Guided Diffusion Monte Carlo Approaches For Studies Of Water Clusters: Applications To Water Hexamer

Water clusters provide an opportunity to explore the effects of nuclear quantum effects on the stability of hydrogen-bonded networks. Because of their well-defined size, such studies provide an opportunity to make detailed comparisons between experiment and calculation and explore experimental measurable consequences of nuclear quantum effects through explorations of changes in zero-point structures upon partial or full deuteration. Such studies are challenging due to the large number of relevant degrees of freedom, as the changes in the anharmonic frequencies of OH stretching vibrations upon hydrogen bond formation are comparable to the zero-point energy in the low-frequency intermolecular vibrations. This also makes these systems challenging for calculations by Diffusion Monte Carlo (DMC). Earlier studies indicated that ensemble sizes of upwards of 10$^6$ {\it {walkers}} are needed to obtain reliable energies.\footnote{Mallory, J. D. and Mandelshtam, V. A., {\it{J. Phys. Chem. A}} (2015), {\bf{119}}, 6504-6515.} In this presentation, we will describe recent work in our group in developing a modified DMC approach in which guiding functions are used to improve the sampling of the high-frequency intramolecular vibrations (OH stretches and HOH bends). With this modification, the energies and wave functions can be obtained using ensembles that are more than an order of magnitude smaller compared to those used in earlier studies.\footnote{Lee, V. G. M.; Vetterli, N. J.; Boyer, M. A. and McCoy, A. B., {\it{J. Phys. Chem. A}} (2020), {\bf{124}}, 6903-6912.} With this more efficient algorithm, we explore the effects of nuclear quantum effects on the relative energies of the low-energy prism and cage structures, as well as the relative energies of the partially deuterated (H$_2$O)$_5$(D$_2$O) and (H$_2$O)(D$_2$O)$_5$ clusters