Fixed-node quantum Monte Carlo

Abstract

Quantum Monte Carlo methods cannot at present provide exact solutions of the Schrödinger equation for systems with more than a few electrons. But, quantum Monte Carlo calculations can provide very low energy, highly accurate solutions for many systems ranging up to several hundred electrons. These systems include atoms such as Be and Fe, molecules such as H₂O, CH₄, and HF, and condensed materials such as solid N₂ and solid silicon. The quantum Monte Carlo predictions of their energies and structures may not be ‘exact’, but they are the best available. Most of the Monte Carlo calculations for these systems have been carried out using approximately correct fixed nodal hypersurfaces and they have come to be known as ‘fixed-node quantum Monte Carlo’ calculations. In this paper we review these ‘fixed node’ calculations and the accuracies they yield.