Therefore the storage requirement for one walker is n b + 1 32-bit integers. The sign array is also a 4 byte integer array.
Such a (bit) string requires n b = ⌈ 2 M / 32 ⌉ 32-bit integers to encode. A determinant is uniquely specified by a binary string of length 2 M, with 0 to signify an empty spin orbital and a 1 to specify a filled spin orbital. The position of a walker in the list of walkers is determined by the string of n b integers which define the determinant on which the walker is located. Schaefer ( Taylor and Francis, London, 2004). Molecular Quantum Mechanics: Selected Papers of N. Saad, Iterative Methods for Sparse Linear Systems ( SIAM, Seattle, 2004). Kalos, Applications of the Monte Carlo method in Statistical Physics ( Springer-Verlag, Berlin, 1984), Vol. In addition, we report on a number of new systems, including CO, O 2, CH 4, and NaH-with FCI spaces ranging from 10 9 to 10 14, whose FCI energies we compute using modest computational resources. We have verified the method by performing calculations on systems for which FCI calculations already exist. 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.
The pattern of walker growth exhibits a characteristic plateau once a critical (system-dependent) number of walkers has been reached. Walker annihilation is shown to play a key role. 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. 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. 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. We have developed a new quantum Monte Carlo method for the simulation of correlated many-electron systems in full configuration-interaction (Slater determinant) spaces.
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