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首页> 外文期刊>International Journal of Quantum Chemistry >On Rudenberg's integral approximations and their unrestricted and combined use in molecular orbital theories of Hartree-Fock type
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On Rudenberg's integral approximations and their unrestricted and combined use in molecular orbital theories of Hartree-Fock type

机译：关于鲁登伯格的积分近似及其在Hartree-Fock型分子轨道理论中的无限制和组合使用

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摘要

Rudenberg's well-known letter of 1951 contains two implications which still have not been employed so far in numerical computations: (1) Whenever all types of attraction and repulsion integrals are subject to the Rudenberg approximations in its simplest form partially known already from Mulliken, the attractive, the Coulomb, as well as the exchange part of the restricted Hartree-Fock-Roothaan equation can be led back to the calculation of corresponding diagonal elements, only. Using Rudenberg's more elaborate concepts, which are invariant with respect to the rotation of local coordinate axes, the complete Fock-matrix representation can be constructed equivalently from only its own diagonal blocks, each belonging to one atom. Similar formulas are valid for the unrestricted Hartree-Fock theory of Pople and Nesbet. (2) If, however, one prefers to calculate all types of one- and two-center integrals exactly as suggested in Rudenberg's headline, the original simplicity of both representations is lost. Instead, one is led to more complicated expressions, which arise from the fact that Rudenberg's integral formulas, when applied to certain kinds of three-center repulsion integrals, imply considerable oversimplifications. In spite of this critical result, Rudenberg's ideas offer an extension together with an interpretation of the semiempirical Wolfsberg and Helmholz recipe (better known from Hoffmann's "extended Huckel" theory), on the one hand, and of the "neglect of differential overlap" schemes ZDO and NDDO, on the other, from a common point of view. (C) 2000 John Wiley & Sons, Inc. [References: 29]
机译：鲁登贝格（Rudenberg）1951年的著名信包含两个含义，到目前为止，它们尚未在数值计算中使用：（1）每当所有类型的吸引和排斥积分都以最简单的形式服从鲁登贝格近似时，这是穆尔肯（Mulliken）所知的，即吸引人的是，库仑以及受限制的Hartree-Fock-Roothaan方程的交换部分只能被引导回相应的对角线元素的计算。使用Rudenberg的更详细的概念（相对于局部坐标轴的旋转是不变的），可以仅由其自己的对角线块等效地构建完整的Fock-矩阵表示，每个对角线块属于一个原子。类似的公式对于Pople和Nesbet的不受限制的Hartree-Fock理论是有效的。 （2）但是，如果人们倾向于完全按照Rudenberg的标题所建议的那样计算所有类型的一中心积分和两中心积分，那么这两种表示的原始简单性就会丧失。取而代之的是，导致更为复杂的表达式，这是由于Rudenberg积分公式在应用于某些类型的三中心斥力积分时暗示了相当大的简化。尽管取得了如此重要的结果，但鲁登伯格的思想一方面提供了扩展，同时又对半经验性的沃尔夫斯伯格和亥姆霍兹配方（从霍夫曼的“扩展的赫克尔”理论中得到了更好的理解）以及“对差异重叠的忽略”方案的解释提供了扩展。另一方面，从共同的角度来看，ZDO和NDDO。 （C）2000 John Wiley＆Sons，Inc. [参考：29]

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