物理化学学报 >> 2000, Vol. 16 >> Issue (08): 681-688.doi: 10.3866/PKU.WHXB20000803

研究论文 上一篇    下一篇

量子Monte Carlo处理激发态

黄宏新, 曾宪标   

  1. 湖南师范大学化学系,长沙 410081
  • 收稿日期:1999-11-30 修回日期:2000-01-13 发布日期:2000-08-15
  • 通讯作者: 黄宏新 E-mail:xieqj@public.cs.hn.cn

Quantum Monte Carlo Approach Process Excited State

Huang Hong-Xin, Zeng Xian-Biao   

  1. Department of Chemistry,Hunan Normal University,Changsha 410081
  • Received:1999-11-30 Revised:2000-01-13 Published:2000-08-15
  • Contact: Huang Hong-Xin E-mail:xieqj@public.cs.hn.cn

摘要:

提出了用于电子激发态的剩余函数变分量子Monte Carlo(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,则基态的SFVMC方法亦可推广到该激发态的情况.文章导出了这第二类激发态的SFVMC方法的详细计算公式.一套完整的用于基态和激发态的 SFVMC方法已经被建立.并用该方法计算了 CH_2分子的 X3B_1态、11A_1态和21 A_1态的能量值.计算结果表明:对于 CH_2分子的这三个态, SFVMC方法只需要迭代到三级能量值即可达到FCI方法的精度;SFVMC方法的四级能量值和五级能量值其相关能百分率可分别达到80%和90%以上.这说明SFVMC方法对于基态和激发态的处理都是非常成功的.

关键词: 变分量子Monte Carlo方法, 剩余函数, 激发态

Abstract:

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 3B_1, state, 1 1A_1 state, and 2 1A_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. 

Key words: Variational Quantum Monte Carlo approach, Surplus function, Excited state