Benchmarking TD-DFT and Wave Function Methods for Oscillator Strengths and Excited-State Dipole Moments

Using a set of oscillator strengths and excited-state dipole moments of near full configuration interaction quality determined for small compounds, we benchmark the performances of several single-reference wave function methods CC2, CCSD, CC3, CCSDT, ADC(2), and ADC(3/2) and time-dependent density-functional theory (TD-DFT) with various functionals (B3LYP, PBE0, M06-2X, CAM-B3LYP, and ωB97X-D). We consider the impact of various gauges (length, velocity, and mixed) and formalisms: equation of motion versus linear response, relaxed versus unrelaxed orbitals, and so forth. Beyond the expected accuracy improvements and a neat decrease of formalism sensitivity when using higher-order wave function methods, the present contribution shows that, for both ADC(2) and CC2, the choice of gauge impacts more significantly the magnitude of the oscillator strengths than the choice of formalism and that CCSD yields a notable improvement on this transition property as compared to CC2. For the excited-state dipole moments, switching on orbital relaxation appreciably improves the accuracy of both ADC(2) and CC2 but has a rather small effect at the CCSD level. Going from ground to excited states, the typical errors on dipole moments for a given method tend to roughly triple. Interestingly, the ADC(3/2) oscillator strengths and dipoles are significantly more accurate than their ADC(2) counterparts, whereas the two models do deliver rather similar absolute errors for transition energies. Concerning TD-DFT, one finds: (i) a rather negligible impact of the gauge on oscillator strengths for all tested functionals (except for M06-2X); (ii) deviations of ca. 0.10 D on ground-state dipoles for all functionals; (iii) strong differences between excited-state dipoles obtained with, on the one hand, B3LYP and PBE0 and, on the other hand, M06-2X, CAM-B3LYP, and ωB97X-D, the latter group being markedly more accurate with the selected basis set; and (iv) the better overall performance of CAM-B3LYP for the two considered excited-state properties. Finally, for all investigated properties, both the accuracy and consistency obtained with the second-order wave function approaches, ADC(2) and CC2, do not clearly outperform those of TD-DFT, hinting that assessing the accuracy of the latter (or selecting a specific functional) on the basis of the results of the former is not systematically a well-settled strategy.