Purpose

First, we define the problem, beginning with the Schrödinger equation

Our goal is to come up with an analytic equation for the energy which can be minimized with respect to some variational parameter(s) to give an upper bound on the energy. To do this, we must

1. Understand the hamiltonian operater .
2. Find an appropriate wave function which allows simple calculation of the electronic energy.
3. Examine potential variational parameters to figure out how to minimize the energy.

It will likely be convenient to have an outline of where we're going, so here it is:

1. Puropse (which we've been through)
2. The Hamiltonian,
   • Kinetic energy operators
   • Coulombic potential operators
3. The Wave Function,
   • 1 electron orbitals
   • Hartree products
   • Slater determinants
4. Hamiltonian as Energy Operator, Schrödinger Equation
   • 
   • Integrals over one electron operators
   • Integrals over two electron operators
   • Specific case energy expressions
   • General form of HF energy
5. What Variational Parameter?
   • LCAO-MO theory, energy in AO basis
   • Density Matrices
6. Hartree-Fock Equations
   • Lagrangs's Undetermined Multipliers
   • A load 'o math
7. Matrix Formalism
8. Program Outline