Atomic and Molecular Calculations Using Quasirandom Numbers

Abstract

We have calculated the total ground-state energy, kinetic energy, and potential energy of He, H2, Li, and Be using explicitly correlated wavefunctions and two numerical integration procedures. The first integration procedure uses pseudorandom numbers and converges as N−0.5. The second uses a set of quasirandom numbers generated by Halton's algorithm. Under some circumstances the convergence of this integration procedure can be as fast as N−1. When a small to intermediate number of quasirandom numbers are used, most of our expectation values converge faster than those computed using pseudorandom numbers. When a large number of quasirandom numbers are used, however, we find that most of the expectation values converge at roughly the same rate as those computed using pseudorandom numbers.