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

by Christopher J. Cramer (University of Minnesota)

• ISBN13: 9780470091814
• ISBN10: 0470091819
• Edition: 2nd
• Format: Hardcover
• Copyright: 2004-11-01
• Publisher: WILEY

Summary

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
What are Theory, Computation, and Modeling?	1	(16)
Definition of Terms	1	(3)
Quantum Mechanics	4	(1)
Computable Quantities	5	(6)
Structure	5	(1)
Potential Energy Surfaces	6	(4)
Chemical Properties	10	(1)
Cost and Efficiency	11	(4)
Intrinsic Value	11	(1)
Hardware and Software	12	(2)
Algorithms	14	(1)
Note on Units	15	(2)
Bibliography and Suggested Additional Reading	15	(1)
References	16	(1)
Molecular Mechanics	17	(52)
History and Fundamental Assumptions	17	(2)
Potential Energy Functional Forms	19	(20)
Bond Stretching	19	(2)
Valence Angle Bending	21	(1)
Torsions	22	(5)
van der Waals Interactions	27	(3)
Electrostatic Interactions	30	(4)
Cross Terms and Additional Non-bonded Terms	34	(2)
Parameterization Strategies	36	(3)
Force-field Energies and Thermodynamics	39	(1)
Geometry Optimization	40	(10)
Optimization Algorithms	41	(5)
Optimization Aspects Specific to Force Fields	46	(4)
Menagerie of Modern Force Fields	50	(12)
Available Force Fields	50	(9)
Validation	59	(3)
Force Fields and Docking	62	(2)
Case Study: (2R*,4S*)-1-Hydroxy-2,4-dimethylhex-5-ene	64	(5)
Bibliography and Suggested Additional Reading	66	(1)
References	67	(2)
Simulations of Molecular Ensembles	69	(36)
Relationship Between MM Optima and Real Systems	69	(1)
Phase Space and Trajectories	70	(2)
Properties as Ensemble Averages	70	(1)
Properties as Time Averages of Trajectories	71	(1)
Molecular Dynamics	72	(8)
Harmonic Oscillator Trajectories	72	(2)
Non-analytical Systems	74	(3)
Practical Issues in Propagation	77	(2)
Stochastic Dynamics	79	(1)
Monte Carlo	80	(2)
Manipulation of Phase-space Integrals	80	(1)
Metropolis Sampling	81	(1)
Ensemble and Dynamical Property Examples	82	(6)
Key Details in Formalism	88	(10)
Cutoffs and Boundary Conditions	88	(2)
Polarization	90	(1)
Control of System Variables	91	(2)
Simulation Convergence	93	(3)
The Multiple Minima Problem	96	(2)
Force Field Performance in Simulations	98	(1)
Case Study: Silica Sodalite	99	(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