How Accurate Are TD-DFT Excited-state Geometries Compared to DFT Ground-state Geometries?

In this work, we take a different angle to the benchmarking of time-dependent density functional theory (TD-DFT) for the calculation of excited-state geometries by extensively assessing how accurate such geometries are compared to ground-state geometries calculated with ordinary DFT. To this end, we consider 20 medium-sized aromatic organic compounds whose lowest singlet excited states are ideally suited for TD-DFT modeling and are very well described by the approximate coupled-cluster singles and doubles (CC2) method, and then use this method and six different density functionals (BP86, B3LYP, PBE0, M06-2X, CAM-B3LYP, and ωB97XD) to optimize the corresponding ground- and excited-state geometries. The results show that although each hybrid functional reproduces the CC2 excited-state bond lengths very satisfactorily, achieving an overall root mean square error of 0.011 Å for all 336 bonds in the 20 molecules, these errors are distinctly larger than those of only 0.004-0.006 Å with which the hybrid functionals reproduce the CC2 ground-state bond lengths. Furthermore, for each functional employed, the variation in the error relative to CC2 between different molecules is found to be much larger (by at least a factor of 3) for the excited-state geometries than for the ground-state geometries, despite the fact that the molecules/states under investigation have rather uniform chemical and spectroscopic character. Overall, the study finds that even in favorable circumstances, TD-DFT excited-state geometries appear intrinsically and comparatively less accurate than DFT ground-state ones.