Initial Guess

HF Theory assumes that an electron moves in a potential which is the average of the potentials due to all the other electrons and nuclei, so a trial wavefunction is required for the potential before the energy can be calculated. The optimal wavefunction is then found by iteratively solving the Schrödinger equation. This initial guess must be close enough to the optimum wavefunction for the equations to converge to the correct electronic state.

There are several ways to obtain a guess for the wavefunction, the simplest of which is to guess the MO coefficients by diagonalising the core Hamiltonian matrix [17]. In 1952 Wolfsberg and Helmholtz presented a more sophisticated procedure which also uses the overlap matrix [18]
$$\begin{align}H_{\mu \nu} = c_{x} S_{\mu \nu} ( H_{\mu \mu} + H_{\nu \nu} ) / 2 \end{align}$$
where c_x is a constant. Obviously, with the guess playing such a crucial role in the efficiency of HF theory, it is an area of much research; one of the latest (and more successful) methods uses a superposition of atomic densities (SAD) [19].