Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota , Minneapolis, Minnesota 55455, United States.
J Chem Theory Comput. 2017 Jun 13;13(6):2823-2830. doi: 10.1021/acs.jctc.7b00325. Epub 2017 May 24.
Band shape is an essential ingredient in the simulation of electronic absorption spectra. The excitation of multiple series of vibrational levels during an electronic excitation is a main contributor to band shapes. Here we present two simple models based on the Franck-Condon displaced-harmonic-oscillator model. The models are both derived from the time-dependent formulation of electronic spectroscopy. They assume that the transition dipoles do not depend on geometry and that the potential energy surfaces are locally quadratic; one model is second order in time and is called LQ2, and the other is third order in time and is called LQ3. These models are suitable for simulating the unresolved vibronic band shapes of electronic spectra that involve many vibrational modes. The models are straightforward and can be easily applied to simulate absorption spectra that are composed of many electronic transitions. As compared to carrying out molecular dynamics simulations, they require relatively few electronic structure calculations, and the additional cost for constructing the spectra is negligible. Therefore, the models are suitable for simulating the spectra of complex systems such as transition-metal complexes.
谱带形状是模拟电子吸收光谱的一个重要组成部分。在电子激发过程中，多个振动能级系列的激发是谱带形状的主要贡献者。在这里，我们提出了两个基于 Franck-Condon 位移谐振子模型的简单模型。这些模型都是从电子光谱的时间相关公式推导出来的。它们假设跃迁偶极子不依赖于几何形状，并且势能面是局部二次的；一个模型是二阶时间的，称为 LQ2，另一个是三阶时间的，称为 LQ3。这些模型适用于模拟涉及多个振动模式的未解析的电子光谱的振子带形状。这些模型简单直接，可以轻松应用于模拟由许多电子跃迁组成的吸收光谱。与进行分子动力学模拟相比，它们需要相对较少的电子结构计算，并且构建光谱的额外成本可以忽略不计。因此，这些模型适用于模拟过渡金属配合物等复杂体系的光谱。
