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J. Phys. Chem. B 2007, 111, 3782-3788
Photochemistry of Visual Pigment Chromophore Models by Ab Initio Molecular Dynamics Oliver Weingart, Igor Schapiro, and Volker Buss* Department of Chemistry, UniVersity of Duisburg-Essen, 47048 Duisburg, Germany ReceiVed: December 4, 2006; In Final Form: February 6, 2007
Ab initio excited-state molecular dynamics calculations have been performed to study the effect of methyl substitution and chromophore distortion on the photoreaction of different four-double-bond retinal model chromophores. Randomly distributed starting geometries were generated by zero-point energy sampling; after Franck-Condon excitation the reaction was followed on the S1 surface. For determining the photoproduct and its configuration, a simplified approachstorsion angle followingsis discussed and applied. We find that chromophore distortion significantly affects the outcome of the photoreaction: with dihedral angles taken from the rhodopsin-embedded 11-cis-retinal chromophore, the reaction rate of the model chromophore is increased by a factor of 3 compared to that of the relaxed chromophore. Also, the reaction proceeds in a completely stereoselective manner involving only the cis double bond and with a minimum quantum yield of 72%. Bond torsion is more effective than methyl substitution for fast and selective photochemistry, which is in agreement with photophysical measurements on rhodopsin analogues. We conclude that apart from the geometric distortions caused by the protein pocket it is not necessary to postulate other specific interactions between the protein and the chromophore to effect the selective and ultrafast photoreaction in rhodopsin.
Introduction Rhodopsin is the membrane-bound protein in the rod cells of the vertebrate retina which mediates the transformation of light into vision: photons of 500 nm induce the isomerization of the chromophore of rhodopsin, 11-cis-retinal protonated Schiff base (pSb), to all-trans, forming the first intermediate of the rhodopsin visual cycle, bathorhodopsin.1 The energy captured in the photoreactionsabout 35 kcal‚mol-1sis used to drive the subsequent dark reactions toward formation of the signaling state which starts the self-amplifying visual cascade and eventually leads to excitation of the visual nerve.2,3 The photoreaction of rhodopsin is ultrafast, highly efficient, and very selective.4 Bathorhodopsin is formed within 200 fs with a quantum yield of 0.67, and according to the X-ray structure5 only the C11dC12 bond is affected, leaving the chromophore in an extended though significantly twisted conformation. In solution, retinal pSb’s behave completely different toward light: the reaction rate is reduced6,7 and is not stereoselective, giving a mixture of isomers instead.8,9 It is generally accepted, therefore, that there must exist specific interactions of the chromophore with the protein binding pocket which are responsible for the unique photoreaction. The rhodopsin photoreaction has been the subject of several theoretical studies in which minimum energy path (MEP) calculations were performed on bare model chromophores with three10 and four double bonds.11 The major finding of these studiessthat rotation of the cis double bond is preceded by activation of a bond stretching coordinate which moves the molecule fast out of the Franck-Condon region toward a region of surface crossing (conical intersection)swas confirmed in later studies on the complete chromophore within the binding pocket.12,13 Two of the present authors were involved in an effort to characterize in more detail the topology of the intersection * To whom correspondence should be addressed. E-mail: Volker.Buss@ uni-due.de.
space between the S0 and S1 surfaces of the three-double-bond (Z)-pentadieniminium model chromophore14,15 by ab initio molecular dynamics (MD). Starting with a large number of independently generated geometries, trajectories were calculated on the basis of CASSCF potential energy surfaces taking into account the full set of vibrational degrees of freedom. According to the statistics, the grand majority of the reactions (92%) involved rotation of the central double bond, leading in more than 80% to successful Z-E isomerization. The average time to reach the surface hopping region was 80 fs; in other words, the vacuum photoreaction was highly selective and very fast. To probe how a distortion of the kind observed in the rhodopsin chromophore would affect the outcome of the reaction, a second study was performed16 which showed that pretwisting the chromophore increased significantly the reaction rate and the quantum yield, which clearly demonstrated the importance of nonplanar distortions on the selectivity of the photoreaction. However, whether these results can be transferred to the photochemistry of rhodopsin is still questionable. With only three double bonds in the molecule, the number of isomerization sites is limited and there appears to be an inherent tendency of the model to rotate about the central bond. While these studies agree that fast photoisomerization in the 100 fs range is possible without any explicit assistance by the protein, they do not rule out the possibility that the high selectivity for isomerization of the C11dC12 bond in the rhodopsin chromophore is brought about by electrostatic effects, as has been suggested in recent work.17-19 To deal with these questions, we have extended the chromophore by an additional double bond to a four-doublebond model and studied four structures mimicking the retinal segment from C9 to N16 of 11-cis-retinal and two retinal analogues (Scheme 1). In 1 and 2, the methyl substitution is the same as in rhodopsin; however, 1 is planar, while 2 has the twisted geometry found in the protein. Models 3 and 4, in which the methyl group is moved from C4 to C7 or is omitted altogether, will be discussed in connection with two retinal
10.1021/jp0683216 CCC: $37.00 © 2007 American Chemical Society Published on Web 03/23/2007
Photochemistry of Visual Pigment Chromophore Models
J. Phys. Chem. B, Vol. 111, No. 14, 2007 3783
SCHEME 1
Figure 1. Relationship between the phase of the HOOP mode of a cis double bond and the configuration of the photoproduct. The reaction is unproductive when at the decay point the H-CdC-H angle decreases (a). When this angle increases, the trans configuration is obtained (b).
analogues, 13-demethyl-10-methyl- and 13-demethylretinal, whose photochemistry in rhodopsin has been studied in the groups of Ga¨rtner20,21 and Lugtenburg and Mathies.22,23 For each of the four model chromophores, ensembles of trajectories with randomly assigned starting conditions were generated and analyzed. On the basis of these data, the effect of chromophore distortion and methyl substitution on the selectivity and effectivity of the photoreaction will be discussed. Methods Calculations of the dynamics of electronically excited molecules, especially the treatment of surface hopping events, present a grand challenge to computational chemistry. Current trajectory surface hopping (TSH) algorithms include the calculation of the time-dependent (TD) wave function along with trajectory propagation, to define at every step of the simulation the state in which the system resides.24,25 In regions of strong nonadiabatic coupling or very small energy differences, the state probabilities may oscillate rapidly. This requires integration over short time steps,26,27 leading to computation times of up to several months for only one trajectory. Such algorithms cannot be efficiently applied to polyenic systems involving more than three double bonds. A different approach is followed in the socalled ab initio multiple spawning (AIMS) method, where the nuclei are described fully quantum mechanically.28 In this study we have adopted a simple and effective method to locate possible decay points which is based on the analysis of the configuration-interaction (CI) vectors during an MD simulation.29 These vectors, which hold the CI coefficients of the two particular electronic states, change only slowly in regions far away from surface crossings. An abrupt change of their composition in the vicinity of a surface crossing indicates a reordering of ground- and excited-state determinants. This can be interpreted as a nearly diabatic changeover to the lower state. The method will, however, always underestimate the true quantum yield of a photoreaction, because surface hops are generally possible earlier and at higher S0/S1 state energy differences. In a study of the pentadieniminium cation,14 where we have used a more sophisticated time-dependent surface hopping scheme, we found that surface hops can occur before the surfaces actually cross, even at values as high as 13 kcal‚mol-1. The importance of surface hops involving nonzero energy gaps has been underlined in a recent review.30 At a true surface crossing, however, the hopping probability becomes equal to one and the molecule will definitely pass to the lower surface at this point.
Both assumptions, that all molecules of a molecular ensemble decay to the ground state at the first approach below a certain threshold or that they pass over only near a surface intersection, will lead to an unbalanced though defined description of the reaction. They will also result in different product ratios, as we have shown in the cited work:16 the highest quantum yield was found when hopping occurred at the first close approach, while the yield dropped significantly when the molecules were allowed to hop only in the close vicinity of a surface crossing. These values correspond, accordingly, to the upper and the lower bounds of the calculated quantum yield of the reaction, and they will be quoted as such in the Results. In the simulations the quantum yields are determined as follows: For the lower bound the trajectories are propagated in the excited state until the CI vectors of two subsequent MD steps indicate a hop in the vicinity of a surface crossing.29 A hop to the ground state is induced when the scalar products deviate by more than 0.25 from orthonormality. The reactions are then allowed to continue on the ground-state surface until the configuration of the photoproduct can be determined unambiguously. For the upper bound of the quantum yield we locate the first minimum of the S1/S0 energy difference below 13 kcal-1. Then the configuration of the photoproduct to be expected from this hop is determined by inspecting the hydrogen out-of-plane (HOOP) bending mode of the isomerizing double bond at the moment of hop15,16 (Figure 1): Starting from a cisconfigurated double bond, a decrease of the H-CdC-H torsion angle at the point of decay will always be unproductive and return the molecule back to the starting product, while an increasing H-CdC-H angle will lead to the trans product. For a trans configuration the opposite holds true: a decreasing H-CdC-H angle indicates formation of the cis product, while an increasing angle regenerates the trans educt. This rule has been derived from a large number of trajectories of protonated Schiff base chromophores and is almost without exception. It shows that it is not the torsion of the carbon chain that determines the configuration of the resulting photoproduct, but the large amplitude motion of the hydrogen atoms. This can be demonstrated nicely by removing the kinetic energy of the molecule at the point of hopping. At low carbon torsion angles (
