Quantum Monte Carlo with very large multideterminant wavefunctions

Abstract

An algorithm to compute efficiently the first two derivatives of (very) large multideterminant wavefunctions for quantum Monte Carlo calculations is presented. The calculation of determinants and their derivatives is performed using the Sherman-Morrison formula for updating the inverse Slater matrix. An improved implementation based on the reduction of the number of column substitutions and on a very efficient implementation of the calculation of the scalar products involved is presented. It is emphasized that multideterminant expansions contain in general a large number of identical spin-specific determinants: for typical configuration interaction-type wavefunctions the number of unique spin-specific determinants Ndetσ ( σ=↑,↓) with a non-negligible weight in the expansion is of order O(Ndet). We show that a careful implementation of the calculation of the Ndet -dependent contributions can make this step negligible enough so that in practice the algorithm scales as the total number of unique spin-specific determinants, Ndet↑+Ndet↓, over a wide range of total number of determinants (here, Ndet up to about one million), thus greatly reducing the total computational cost. Finally, a new truncation scheme for the multideterminant expansion is proposed so that larger expansions can be considered without increasing the computational time. The algorithm is illustrated with all-electron fixed-node diffusion Monte Carlo calculations of the total energy of the chlorine atom. Calculations using a trial wavefunction including about 750,000 determinants with a computational increase of ∼400 compared to a single-determinant calculation are shown to be feasible. © 2016 Wiley Periodicals, Inc.

Variational and diffusion quantum Monte Carlo calculations with the CASINO code

“…There are a number of dedicated multideterminant wavefunction-evaluation algorithms. [90][91][92][93][94] CASINO implements the compression method of Weerasinghe et al 95 Although this method underperforms some of the other approaches, it can potentially be combined with them for additional efficiency since it does not require modification to the evaluation of the wave function. The compression algorithm is based on combining determinants differing by a single column, e.g.,…”

QMCPACK: an open sourceab initioquantum Monte Carlo package for the electronic structure of atoms, molecules and solids

“…[99,100]. The CIPSI method [98,121,119,120] is implemented in the Quantum Package (QP) code [59] developed by the Caffarel group. QMCPACK does not implement CIPSI, but is able to use output from the QP code via tight integration.…”

Deterministic Construction of Nodal Surfaces within Quantum Monte Carlo: The Case of FeS

“…The multideterminant expansion (2) has been constructed using the sCI algorithm CIPSI, 54,55 which uses a second-order perturbative criterion to select the energetically-important determinants D I in the FCI space. 36,37,[42][43][44][45]65 A n s -state truncated sCI expansion (here n s = 2) is obtained via a natural generalization of the state-specific criterion introduced in Eq. (5): a deter-…”

“…To keep the size of the CI expansion reasonable and retain only the most important determinants, we propose to use selected CI (sCI) algorithms, such as CIPSI (Configuration Interaction using a Perturbative Selection made Iteratively). 42 Using a recently-proposed algorithm to handle large numbers of determinants in FN-DMC 44 we are able to consider up to a few million determinants in our simulations.…”