Nature of the surface crossing process in bacteriorhodopsin: Computer simulations of the quantum dynamics of the primary photochemical event

The quantum dynamics of the primary photoisomerization event in bacteriorho dopsin is studied by a semiclassical trajectory approach. The relevant surf ace crossing probability is evaluated from the wave functions and potential surfaces of a hybrid quantum mechanical/molecular mechanics (QM/MM) Hamilt onian of the complete chromophore-protein-solvent system. The QM/MM model c ombines consistently the quantum mechanical Hamiltonian of the chromophore with the microscopic electric field of the ionized groups and induced dipol es of the protein-solvent system. The QCFF/PI Hamiltonian of the chromophor e is adjusted to reproduce relevant ab initio results. The nonadiabatic cou pling term < psi (1)/partial derivative psi (0)/partial derivativet > calcu lated numerically from the corresponding wave functions. The simulations ar e performed by combining the ENZYMIX and QCFF/PI molecular modeling program s. The effect of the protein on the absorption spectrum of the chromophore is examined. It is found that this spectrum reflects the effect of the prot ein permanent dipoles, ionized residues, water molecules (in and around the protein), and the induced dipoles of the protein plus water system. Next, we probe the motion along the excited state surface. It is demonstrated, in agreement with our early study and more recent works, that the motion star ts with bond vibrations and evolves to a torsional motion. It is also found that we are dealing with an overdumped motion. Major emphasis is placed on the nature of the surface crossing process. In particular, we try to exami ne the origin of the very large probability of crossing in the pi /2 region . A large crossing probability was obtained first in our early simulation ( Warshel, A. Nature 1976, 260, 679), but its origin was not explored in deta ils. Such large crossing probabilities can be obtained by passing through s trict conical intersections (where the, two surfaces "touch" each other) or by passing through regions with large nonadiabatic coupling and small ener gy gap (such regions are usually close to conical intersections). It is fou nd that some trajectories pass through strict conical intersections whereas others cross through regions with nonzero energy gap and a large nonadiaba tic coupling. This feature helps probably to ensure the stability of the ph otobiological process with regards to various mutations. The average surfac e crossing probability and our previously derived expression (Weiss, R. M.; Warshel, A. J. Am. Chem. Soc. 1979, 101, 6131) appear to provide an excell ent approximation for the calculated quantum yield. Furthermore, the calcul ated quantum yield reproduces the corresponding observed value. finally, we examine the behavior of trajectories that cross to the ground state before the pi /2 region. Our finding that these trajectories are deflected backwa rd allow us to exclude models where the surface crossing occurs before the pi /2 region.