Toward an improved control of the fixed-node error in quantum Monte Carlo: The case of the water molecule

Abstract

All-electron Fixed-node Diffusion Monte Carlo (FN-DMC) 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 perturbatively selected Configuration Interaction calculation (CIPSI method) including up to about 1.4 million of determinants. Calculations are made using the cc-pCV$n$Z family of basis sets, with $n$=2 to 5. In contrast with most QMC 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 -76.43744(18) is obtained. The fixed-node energy is found to decrease regularly as a function of the cardinal number $n$ and the Complete Basis Set limit (CBS) associated with {\it exact nodes} is easily extracted. The resulting energy of -76.43894(12) -in perfect agreement with the best experimentally derived value- is the most accurate theoretical estimate reported so far. We emphasize that employing selected CI nodes 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 DMC.

arXiv comment5 pages, 1 figure

References in corpus (7)

• Fixed-Node Diffusion Monte Carlo potential energy curve of the fluorine molecule F2 using selected configuration interaction trial wavefunctions
• Computing the energy of a water molecule using MultiDeterminants: A simple, efficient algorithm
• Spin density distribution in open-shell transition metal systems: A comparative post-Hartree-Fock, Density Functional Theory and quantum Monte Carlo study of the CuCl2 molecule
• Accurate nonrelativistic ground-state energies of 3d transition metal atoms
• Quantum Monte Carlo with very large multideterminant wavefunctions
• A Fast and Efficient Algorithm for Slater Determinant Updates in Quantum Monte Carlo Simulations
• Compression algorithm for multi-determinant wave functions

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