ARC Centre of Excellence for Free- Radical Chemistry and Biotechnology, Research School of Chemistry, Australian National University, Canberra, 0200 ACT, Australia.
J Chem Theory Comput. 2012 Feb 14;8(2):575-84. doi: 10.1021/ct200768b. Epub 2012 Jan 17.
The applicability of time-dependent density functional theory (TD-DFT) is tested in describing (1)La and (1)Lb π-π* states in indole, azaindole, indene, and benzimidazole. Several density functionals including popular three hybrid functionals (B3LYP, PBE0, and mPW1PW91), two meta-GGA functionals (M06-L and M06-2X), and four long-range corrected (CAM-B3LYP, ωB97XD, LC-BLYP, and LC-ωPBE) density functionals have been considered for the present study. The 6-311+G(2d,p) basis set incorporated with two sets of Rydberg sp functions for carbon and nitrogen atoms is utilized. The range-separation parameters for the calculations with the long-range corrected density functionals were tuned by enforcing the DFT version of Koopmans' theorem, and the effect of this tuning on the accuracy of the results is also examined. Results show that all of the hybrid and meta-GGA functionals predict a wrong order of (1)La and (1)Lb π-π* states in indole and azaindole. Although all of the LC functionals correctly predict that (1)Lb is the lowest excited state in indole, the energy gap calculated between the (1)Lb and (1)La state is much smaller than the value observed in the experimental studies. In the case of azaindole, only LC-ωPBE and LC-BLYP functionals could manage to reproduce the correct order of states; however, here too, the calculated energy gap between the two π-π* states is very small compared to the experimental value. Overall, the (1)Lb state excitation energies derived with all of the functionals are overestimated. In contrast, all of the nine selected functionals correctly reproduce the order of states in indene and benzimidazole. The origin of this differing performance is analyzed. Also in the study, oscillator strengths and dipole moments of the excited states are derived, and two other important states, π-σ* and n-π* states, that could play important role in the photochemistry of these molecules are examined.
时间依赖密度泛函理论（TD-DFT）在描述吲哚、氮杂吲哚、茚和苯并咪唑中的（1）La 和（1）Lb π-π* 态的适用性进行了测试。本研究考虑了几种密度泛函，包括流行的三杂交泛函（B3LYP、PBE0 和 mPW1PW91）、两种 meta-GGA 泛函（M06-L 和 M06-2X）以及四种长程校正（CAM-B3LYP、ωB97XD、LC-BLYP 和 LC-ωPBE）密度泛函。使用了包含两套碳和氮原子的 Rydberg sp 函数的 6-311+G(2d,p) 基组。通过强制执行 DFT 版本的 Koopmans 定理来调整长程校正密度泛函计算的范围分离参数，并检查了这种调整对结果准确性的影响。结果表明，所有混合和 meta-GGA 泛函都预测了吲哚和氮杂吲哚中（1）La 和（1）Lb π-π* 态的错误顺序。尽管所有 LC 泛函都正确预测了（1）Lb 是吲哚中最低激发态，但计算得出的（1）Lb 和（1）La 态之间的能隙比实验研究中观察到的值小得多。在氮杂吲哚的情况下，只有 LC-ωPBE 和 LC-BLYP 泛函能够正确地再现状态的顺序；然而，在这里，两个 π-π* 态之间的计算能隙也与实验值相比非常小。总体而言，所有泛函得出的（1）Lb 态激发能都被高估了。相比之下，所有九种选定的泛函都正确地再现了茚和苯并咪唑中的状态顺序。分析了这种不同性能的原因。此外，在研究中还推导了激发态的振子强度和偶极矩，并研究了另外两个重要的态，π-σ* 和 n-π* 态，它们可能在这些分子的光化学中发挥重要作用。
