广义优化轨道及其对称性

GENERALIZED OPTIMUM ORBITA AND THEIR SYMMETRY PROPERT

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.