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arXiv 2104.11947physics.chem-ph
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分子电子跃迁的自然轨道表示

Natural-orbital representation of molecular electronic transitions

Thibaud Etienne

摘要:

本文介绍了约化密度矩阵理论和格林函数理论在分子电子跃迁分析中应用的形式基础。为此,他们的力学,适用于特定的对象,包含有关的通道和电子状态之间的干扰信息-差异和跃迁密度算子-严格介绍了一个独立的方式。在减少相应的$N$体运营商(其中$N$是在系统中的电子数)使用运营商部分跟踪程序后,我们推导出减少的单体差分和跃迁密度运营商的核,以及这些运营商在有限维单粒子态的基础上的矩阵表示。为了完整起见,这些推导是在第一和第二量化中完成的-这两个公式在文献中是等价的-并且因为第二量化在本文的第二部分中被广泛使用。自然轨道被引入作为适当的基础,以减少问题的维数和过渡现象的分析的复杂性。密度算符的自然轨道表示通常用作表征分子电子跃迁性质的工具,因此我们建议通过这一贡献重新审视它们的理论基础,以便更好地理解这些工具的起源和性质。

英文摘要:

This paper aims at introducing the formal foundations of the application of reduced density-matrix theory and Green's function theory to the analysis of molecular electronic transitions. For this sake, their mechanics, applied to specific objects containing information related to the passage and the interference between electronic states - the difference and the transition density operators - are rigorously introduced in a self-contained way. After reducing the corresponding $N$-body operators (where $N$ is the number of electrons in the system) using an operator partial-trace procedure, we derive the kernel of the reduced one-body difference and transition density operators, as well as the matrix representation of these operators in a finite-dimensional one-particle-state basis. These derivations are done in first and second quantization for the sake of completeness - the two formulations are equivalently present in the literature - and because second quantization is extensively used in a second part of the paper. Natural orbitals are introduced as appropriate bases for reducing the dimensionality of the problem and the complexity of the analysis of the transition phenomenon. Natural-orbital representation of density operators are often used as a tool to characterize the nature of molecular electronic transitions, so we suggest with this contribution to revisit their theoretical foundations in order to better understand the origin and nature of these tools.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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