The density matrix in many-electron quantum mechanics I. Generalized product functions. Factorization and physical interpretation of the density matrices
The density matrix in many-electron quantum mechanics I. Generalized product functions. Factorization and physical interpretation of the density matrices
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多电子量子力学中的密度矩阵 I. 广义乘积函数。
DOI：
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发表时间：
1959
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通讯作者：
R. Mcweeny
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作者：
R. Mcweeny
多电子波函数通常由单电子轨道（行列式）的反对称乘积构成，能量计算基于斯莱特（1931）的矩阵元表达式。在本文中，轨道在这样的产品被取代的“群函数”，每个描述任何数量的电子，和必要的推广斯莱特的结果进行。首先必须发展N粒子系统的密度矩阵理论，并表明对于用“广义乘积函数”描述的系统，整个系统的密度矩阵可以用组成电子群的密度矩阵来表示。广义乘积函数之间的哈密顿量的矩阵元素，然后给出的表达式类似的斯莱特，“库仑”和“交换”积分被替换的积分包含一个电子密度矩阵的各个群体。通过建立一个“有效”的哈密顿量为每个电子群的存在下，其他人，讨论一个多粒子系统，其中集团或“壳”可以区分（e。G.原子K，L，M，...，壳）可以严格地减少到更小的子系统的讨论。一个单一的广义产品（cf。Hartree-Fock理论的单一行列式）提供了一个方便的第一近似;和承认“激发”产品的效果（参见。构型相互作用）可以通过微扰方法来估计。然后，可以根据电子密度和“对”函数来讨论能量表达式。能量是由相互作用项补充的组能量的总和，所述相互作用项表示（i）电荷云之间的静电排斥，（ii）每个组在其他组的场中的极化，以及（iii）由伦敦定义的类型的“色散”效应。对于任何类型的群函数，所有这些项都可以用各个群的密度矩阵来计算。应用分子间力的理论和π-电子系统也进行了讨论。
Many-electron wave functions are usually constructed from antisymmetrized products of one-electron orbitals (determinants) and energy calculations are based on the matrix element expressions due to Slater (1931). In this paper, the orbitals in such a product are replaced by ‘group functions’, each describing any number of electrons, and the necessary generalization of Slater’s results is carried out. It is first necessary to develop the density matrix theory of N-particle systems and to show that for systems described by ‘generalized product functions’ the density matrices of the whole system may be expressed in terms of those of the component electron groups. The matrix elements of the Hamiltonian between generalized product functions are then given by expressions which resemble those of Slater, the ‘coulomb’ and ‘exchange’ integrals being replaced by integrals containing the one-electron density matrices of the various groups. By setting up an ‘effective’ Hamiltonian for each electron group in the presence of the others, the discussion of a many-particle system in which groups or ‘shells’ can be distinguished (e. g. atomic K, L, M, ..., shells) can rigorously be reduced to a discussion of smaller subsystems. A single generalized product (cf. the single determinant of Hartree—Fock theory) provides a convenient first approximation; and the effect of admitting ‘excited’ products (cf. configuration interaction) can be estimated by a perturbation method. The energy expression may then be discussed in terms of the electon density and ‘pair’ functions. The energy is a sum of group energies supplemented by interaction terms which represent (i) electrostatic repulsions between charge clouds, (ii) the polarization of each group in the field of the others, and (iii) ‘dispersion’ effects of the type defined by London. All these terms can be calculated, for group functions of any kind, in terms of the density matrices of the separate groups. Applications to the theory of intermolecular forces and to π-electron systems are also discussed.