A novel quantum Monte Carlo strategy: Surplus function approach

A concept of surplus function for the Schrödinger equation is put forward. A novel quantum Monte Carlo approach, namely, the surplus function method, is suggested with use of a novel trial function of significant physical meaning which is based on the proposed surplus function. The trial function is an iteration type, as given in the text. It is theoretically proved that the energy expectation value obtained from the proposed trial function decreases step by step in iterations. In addition, computation formulas and concrete procedures for energy expectation value are presented. Calculations for ${\mathrm{H}}_{\mathrm{2}},$ LiH, ${\mathrm{Li}}_{\mathrm{2}},$ and ${\mathrm{H}}_{\mathrm{2}}\mathrm{O}$ molecules indicate that the energy expectation values after only 4–5 iterations achieve over 90% of the correlation energy, indicating that the convergence rates are rapid. The trial function used in the present paper requires no parameter optimization and is of the highest accuracy.