Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis

Abstract

We extend the recently introduced phaseless auxiliary-field quantum Monte Carlo (QMC) approach to any single-particle basis, and apply it to molecular systems with Gaussian basis sets. QMC methods in general scale favorably with system size, as a low power. A QMC approach with auxiliary fields in principle allows an exact solution of the Schrödinger equation in the chosen basis. However, the well-known sign/phase problem causes the statistical noise to increase exponentially. The phaseless method controls this problem by constraining the paths in the auxiliary-field path integrals with an approximate phase condition that depends on a trial wave function. In the present calculations, the trial wave function is a single Slater determinant from a Hartree-Fock calculation. The calculated all-electron total energies show typical systematic errors of no more than a few milli-Hartrees compared to exact results. At equilibrium geometries in the molecules we studied, this accuracy is roughly comparable to that of coupled-cluster with single and double excitations and with non-iterative triples, CCSD(T). For stretched bonds in H2O, our method exhibits better overall accuracy and a more uniform behavior than CCSD(T).

Coupling quantum Monte Carlo and independent-particle calculations: Self-consistent constraint for the sign problem based on the density or the density matrix

“…Previous studies in a variety of systems have shown that the bias tends to be small, in both models 10,24-27 and realistic materials 13,17,21,23 , making this one of the most accurate many-body approaches for general interacting fermion systems. In this work, we introduce a self-consistent method to further reduce the bias introduced by the constraint from the trial wave function.…”

“…A constraint is applied in some space to restrict the Monte Carlo sampling, which introduces a systematic bias but in turn removes the exponential growth in variance and restores the algebraic complexity of the algorithm. The majority of QMC calculations have employed this approach, including many on spin and fermion models 9,10 , and almost all on realistic systems in condensed matter physics [11][12][13] , nuclear physics 14 , and quantum chemistry [15][16][17] .…”

A study of H+H2 and several H-bonded molecules by phaseless auxiliary-field quantum Monte Carlo with plane wave and Gaussian basis sets

“…The auxiliary-field quantum Monte Carlo method has been described elsewhere [2,3]. Here we outline the relevant formulas to facilitate the ensuing discussion.…”

“…The Fermion sign/phase problem is controlled approximately according to the overlap of each random walker (Slater determinant) with a trial wave function. Applications of the phaseless AF QMC method to date, including second-row systems [2] and transition metal molecules [13] with planewave basis sets, and first-row [3] and postd [14] molecular systems with Gaussian basis sets, indicate that this often reduces the reliance of the results on the quality of the trial wave function. For example, with single determinant trial wave functions, the calculated total energies at equilibrium geometries in molecules show typical systematic errors of no more than a few milliHartrees compared to exact/experimental results.…”

“…Recently, a new phaseless auxiliary-field QMC (AF QMC) method has been developed and applied for electronic structure calculations [2,3]. This method is formulated in a many-particle Hilbert space whose span is defined by a single-particle basis set.…”