Benchmarking density functional approximations in nonadiabatic dynamics: trans-cis isomerization in retinal model

An exhaustive benchmark of density functional approximations (DFAs) for nonadiabatic dynamics is reported on the trans-cis photoisomerization of the protonated Schiff base 3 (PSB3), which presents numerous challenges for time-dependent density functional theory (TD-DFT). We introduce a rigorous protocol for benchmarking DFAs for nonadiabatic dynamics regarding the initialization, the dynamics, and its evaluation. Different families of DFAs were compared with a high-level reference, highlighting that electronic populations are an unsuitable metric for evaluating the accuracy of dynamics. We found that several local functionals showed the best agreement of the population decay with the reference RMS-CASPT2, but strictly passed through a deactivation channel dominated by a single-bond torsion that is not accessible in the reference and in the literature. While using 100% Hartree-Fock exchange in the functional yields the only correct isomerization behaviour, the time scales and quantum yields are far off the reference values, due to an artificial local minimum being predicted along the wrong torsion coordinate. Static energy scans suggest that this issue can be circumvented by double hybrid functionals, in particular those balancing nonlocal exchange and correlation combined with range-separation. Indeed, they predict energy profiles along the two torsion coordinates in close agreement with the RMS-CASPT2 reference. This emphasizes the impact these DFAs will have on the field of nonadiabatic dynamics once analytical gradients are introduced.