笛卡尔网格KS DFT中Becke激子模型的激发能
Excitation energies through Becke's exciton model within a Cartesian-grid KS DFT
摘要：
光子诱导的电子激发在有机生色团中普遍存在。在这种情况下，我们提出了一个简单的，替代的时间无关的DFT程序，计算单粒子激发能，特别是，在光化学的主要兴趣的下界激发单重态。这需要灵感来自最近开发的贝克的激子模型，其中一个关键步骤构成了相关的单重态-三重态分裂能量的准确评估。介绍了一种非经验模型，从“绝热连接定理”和“维里定理”两方面分析了2 e $^-$积分在这类计算中的作用。后一个量被有效地映射到一个真实的网格上，并使用纯数值策略精确计算。说明性的计算进行10 $π$ -电子有机生色团内的笛卡尔网格实施赝势Kohn-Sham（KS）DFT，在我们的实验室开发的，在B3 LYP近似SBKJC型基函数。第一单激发态对应的三重态和单重态激发能与TD-B3 LYP计算结果吻合较好。此外，除了B3 LYP，我们还使用渐近校正的LC-BLYP对一组较大的分子系统进行了相同的计算。与理论最佳估计的系统比较表明，目前的方法在确定光学间隙的可行性和适用性，结合预测精度与适度的计算成本。
英文摘要：
Photon-induced electronic excitations are ubiquitously observed in organic chromophore. In this context, we present a simple, alternative time-independent DFT procedure, for computation of single-particle excitation energies, in particular, the lower bound excited singlet states, which are of primary interest in photochemistry. This takes inspiration from recently developed Becke's exciton model, where a key step constitutes the accurate evaluation of correlated singlet-triplet splitting energy. It introduces a non-empirical model, both from "adiabatic connection theorem" and "virial theorem" to analyze the role of 2e$^-$ integral in such calculations. The latter quantity is efficiently mapped onto a real grid and computed accurately using a purely numerical strategy. Illustrative calculations are performed on 10 $π$-electron organic chromophores within a Cartesian-grid implementation of pseudopotential Kohn-Sham (KS) DFT, developed in our laboratory, taking SBKJC-type basis functions within B3LYP approximation. The triplet and singlet excitation energies corresponding to first singly excited configuration, are found to be in excellent agreement with TD-B3LYP calculations. Further, we perform the same for a set of larger molecular systems using the asymptotically corrected LC-BLYP, in addition to B3LYP. A systematic comparison with theoretical best estimates demonstrates the viability and suitability of current approach in determining optical gaps, combining predictive accuracy with moderate computational cost.
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