发表机构
College of Chemistry and Molecular Engineering, Peking University; Department of Chemistry, The University of Hong Kong（北京大学化学与分子工程学院; 香港大学化学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究开发了严格保留自旋对称性的有限温度ROKS和自旋适配TDDFT扩展框架，分别用于基态和激发态描述，并通过双自由基分子的变温UV/Vis光谱实验验证了其解释热活化吸收的能力。
AI 中文摘要
有限温度条件是量子化学中受关注的核心研究体系。然而，在严格保留与$\boldsymbol{\text{Ŝ}}^2$算符相关的自旋对称性的前提下，将有限温度效应一致地纳入描述基态和激发态的密度泛函理论（DFT）中，这一目标尚未实现。本工作中，我们开发了限制性开壳层Kohn-Sham（ROKS）理论和自旋适配的含时密度泛函理论（TDDFT）的有限温度扩展版本，分别为基态和激发态的描述提供了统一框架。对于有限温度ROKS，我们利用整数高自旋ROKS分量构建正则系综，其中每个分量$I$具有相同的自旋数$|SS\rangle$，其权重$w_I$服从玻尔兹曼分布。对于有限温度自旋适配TDDFT，每个整数分量$I$提供一组常规零温自旋适配TDDFT矩阵对$(\boldsymbol{\text{M}}_I,\boldsymbol{\text{N}}_I)$，这些矩阵按统一的空间轨道顺序排列后进行平均。在零温单分量极限下，该理论退化为常规高自旋ROKS及对应的自旋适配TDDFT。作为数值应用，我们将该理论应用于一种双自由基类分子，并利用计算得到的激发态解释了变温紫外-可见（UV/Vis）光谱中观测到的热活化吸收现象。
英文摘要
Low-lying electronic states of different spins can be thermally populated in open-shell molecules, allowing optical absorption to begin from several initial states. We formulate their canonical optical response using the electronic levels and one-body matrices of spin-adapted time-dependent density functional theory. Boltzmann populations determine the contribution of each initial state, while transition density matrices determine its coupling to the final states. Absorption and stimulated emission then give the temperature-dependent strength of every allowed transition. Transition matrices are evaluated from the calculated first-order excitation amplitudes, with the additional mixed second-order electronic response omitted by this approximation identified explicitly. The resulting response function provides spin-resolved polarizabilities and absorption spectra with definite total spin assigned to each participating electronic state. Applications to diradicals provide a qualitative interpretation of their temperature-dependent absorption spectra.
Comments15 pages, 58 equations
