物理化学学报 >> 2007, Vol. 23 >> Issue (04): 543-548.doi: 10.1016/S1872-1508(07)60036-9

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两种约化密度矩阵重构方法的理论分析

高新秀; 陈飞武   

  1. 北京科技大学化学系, 北京 100083
  • 收稿日期:2006-10-20 修回日期:2006-11-13 发布日期:2007-04-05
  • 通讯作者: 陈飞武 E-mail:chenfeiwu@sas.ustb.edu.cn

Theoretical Analysis of Two Reconstruction Schemes of Reduced DensityMatrices

GAO Xin-Xiu; CHEN Fei-Wu   

  1. Department of Chemistry, University of Science and Technology Beijing, Beijing 100083, P. R. China
  • Received:2006-10-20 Revised:2006-11-13 Published:2007-04-05
  • Contact: CHEN Fei-Wu E-mail:chenfeiwu@sas.ustb.edu.cn

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摘要： 利用Harris模型, 详细分析了Mazziotti提出的重构方法和Chen提出的一种由低阶约化密度矩阵重构高阶约化密度矩阵的系统方法(Science in China B, 2006, 49: 402)的差异. 如果忽略Mazziotti 方法中的3△M、4△M和Chen方法中的3△、4△, 计算结果显示两种方法的计算误差相近. 更好的近似是只忽略四级项4△M、4△, 而三级项由相应的四级项通过简缩来计算. 采用Mazziotti方法计算出来的有些近似值和精确值连正负号都不同, 而用Chen方法计算出来的近似值和精确值不仅正负符号一致, 而且数值大小也很接近.

关键词: 约化密度矩阵, 简缩Schrodinger 方程, 正规乘积, 累计量

Abstract: The effectiveness of the approach for systematical reconstruction of higher order reduced density matrices with lower order ones, which was developed by Chen (Science in China B, 2006, 49: 402), was compared theoretically with that of Mazziotti's method through Harris model. In the case of omitting the cumulant terms 3△M, 4△M in the latter and the normal product terms 3△, 4△in the former, it was found that the errors from both approaches were comparable. As a better approximation, if only fourth-order terms 4△M and 4△ in both methods are neglected whereas the third-order terms 3△M and 3△are computed from their corresponding fourth-order terms 4△M and 4△ respectively through contractions, the results calculated with Chen's approach not only have the correct signs but also are very close to the exact normal products 3△ whereas some of the results calculated with Mazziotti's method do not even have the correct signs with respect to the exact cumulants 3△M.

Key words: Reduced density matrix, Contracted Schrodinger equation, Normal product, Cumulant