Diffusion Monte Carlo study of electronic properties for hydrogen and beryllium atoms

We examined three different, algorithms used in diffusion Monte Carlo (DMC) to study their precisions and accuracies in predicting properties of isolated atoms, which are H atom ground state, Be atom ground state and H atom first excited state.; All three algorithms---basic DMC, minimal stochastic reconfiguration DMC, and pure DMC, each with future-walking, are successfully impletmented in ground state energy and simple moments calculations with satisfactory results. Pure diffusion Monte Carlo with future-walking algorithm is proven to be the simplest approach with the least variance.; Polarizabilities for Be atom ground state and H atom first excited state are not satisfactorily estimated in the infinitesimal differentiation approach. Likewise, an approach using the finite field approximation with an unperturbed wavefunction for the latter system also fails. However, accurate estimations for the alpha-polarizabilities are obtained by using wavefunctions that come from the time-independent perturbation theory. This suggests the flaw in our approach to polarizability estimation for these difficult case rests with our having assumed the trial function is unaffected by infinitesimal perturbations in the Hamiltonian.