Essentials of Computational Chemistry: Theories and Models, 2nd Edition

, by Christopher J. Cramer (University of Minnesota)

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ISBN: 9780470091814 | 0470091819
Cover: Hardcover
Copyright: 11/1/2004

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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.

Preface to the First Edition

Preface to the Second Edition

xix

Acknowledgments

xxi

What are Theory, Computation, and Modeling?

(16)

Definition of Terms

(3)

Quantum Mechanics

(1)

Computable Quantities

(6)

Structure

(1)

Potential Energy Surfaces

(4)

Chemical Properties

(1)

Cost and Efficiency

(4)

Intrinsic Value

(1)

Hardware and Software

(2)

Algorithms

(1)

Note on Units

(2)

Bibliography and Suggested Additional Reading

(1)

References

(1)

Molecular Mechanics

(52)

History and Fundamental Assumptions

(2)

Potential Energy Functional Forms

(20)

Bond Stretching

(2)

Valence Angle Bending

(1)

Torsions

(5)

van der Waals Interactions

(3)

Electrostatic Interactions

(4)

Cross Terms and Additional Non-bonded Terms

(2)

Parameterization Strategies

(3)

Force-field Energies and Thermodynamics

(1)

Geometry Optimization

(10)

Optimization Algorithms

(5)

Optimization Aspects Specific to Force Fields

(4)

Menagerie of Modern Force Fields

(12)

Available Force Fields

(9)

Validation

(3)

Force Fields and Docking

(2)

Case Study: (2R*,4S*)-1-Hydroxy-2,4-dimethylhex-5-ene

(5)

Bibliography and Suggested Additional Reading

(1)

References

(2)

Simulations of Molecular Ensembles

(36)

Relationship Between MM Optima and Real Systems

(1)

Phase Space and Trajectories

(2)

Properties as Ensemble Averages

(1)

Properties as Time Averages of Trajectories

(1)

Molecular Dynamics

(8)

Harmonic Oscillator Trajectories

(2)

Non-analytical Systems

(3)

Practical Issues in Propagation

(2)

Stochastic Dynamics

(1)

Monte Carlo

(2)

Manipulation of Phase-space Integrals

(1)

Metropolis Sampling

(1)

Ensemble and Dynamical Property Examples

(6)

Key Details in Formalism

(10)

Cutoffs and Boundary Conditions

(2)

Polarization

(1)

Control of System Variables

(2)

Simulation Convergence

(3)

The Multiple Minima Problem

(2)

Force Field Performance in Simulations

(1)

Case Study: Silica Sodalite

(6)

Bibliography and Suggested Additional Reading

101

(1)

References

102

(3)

Foundations of Molecular Orbital Theory

105

(26)

Quantum Mechanics and the Wave Function

105

(1)

The Hamiltonian Operator

106

(5)

General Features

106

(2)

The Variational Principle

108

(2)

The Born-Oppenheimer Approximation

110

(1)

Construction of Trial Wave Functions

111

(4)

The LCAO Basis Set Approach

111

(2)

The Secular Equation

113

(2)

Huckel Theory

115

(4)

Fundamental Principles

115

(1)

Application to the Allyl System

116

(3)

Many-electron Wave Functions

119

(12)

Hartree-product Wave Functions

120

(1)

The Hartree Hamiltonian

121

(1)

Electron Spin and Antisymmetry

122

(2)

Slater Determinants

124

(2)

The Hartree-Fock Self-consistent Field Method

126

(3)

Bibliography and Suggested Additional Reading

129

(1)

References

130

(1)

Semiempirical Implementations of Molecular Orbital Theory

131

(34)

Semiempirical Philosophy

131

(3)

Chemically Virtuous Approximations

131

(2)

Analytic Derivatives

133

(1)

Extended Huckel Theory

134

(2)

CNDO Formalism

136

(3)

INDO Formalism

139

(4)

INDO and INDO/S

139

(2)

MINDO/3 and SINDO1

141

(2)

Basic NDDO Formalism

143

(4)

MNDO

143

(2)

AM1

145

(1)

PM3

146

(1)

General Performance Overview of Basic NDDO Models

147

(5)

Energetics

147

(3)

Geometries

150

(1)

Charge Distributions

151

(1)

Ongoing Developments in Semiempirical MO Theory

152

(7)

Use of Semiempirical Properties in SAR

152

(1)

d Orbitals in NDDO Models

153

(2)

SRP Models

155

(2)

Linear Scaling

157

(1)

Other Changes in Functional Form

157

(2)

Case Study: Asymmetric Alkylation of Benzaldehyde

159

(6)

Bibliography and Suggested Additional Reading

162

(1)

References

163

(2)

Ab Initio Implementations of Hartree-Fock Molecular Orbital Theory

165

(38)

Ab Initio Philosophy

165

(1)

Basis Sets

166

(14)

Functional Forms

167

(1)

Contracted Gaussian Functions

168

(2)

Single-ζ, Multiple-ζ, and Split-Valence

170

(3)

Polarization Functions

173

(3)

Diffuse Functions

176

(1)

The HF Limit

176

(2)

Effective Core Potentials

178

(2)

Sources

180

(1)

Key Technical and Practical Points of Hartree-Fock Theory

180

(12)

SCF Convergence

181

(1)

Symmetry

182

(6)

Open-shell Systems

188

(2)

Efficiency of Implementation and Use

190

(2)

General Performance Overview of Ab Initio HF Theory

192

(7)

Energetics

192

(4)

Geometries

196

(2)

Charge Distributions

198

(1)

Case Study: Polymerization of 4-Substituted Aromatic Enynes

199

(4)

Bibliography and Suggested Additional Reading

201

(1)

References

201

(2)

Including Electron Correlation in Molecular Orbital Theory

203

(46)

Dynamical vs. Non-dynamical Electron Correlation

203

(2)

Multiconfiguration Self-Consistent Field Theory

205

(6)

Conceptual Basis

205

(2)

Active Space Specification

207

(4)

Full Configuration Interaction

211

(1)

Configuration Interaction

211

(5)

Single-determinant Reference

211

(5)

Multireference

216

(1)

Perturbation Theory

216

(8)

General Principles

216

(3)

Single-reference

219

(4)

Multireference

223

(1)

First-order Perturbation Theory for Some Relativistic Effects

223

(1)

Coupled-cluster Theory

224

(3)

Practical Issues in Application

227

(10)

Basis Set Convergence

227

(3)

Sensitivity to Reference Wave Function

230

(5)

Price/Performance Summary

235

(2)

Parameterized Methods

237

(7)

Scaling Correlation Energies

238

(1)

Extrapolation

239

(1)

Multilevel Methods

239

(5)

Case Study: Ethylenedione Radical Anion

244

(5)

Bibliography and Suggested Additional Reading

246

(1)

References

247

(2)

Density Functional Theory

249

(56)

Theoretical Motivation

249

(3)

Philosophy

249

(1)

Early Approximations

250

(2)

Rigorous Foundation

252

(3)

The Hohenberg-Kohn Existence Theorem

252

(2)

The Hohenberg-Kohn Variational Theorem

254

(1)

Kohn-Sham Self-consistent Field Methodology

255

(2)

Exchange-correlation Functionals

257

(14)

Local Density Approximation

258

(5)

Density Gradient and Kinetic Energy Density Corrections

263

(1)

Adiabatic Connection Methods

264

(4)

Semiempirical DFT

268

(3)

Advantages and Disadvantages of DFT Compared to MO Theory

271

(9)

Densities vs. Wave Functions

271

(2)

Computational Efficiency

273

(1)

Limitations of the KS Formalism

274

(4)

Systematic Improvability

278

(1)

Worst-case Scenarios

278

(2)

General Performance Overview of DFT

280

(19)

Energetics

280

(11)

Geometries

291

(3)

Charge Distributions

294

(5)

Case Study: Transition-Metal Catalyzed Carbonylation of Methanol

299

(6)

Bibliography and Suggested Additional Reading

300

(1)

References

301

(4)

Charge Distribution and Spectroscopic Properties

305

(50)

Properties Related to Charge Distribution

305

(25)

Electric Multipole Moments

305

(3)

Molecular Electrostatic Potential

308

(1)

Partial Atomic Charges

309

(15)

Total Spin

324

(1)

Polarizability and Hyperpolarizability

325

(2)

ESR Hyperfine Coupling Constants

327

(3)

Ionization Potentials and Electron Affinities

330

(1)

Spectroscopy of Nuclear Motion

331

(13)

Rotational

332

(2)

Vibrational

334

(10)

NMR Spectral Properties

344

(5)

Technical Issues

344

(1)

Chemical Shifts and Spin--spin Coupling Constants

345

(4)

Case Study: Matrix Isolation of Perfluorinated p-Benzyne

349

(6)

Bibliography and Suggested Additional Reading

351

(1)

References

351

(4)

Thermodynamic Properties

355

(30)

Microscopic-macroscopic Connection

355

(1)

Zero-point Vibrational Energy

356

(1)

Ensemble Properties and Basic Statistical Mechanics

357

(9)

Ideal Gas Assumption

358

(1)

Separability of Energy Components

359

(1)

Molecular Electronic Partition Function

360

(1)

Molecular Translational Partition Function

361

(1)

Molecular Rotational Partition Function

362

(2)

Molecular Vibrational Partition Function

364

(2)

Standard-state Heats and Free Energies of Formation and Reaction

366

(9)

Direct Computation

367

(3)

Parametric Improvement

370

(2)

Isodesmic Equations

372

(3)

Technical Caveats

375

(6)

Semiempirical Heats of Formation

375

(1)

Low-frequency Motions

375

(2)

Equilibrium Populations over Multiple Minima

377

(1)

Standard-state Conversions

378

(1)

Standard-state Free Energies, Equilibrium Constants, and Concentrations

379

(2)

Case Study: Heat of Formation of H2NOH

381

(4)

Bibliography and Suggested Additional Reading

383

(1)

References

383

(2)

Implicit Models for Condensed Phases

385

(44)

Condensed-phase Effects on Structure and Reactivity

385

(8)

Free Energy of Transfer and Its Physical Components

386

(3)

Solvation as It Affects Potential Energy Surfaces

389

(4)

Electrostatic Interactions with a Continuum

393

(13)

The Poisson Equation

394

(8)

Generalized Born

402

(2)

Conductor-like Screening Model

404

(2)

Continuum Models for Non-electrostatic Interactions

406

(4)

Specific Component Models

406

(1)

Atomic Surface Tensions

407

(3)

Strengths and Weaknesses of Continuum Solvation Models

410

(12)

General Performance for Solvation Free Energies

410

(6)

Partitioning

416

(1)

Non-isotropic Media

416

(3)

Potentials of Mean Force and Solvent Structure

419

(1)

Molecular Dynamics with Implicit Solvent

420

(1)

Equilibrium vs. Non-equilibrium Solvation

421

(1)

Case Study: Aqueous Reductive Dechlorination of Hexachloroethane

422

(7)

Bibliography and Suggested Additional Reading

424

(1)

References

425

(4)

Explicit Models for Condensed Phases

429

(28)

Motivation

429

(1)

Computing Free-energy Differences

429

(15)

Raw Differences

430

(2)

Free-energy Perturbation

432

(3)

Slow Growth and Thermodynamic Integration

435

(2)

Free-energy Cycles

437

(2)

Potentials of Mean Force

439

(4)

Technical Issues and Error Analysis

443

(1)

Other Thermodynamic Properties

444

(1)

Solvent Models

445

(3)

Classical Models

445

(2)

Quantal Models

447

(1)

Relative Merits of Explicit and Implicit Solvent Models

448

(4)

Analysis of Solvation Shell Structure and Energetics

448

(2)

Speed/Efficiency

450

(1)

Non-equilibrium Solvation

450

(1)

Mixed Explicit/Implicit Models

451

(1)

Case Study: Binding of Biotin Analogs to Avidin

452

(5)

Bibliography and Suggested Additional Reading

454

(1)

References

455

(2)

Hybrid Quantal/Classical Models

457

(30)

Motivation

457

(1)

Boundaries Through Space

458

(9)

Unpolarized Interactions

459

(2)

Polarized QM/Unpolarized MM

461

(5)

Fully Polarized Interactions

466

(1)

Boundaries Through Bonds

467

(10)

Linear Combinations of Model Compounds

467

(6)

Link Atoms

473

(2)

Frozen Orbitals

475

(2)

Empirical Valence Bond Methods

477

(5)

Potential Energy Surfaces

478

(2)

Following Reaction Paths

480

(1)

Generalization to QM/MM

481

(1)

Case Study: Catalytic Mechanism of Yeast Enolase

482

(5)

Bibliography and Suggested Additional Reading

484

(1)

References

485

(2)

Excited Electronic States

487

(32)

Determinantal/Configurational Representation of Excited States

487

(5)

Singly Excited States

492

(7)

SCF Applicability

493

(3)

CI Singles

496

(2)

Rydberg States

498

(1)

General Excited State Methods

499

(5)

Higher Roots in MCSCF and CI Calculations

499

(2)

Propagator Methods and Time-dependent DFT

501

(3)

Sum and Projection Methods

504

(3)

Transition Probabilities

507

(4)

Solvatochromism

511

(2)

Case Study: Organic Light Emitting Diode Alq3

513

(6)

Bibliography and Suggested Additional Reading

515

(1)

References

516

(3)

Adiabatic Reaction Dynamics

519

(30)

Reaction Kinetics and Rate Constants

519

(3)

Unimolecular Reactions

520

(1)

Bimolecular Reactions

521

(1)

Reaction Paths and Transition States

522

(2)

Transition-state Theory

524

(14)

Canonical Equation

524

(7)

Variational Transition-state Theory

531

(2)

Quantum Effects on the Rate Constant

533

(5)

Condensed-phase Dynamics

538

(1)

Non-adiabatic Dynamics

539

(5)

General Surface Crossings

539

(2)

Marcus Theory

541

(3)

Case Study: Isomerization of Propylene Oxide

544

(5)

Bibliography and Suggested Additional Reading

546

(1)

References

546

(3)

Appendix A Acronym Glossary

549

(8)

Appendix B Symmetry and Group Theory

557

(8)

Symmetry Elements

557

(2)

Molecular Point Groups and Irreducible Representations

559

(2)

Assigning Electronic State Symmetries

561

(1)

Symmetry in the Evaluation of Integrals and Partition Functions

562

(3)

Appendix C Spin Algebra

565

(10)

Spin Operators

565

(1)

Pure- and Mixed-spin Wave Functions

566

(5)

UHF Wave Functions

571

(1)

Spin Projection/Annihilation

571

(4)

Reference

574

(1)

Appendix D Orbital Localization

575

(6)

Orbitals as Empirical Constructs

575

(3)

Natural Bond Orbital Analysis

578

(3)

References

579

(2)

Index

581

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Essentials of Computational Chemistry: Theories and Models, 2nd Edition

Summary

Table of Contents

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