Comparison of vertical and adiabatic harmonic approaches for the calculation of the vibrational structure of electronic spectra
Comparison of vertical and adiabatic harmonic approaches for the calculation of the vibrational structure of electronic spectra
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DOI：
10.1039/c2cp41169e
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发表时间：
2012-01-01
影响因子：
3.3
通讯作者：
Santoro, Fabrizio
中科院分区：
文献类型：
--
作者：
Ferrer, Francisco Jose Avila;Santoro, Fabrizio
与大分子电子光谱相关的振动结构的计算需要对一些参考核结构周围的初始和最终状态势能表面（PES）进行泰勒展开。垂直 (V) 和绝热 (A) 方法围绕初始状态 (V) 或最终状态 (A) 平衡结构扩展最终状态 PES。最简单的模型仅考虑初始状态和最终状态最小值的位移，中间模型还考虑频率差异，更准确的模型通过计算初始状态和最终状态的 Hessians 引入杜辛斯基效应。在这篇文章中，我们总结并比较了 V 和 A 谐波模型完整层次结构的数学表达式，并以数字代码实现它们，详细比较了它们在许多原型系统上的性能。我们还通过作为核坐标函数的过渡偶极子的线性展开（赫兹伯格-特勒效应）来解决非康顿效应，并比较初始和最终状态平衡几何形状的展开结果。通过对结果的全面分析，我们强调了模型相对性能的一些总体趋势，这些趋势可以为正确选择提供提示。此外，我们表明，包括最终状态 PES Hessian 的 A 和 V 模型优于更简单的模型，并且它们的预测差异可以诊断谐波近似和/或 Born-Oppenheimer 近似的失败（存在显着的依赖于几何的电子态混合）。
The calculation of the vibrational structure associated to electronic spectra in large molecules requires a Taylor expansion of the initial and final state potential energy surface (PES) around some reference nuclear structure. Vertical (V) and adiabatic (A) approaches expand the final state PES around the initial-state (V) or final-state (A) equilibrium structure. Simplest models only take into account displacements of initial-and final-state minima, intermediate ones also allow for difference in frequencies and more accurate models introduce the Dushinsky effect through the computation of the Hessians of both the initial and final state. In this contribution we summarize and compare the mathematical expressions of the complete hierarchy of V and A harmonic models and we implement them in a numerical code, presenting a detailed comparison of their performance on a number of prototypical systems. We also address non-Condon effects through linear expansions of the transition dipole as a function of nuclear coordinates (Herzberg-Teller effect) and compare the results of expansions around initial and final state equilibrium geometries. By a throughout analysis of our results we highlight a number of general trends in the relative performance of the models that can provide hints for their proper choice. Moreover we show that A and V models including final state PES Hessian outperform the simpler ones and that discrepancies in their predictions are diagnostic for failure of harmonic approximation and/or of Born-Oppenheimer approximation (existence of remarkable geometry-dependent mixing of electronic states).