Plötner Jürgen, Tozer David J, Dreuw Andreas
Institute of Physical and Theoretical Chemistry, Goethe-University Frankfurt, Max von Laue-Strasse 7, 60438 Frankfurt, Germany, and Department of Chemistry, University of Durham, South Road, Durham DH1 3LE, United Kingdom.
J Chem Theory Comput. 2010 Aug 10;6(8):2315-24. doi: 10.1021/ct1001973.
Time-dependent density functional theory (TDDFT) with standard GGA or hybrid exchange-correlation functionals is not capable of describing the potential energy surface of the S1 state of Pigment Yellow 101 correctly; an additional local minimum is observed at a twisted geometry with substantial charge transfer (CT) character. To investigate the influence of nonlocal exact orbital (Hartree-Fock) exchange on the shape of the potential energy surface of the S1 state in detail, it has been computed along the twisting coordinate employing the standard BP86, B3LYP, and BHLYP xc-functionals as well as the long-range separated (LRS) exchange-correlation (xc)-functionals LC-BOP, ωB97X, ωPBE, and CAM-B3LYP and compared to RI-CC2 benchmark results. Additionally, a recently suggested Λ-parameter has been employed that measures the amount of CT in an excited state by calculating the spatial overlap of the occupied and virtual molecular orbitals involved in the transition. Here, the error in the calculated S1 potential energy curves at BP86, B3LYP, and BHLYP can be clearly related to the Λ-parameter, i.e., to the extent of charge transfer. Additionally, it is demonstrated that the CT problem is largely alleviated when the BHLYP xc-functional is employed, although it still exhibits a weak tendency to underestimate the energy of CT states. The situation improves drastically when LRS-functionals are employed within TDDFT excited state calculations. All tested LRS-functionals give qualitatively the correct potential energy curves of the energetically lowest excited states of P. Y. 101 along the twisting coordinate. While LC-BOP and ωB97X overcorrect the CT problem and now tend to give too large excitation energies compared to other non-CT states, ωPBE and CAM-B3LYP are in excellent agreement with the RI-CC2 results, with respect to both the correct shape of the potential energy curve as well as the absolute values of the calculated excitation energies.
采用标准广义梯度近似（GGA）或杂化交换相关泛函的含时密度泛函理论（TDDFT）无法正确描述颜料黄101的S1态势能面；在具有大量电荷转移（CT）特征的扭曲几何结构处观察到一个额外的局部最小值。为了详细研究非局部精确轨道（哈特里 - 福克）交换对S1态势能面形状的影响，沿着扭曲坐标计算了采用标准BP86、B3LYP和BHLYP交换相关泛函以及长程分离（LRS）交换相关（xc）泛函LC - BOP、ωB97X、ωPBE和CAM - B3LYP的情况，并与RI - CC2基准结果进行了比较。此外，还采用了最近提出的Λ参数，该参数通过计算跃迁中占据和虚拟分子轨道的空间重叠来测量激发态中的电荷转移量。在此，BP86、B3LYP和BHLYP计算的S1势能曲线中的误差与Λ参数明显相关，即与电荷转移程度相关。此外，结果表明，尽管采用BHLYP交换相关泛函时仍有轻微低估CT态能量的趋势，但电荷转移问题在很大程度上得到了缓解。当在TDDFT激发态计算中采用LRS泛函时，情况有了显著改善。所有测试的LRS泛函在沿着扭曲坐标的情况下，定性地给出了颜料黄101能量最低激发态的正确势能曲线。虽然LC - BOP和ωB97X过度校正了电荷转移问题，与其他非CT态相比现在往往给出过大的激发能，但ωPBE和CAM - B3LYP在势能曲线形状以及计算的激发能绝对值方面都与RI - CC2结果非常吻合。
