Peach Michael J G, Le Sueur C Ruth, Ruud Kenneth, Guillaume Maxime, Tozer David J
Department of Chemistry, University of Durham, South Road, Durham, UK DH1 3LE.
Phys Chem Chem Phys. 2009 Jun 14;11(22):4465-70. doi: 10.1039/b822941d. Epub 2009 Mar 3.
A simple diagnostic test based on orbital overlap [M. J. G. Peach et al., J. Chem. Phys., 2008, 128, 044118] may be used to help judge the reliability of excitation energies in time-dependent density functional theory (TDDFT) when using generalized gradient approximation (GGA) and hybrid functionals. Orbital plots are used to illustrate the test for a model tripeptide and for 4-(N,N-dimethylamino)benzonitrile, which are representative of systems containing low- and high-overlap charge-transfer excitations. The scheme is then applied to a series of triazene chromophores in solvent, highlighting the relationship between overlap and oscillator strength and its implications for theoretical absorption spectra. No low-overlap excitations are observed with a hybrid functional; a single one is identified using a GGA. To assess the diagnostic test and to judge functional performance, gas phase triazene TDDFT excitations are compared with correlated ab initio values. The diagnostic test correctly identifies two low-overlap problematic GGA excitations. However, it does not identify another problematic excitation where the electron is excited to a spatially extended orbital, which necessarily has reasonable overlap with the occupied orbital; an improved diagnostic quantity is required for such cases. The best agreement between TDDFT and correlated ab initio excitations is obtained using a Coulomb-attenuated functional; the errors are significantly smaller than from the GGA and hybrid functionals. The study provides further support for the high quality excitations from Coulomb-attenuated functionals, negating the need for diagnostic tests.
一种基于轨道重叠的简单诊断测试方法[M. J. G. Peach等人，《化学物理杂志》，2008年，128卷，044118期]可用于在使用广义梯度近似（GGA）和杂化泛函时，帮助判断含时密度泛函理论（TDDFT）中激发能的可靠性。轨道图用于说明对一种模型三肽和4-（N，N-二甲基氨基）苯甲腈的测试，它们分别代表含有低重叠和高重叠电荷转移激发的体系。然后将该方案应用于一系列溶剂中的三氮烯发色团，突出了重叠与振子强度之间的关系及其对理论吸收光谱的影响。使用杂化泛函未观察到低重叠激发；使用GGA识别出了一个。为了评估诊断测试并判断泛函性能，将气相三氮烯TDDFT激发与相关的从头算值进行了比较。诊断测试正确识别出两个低重叠的有问题的GGA激发。然而，它没有识别出另一个有问题的激发，即电子被激发到一个空间扩展的轨道，该轨道必然与占据轨道有合理的重叠；对于这种情况，需要一个改进的诊断量。使用库仑衰减泛函可获得TDDFT与相关从头算激发之间的最佳一致性；误差明显小于GGA和杂化泛函。该研究为库仑衰减泛函的高质量激发提供了进一步支持，不再需要诊断测试。
