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, , , and NaH—with FCI spaces ranging from to , whose FCI energies we compute using modest computational resources.
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7 August 2009
Research Article|
August 04 2009
Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space
George H. Booth;
George H. Booth
1Department of Chemistry,
University of Cambridge
, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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Alex J. W. Thom;
Alex J. W. Thom
1Department of Chemistry,
University of Cambridge
, Lensfield Road, Cambridge CB2 1EW, United Kingdom
2Department of Chemistry,
University of California Berkeley
, Berkeley, California 94720, USA
Search for other works by this author on:
a)
Author to whom correspondence should be addressed. Electronic mail: asa10@cam.ac.uk.
J. Chem. Phys. 131, 054106 (2009)
Article history
Received:
May 15 2009
Accepted:
July 13 2009
Citation
George H. Booth, Alex J. W. Thom, Ali Alavi; Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space. J. Chem. Phys. 7 August 2009; 131 (5): 054106. https://doi.org/10.1063/1.3193710
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