AN APPROACH FOR IMPROVED VARIATIONAL QUANTUM MONTE-CARLO

Sampling of core electrons in Monte Carlo approaches to electronic structure is a major bottleneck to efficient studies of large molecules. To overcome this problem, we propose an improved Metropolis algorithm for variational Monte Carlo which includes the second derivatives (Hessian matrix) of the pseudopotential P=-ln\Psi(T)\(2) in its transition probability in addition to the commonly used first derivatives (or quantum force). To minimize computational effort, we use only the diagonal elements of the Hessian matrix, which are readily obtained from information already available in the Monte Carlo computation. We analyze the effect of these diagonal terms on the transition probability and core-electron sampling. The approach automatically reduces the step sizes of the innermost electrons and does not require further considerations such as choice of coordinate system or assignment of electrons to specific shells. In addition, heteronuclear molecules pose no difficulty for the present algorithm. Application of the method to representative systems, Ne, Ar, and KCl, has shown that it increases the acceptance ratio of the innermost core electrons by a factor of 5 over previous algorithms.