Abstract:

 A concept of surplus function for Schrodinger equation is put forward. A novel quantum Monte Carlo approach entitled 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 of an iteration-type and suffers no time-consuming parameter optimum in a quantum Monte Carlo process. It is theoretically proved that the energy expectation value obtained from the proposed trial function converges to the exact energy value of the system investigated. In addition, computation formulas and procedures for energy expectation value are presented. Calculations for several molecules indicate that the energy expectation value obtained from the trial function does converge to the exact energy value of the investigated system and the converging rate is very fast as generally only 4-5 iterations achieves over 90% correlation energy. To our knowledge, both the calculating precision and converging rate of the trial function proposed are the highest one in the quantum Monte Carlo approach at present time. 

Key words: Quantum Monte Carlo approach, Surplus function for Schrdinger equation, Energy expectation value