Computing upper and lower bounds using Monte Carlo methods

We computed lower bounds for some ground and excited states of the helium atom using variational Monte Carlo and the Weinstein, Temple, and Stevenson formulas. For these systems, the Temple and Stevenson bounds are approximately the same and have similar standard deviations. The Weinstein bounds are much further from the actual energies and have much larger standard deviations, We also investigated the reliability of these lower bound formulas when nonorthogonal wave functions are used. The Temple formula has been shown to produce an accurate lower bound even under such circumstances, while the Weinstein and Stevenson formulas are shown to yield incorrect results. (C) 2002 Wiley Periodicals, Inc.