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Physical Review Letters

Linear-Scaling Quantum Monte Carlo Calculations

Andrew Williamson, Randolph Q. Hood, Jeffrey C. Grossman

Published Nov 26, 2001• 157 citations
Publisher

Abstract

A method is presented for using truncated, maximally localized Wannier functions to introduce sparsity into the Slater determinant part of the trial wave function in quantum Monte Carlo calculations. When combined with an efficient numerical evaluation of these localized orbitals, the dominant cost in the calculation, namely, the evaluation of the Slater determinant, scales linearly with system size. This technique is applied to accurate total energy calculation of hydrogenated silicon clusters and carbon fullerenes containing 20-1000 valence electrons.

DOI
10.1103/physrevlett.87.246406

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Abstract This paper describes the use of localized orbitals and shortrange correlation functions to achieve near linear scaling in fixednode diffusion QMC calculations. The success of the method is demonstrated with a series of all-electron calculations for linear hydrocarbons in the range of C2H6 to C2sHs2 with 18 to 202 electrons. The procedure used was not very different from that of earlier all-electron calculations for systems of these sizes. Some changes were needed for evaluation of the trial wave functions and their derivatives. The molecular orbitals for the determinantal wavefunction were composed of contracted Gaussian functions decaying rapidly with distance but limited by a cut-off radius. The resulting determinants were sparse and could be evaluated by a standard matrix LU decomposition package. The standard Schmidt Moskowitz correlation function was modified with use of a short-range scaled distance to allow short cut-off radii.