Three electronic state model of the primary phototransformation of bacteriorhodopsin

The primary all-trans → 13-cis photoisomerization of retinal in bacteriorhodopsin has been investigated by means of quantum chemical and combined classical/quantum mechanical simulations employing the density matrix evolution method. Ab initio calculations on an analog of a protonated Schiff base of retinal in vacuo reveal two excited states St and S₂, the potential surfaces of which intersect along the reaction coordinate through an avoided crossing, and then exhibit a second, weakly avoided, crossing or a conical intersection with the ground state surface. The dynamics governed by the three potential surfaces, scaled to match the in situ level spacings and represented through analytical functions, are described by a combined classical/quantum mechanical simulation. For a choice of nonadiabatic coupling constants close to the quantum chemistry calculation results, the simulations reproduce the observed photoisomerization quantum yield and predict the time needed to pass the avoided crossing region between S₁ and S₂ states at τ₁ = 330 fs and the S₁ → ground state crossing at τ₂ = 460 fs after light absorption. The first crossing follows after a 30°torsion on a flat S₁ surface, and the second crossing follows after a rapid torsion by a further 60°. τ₁ matches the observed fluorescence lifetime of S₁. Adjusting the three energy levels to the spectral shift of D85N and D212N mutants of bacteriorhodospin changes the crossing region of S₁ and S₂ and leads to an increase in τ₁ by factors 17 and 10, respectively, in qualitative agreement with the observed increase in fluorescent lifetimes.