Quantum chemistry without wave functions: Diffusion Monte Carlo applied to H and H_2~+

摘要

In quantum theory, H atom and H_2~+ can be solved via Schrodinger equation using computer simulation method known as `diffusion Monte Carlo'. The time-dependent Schrodinger equation in atomic units and in 1D in the form (3), can be viewed as a diffusion equation to which a first-order term is added: (4), where D is the diffusion coefficient, k is the rate constant for their disappearance or multiplication. The gist of diffusion Monte Carlo is that one can simulate the Schrodinger equation by a process of diffusion, whereby each walker is moved at random a distance determined by D, followed by a process of `branching', where each is allowed to multiply or disappear with a probability depending on the value of k.