Question

Explain the assumptions made in the Hartree Fock method. Please explain it, and not copy the incorrect assumptions from Wikipedia (I asked this question twice before, this actually happened), a basic explanation of the assumptions is just dandy, as I don't really understand the method. Thank you!

Answer 1

Hartree-Fock (SCF) Theory

In Hartree-Fock theory, the variational principle is used to determine the cui's. The best possible solution to the problem is when the energy is at a minimum. Therefore, the coefficients just need to be varied until the energy is at a minimum. This corresponds to when the first derivative is zero:

This set of c's give the best possible estimate of energy under the limitations we have imposed:

1. Single determinant wavefunction
2. Basis set used (Hartree-Fock limit when an infinite basis set is used.)



* Hartree-Fock Theory in Detail

We want to determine the best spin orbitals that minimize the energy:

In the Hartree-Fock approximation, the Hamiltonian Ĥ is replace with an effective one-electron operator called the Fock operator:



i.e. The HF approach is to replace the many electron problem by a one electron problem in which the electron-electron repulsion is treated in an average way.

Giving:

The HF potential depends on the spin orbitals c thus the equation must be solved iteratively. This procedure is called the SCF method.