OPTIMIZATION OF QUANTUM MONTE CARLO WAVE FUNCTION: STEEPEST DESCENT METHOD

Abstract

We have employed the steepest descent method to optimize the variational groundstate quantum Monte Carlo wave function for He , Li , Be , B and C atoms. We have used both the direct energy minimization and the variance minimization approaches. Our calculations show that in spite of receiving insufficient attention, the steepest descent method can successfully minimize the wave function. All the derivatives of the trial wave function respect to spatial coordinates and variational parameters have been computed analytically. Our groundstate energies are in a very good agreement with those obtained with diffusion quantum Monte Carlo method (DMC) and the exact results.