Group Theoretical Structure of a Solution of the Unrestricted Hartree-Fock Equation in Molecular Systems with a Spatial Point Symmetry
Group Theoretical Structure of a Solution of the Unrestricted Hartree-Fock Equation in Molecular Systems with a Spatial Point Symmetry
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空间点对称分子体系中无限制Hartree-Fock方程解的群论结构
DOI：
10.1143/ptp.62.1183
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发表时间：
1979
影响因子：
--
通讯作者：
Masa–aki Ozaki
中科院分区：
文献类型：
--
作者：
Masa–aki Ozaki
提出了一种确定具有空间点对称的分子体系中超高频溶液的群理论结构的理论。证明了UHF解的不变性群G至少有一系列减半子群G=Ho~H，···~H。使得H，+是H的一个减半子群，而H是一个其不可约表示可以很容易地得到或在标准教科书中可用的群。在此减半级数的基础上，导出了UHF解的不变性群的所有不可约双值表示及其基的一般方法，这些基提供了UHF解的轨道的标准形式。给出了自旋和时间反转对称中除扭转自旋波外的7类超高频解的不变性群的不可约表示及其基，即TSW型群或点群的不变性群的不可约表示。
A theory is developed to determine the group theoretical structure of a UHF solution in molecular systems with a spatial point symmetry. It is shown that the invariance group G of a UHF solution has at least a series of halving subgroups G=Ho~H,···~H. such that H,+, is a halving subgroup of H, and H. is a group whose irreducible representations can be easily obtained or are available in standard text books. On the basis of this halving series, a general procedure is derived to obtain all the irreducible double valued representations of the invariance group of a UHF solution and their bases which provide a standard form of the orbitals of the UHF solution. The irreducible representations and their bases of the invariance groups of the seven classes of UHF solutions in spin and time reversal symmetry except the torsional spin wave (TSW) one are given in terms of those of the group of TSW type or the point group.