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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。
In this paper, we generalize the optimization problem in linear space and derive a set of uniform equations for constructing orbit optimization and calculating corresponding optimization values. The obtained equations show that any optimal orbit is the essential vector of an operator and the coefficient of the optimal orbit Matrices are the sagittal matrices of some representation matrix related to this operator, and the corresponding optimization values are the eigenvalues corresponding to these eigenvectors. It has been proved that if the q fundamental vectors used to construct the optimal orbit and r The basis vectors form the bases of the q-dimensional and r-dimensional representations of the molecular point groups, respectively, and all the operators appearing in the expressions of the optimization values are linear, Hermitian, and transformed in accordance with the full symmetry operation of the molecular point group Then the optimal orbit corresponding to the same optimization value forms the basis of the representation of the point group In general, if the optimization value is closely related to the orbital energy, the representation of the point group opposite the keyed orbit optimization is irreducible , The representation of the group of points corresponding to the non-key optimization orbit may be reducible, and this reducible representation needs to be further reduced.