An Introduction to

Theoretical Chemistry

Jack Simons


Chemistry Department

University of Utah

Salt Lake City, Utah





Table of Contents


Part 1. Background Material


Chapter 1 (79 pages) The Basics of Quantum Mechanics

Why Quantum Mechanics is Necessary for Describing Molecular Properties

I. The Schrödinger Equation and Its Components

A. Operators

B. Wave functions

C. The Schrödinger Equation

1. The Time-Dependent Equation

2. The Time-Independent Equation

3. The Born-Oppenheimer Approximation

II. Your first application of quantum mechanics- motion of a particle in one dimension.

A. The Classical Probability Density

B. The Quantum Treatment

C. The Energies and Wavefunctions

D. The Probability Densities

E. Classical and Quantum Probability Densities

F. Time Propagation of Wavefunctions

III. Free Particle Motions in More Dimensions

A. The Schrödinger Equation

B. Boundary Conditions

C. Energies and Wave functions for Bound States

D. Quantized Action Can Also be Used to Derive Energy Levels

E. Quantized Action Does Not Always Work


Chapter 2 (117 pages) Model Problems That Form Important Starting Points

I. Free Electron Model of Polyenes

II. Bands of Orbitals in Solids

III. Densities of States in 1, 2, and 3 dimensions.

IV. The Most Elementary Model of Orbital Energy Splittings: Hückel

or Tight-Binding Theory

V. Hydrogenic Orbitals

VI. Electron Tunneling

VII. Angular Momentum

VIII. Rotations of Molecules

1. Rotational Motion For Rigid Diatomic and Linear Polyatomic Molecules

2. Rotational Motions of Rigid Non-Linear Molecules

IX. Vibrations of Molecules


Chapter 3 (20 pages) Characteristics of Energy Surfaces

I. Strategies for Geometry Optimization

II. Normal Modes of Vibration

A. The Newton Equations of Motion for Vibration

1. The Kinetic and Potential Energy Matrices

2. The Harmonic Vibrational Energies and Normal Mode Eigenvectors

B. The Use of Symmetry

1. Symmetry Adapted Modes

2. Point Group Symmetry of the Harmonic Potential


Chapter 4 (59 pages) Some Important Tools of Theory

I. Perturbation Theory and the Variational Method

II. Point Group Symmetry

Character Tables


Part 2. Three Primary Areas of Theoretical Chemistry


Chapter 5 (73 pgs) An Overview of Theoretical Chemistry

I. What is Theoretical Chemistry About?

A. Molecular Structure- bonding, shapes, electronic structures

B. Molecular Change- reactions, isomerization, interactions

1. Changes in Bonding

2. Energy Conservation

3. Conservation of Orbital Symmetry: Woodward-Hoffmann Rules

4. Rates of change

C. Statistical Mechanics: Treating Large Numbers of Molecules in Close Contact

II. Molecular Structure: Theory and Experiment

A. Experimental Probes of Molecular Shapes

1. Rotational Spectroscopy

2. Vibrational Spectroscopy

3. X-Ray Crystallography

4. NMR Spectroscopy

B. Theoretical Simulation of Structures

III. Chemical Change

A. Experimental Probes of Chemical Change

B. Theoretical Simulation of Chemical Change


Chapter 6 (134 pgs) Electronic Structures

I. Theoretical Treatment of Electronic Structure: Atomic and Molecular Orbital Theory

A. Orbitals

1. The Hartree Description

2. The LCAO-Expansion

3. AO Basis Sets

a. STOs and GTOs

b. The Fundamental Core and Valence Basis

c. Polarization Functions

d. Diffuse Functions

4. The Hartree-Fock Approximation

a. Koopmans' Theorem

b. Orbital Energies and the Total Energy

5. Molecular Orbitals

a. Shapes, Sizes, and Energies of Orbitals

b. Bonding, Anti-bonding, Non-bonding, and Rydberg Orbitals

B. Deficiencies in the Single Determinant Model

1. Electron Correlation

2. Essential Configuration Interaction

3. Various Approaches to Electron Correlation

a. The CI Method

b. Perturbation Theory

c. The Coupled-Cluster Method

d. The Density Functional Method

e. Energy Difference Methods

f. The Slater-Condon Rules

g. Atomic Units

C. Molecules Embedded in Condensed Media

D. High-End Methods for Treating Electron Correlation

II. Experimental Probes of Electronic Structure

A. Visible and Ultraviolet Spectroscopy

1. The Electronic Transition Dipole and Use of Point Group Symmetry

2. The Franck-Condon Factors

3. Time Correlation Function Expressions for Transition Rates

4. Line Broadening Mechanisms

B. Photoelectron Spectroscopy

C. Probing Continuum Orbitals


Chapter 7 (79 pgs) Statistical Mechanics

I. Collections of Molecules at or Near Equilibrium

A. The Distribution of Energy Among Levels

B. Partition Functions and Thermodynamic Properties

C. Equilibrium Constants in Terms of Partition Functions

D. Monte-Carlo Evaluation of Properties

E. Molecular Dynamics Simulations of Properties

II. Time Correlation Functions

III. Some Important Chemical Applications of Statistical Mechanics

A. Gas-Molecule Thermodynamics

B. Einstein and Debye Models of Solids

C. Lattice Theories of Surfaces and Liquids

D. Virial Corrections to Ideal-Gas Behavior


Chapter 8 (50 pgs) Chemical Dynamics

I. Theoretical Treatment of Chemical Change and Dynamics

A. Transition State Theory

B. Variational Transition State Theory

C. Reaction Path HamiltonianTheory

D. Classical Dynamics Simulation of Rates

E. RRKM Theory

F. Correlation Function Expressions for Rates

G. Wave Packet Propagation

H. Surface Hopping Dynamics

II. Experimental Probes of Reaction Dynamics

A. Spectroscopic Methods

B. Beam Methods

C. Other Methods


Problems (64 pgs)

Solutions (159 pgs)