Fluorescent Rhodopsins: a challenging test for cost-effective QM/MM approaches

In this study, we evaluate the performance of two cost-effective models, namely TD-DFT and ∆SCF methods, combined with different Molecular Mechanics models, to predict photophysical and photochemical properties of a set of fluorescent mutants of the microbial rhodopsin Archaerhodopsin3. We investigate absorption energies and excited state isomerization barriers of the embedded retinal protonated Schiff-base chromophore by comparing different DFT functionals as well as different approximations of the embedding model. For absorption energies, CAM-B3LYP demonstrates the most consistent alignment with experiments among the functionals tested whereas the embedding potentials exhibit similar accuracy. However, incorporating linear response corrections within the polarizable TD-DFT/MM framework enhances accuracy. The photoisomerization barriers, instead, exhibit a pronounced sensitivity to the choice of embedding model, underscoring the complex role that environmental factors play in modulating predictions of excited-state processes. For the two properties here investigated, ∆SCF/MM presents a qualitatively similar behavior with respect to TD-DFT for all the tested embedding models.