摘要
提出变分量子ＭｏｎｔｅＣａｒｌｏ（ＶＭＣ）计算的新算法极小化方差（ＭＶ）方法．它从局域能的内部结构出发，直接削减其波动以达到将ＶＭＣ的方差减到极小的目的．给出了局域能的分析表达式，导出ＶＭＣ的极小方差原理，并建立方差极小化的计算步骤．这一新算法被用到ＣＨ２的Ｘ３Ｂ１态和ａ１Ａ１态以及ＮＨ２的π－Ｘ２Ｂ１态和σ－Ａ２Ａ１态总能量的计算，得到ＣＨ２单－三重态的“劈裂”能ΔＥＳ－Ｔ＝（４８．５４２８±２．３６２９）ｋＪ／ｍｏｌ和ＮＨ２的σ－π“劈裂”能ΔＥσ－π＝（１４０．８８５５±４．４６３０）ｋＪ／ｍｏｌ．结果表明，在只增加１０％～１５％的计算量下，ＭＶ法比一般ＶＭＣ过程统计误差要小７２％～８７％．
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 X 3B 1 and a 1A 1 of CH 2, π X 2B 1 and σ A 2A 1 of NH 2. The singlet triplet energy splitting(Δ E S T ) in CH 2 and σ π energy splitting Δ E σ π in NH 2 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%￣15% increase in computation amount, one is able to reduce 72%￣87% of the statistical error reported in the conventional VMC runs.
出处
《高等学校化学学报》
SCIE
EI
CAS
CSCD
北大核心
1998年第10期1636-1639,共4页
Chemical Journal of Chinese Universities
基金
国家自然科学基金
关键词
变分量子
局域能
方差极小化
能级裂分
VMC
MV
Variational quantum Monte Carlo method, Local energy, Minimum variance, Energy splitting
