Goerigk Lars, Moellmann Jonas, Grimme Stefan
Theoretische Organische Chemie, Organisch-Chemisches Institut der Universität Münster, Corrensstrasse 40, D-48149, Münster, Germany.
Phys Chem Chem Phys. 2009 Jun 14;11(22):4611-20. doi: 10.1039/b902315a. Epub 2009 Mar 23.
Time-dependent double-hybrid density functional methods are evaluated for the calculation of vertical singlet-singlet valence excitation energies of a wide variety of organic molecules. Beside the already published TD-B2-PLYP method, an analogous approach based on the recently published ground state B2GP-PLYP functional is presented for the first time. Double-hybrid functionals contain a hybrid-GGA-like part for which a conventional TDDFT linear response treatment is carried out. The thus obtained excitation energies are afterwards corrected by adding a non-local correlation portion, which is based on an CIS(D) type excited state perturbative correction. Both, TD-B2-PLYP and TD-B2GP-PLYP, are first applied to the 142 vertical singlet excitation energies in a benchmark set by Schreiber et al., that contains small and medium sized organic molecules. In a second part, a new benchmark set composed of five large organic dyes is proposed. Accurate reference values are derived from experimental 0-0 excitation energies in solution. A back-correction scheme based on TDDFT computations is presented by which solvent, relaxation and vibrational effects are removed, yielding experimental vertical gas phase excitation energies with an estimated accuracy of about +/-0.1 eV. The TD-B2-PLYP, TD-B2GP-PLYP and a variety of conventional TDDFT methods are then applied to this new benchmark set. The results for both considered test sets show that the new double-hybrid approaches yield the smallest mean absolute deviations of 0.22 eV for the first benchmark set and 0.19 eV (TD-B2-PLYP) and 0.16 eV (TD-B2GP-PLYP) for the new organic dye test set. Apart from a break-down of the perturbative correction for very high-lying transitions (larger than 8 eV), it is generally found that the double-hybrid functionals show high robustness and accuracy that cannot be obtained with conventional density functionals (e.g. B3-LYP).
对含时双杂化密度泛函方法进行了评估，以计算各种有机分子的垂直单重态 - 单重态价激发能。除了已发表的TD - B2 - PLYP方法外，首次提出了一种基于最近发表的基态B2GP - PLYP泛函的类似方法。双杂化泛函包含一个类似杂化广义梯度近似（hybrid - GGA）的部分，对其进行常规的含时密度泛函理论（TDDFT）线性响应处理。然后通过添加基于耦合簇单双激发（CIS(D)）型激发态微扰校正的非局部相关部分来校正由此获得的激发能。TD - B2 - PLYP和TD - B2GP - PLYP首先应用于Schreiber等人的基准集中的142个垂直单重态激发能，该基准集包含中小尺寸有机分子。在第二部分中，提出了一个由五种大型有机染料组成的新基准集。准确的参考值源自溶液中的实验0 - 0激发能。提出了一种基于TDDFT计算的反校正方案，通过该方案消除溶剂、弛豫和振动效应，得到估计精度约为±0.1 eV的实验垂直气相激发能。然后将TD - B2 - PLYP、TD - B2GP - PLYP和各种传统的TDDFT方法应用于这个新基准集。两个考虑的测试集的结果表明，新的双杂化方法对于第一个基准集产生的最小平均绝对偏差为0.22 eV，对于新的有机染料测试集产生的最小平均绝对偏差为0.19 eV（TD - B2 - PLYP）和0.16 eV（TD - B2GP - PLYP）。除了对于非常高激发态跃迁（大于8 eV）微扰校正失效外，一般发现双杂化泛函表现出高稳健性和准确性，这是传统密度泛函（如B3 - LYP）无法获得的。
