James F Harrison

Emeritus Professor of Chemistry

Chemistry Department

Michigan State University

East Lansing Michigan 48824

harrison@chemistry.msu.edu

Courses taught 1968-2103

Publications 1967-2017

Over the years I have taught many courses and the notes for a few of the topics discussed are collected below.

This first grouping includes some basic classical physics the understanding of which is vital for success in Advanced Physical Chemistry.

Electrostatics

Electrostatic potential & electric field due to a collection of point charges

Potential energy of a collection of N point charges

Potential energy of N point charges in an external potential

Multipole moments of a charge distribution

Multipole expansion of a charge distribution

Interaction energy between two disjoint charge distributions

Angular Momentum

Introduction

Orbital angular momentum operators

Angular momentum in a central field

Commutators

Eigenvalues and Eigenfunctions of Orbital Angular Momentum

Operator Derivation of Eigenvalue and Eigenfunctions

A spin ½ particle in a Central Potential

Coupling of Angular Momenta

Wigner or Clebsch-Gordon Coeffficients

Perturbation theory

Non-degenerate theory

Non-degenerate examples

Harmonic oscillator with a cubic perturbation

Harmonic oscillator in a constant electric field

Moller-Plesset second order theory

Degenerate theory

Hydrogen-like atoms/ions

Schrodinger equation

Center of Mass Separation

Energy and Structure of Wavefunctions

Radial Distribution Functions

Average values of rⁿ

Comparison with experiment

One-electron Atoms in an Electric Field

Ground state (Stark Effect, dipole & quadrupole polarizabilities)

Excited State (Stark Effect)

Spin-orbit Interaction

Form of the Hamiltonian

Angular and Radial Wave-functions

PerturbationTreatment (numerical results)

One-electron atoms in a magnetic field

More Relativistic Effects

Dirac equation for a one-electron atom

Pauli Hamiltonian and the Mass Velocity, Spin Orbit & Darwin Terms

First-order perturbation results using Pauli Hamiltonian

Exact Energy Eigenvalues of Dirac equation

Compilation

Hydrogen wavefunctions (1s-6h)

Hartree-Fock Theory

Introduction

General Equations

Unrestricted open-shell

Closed-shell

Restricted open-shell

Physical interpretation

Relationship between Hartree-Fock eigenvalues and the Energy

Matrix Hartree-Fock equations

Spin Contamination in UHF

Density Matrices, Natural Orbitals & Electron Density

Introduction

One and Two Particle Density Matrices-Definitions

One and Two Particle Density Matrices for Hartree-Fock wavefunctions

Electron Density and one Particle Density Matrix

Natural Orbitals and One Particle Density Matrix

Natural Orbitals for Heitler-London H2

Slater Determinants

Slater Determinants and Antisymmeteriizing Operator

Matrix Elements Between Slater Determinants (Slater-Condon Rules)

Spin and Many Electron Systems

One Electron Spin Operators

Many Electron Spin Operators

Two Electron Spin Eigenfunctions

Many Electron Spin Eigenfunctions

He and Two Electron Atoms

Introduction

Orbital Models

Hartree-Fock equations

Correlation Energy

Hylleraas Equation