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广义优化轨道及其对称性(英文)

GENERALIZED OPTIMUM ORBITA AND THEIR SYMMETRY PROPERT
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摘要 本文是线性空间的优化课题的一般化处理,导出了构造优化轨道并计算相应优化值的一组统一的方程,所得方程表明,任何优化轨道都是某一算符的本性矢,优化轨道的系数矩阵均为与该算符相关的某一表象矩阵的本性矢矩阵,且相应的优化值就是与这些本征矢对应的本征值,已证明,如果用于构造优化轨道的q个基矢与r个基矢分别构成分子点群的q维与r维表示的基,并且出现在优化值的表达式中的所有算符都是线性,厄米,与分子点群的全部对称操作相应的变换算符对易的,那么与相同优化值对应的优化轨道形成该点群的表示的基.通常,如果优化值与轨道能量紧密相关,那么与成键优化轨道对立的点群的表示是不可约的,与非键优化轨道对应的点群的表示可能是可约的,这种可约表示还需进一步约化。 This paper presents a generalized treatment of optimization problems in linear spaces. A set of generalized equations are derived for constructing optimum orbitals and for calculating the corresponding optimum values. The obtained equations show that anyone of the optimum orbitals is an eigenvector of an operator, and the coefficient matrices of the optimum orbitals are all eigenvector matrices of the related matrices. The optimum values are all the corresponding eigenvalues. It is shown that if the q and r basis vectors used for construction of the optimum orbitals form bases for q- and r-dimensional representations of a symmetry group, respectively, and the all operators appearing in the expression of the optimum value are linear, Hermitian and commute with the all elements of the symmetry group, then the optimum orbitals associated with the same optimum values form bases for representations of the group, Generally, if the optimum values are closely related to the orbital energies, then the representations corresponding to the bonding optimum orbitals are irreducible, and that corresponding to the non-bonding optimum orbitals may be reducible and should be further reduced.
作者 湛昌国
出处 《华中师范大学学报(自然科学版)》 CAS CSCD 1992年第3期307-313,共7页 Journal of Central China Normal University:Natural Sciences
基金 The Project Supported by National Scjence Foundation of China
关键词 广义优化标准 优化轨道 对称性 Generalized Optimization Criterion Optimum Orbital Symmetry Property of Optimum Orbital Construction of Optimum Orbital Calculation of Optimum Value
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  • 1Chang-Guo Zhan,Qiong-Lin Wang,Fang Zheng. Calculation of the maximum bond order[J] 1990,Theoretica Chimica Acta(2):129~131
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