Laboratoire de Chimie Théorique Appliquée, Groupe de Chimie-Physique Théorique et Structurale, Facultés Universitaires Notre-Dame de la Paix, rue de Bruxelles, 61, B-5000 Namur, Belgium, Department of Chemistry, Rice University, Houston, Texas 77005, and Ecole Nationale Supérieure de Chimie de Paris, Laboratoire Electrochimie et Chimie Analytique, UMR CNRS-ENSCP no. 7575, 11, rue Pierre et Marie Curie, F-75321 Paris Cedex 05, France.
J Chem Theory Comput. 2008 Jan;4(1):123-35. doi: 10.1021/ct700187z.
The π → π* transitions of more than 100 organic dyes from the major classes of chromophores (quinones, diazo, ...) have been investigated using a Time-Dependent Density Functional Theory (TD-DFT) procedure relying on large atomic basis sets and the systematic modeling of solvent effects. These calculations have been performed with pure (PBE) as well as conventional (PBE0) and long-range (LR) corrected hybrid functionals (LC-PBE, LC-ωPBE, and CAM-B3LYP). The computed wavelengths are systematically guided by the percentage of exact exchange included at intermediate interelectronic distance, i.e., the λmax value always follows the PBE > PBE0 > CAM-B3LYP > LC-PBE > LC-ωPBE > HF sequence. The functional giving the best estimates of the experimental transition energies may vary, but PBE0 and CAM-B3LYP tend to outperform all other approaches. The latter functional is shown to be especially adequate to treat molecules with delocalized excited states. The mean absolute error provided by PBE0 is 22 nm (0.14 eV) with no deviation exceeding 100 nm (0.50 eV): PBE0 is able to deliver reasonable estimates of the color of most organic dyes of practical or industrial interest. By using a calibration curve, we found that the LR functionals systematically allow an even more consistent description of the low-lying excited-state energies than the conventional hybrids. Indeed, linearly corrected LR approaches yield an average error of 10 nm for each dye family. Therefore, when such statistical treatments can be designed for given sets of dyes, a simple and rapid theoretical procedure allows both a chemically sound and a numerically accurate description of the absorption wavelengths.
超过 100 种有机染料的π→π*跃迁，这些染料来自主要发色团（醌、重氮、...），已经使用基于大原子基组和溶剂效应系统建模的时间相关密度泛函理论（TD-DFT）程序进行了研究。这些计算是使用纯（PBE）以及常规（PBE0）和长程（LR）校正混合泛函（LC-PBE、LC-ωPBE 和 CAM-B3LYP）进行的。计算的波长系统地由中间电子距离处包含的精确交换百分比指导，即 λmax 值始终遵循 PBE>PBE0>CAM-B3LYP>LC-PBE>LC-ωPBE>HF 序列。给出实验跃迁能量最佳估计的函数可能会有所不同，但 PBE0 和 CAM-B3LYP 往往优于所有其他方法。后者功能特别适合处理具有离域激发态的分子。PBE0 提供的平均绝对误差为 22nm（0.14eV），没有超过 100nm（0.50eV）的偏差：PBE0 能够合理估计大多数具有实际或工业意义的有机染料的颜色。通过使用校准曲线，我们发现 LR 函数甚至比常规混合更能一致地描述低能激发态能量。实际上，线性校正 LR 方法使每种染料家族的平均误差为 10nm。因此，当可以为给定的染料集设计这种统计处理时，简单而快速的理论程序可以对吸收波长进行化学合理且数值准确的描述。
