Permanent dipole moments and energies of excited states from density functional theory compared with coupled cluster predictions: Case of para-nitroaniline

Different ways to extract properties of excited states from time-dependent density functional theory (TD-DFT) calculations are compared to ab initio results obtained with the Equation of Motion Coupled Cluster approach. The recently proposed a posteriori Tamm–Dancoff approximation (ATDA) predicts the permanent dipole moments to be underestimated by 25% on average, close to the results of the relaxed density TD-DFT formalism, quadratic response formalism, and numerical energy derivatives, while the unrelaxed density approximation results are less accurate (40% overestimate). We also propose a correction for TD-DFT excitation energies, which are known to be problematic for charge transfer states. The static DFT energies evaluated on the relaxed densities of the excited states are found to be more accurate than TD-DFT excitation energies (RMSD is 0.7 eV vs. 1.1 eV, while maximum deviation is −1.0 eV vs. −2.0 eV). This validates ATDA for description of nonlinear optical properties of donor–acceptor molecules, exemplified by para-nitroaniline, and extends this method to improve the excitation energy predictions.