The importance of the trial/guiding wavefunction in determining the accuracy of VMC calculations is illustrated by recent work  to calculate the total energy of solid germanium in the diamond structure using a 2x2x2 supercell containing 16 Ge atoms and 64 valence electrons within both the VMC and DMC formalisms. The results are illustrated in Figure .
Figure: Difference in the energy of VMC and DMC results for 2x2x2 bulk germanium in the diamond structure.
The VMC energy and DMC energy are defined as
where is the wavefunction that propagates to during the diffusion process.
It has already been stressed in section that the DMC energy is in principle exact (apart from the fixed-node approximation), i.e. for a given trial/guiding wavefunction , the DMC energy is equivalent to the lowest variational energy for all wavefunctions with the same nodal surface as . As the DMC and VMC  calculations share the same trial wavefunction, and hence have the same nodal surface, the difference in energy is due only to the difference between the VMC trial wavefunction and the wavefunction, , to which the DMC calculation converges to in the long time approximation. This energy difference acts as a measure of the quality of , where the quality describes how closely matches the converged DMC ground state wavefunction, , throughout all of configuration space. If one is able to optimise the trial/guiding wavefunction and therefore improve its quality, then the difference will be reduced and the accuracy of the VMC calculations is improved.
It is not only the value of the total energy which reflects the quality of a trial/guiding wavefunction. The intrinsic variance of the energy estimator, as defined by
is also important. If one is able to reduce the intrinsic variance, , of the VMC energy by improving the quality of , then the number of VMC moves required to achieve a specific variance of the mean, , decreases linearly with the variance. i.e. , where N is the number of moves.