A VMC calculation requires the evaluation of the local energy after moving each of the electrons. In practice, the energy is not evaluated after every move because the energies are strongly correlated from one move to the next. As the evaluation of the local energy for a given configuration is considerably more computationally expensive than the process of accepting or rejecting the set of moves to the next configuration, the local energy is only evaluated every few configurations. In our calculations the correlation length of the energy varies between 1 and 100 moves depending on the step size of the moves and the number of electrons in the system. Methods for calculating this correlation length are described in chapter 4.
The method used to calculate the local energy closely follows the work of Fahy, Wang and Louie [26]. The energy is calculated in two distinct parts: the kinetic energy and the electrostatic interaction energy. The kinetic energy is dependent upon the form of the wavefunction and the electronic positions whereas the electrostatic energy only depends upon the positions of the charges in the system.