Surplus function variational quantum Monte Carlo approach: Excited state processing

Abstract

Surplus function variational quantum Monte Carlo approach used for the excited state of electrons has been proposed. If the initial wave functions of both the excited state and ground state belong to the irreducible representation with different symmetries, the surplus function variational quantum Monte Carlo approach of the excited state is identical to that of the ground state, and if they belong to the irreducible representation with an identical symmetry, the surplus function variational quantum Monte Carlo approach of the ground state can also be applied to the excited state only by orthogonal revision for the initial wave function of the excited state. The detailed calculations formulas on the surplus function variational quantum Monte Carlo approach of the excited state have been deduced. A complete set of the surplus function variational quantum Monte Carlo approach for both the ground state and excited state has been established. The energy values of X 3B1, 1 1A1, and 2 1A1 states of CH2 have been calculated using this approach. The calculation results show that the precision of the surplus function variational quantum Monte Carlo approach is comparable to that of FCI approach only by iteration to the third-order energy value for three states of CH2. The correlation energy percentages of the fourth- and the fifth-order energy obtained by the surplus function variational quantum Monte Carlo approach are over 80% and 90%, respectively. This indicates that the approach is successful both in the ground state and in the excited state.