SCF

The varational principle & method

The variational principle essentially states that the energy for the approximate Hartree-Fock wavefunction is always greater than or equal to the exact ground state energy of the system in question.

Given this principle, we

The Self-Consistent Field method

Sketch of the procedure

Overall an SCF involves the following steps:

1. Compute/load an initial guess for the wavefunction
2. Determine the potential energy of the current wavefunction i.e. the Fock matrix $F$
3. Solve the Roothaan equations $F C = S C \epsilon$, yielding the molecular orbital coefficients $C$
4. Repeat from step 2. until convergence is achieved.