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Communication: Toward an improved control of the fixed-node error in quantum Monte Carlo: The case of the water molecule
1. Here, by uncontrolled it is meant that there does not exist a systematic way of arbitrarily reducing the fixed-node error.
14.R. J. Buenker, S. D. Peyerimholf, and P. J. Bruna, Computational Theoretical Organic Chemistry (Reidel, Dordrecht, 1981), p. 55.
22.A. Scemama, T. Applencourt, E. Giner, and M. Caffarel, “Quantum Monte Carlo with very large multideterminant wavefunctions,” J. Comput. Chem. (in press).
23. An increase in the fixed-node energy may be sometimes observed at small number of determinants, (say, less than a few thousands) when large basis sets and/or canonical orbitals are used. This transient behavior has been found to systematically disappear when natural orbitals are used and/or larger expansions are considered.
24.H. J. Flad, M. Caffarel, and A. Savin, Recent Advances in Quantum Monte Carlo Methods (World Scientific Publishing, 1997).
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All-electron Fixed-node DiffusionMonte Carlo calculations for the nonrelativistic ground-state energy of the water molecule at equilibrium geometry are presented. The determinantal part of the trial wavefunction is obtained from a selected Configuration Interaction calculation[Configuration Interaction using a Perturbative Selection done Iteratively (CIPSI) method] including up to about 1.4 × 106 of determinants. Calculations are made using the cc-pCVnZ family of basis sets, with n = 2 to 5. In contrast with most quantum Monte Carlo works no re-optimization of the determinantal part in presence of a Jastrow is performed. For the largest cc-pCV5Z basis set the lowest upper bound for the ground-state energy reported so far of −76.437 44(18) is obtained. The fixed-node energy is found to decrease regularly as a function of the cardinal numbern and the Complete Basis Set limit associated with exact nodes is easily extracted. The resulting energy of −76.438 94(12) — in perfect agreement with the best experimentally derived value — is the most accurate theoretical estimate reported so far. We emphasize that employing selected configuration interactionnodes of increasing quality in a given family of basis sets may represent a simple, deterministic, reproducible, and systematic way of controlling the fixed-node error in diffusionMonte Carlo.
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