Quantum dynamics of multi-dimensional rhodopsin photoisomerization models: Approximate versus accurate treatment of the secondary modes

Abstract

We numerically investigate the quantum dynamics of the high-dimensional rhodopsin photoisomerization models of Hahn and Stock using the multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) method. The original two-state two-mode model is augmented with additional Raman-active modes observed experimentally and by a bath of low frequency modes that accounts in a generic fashion for the effect the protein and solvent environment. A previously used approximate method in which the two primary modes are treated using an accurate quantum dynamical method while the secondary modes are treated using the time-dependent Hartree (TDH) method is tested against ML-MCTDH calculations. It is shown that the former method does not capture the main effect of these modes on the electronic populations, on the coherent torsional dynamics and on the quantum yield of the photoisomerization reaction. Our ML-MCTDH calculations predict small photoisomerization quantum yields, in contradiction with the experiments, and call for a revision of the model.