A new algorithm for variational quantum Monte Carlo method

Abstract

A new algorithm of the variational quantum Monte Carlo(VMC) calculations , called the minimum variance(MV) method, is reported in this paper. This algorithm takes the internal structure Of a local energy as starting point, and directly reduces its fluctuation in order to make the variance decrease to the minimum. An analytical expression of the local energy is presented, The principle of variance minimization for VMC is deduced, and the steps of variance minimization are established. We then apply the new algorithm to calculate the total energies of the states (XB1)-B-3 and a(1)A(1) of CH2, pi-(XB1)-B-2 and sigma-A(2)A(1) of NH2. The singlet-triplet energy splitting(Delta ES-T) in CH2 and sigma-pi energy splitting Delta Esigma-pi in NH2 obtained with this present method are (48.542 8+/-2. 362 9) kJ/mol and (140. 885 5+/-4. 463 0) kJ/mol, respectively. It is shown that at the cost of only 10%similar to 15% increase in computation amount, one is able to reduce 72%similar to 87% of the statistical error reported in the conventional VMC runs.