Variational Monte Carlo (VMC)

VCM calculations use a trial function whose parameters are determined from the minimisation of the average energy or its variance:

 (1)

A typical trial function for an electronic system is the product between the Slater determinants of one particle orbitals (OPO), obtained from a DFT calculation, multiplied by a function that describes the particle correlations.

 (2) (3)

where are the Slater determinants of the electrons with spin up() or down( ). The simplest Jastrow factor is a sum of two-electron functions

 (4)

where u is taken from the homogeneous electron gas. Over the years more elaborate extensions of have been developed in order to include three electron correlations and electron ion correlations [4].

Many studies have shown that VMC calculations recover up to of the correlation energy but the remaining contributions are hard to conquer because the results cannot be improved systematically in the VMC framework. As a matter of fact the main use of VMC calculations in CASINO is to generate the configuration set needed for the Diffusion Monte Carlo calculation.