A random-walk simulation of the Schrödinger equation: H+3

A simple random-walk method for obtaining ab initio solutions of the Schrödinger equation is examined in its application to the case of the molecular ion H+3 in the equilateral triangle configuration with side length R=1.66 bohr. The method, which is based on the similarity of the Schrödinger equation and the diffusion equation, involves the random movement of imaginary particles (psips) in electron configuration space subject to a variable chance of multiplication or disappearance. The computation requirements for high accuracy in determining energies of H+3 are greater than those of existing LCAO–MO–SCF–CI methods. For more complex molecular systems the method may be competitive.