connections between the Dirac and Schrödinger Equations 302

9.3 Many-Particle Systems 306

9.4 Four-Component Calculations 309

9.5 Two-Component Calculations 310

9.6 Relativistic Effects 313

References 315

10 Wave Function Analysis 317

10.1 Population Analysis Based on Basis Functions 317

10.2 Population Analysis Based on the Electrostatic Potential 320

10.3 Population Analysis Based on the Electron Density 323

10.4 Localized Orbitals 329

10.5 Natural Orbitals 333

10.6 Computational Considerations 337

10.7 Examples 338

References 339

11 Molecular Properties 341

11.1 Examples of Molecular Properties 343

11.2 Perturbation Methods 347

11.3 Derivative Techniques 349

11.4 Response and Propagator Methods 351

11.5 Lagrangian Techniques 351

11.6 Wave Function Response 353

11.7 Electric Field Perturbation 357

11.8 Magnetic Field Perturbation 358

11.9 Geometry Perturbations 367

11.10 Time-Dependent Perturbations 372

11.11 Rotational and Vibrational Corrections 377

11.12 Environmental Effects 378

11.13 Relativistic Corrections 378

References 378

12 Illustrating the Concepts 380

12.1 Geometry Convergence 380

12.2 Total Energy Convergence 383

12.3 Dipole Moment Convergence 385

12.4 Vibrational Frequency Convergence 386

12.5 Bond Dissociation Curves 389

12.6 Angle Bending Curves 394

12.7 Problematic Systems 396

12.8 Relative Energies of C4H6 Isomers 399

References 402

13 Optimization Techniques 404

13.1 Optimizing Quadratic Functions 405

13.2 Optimizing General Functions: Finding Minima 407

13.3 Choice of Coordinates 415

13.4 Optimizing General Functions: Finding Saddle Points (Transition Structures) 418

13.5 Constrained Optimizations 431

13.6 Global Minimizations and Sampling 433

13.7 Molecular Docking 440

13.8 Intrinsic Reaction Coordinate Methods 441

References 444

14 Statistical Mechanics and Transition State Theory 447

14.1 Transition State Theory 447

14.2 Rice–Ramsperger–Kassel–Marcus Theory 450

14.3 Dynamical Effects 451

14.4 StatisticalMechanics 452

14.5 The Ideal Gas, Rigid-Rotor Harmonic-Oscillator Approximation 454

14.6 Condensed Phases 464

References 468

15 Simulation Techniques 469

15.1 Monte Carlo Methods 472

15.2 Time-Dependent Methods 474

15.3 Periodic Boundary Conditions 491

15.4 Extracting Information from Simulations 494

15.5 Free Energy Methods 499

15.6 Solvation Models 502

References 511

16 Qualitative Theories 515

16.1 Frontier Molecular Orbital Theory 515

16.2 Concepts from Density Functional Theory 519

16.3 Qualitative Molecular Orbital Theory 522

16.4 Energy Decomposition Analyses 524

16.5 Orbital Correlation Diagrams: TheWoodward–Hoffmann Rules 526

16.6 The Bell–Evans–Polanyi Principle/Hammond Postulate/Marcus Theory 534

16.7 More O’Ferrall–Jencks Diagrams 538

References 541

17 Mathematical Methods 543

17.1 Numbers, Vectors, Matrices and Tensors 543

17.2 Change of Coordinate System 549

17.3 Coordinates, Functions, Functionals, Operators and Superoperators 560

17.3.1 Differential Operators 562

17.4 Normalization, Orthogonalization and Projection 563

17.5 Differential Equations 565

17.6 Approximating Functions 568

17.7 Fourier and Laplace Transformations 577

17.8 Surfaces 577

References 580

18 Statistics and QSAR 581

18.1 Introduction 581

18.2 Elementary Statistical Measures 583

18.3 Correlation between Two Sets of Data 585

18.4 Correlation between Many Sets of Data 588

18.5 Quantitative Structure–Activity Relationships (QSAR) 595

18.6 Non-linear Correlation Methods 597

18.7 Clustering Methods 598

References 604

19 Concluding Remarks 605

Appendix A 608

Notation 608

Appendix B 614

The Variational Principle 614

The Hohenberg–Kohn Theorems 615

The Adiabatic Connection Formula 616

Reference 617

Appendix C 618

Atomic Units 618

Appendix D 619

Z Matrix Construction 619

Appendix E 627

First and Second Quantization 627

References 628

Index 629

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