Quantum Monte Carlo Calculation of Correlation Energy

Abstract

Over a long period two systematic methods have provided the main routes to the calculation of correlation energies for many-electron systems at zero temperature; namely; configuration interaction (CI) and many-body perturbation theory. The second of these approaches applied to molecules has been dealt with in the review by Wilson (1981). Therefore that ground will not be covered in this chapter. However, there has been much progress using the so-called Quantum Monte Carlo (QMC) method. The goal of this approach [see, e.g., Ceperley and Alder (1984)] is to obtain the exact ground-state wave function of a many-body system by numerically solving the Schrodinger equation in one of its equivalent forms. In practice, this is achieved by means of iterative algorithms, that propagate the wave function from a suitable starting estimate to the exact ground-state result. Thus, in the Diffusion Monte Carlo (DMC) method, one is directly concerned with the evolution in imaginary time of the wave function, which corresponds to a diffusion process in configuration space. In the Green Function Monte Carlo (GFMC) technique, on the other hand, a time-integrated form of the Green function or resolvent is used to propagate the wave function. In fact, in either case the sampling of an appropriate Green function is required, and this is achieved by means of suitable random-walk algorithms.