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Summary: Quantum chemistry by random walk: Exact treatment of many-electron
systems
James B. Anderson and Carol A. Traynor
Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802
Bruce M. Boghosian
Thinking Machines Corporation, Cambridge, Massachusetts 02142-1264
(Received 10 June 1991; accepted 2 August 1991)
We report an improved Monte Carlo method for quantum chemistry which permits the exact
treatment of many-electron systems. The method combines many of the best features of earlier
fixed-node, released-node, and positive/negative cancellation methods with new ideas for
relocation after node crossing, self-cancellations, multiple cancellations, maximum use of
symmetry in promoting cancellations, and rigorous evaluation of energies using importance
sampling with trial wave functions. The method is illustrated with applications to the problems
of the first excited state of a particle in a two-dimensional box, the two-electron system of
excited H, "I,+ , and the three-electron system of linear symmetric HHH, the intermediate for
the reaction H + H, -+H2 + H.
INTRODUCTION
Random-walk methods of solving the Schrodinger
equation, including diffusion Monte Carlo (DMC) and
Green's-function Monte Carlo (GFMC) methods, offer an
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