Theory and Application of a Pure-sampling Quantum Monte Carlo Algorithm

Abstract

The objective of pure-sampling quantum Monte Carlo is to calculate physical properties that are independent of the importance sampling function being employed in the calculation, save for the mismatch of its nodal hypersurface with that of the exact wave function. To achieve this objective, we describe a pure-sampling algorithm that combines features of forward-walking methods of pure-sampling and reptation quantum Monte Carlo. The importance sampling is performed by using a single-determinant basis set composed of Slater-type orbitals. We implement our algorithm by systematically increasing an algorithmic parameter until the properties sampled from the electron distributions converge to statistically equivalent values, extrapolated in the limit of zero time-step. In doing so, we are able to unambiguously determine the values for the ground-state fixed-node energies and one-electron properties of various molecules. These quantities are free from importance sampling bias, population control bias, time-step bias, extrapolation-model bias, and the finite-field approximation. We applied our algorithm to the ground-states of lithium hydride, water and ethylene molecules, and found excellent agreement with the accepted literature values for the energy and a variety of other properties for those systems. Some of our one-electron properties of ethylene had not been calculated before at any level of theory. In a detailed comparison, we found reptation quantum Monte Carlo, our closest competitor, to be less efficient by at least a factor of two. It requires different sets of time-steps to accurately determine the ground-state energy and one-electron properties, whereas our algorithm can achieve the same objective by using a single set of time-step values.