DOI: 10.1063/1.3193710. Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space

Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space

10.1063/1.3193710

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

We have developed a new quantum Monte Carlo method for the simulation of correlated many-electron systems in full configuration-interaction (Slater determinant) spaces. The new method is a population dynamics of a set of walkers, and is designed to simulate the underlying imaginary-time Schrödinger equation of the interacting Hamiltonian. The walkers (which carry a positive or negative sign) inhabit Slater determinant space, and evolve according to a simple set of rules which include spawning, death and annihilation processes. We show that this method is capable of converging onto the full configuration-interaction (FCI) energy and wave function of the problem, without any a priori information regarding the nodal structure of the wave function being provided. Walker annihilation is shown to play a key role. The pattern of walker growth exhibits a characteristic plateau once a critical (system-dependent) number of walkers has been reached. At this point, the correlation energy can be measured using two independent methods—a projection formula and a energy shift; agreement between these provides a strong measure of confidence in the accuracy of the computed correlation energies. We have verified the method by performing calculations on systems for which FCI calculations already exist. In addition, we report on a number of new systems, including CO, O2, CH4, and NaH—with FCI spaces ranging from 109 to 1014, whose FCI energies we compute using modest computational resources.

Bibliography

Booth, G. H., Thom, A. J. W., & Alavi, A. (2009). Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space. The Journal of Chemical Physics, 131(5).

Authors 3

George H. Booth (first)
Alex J. W. Thom (additional)
Ali Alavi (additional)

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Dates

Type	When
Created	16 years ago (Aug. 5, 2009, 6:56 p.m.)
Deposited	2 years ago (July 30, 2023, 7:28 p.m.)
Indexed	5 hours, 19 minutes ago (Aug. 28, 2025, 8:42 a.m.)
Issued	16 years ago (Aug. 4, 2009)
Published	16 years ago (Aug. 4, 2009)
Published Online	16 years ago (Aug. 4, 2009)
Published Print	16 years ago (Aug. 7, 2009)

Funders 0

None

BibTeX

@article{Booth_2009, title={Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space}, volume={131}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.3193710}, DOI={10.1063/1.3193710}, number={5}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Booth, George H. and Thom, Alex J. W. and Alavi, Ali}, year={2009}, month=aug }

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  "abstract": "<jats:p>We have developed a new quantum Monte Carlo method for the simulation of correlated many-electron systems in full configuration-interaction (Slater determinant) spaces. The new method is a population dynamics of a set of walkers, and is designed to simulate the underlying imaginary-time Schr\u00f6dinger equation of the interacting Hamiltonian. The walkers (which carry a positive or negative sign) inhabit Slater determinant space, and evolve according to a simple set of rules which include spawning, death and annihilation processes. We show that this method is capable of converging onto the full configuration-interaction (FCI) energy and wave function of the problem, without any a priori information regarding the nodal structure of the wave function being provided. Walker annihilation is shown to play a key role. The pattern of walker growth exhibits a characteristic plateau once a critical (system-dependent) number of walkers has been reached. At this point, the correlation energy can be measured using two independent methods\u2014a projection formula and a energy shift; agreement between these provides a strong measure of confidence in the accuracy of the computed correlation energies. We have verified the method by performing calculations on systems for which FCI calculations already exist. In addition, we report on a number of new systems, including CO, O2, CH4, and NaH\u2014with FCI spaces ranging from 109 to 1014, whose FCI energies we compute using modest computational resources.</jats:p>",
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