TDDFT diagnostic testing and functional assessment for triazene chromophores

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.