Optimizing the Energy with Quantum Monte Carlo: A Lower Numerical Scaling for Jastrow-Slater Expansions

Roland Assaraf; S Moroni; Claudia Filippi

doi:10.1021/acs.jctc.7b00648

Optimizing the Energy with Quantum Monte Carlo: A Lower Numerical Scaling for Jastrow-Slater Expansions

J Chem Theory Comput. 2017 Nov 14;13(11):5273-5281. doi: 10.1021/acs.jctc.7b00648. Epub 2017 Oct 5.

Authors

Roland Assaraf¹, S Moroni², Claudia Filippi³

Affiliations

¹ Sorbonne Universités, UPMC Univ Paris 06, CNRS, Laboratoire de Chimie Théorique (UMR7616), 4 place Jussieu F-75252 Paris, France.
² CNR-IOM DEMOCRITOS, Istituto Officina dei Materiali, and SISSA Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, I-34136 Trieste, Italy.
³ MESA+ Institute for Nanotechnology, University of Twente , P.O. Box 217, 7500 AE Enschede, The Netherlands.

PMID: 28873307
DOI: 10.1021/acs.jctc.7b00648

Abstract

We present an improved formalism for quantum Monte Carlo calculations of energy derivatives and properties (e.g., the interatomic forces), with a multideterminant Jastrow-Slater function. As a function of the number N_e of Slater determinants, the numerical scaling of O(N_e) per derivative we have recently reported is here lowered to O(N_e) for the entire set of derivatives. As a function of the number of electrons N, the scaling to optimize the wave function and the geometry of a molecular system is lowered to O(N³) + O(NN_e), the same as computing the energy alone in the sampling process. The scaling is demonstrated on linear polyenes up to C₆₀H₆₂ and the efficiency of the method is illustrated with the structural optimization of butadiene and octatetraene with Jastrow-Slater wave functions comprising as many as 200 000 determinants and 60 000 parameters.