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首页> 外文期刊>The Journal of Chemical Physics >Nonorthogonal orbital based N-body reduced density matrices and their applications to valence bond theory. I. Hamiltonian matrix elements between internally contracted excited valence bond wave functions
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Nonorthogonal orbital based N-body reduced density matrices and their applications to valence bond theory. I. Hamiltonian matrix elements between internally contracted excited valence bond wave functions

机译：基于非正交轨道的N体约化密度矩阵及其在价键理论中的应用。一，内部收缩的激发价键波函数之间的哈密顿矩阵元

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摘要

In this series, the n-body reduced density matrix (n-RDM) approach for nonorthogonal orbitals and their applications to ab initio valence bond (VB) methods are presented. As the first paper of this series, Hamiltonian matrix elements between internally contracted VB wave functions are explicitly provided by means of nonorthogonal orbital based RDM approach. To this end, a more generalized Wicks theorem, called enhanced Wicks theorem, is presented both in arithmetical and in graphical forms, by which the deduction of expressions for the matrix elements between internally contracted VB wave functions is dramatically simplified, and the matrix elements are finally expressed in terms of tensor contractions of electronic integrals and n-RDMs of the reference VB self-consistent field wave function. A string-based algorithm is developed for the purpose of evaluating n-RDMs in an efficient way. Using the techniques presented in this paper, one is able to develop new methods and efficient algorithms for nonorthogonal orbital based many-electron theory much easier than by use of the first quantized formulism.
机译：在本系列中，介绍了用于非正交轨道的n体降密度矩阵（n-RDM）方法及其在从头价键（VB）方法中的应用。作为该系列的第一篇论文，通过基于非正交轨道的RDM方法显式提供了内部收缩VB波函数之间的哈密顿矩阵元素。为此，以算术形式和图形形式提出了一种更广义的维克斯定理，称为增强维克斯定理，从而大大简化了内部收缩VB波函数之间矩阵元素的表达式推导，并且简化了矩阵元素。最后用参考VB自洽场波函数的电子积分和n-RDM的张量收缩表示。为了有效评估n-RDM，开发了基于字符串的算法。使用本文中介绍的技术，与使用第一个量化公式相比，它能够为基于非正交轨道的多电子理论开发新方法和高效算法。

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