Deterministic Construction of Nodal Surfaces within Quantum Monte Carlo: The Case of FeS.

In diffusion Monte Carlo (DMC) methods, the nodes (or zeroes) of the trial wave function dictate the magnitude of the fixed-node (FN) error. In standard DMC implementations, the nodes are optimized by stochastically optimizing a short multideterminant expansion in the presence of an explicitly correlated Jastrow factor. Here, following a recent proposal, we pursue a different route and consider the nodes of selected configuration interaction (sCI) expansions built with the CIPSI (Configuration Interaction using a Perturbative Selection made Iteratively) algorithm. By increasing the size of the sCI expansion, these nodes can be systematically and deterministically improved. The present methodology is used to investigate the properties of the transition metal sulfide molecule FeS. This apparently simple molecule has been shown to be particularly challenging for electronic structure theory methods due to the proximity of two low-energy quintet electronic states of different spatial symmetry and the difficulty to treat them on equal footing from a one-electron basis set point of view. In particular, we show that, at the triple-ζ basis set level, all sCI results-including those extrapolated at the full CI (FCI) limit-disagree with experiment, yielding an electronic ground state of 5Σ+ symmetry. Performing FN-DMC simulation with sCI nodes, we show that the correct 5Δ ground state is obtained if sufficiently large expansions are used. Moreover, we show that one can systematically get accurate potential energy surfaces and reproduce the experimental dissociation energy as well as other spectroscopic constants.