On quantum Monte Carlo for the electronic structure of molecules

Abstract

We present recent advances in the quantum Monte Carlo (QMC) method for the electronic structure of atoms and molecules. The QMC method used here is a procedure for solving the Schrödinger equation stochastically based on the formal similarity between the Schrödinger equation and the classical diffusion equation. Quantum mechanical expectation values are obtained as Monte Carlo averages over an ensemble of random walkers undergoing diffusion, drift (from importance sampling), and branching. The power of the QMC method is that it is inherently an N-body method which can capture all of the dynamic correlation of the electrons. The approach yields highly accurate energies and has been used to determine other properties, including dipole moments and molecular geometry energy gradients. Here we present a description of the QMC method that we employ and give representative results. In addition we discuss recent progress on the calculation of transition dipole moments and developments with the “damped-core” QMC method which enables studies of molecular systems containing heavy atoms without reliance on Pseudopotentials.