Analytical Energy Gradients of Coulomb-Attenuated Time-Dependent Density Functional Methods for Excited States

We present an implementation and validation of the analytical energy gradient of time-dependent density functional theory (TDDFT) using Coulomb-attenuated (CA) functionals for excited state energies, dipole moments, geometries, and vibrational frequencies. The CA-TDDFT gradient is based on the previous long-range corrected TDDFT of (Chiba et al. J Chem Phys 2006, 124, 144106) and the Z-vector formalism of (Furche and Ahlrichs J Chem Phys 2002, 117, 7433). Geometry optimization using CA-TDDFT was carried out for molecules (substituted stilbenes and coumarins) having intramolecular charge-transfer excited states and for a series of small molecules (CO, HCN, CH2O, CH2S, CCl2, C2H2, trans-(CHO)(2)). We assess the results of the CA functionals, the long-range corrected LC-BLYP functional, and the B3LYP hybrid functional, by comparing to accurate experimental data. The results highlight the applicabilty of different functionals for excited state properties. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110:2247-2255, 2010