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Three-dimensional functions f(r) = g(r) · Y
m
l
(, ø), which transform like an irreducible tensor, are transformed simultaneously under rotations and translations. The relationships governing the transformation reveal some general properties. If the addition theorem of a function f(r) can be represented by a one-center expansion in terms of surface spherical harmonics Y
m
l
, each expansion coefficient is given by a Clebsch-Gordan coefficient and a radial function.Because of these properties, addition theorems are especially helpful for the simplification and evaluation of quantum-mechanical matrix elements and multi-center energy integrals in molecular LCAO calculations. The application of addition theorems has two major advantages: First, because addition theorems are equivalent to translation formulas, the number of centers of an integral can be reduced by translation of orbitals and operators. Second, due to the typical analytical structure of the series expansion representing the addition theorem, the dimensionality of a molecular integral can be reduced, because the integration over the angular variables can be executed. Then, a molecular multi-center integral is represented by a series of one-center integrals over functions of the radial variable only.
Herrn Professor Dr. H. Hartmann zum 65. Geburtstag gewidmet. 相似文献
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大体系多电子相关研究中应用群对称定域轨道的构想周泰锦,刘爱民(厦门大学化学系,厦门361005)关键词:组态相关,多构型自治叠代,多中心积分,群对称定域轨道,对称约化有关原子簇化合物及化学吸附、过渡态、激发态、催化反应等大体系的量子化学研究,对于探讨... 相似文献
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