量子Monte Carlo处理激发态

Quantum Monte Carlo Approach Process Excited State

提出了用于电子激发态的剩余函数变分量子ＭｏｎｔｅＣａｒｌｏ（ＳＦＶＭＣ）方法，已经证明：若激发态的初始波函数与基态的初始波函数属于对称性不同的不可约表示时，该激发态的ＳＦＶＭＣ方法与基态的ＳＦＶＭＣ方法完全相同；若激发态的初始波函数与基态的初始波函数有相同的对称性时，只要对激发态的初始波函数作正交性修正，则其态的ＳＦＶＭＣ方法亦可推到该激发态的情况。

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 establised in combination of the ground state's SFVMC approach which was deduced in our previous paper[1]. The energy values of X 3~B_1, state, 1 1~A_1 state, and 2 1~A_1 state of CH_2 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 CH_2 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.