Correlated sampling of Monte Carlo derivatives with iterative-fixed sampling

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Abstract
A correlated sampling method for determining the energy and other property derivatives by finite difference is implemented within variational Monte Carlo. Determination of derivatives takes place over a fixed sample of electronic coordinates, so it is possible to distinguish small energy or other property differences accurately. Using finite differences avoids the evaluation of complicated derivative expressions and can be applied directly to Green’s function Monte Carlo methods without the need for derivatives of the Green’s function. The algorithm can be used to evaluate derivatives with respect to any parameters in the Hamiltonian or in the trial function. In this paper, it is applied to H2 and Li2 for their energy derivatives with respect to nuclear coordinates. Results are in agreement with experimental data.