A diffusion Monte Carlo algorithm with very small time-step errors

Abstract

Quantum chemistry by random walk.

QWalk: A quantum Monte Carlo program for electronic structure

“…[11], although developed independently, and for full-core calculations, we use the accelerated Metropolis method from Ref. [12]. The total energy and its components are evaluated, as well as other properties.…”

“…In QWalk, two versions of the projector method are implemented: Diffusion Monte Carlo, which has the advantage that the large N limit is easily obtained, and Reptation Monte Carlo, which makes the 'pure' distribution Φ 2 0 available. Diffusion Monte Carlo has been discussed by many authors [1,12], and suffice it to say that it attains the mixed distribution by starting with a distribution of Ψ 2 T and interpreting the action of the Green's function as a stochastic process with killing and branching, eventually ending up with Ψ T Φ 0 . It has the advantage that the τ → ∞ limit is easy to achieve, but the disadvantage of not having access to the pure distribution.…”

van der Waals clusters in the ultraquantum limit: A Monte Carlo study

“…The corresponding freedom can be exploited to extend the range in over which the approximate short-time Green function agrees with the exact expression to some given accuracy. 2 In other words, the time-step error of the diffusion Monte Carlo algorithm can be reduced by adapting the algorithm so that it can deal more accurately with singular regions of configuration space. In this way, one can make simple algorithmic changes essentially without computational cost to improve the efficiency of the algorithm dramatically.…”

“…II we review diffusion Monte Carlo and the modifications we made to the algorithm given in Ref. 2 to make it applicable to Lennard-Jones bosons. Trial functions are optimized by minimizing the variance of the local energy.…”

Comparison of rotational energies and rigidity of OCS–para-H2 and OCS–4He complexes

“…The theory and implementation of DMC has been described extensively in the literature [20,21,22]. We employ here a mixed branching-weighting algorithm.…”