Cramer Christopher J. Essentials of Computational Chemistry. Theories and Models

2nd Edition. John Wiley & Sons Ltd, 2004. – 596 p.
This books contains the foundations of computational and quantum chemistry, including description of molecular mechanics, molecular orbital theory (semiempirical, ab initio implementations), density functional theory, modeling of thermodynamic properties, implicit and explicit models for condensed phases, excited electronic states and adiabatic reaction dynamicsPreface to the First Edition
Preface to the Second EditionWhat are Theory, Computation, and Modeling?Definition of Terms
Quantum Mechanics
Computable Quantities
Structure
Potential Energy Surfaces
Chemical Properties
Cost and Efficiency
Intrinsic Value
Hardware and Software
Algorithms
Note on Units
Bibliography and Suggested Additional ReadingMolecular MechanicsHistory and Fundamental Assumptions
Potential Energy Functional Forms
Bond Stretching
Valence Angle Bending
Torsions
Van der Waals Interactions
Electrostatic Interactions
Cross Terms and Additional Non-bonded Terms
Parameterization Strategies
Force-field Energies and Thermodynamics
Geometry Optimization
Optimization Algorithms
Optimization Aspects Specific to Force Fields
Menagerie of Modern Force Fields
Available Force Fields
Validation
Force Fields and Docking Case Study: (2R*,4S*)-1-Hydroxy-2,4-dimethylhex-5-ene
Bibliography and Suggested Additional ReadingSimulations of Molecular EnsemblesRelationship Between MM Optima and Real Systems
Phase Space and Trajectories
Properties as Ensemble Averages
Properties as Time Averages of Trajectories
Molecular Dynamics
Harmonic Oscillator Trajectories
Non-analytical Systems
Practical Issues in Propagation
Stochastic Dynamics
Monte Carlo
Manipulation of Phase-space Integrals
Metropolis Sampling
Ensemble and Dynamical Property Examples
Key Details in Formalism
Cutoffs and Boundary Conditions
Polarization
Control of System Variables
Simulation Convergence
The Multiple Minima Problem
Force Field Performance in Simulations
Case Study: Silica Sodalite
Bibliography and Suggested Additional ReadingFoundations of Molecular Orbital TheoryQuantum Mechanics and the Wave Function
The Hamiltonian Operator
General Features
The Variational Principle
The Born–Oppenheimer Approximation
Construction of Trial Wave Functions
The LCAO Basis Set Approach
The Secular Equation
Hёuckel Theory
Fundamental Principles
Application to the Allyl System
Many-electron Wave Functions
Hartree-product Wave Functions
The Hartree Hamiltonian
Electron Spin and Antisymmetry
Slater Determinants
The Hartree-Fock Self-consistent Field Method
Bibliography and Suggested Additional ReadingSemiempirical Implementations of Molecular Orbital TheorySemiempirical Philosophy
Chemically Virtuous Approximations
Analytic Derivatives
Extended Hёuckel Theory
CNDO Formalism
INDO Formalism
INDO and INDO/S
MINDO/3 and SINDO1
Basic NDDO Formalism
MNDO
AM1
PM3
General Performance Overview of Basic NDDO Models
Energetics
Geometries
Charge Distributions
Ongoing Developments in Semiempirical MO Theory
Use of Semiempirical Properties in SAR
d Orbitals in NDDO Models
SRP Models
Linear Scaling
Other Changes in Functional Form
Case Study: Asymmetric Alkylation of Benzaldehyde
Bibliography and Suggested Additional ReadingAb Initio Implementations of Hartree–Fock Molecular Orbital TheoryAb Initio Philosophy
Basis Sets
Functional Forms
Contracted Gaussian Functions
Single-ζ , Multiple-ζ , and Split-Valence
Polarization Functions
Diffuse Functions
The HF Limit
Effective Core Potentials
Sources
Key Technical and Practical Points of Hartree–Fock Theory
SCF Convergence
Symmetry
Open-shell Systems
Efficiency of Implementation and Use
General Performance Overview of Ab Initio HF Theory
Energetics
Geometries
Charge Distributions
Case Study: Polymerization of 4-Substituted Aromatic Enynes
Bibliography and Suggested Additional ReadingIncluding Electron Correlation in Molecular Orbital TheoryDynamical vs. Non-dynamical Electron Correlation
Multiconfiguration Self-Consistent Field Theory
Conceptual Basis
Active Space Specification
Full Configuration Interaction
Configuration Interaction
Single-determinant Reference
Multireference
Perturbation Theory
General Principles
Single-reference
Multireference
First-order Perturbation Theory for Some Relativistic Effects
Coupled-cluster Theory
Practical Issues in Application
Basis Set Convergence
Sensitivity to Reference Wave Function
Price/Performance Summary
Parameterized Methods
Scaling Correlation Energies
Extrapolation
Multilevel Methods
Case Study: Ethylenedione Radical Anion
Bibliography and Suggested Additional ReadingDensity Functional TheoryTheoretical Motivation
Philosophy
Early Approximations
Rigorous Foundation
The Hohenberg–Kohn Existence Theorem
The Hohenberg–Kohn Variational Theorem
Kohn–Sham Self-consistent Field Methodology
Exchange-correlation Functionals
Local Density Approximation
Density Gradient and Kinetic Energy Density Corrections
Adiabatic Connection Methods
Semiempirical DFT
Advantages and Disadvantages of DFT Compared to MO Theory
Densities vs. Wave Functions
Computational Efficiency
Limitations of the KS Formalism
Systematic Improvability
Worst-case Scenarios
General Performance Overview of DFT
Energetics
Geometries
Charge Distributions
Case Study: Transition-Metal Catalyzed Carbonylation of Methanol
Bibliography and Suggested Additional ReadingCharge Distribution and Spectroscopic PropertiesProperties Related to Charge Distribution
Electric Multipole Moments
Molecular Electrostatic Potential
Partial Atomic Charges
Total Spin
Polarizability and Hyperpolarizability
ESR Hyperfine Coupling Constants
Ionization Potentials and Electron Affinities
Spectroscopy of Nuclear Motion
Rotational
Vibrational
NMR Spectral Properties
Technical Issues
Chemical Shifts and Spin–spin Coupling Constants
Case Study: Matrix Isolation of Perfluorinated p-Benzyne
Bibliography and Suggested Additional ReadingThermodynamic PropertiesMicroscopic–macroscopic Connection
Zero-point Vibrational Energy
Ensemble Properties and Basic Statistical Mechanics
Ideal Gas Assumption
Separability of Energy Components
Molecular Electronic Partition Function
Molecular Translational Partition Function
Molecular Rotational Partition Function
Molecular Vibrational Partition Function
Standard-state Heats and Free Energies of Formation and Reaction
Direct Computation
Parametric Improvement
Isodesmic Equations
Technical Caveats
Semiempirical Heats of Formation
Low-frequency Motions
Equilibrium Populations over Multiple Minima
Standard-state Conversions
Standard-state Free Energies, Equilibrium Constants, and Concentrations
Case Study: Heat of Formation of NH₂OH
Bibliography and Suggested Additional ReadingImplicit Models for Condensed PhasesCondensed-phase Effects on Structure and Reactivity
Free Energy of Transfer and Its Physical Components
Solvation as It Affects Potential Energy Surfaces
Electrostatic Interactions with a Continuum
The Poisson Equation
Generalized Born
Conductor-like Screening Model
Continuum Models for Non-electrostatic Interactions
Specific Component Models
Atomic Surface Tensions
Strengths and Weaknesses of Continuum Solvation Models
General Performance for Solvation Free Energies
Partitioning
Non-isotropic Media
Potentials of Mean Force and Solvent Structure
Molecular Dynamics with Implicit Solvent
Equilibrium vs. Non-equilibrium Solvation
Case Study: Aqueous Reductive Dechlorination of Hexachloroethane
Bibliography and Suggested Additional ReadingExplicit Models for Condensed PhasesMotivation
Computing Free-energy Differences
Raw Differences
Free-energy Perturbation
Slow Growth and Thermodynamic Integration
Free-energy Cycles
Potentials of Mean Force
Technical Issues and Error Analysis
Other Thermodynamic Properties
Solvent Models
Classical Models
Quantal Models
Relative Merits of Explicit and Implicit Solvent Models
Analysis of Solvation Shell Structure and Energetics
Speed/Efficiency
Non-equilibrium Solvation
Mixed Explicit/Implicit Models
Case Study: Binding of Biotin Analogs to Avidin
Bibliography and Suggested Additional ReadingHybrid Quantal/Classical ModelsMotivation
Boundaries Through Space
Unpolarized Interactions
Polarized QM/Unpolarized MM
Fully Polarized Interactions
Boundaries Through Bonds
Linear Combinations of Model Compounds
Link Atoms
Frozen Orbitals
Empirical Valence Bond Methods
Potential Energy Surfaces
Following Reaction Paths
Generalization to QM/MM
Case Study: Catalytic Mechanism of Yeast Enolase
Bibliography and Suggested Additional ReadingExcited Electronic StatesDeterminantal/Configurational Representation of Excited States
Singly Excited States
SCF Applicability
CI Singles
Rydberg States
General Excited State Methods
Higher Roots in MCSCF and CI Calculations
Propagator Methods and Time-dependent DFT
Sum and Projection Methods
Transition Probabilities
Solvatochromism
Case Study: Organic Light Emitting Diode Alq3
Bibliography and Suggested Additional ReadingAdiabatic Reaction DynamicsReaction Kinetics and Rate Constants
Unimolecular Reactions
Bimolecular Reactions
Reaction Paths and Transition States
Transition-state Theory
Canonical Equation
Variational Transition-state Theory
Quantum Effects on the Rate Constant
Condensed-phase Dynamics
Non-adiabatic Dynamics
General Surface Crossings
Marcus Theory
Case Study: Isomerization of Propylene Oxide
Bibliography and Suggested Additional ReadingAppendix A Acronym Glossary
Appendix B Symmetry and Group Theory
Symmetry Elements
Molecular Point Groups and Irreducible Representations
Assigning Electronic State Symmetries
Symmetry in the Evaluation of Integrals and Partition Functions
Appendix C Spin Algebra
Spin Operators
Pure- and Mixed-spin Wave Functions
UHF Wave Functions
Spin Projection/AnnihilationAppendix D Orbital Localization
Orbitals as Empirical Constructs
Natural Bond Orbital Analysis