A spline approach to trial wave functions for variational and diffusion Monte Carlo

We describe how to combine the variational Monte Carlo method with a spline description of the wave function to obtain a powerful and flexible method to optimize electronic and nuclear wave functions. A property of this method is that the optimization is performed "locally": During the optimization, the attention is focused on a region of the wave function at a certain time, with little or no perturbation in far away regions. This allows a fine tuning of the wave function even in cases where there is no experience on how to choose a good functional form and a good basis set. After the optimization, the splines were fitted using more familiar analytical global functions. The flexibility of the method is shown by calculating the electronic wave function for some two and three electron systems, and the nuclear wave function for the helium trimer. For He-4(3), using a two-body helium-helium potential, we obtained the best variational function to date, which allows us to estimate the exact energy with a very small variance by a diffusion Monte Carlo simulation. (C) 1999 American Institute of Physics. [S0021-9606(99)30537-7].