Electronic Structure Modeling

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