Quantum Monte Carlo approach process excited state

Surplus function variational quantum Monte Carlo (SFVMC) approach for the electronic excited state has been established in this paper. It is demonstrated that if the initial wave functions of the excited state and ground state belong to the irreducible representation with different symmetry, SFVMC approach of excited state is identical to that of ground state, if they belong to the irreducible representation with identical symmetry, SFVMC approach of the ground state can also be applied to the excited state only the initial wave function of excited state requiring orthogonal adjustment. The detailed calculations of SFVMC approach of the excited state are also deduced in this paper. A complete set of SFVMC approach for the ground state and excited state has been established in combination of the ground state's SFVMC approach which was deduced in our previous paper([1]). The energy values of X B-3(1) state, 1 (1)A(1) state, and 2 (1)A(1) state of CH2 molecule have been calculated by this approach as an example. The calculation results (to see Table 1) show that the precision of SFVMC approach can achieve that of FCI approach by only iteration to the third order energy value for three states of CH2 molecule. The correlation energy percentages of the fourth order energy and the fifth order energy are above 80% and 90% by SFVMC approach, respectively. This discloses that SFVMC approach is successful not only for the ground state but also for the excited state.