Fixed-node quantum Monte Carlo: A novel approach

In this paper, a novel method for fixed-node quantum Monte Carlo is given. We have derived an expansion of the eigenvalue of the energy for a system and proved that the value of the energy calculated using the traditional fixed-node quantum Monte Carlo method is only the zero order approximation of the eigenvalue of the energy But when using our novel method, in the case of only increasing less computing amounts (<1%), we can obtain conveniently the first order approximation, second order approximation, and so on. We have calculated the values of the zero, first and second approximation (ε(0), ε(1) and ε(2)) of the energies of 1(1)A(1) state of CH2, (1)A(g) (C-4h, acet) state of C-8 and the ground-state of H2O using this novel method. The results indicate that for 1(1)A(1) state of CH2, (1)A(g) (C-4h, acet) state of C-8 and the ground-state of H2O it needs only the second order approximation to obtain electronic correlation energy with over 97%. This demonstrates that this novel method is very excellent in both the computing accuracy and the amount of calculation required.