AI 中文总结
本文研究分子电子跃迁的TDDFRT表示是否唯一，通过单粒子约化差密度矩阵展开分析，采用新型图解语言，对比含时Hartree-Fock与TDDFRT的差异，质疑其唯一性。
AI 中文摘要
本文通过单粒子约化差密度矩阵，研究了参考含时密度泛函响应理论（TDDFRT）的分子电子跃迁表示的一部分。文献中已报道该物理量的一种推导途径，基于将TDDFRT相关量代入一个精确泛函表达式。本文证明提供该精确物理量的泛函并非唯一，并质疑将相同TDDFRT相关量代入替代泛函表达式是否能得到近似TDDFRT单粒子约化差密度矩阵的可接受候选，这会对分子电子跃迁的TDDFRT表示的明确性提出质疑。本文首先利用一种受Dyck语言启发、专门用于处理此类问题的新型图解语言直接解决该问题；最后质疑是否可将该问题重述为更通用的框架——运动方程框架。全文对比了含时Hartree-Fock与TDDFRT的情况，以凸显这些问题存在时二者的差异。
英文摘要
In this article a piece of the reference time-dependent density-functional response theory (TDDFRT) representation of molecular electronic transitions is studied through the one-body reduced difference density matrix. A first derivation route for that object has been reported in the literature based on the substitution of TDDFRT-related objects into an exact functional expression. We show in the text that the functional providing the exact object is not unique, and we question whether substituting the same TDDFRT-related objects into the alternative functional expressions leads to acceptable candidates for the approximate TDDFRT one-body reduced difference density matrix, which would question the unequivocality of the TDDFRT representation of molecular electronic transitions. We first directly address the problem using a novel diagrammatic language, inspired by Dyck languages, and specifically designed for dealing with this kind of issue. In the last part of the article we question whether it is possible or not to recast the problem in a more general framework - the equations-of-motion framework. Through all the text, the case of time-dependent Hartree-Fock is compared with that of TDDFRT to highlight what makes them so different when those questions are at stake.
