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DMC Calculations

The quality of the trial/guiding wavefunction does not directly affect the final DMC estimate of the total energy of a given system (apart from the fixed node approximation). However, the intrinsic variance of tex2html_wrap_inline6909 determines the variance of the estimate of the total energy at each step of the diffusion process. Therefore, as in the VMC technique, the number of DMC moves required to achieve a specific variance of the mean, tex2html_wrap_inline6903 , decreases linearly with the intrinsic variance of tex2html_wrap_inline6909 . As the computational cost of a DMC calculation is roughly an order of magnitude greater than that of a comparable VMC calculation, reducing this intrinsic variance is very important.

Reducing the intrinsic variance of the trial/guiding wavefunction by optimisation also improves the numerical stability of a DMC calculation. As described in section gif, the multiplicity of a walker at the end of each DMC move is determined by its excess local energy, tex2html_wrap_inline6915 ]. Therefore, any reduction in the intrinsic variance of tex2html_wrap_inline6049 will reduce the deviation of the individual multiplicities of the walkers from unity and help to produce a more stable population.

Finally, any improvement in the quality of tex2html_wrap_inline6049 should reduce the time taken for a DMC calculation to reach a converged energy. If tex2html_wrap_inline6049 is closer to tex2html_wrap_inline6875 the probability distribution tex2html_wrap_inline6925 (see section gif) starts closer to its converged form. See figure gif and section gif for more details on the convergence of the DMC algorithm.

Andrew Williamson
Tue Nov 19 17:11:34 GMT 1996