Table of Contents

One-Dimensional Quantum Mechanics: A Short Review
The Particle-in-a-Box
Particle-on-a-Ring
Matrices, Representations, and Electronic Structure Modeling
Definition and Properties of Vectors and Matrices
Response Matrices
Symmetry Operations
Methods of Approximation and the SCF Method
The Variation Theorem
Determinantal Wave Functions and HF-SCF Theory
Koopmans’ Theorem
Brillouin’s Theorem
Gaussian-Lobe Basis Sets
Overlap (SAB)
Kinetic Energy (TAB)
 Nuclear Potential (for Z Nuclear Charge Value, at rC)
Electron Repulsion (Coulomb’s Law for Two Charge Distributions)
Dipole Moment
Quadrupole Moment
 Angular Momentum (Imaginary Hermitian Operator)
Spin–Orbit and Spin–Spin Interactions
Frost FSGO Method
Screened Coulomb Potential
Electrostatic Potential Maps
A Very Simple MO Program
Helium in SCF1s
Beryllium Atom in SCF1s STOs
Spherical Gaussian Contraction for Helium: 3G Expansion
Molecular Hydrogen in SCF1s
LiH–Frost Spherical Gaussian Pairs
PCLOBE and Sample Output from RHF Calculations
Li2
N2
N2, CO, BF: An Isoelectronic Series
The Value of Mulliken Charges and Mayer Bond Orders
Bonding in C2 and LiF by Natural Bond Order Analysis
Geometry Optimization and Vibrational Frequencies by SCF
Introduction
The SCF-Roothaan Calculation in PCLOBE
Molecular Structure Determination by Energy Minimization
Derivative of the Hartree–Fock Energy
Search Techniques Using the Gradient
Geometry Optimization in PCLOBE
Second Derivatives of the Hartree–Fock Energy and Vibrational Spectra
SCF Calculation Revisited: Alternatives and Points of Contention
Impure Symmetry of Properties Computed in the Contracted Lobe Basis
Completeness and Linear Dependence in the Lobe Basis
Management of Two-Electron Integrals
Reoptimization of Formaldehyde in an Extended Basis
Historical Landmark: The Accomplishment of Boys
Configuration Interaction and Potential Curves
Configuration Interaction in General
Slater Determinant MO-CI
CI without Canonical Orbitals
Pauling Valence Bond and CI
Boys–Reeves CI (MOVB)
 Resolution of an MOVB-CI Wave Function into Leading Excitations
Sydnone CI
CI and Potential Curves
Three Descriptions of Dissociation of Hydrogen Molecule
MOVB-CI for BH
MOVB-CI of Formaldehyde Dissociation
MCSCF and CASSCF: Achieving Proper Dissociation for Larger Systems
Perturbation Theory
First-Order Correction to a Nondegenerate Reference System
Second-Order Correction—Nondegenerate Case
The Degenerate Case
Perturbation Theory in Approximate MO Theory
MP2 as Perturbation Theory
Time-Dependent Perturbation Theory
Hamiltonian for Matter in an Electromagnetic Field
Time-Dependent Perturbation Theory for Charged Particles
in the Electromagnetic Field
Length–Velocity Relationship
Response Theory
Highly Accurate Methods: Coupled Cluster Calculations, Extrapolation to Chemical Accuracy, and Quantum Monte Carlo Methods
Aspiration to Chemical Accuracy
An Aerial View of CC
Theoretical Foundations
The Size-Consistency Issue in CC and CI
Solving the CC Equations
Beyond CCSD
Performance of CCSD (T)
Thermochemical Standards by Quantum Chemistry
Aspiration to Exact Description: Quantum Monte Carlo Calculations
Random (?) Numbers
Modeling the Coulomb Hole
The Fermi Hole and Exchange–Correlation
Coulomb Correlation Hole
Applying the Correlated-SCF Method to Hydroxlyamine
Density Functional Theory
John Perdew’s Ladder
Refinements to the VWN Exchange–Correlation Functionals
The Adiabatic Connection and Hybrid Functionals
Correlation Effects on Kinetic Energy
The Empirical Thread
Two DFT-Focussed Programs
Summary, Conclusions, and Overview
Appendix: Technical Aspects of DFT Calculations
Calculation of Nuclear Magnetic Resonance Shielding=Shifts
Ramsey Theory
Challenges to Use of Ramsey’s Form
Semiempirical Adaptions of Ramsey’s Formalism
Ditchfield’s Formalism
Use of Localized Orbitals in NMR Shielding Calculations
RPAC Program (LORG)
Correlation Corrections and NMR Shielding: DFT
Practical Use of Calculated Chemical Shifts
Advances in DFT-Based NMR
The Question of Coupling and Fine Structure
Perturbative Correlation-Corrected Methods for Shielding
ACES-II Coupled Cluster Calculation of NMR Properties
Predicting Magnetic Properties with ChemDraw and Gaussian
The Representation of Electronically Excited States
CI-Singles
Practical Use of the CIS Equations
Singlet and Triplet State Energies for the 1G Model
PCLOBE Illustration of CIS
Structural Relaxation in the Excited State
Case Study for Formaldehyde
Correlation Corrections
Time-Dependent Hartree–Fock Treatments of Excitations
Formaldehyde Again
A Case Study—Sulfur Dioxide
Adaptation of the Time-Dependent Formalism to DFT
Applications
CCSD-EOM Treatment of Excited States
Circular Dichroism and Optical Rotatory Dispersion
The Phenomenon of Optical Rotation
Ways to Improve CD and ORD Calculations
Methyloxirane: A Hard Case
A Brighter View
The Phenomenon of Magnetic Circular Dichroism
MCD—A Challenge to Modern Theory