A. Theory provides equations connecting measured quantities to molecule-level properties
1. An example from chemical kinetics
2. An example from spectroscopy

B. Theory provides concepts that help us systematize trends in measured properties

1. Oxidation numbers and electronegativies
2. Lewis acid-base concepts

3. Woodward- Hoffmann rules

C. Theory allows us to simulate molecular behavior using computers

1. Diffusion of gases in a polymer
2. Solvation of anions in water clusters

II. The Laboratory-Theory Interface: What do Experiments Measure?

A. Instrumental responses are often highly precise
B. The relations between experimental signals and molecualr quantities often are imprecise

C. Why Can Experiments Not Directly Determine Molecular Properties?

1. Experiments usually provide quantum-level data
2. Our concepts and molecular models are often cast in classical language

III. What is Present Day Theoretical Chemistry About?

A. Electronic structure theory describes the motions of the electrons and produces energy surfaces
1. The Underlying Theoretical Basis
2. What is Learned from an Electronic Stucture Calculation?

3. Present Day Challenges in Structure Theory

a. Orbitals form the starting point; what are the orbitals?
b. The imperfections in the orbital-level picture are substantial

c. Going beyond the simplest orbital model is sometimes essential

d. For realistic accuracy, improvements to the orbital picture are required

e. Density Functional Theory (DFT) is an alternative that is attracting much attention

f. Efficient and widely disbributed computer programs exist for carrying out electronic structure calculations

B. Molecular and chemical dynamics describes the motions of the atoms within the molecule and the surrounding solvent

1. Classical Newtonian Dynamics Can Often Be Used
a. A collision between an atom and a diatomic molecule
I. The coordinates in which the kinetic energy has no cross terms
II. The Hamiltonian or total energy

III. The conjugate momenta

IV. The equations of motion

V. The initial conditions

VI. Computer time requirements

b. Monitoring the outcome of a classical trajectory

2. Sometimes Quantum Dynamics are Required

a. What needs to be done to apply the Schrödinger equation?
I. An initial wavefunction must be given
II. Time propagation of the wavefunction must be effected- the basis expansion approach

III. Time propagation of the wavefunction can be effected using Feynman path integrals instead

b. How is information extracted from a quantum dynamics simulation?

3. Present Day Challenges in Chemical Dynamics

a. Large Biomolecules and Polymers
b. Mixed Classical and Quantum Dynamics

c. The Car-Parrinello Method

C. Statistical mechanics provides the framework for studying large collections of molecules and tells us how to average positions and velocities to properly simulate the laboratory distribution of molecules

1. The framework of statistical mechanics provides efficient equations for computing thermodynamic properties from molecular properties
a. The Boltzmann population equation
b. The limit for systems containing many molecules

c. The connection with thermodynamics

2. Statistical mechanics gives equations for probability densities in coordinate and momentum space

3. Present Day Challenges in Statistical Mechanics