Ground-state properties of the water molecule by reptation quantum Monte Carlo

Reptation quantum Monte Carlo (RQMC) is a Markov chain and Metropolis-Hastings type algorithm. In this paper RQMC-variants are implemented for the ground-state of water molecule, whereby adjustments are made to the Metropolis decision to utilize the trial density at strategic reptile locations and to impose microscopic reversibility on the electron moves. Our objective is to identify the adjustment which gives one-electron properties of the water molecule which best agree with highly-accurate determinations in the literature. Other than for the energy, RQMC, when implemented with a single-$\zeta$ STO guiding function, does not significantly improve the variational estimates. For a double-$\zeta$ STO case, the RQMC-HT variant that adjusts the Metropolis decision at where new scales are being added clearly provides the most precise estimates with negligible bias. For double-$\zeta$ and triple-$\zeta$ cases, each with polarization, RQMC-HT still outperforms the others, but, as expected, to a much lesser extent.