Tracking the excited-state time evolution of thevisual pigment with multiconfigurationalquantum chemistryLuis Manuel Frutos†, Tadeusz Andruniow‡, Fabrizio Santoro§, Nicolas Ferre¶, and Massimo Olivucci†�††

†Dipartimento di Chimica, Universita di Siena, via Aldo Moro 2, I-53100 Siena, Italy; �Department of Chemistry, Bowling Green State University,Bowling Green, OH 43403; ‡Institute of Physical and Theoretical Chemistry, Department of Chemistry, Wroclaw University of Technology, 27 Wyb.Wyspianskiego, 50-370, Wroclaw, Poland; §Istituto per i Processi Chimico-Fisici, Consiglio Nazionale delle Ricerche, Via Moruzzi 1, I-56124 Pisa,Italy; and ¶Laboratoire de Chimie Theorique et de Modelisation Moleculaire, Unite Mixte de Recherche 6517, Centre National de la RechercheScientifique, Universite de Provence, Case 521, Faculte de Saint-Jerome, Avenue Esc. Normandie Niemen, 13397 Marseille Cedex 20, France

Edited by Ernest R. Davidson, University of Washington, Seattle, WA, and approved March 8, 2007 (received for review February 25, 2007)

The primary event that initiates vision is the photoinduced isomer-ization of retinal in the visual pigment rhodopsin (Rh). Here, we usea scaled quantum mechanics/molecular mechanics potential thatreproduces the isomerization path determined with multiconfigu-rational perturbation theory to follow the excited-state evolutionof bovine Rh. The analysis of a 140-fs trajectory provides a de-scription of the electronic and geometrical changes that preparethe system for decay to the ground state. The data uncover acomplex change of the retinal backbone that, at �60-fs delay,initiates a space saving ‘‘asynchronous bicycle-pedal or crankshaft’’motion, leading to a conical intersection on a 110-fs time scale. Itis shown that the twisted structure achieved at decay features amomentum that provides a natural route toward the photoRhstructure recently resolved by using femtosecond-stimulated Ra-man spectroscopy.

photoisomerization � rhodopsin � vision

The visual pigment rhodopsin (Rh) (1, 2) is a G protein-coupledreceptor containing a 11-cis retinal chromophore (PSB11)

bounded to a lysine residue (Lys-296) via a protonated Schiff baselinkage (see Fig. 1). While the biological activity of Rh is triggeredby the light-induced 11-cis all-trans isomerization of PSB11, thisreaction owes its efficiency (e.g., short time scale and high quantumyields) to the protein cavity (1). Recently, the mechanism of theisomerization of retinal in Rh has been investigated by usingfemtosecond-stimulated Raman spectroscopy (FSRS) (3). Kukuraet al. (3) have reported on experimentally derived structures ofphotoRh and bathoRh, namely the first and second ground-stateintermediates of the Rh photocycle.

While such progress has provided information on the struc-tural changes achieved 200 fs after light absorption, the fasterstructural changes prompting the excited-state decay of PSB11(i.e., the central event of the isomerization mechanism) remainto be established. Indeed, it has been suggested that such decaymay occur on a 60-fs time scale through fast hydrogen out-of-plane (HOOP) motion (3), whereas the traditional view pointsto a slower �150-fs decay driven by cis–trans isomerizationmotion (4). In principle, molecular dynamics simulations fea-turing a quantum chemical description of the chromophore canbe used to address such issues. This fact was shown by Warshel(5) using semiempirical quantum chemistry to describe PSB11and geometrical constraints to account for the protein environ-ment. Later, Birge and Hubbard (6) reported a differentsemiempirical study of an explicit chromophore–counterion pairevolving along a single coordinate. While the first simulation ofthe retinal photoisomerization using a full atomic-level proteinmodel (7) was reported for the related receptor bacterio-Rh(bR), attempts to simulate the PSB11 excited-state motion in acomplete Rh model are more recent (8–10). On the other hand,a quantitative evaluation of the isomerization coordinate and

time scale requires, as a prerequisite, an accurate excited-stateforce field for PSB11 in Rh.

The ab initio (i.e., first-principles) complete-active-space self-consistent-field (CASSCF) method (11) is a multiconfigura-tional method offering maximum flexibility for the unbiaseddescription of the electronic and equilibrium structure of amolecule (i.e., with no empirically derived parameters andavoiding single-reference wavefunctions). Furthermore, theCASSCF wavefunction can be used for subsequent multicon-figurational second-order perturbation theory (CASPT2) (12)computations of the dynamic correlation energy of each state,ultimately leading to a quantitative evaluation of the excitationenergies and excited-state energy differences. Recently, we (13)

Author contributions: L.M.F., F.S., N.F., and M.O. designed research; L.M.F., T.A., F.S., andN.F. performed research; L.M.F., T.A., F.S., and M.O. analyzed data; and M.O. wrote thepaper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Abbreviations: Rh, rhodopsin; bR, bacterio-Rh; FSRS, femtosecond-stimulated Raman spec-troscopy; HOOP, hydrogen out-of-plane; CASSCF, complete-active-space self-consistent-field; CASPT2, multiconfigurational second-order perturbation theory.

††To whom correspondence should be addressed. E-mail: olivucci@unisi.it.

This article contains supporting information online at www.pnas.org/cgi/content/full/0701732104/DC1.

© 2007 by The National Academy of Sciences of the USA

Fig. 1. The structure of Rh. (Upper) View of Rh from the cytoplasmatic side.The Glu-113 carboxylate is the only ionized group in the chromophore cavity.(Lower) Structure of the retinal chromophore.

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have implemented the ab initio CASPT2//CASSCF protocol(where equilibrium geometries and electronic energies are de-termined at the CASSCF and CASPT2 levels, respectively) in aquantum mechanics/molecular mechanics scheme allowing forthe evaluation of the excitation energy of different chro-mophores (treated quantum mechanically) embedded in proteinand solution environments (described by the AMBER forcefield) with a few kcal�mol�1 errors (14) [see supporting infor-mation (SI) Appendix].

Because of their prohibitive computational cost, CASPT2potential energy surfaces cannot be presently used for even asingle trajectory computation on systems as large as PSB11. Onthe other hand, although the CASSCF potential energy could beused, this level of theory is known to overestimate both theexcitation energy and gradient of PSB11 (14). To overcome thesedifficulties, we adopt a scaled-CASSCF/AMBER potential thatreproduces the CASPT2//CASSCF/AMBER profile of the Rhisomerization path with a 0.75 kcal�mol�1 standard deviation.This potential is used to compute a 140-fs adiabatic trajectoryalong the spectroscopic (S1) state of Rh starting at the verticalexcitation (i.e., Franck-Condon) point with zero initial velocities.

We show that our scaled-CASSCF/AMBER trajectory pro-vides a description of the S1 evolution of PSB11 in Rh. Thisevolution is found to involve a complex space-saving motion ofthe –C9AC10–C11AC12–C13AC14- moiety that goes beyondthe previously proposed bicycle-pedal, one-bond-flip, and hula-twist models (15). We found that, after 60-fs evolution, up to50% of the kinetic energy flows along a mode involving theflipping of the C10–C11 unit and pointing to a conical inter-section. Evolution along this mode leads to a sharp increase indecay probability that reaches a maximum after 110 fs when thereactive -C11AC12- bond is �80° twisted.

Results and DiscussionTrajectory Computation and Analysis. The high cost of numericalCASPT2 gradients makes the evaluation of a classical trajectoryimpossible for the retinal chromophore. Such calculation, whenlimited to a few hundred femtoseconds, could be achieved at theCASSCF level. However, CASSCF energies not only do notreproduce the observed spectral properties of Rh but yield a toosteep energy profile (i.e., too large forces). To solve this problemand evaluate a realistic trajectory we noticed that scaling theCASSCF isomerization energy profile yields a curve overlappingwith the corresponding CASPT2 curve (see Fig. 2A). Thereforea scaled-CASSCF potential may provide an excited-state forcefield with near CASPT2 accuracy. Accordingly, for our Rhmodel, the following relationship holds:

��ECASSCF�x�� � �ECASPT2�x��,

where � � 0.795 is a constant. We now seek the solution of theclassic equations of motion [i.e., the trajectory x�(t)] using theCASSCF/6–31G*/AMBER gradient multiplied by �. This com-putation (see SI Appendix) is equivalent to solving the equationsof motion by using the unscaled CASSCF gradients but scalingthe time according to the relationship:

t� � ��1�2t.

t is the unphysical CASSCF time, and t� is the physical CASPT2time. We use the CASSCF/6–31G*/AMBER gradient and theabove time relationship to generate a 140-fs classical trajectorythat approximate a trajectory driven by the CASPT2 potential.Such a computation is performed under the following condi-tions: (i) we keep fixed the protein structure at the crystallo-graphic geometry but release the full retinal chromophore, theLys-296 side chain, and the two water molecules W1 and W2, (ii)we release the trajectory from the ground-state equilibrium

geometry (i.e., from S0-Rh) with no initial momentum. Condi-tion i is related to the assumption that the x-ray structureprovides a representation of the average conformation of theprotein cavity (with respect to the many sampled at roomtemperature) that does not change within the observed 200-fsreaction time (16) (the effects of protein motion are discussed in

Fig. 2. The excited-state trajectory. (A) ��CASSCF/6–31G*/AMBER (scaled-CASSCF) and CASPT2/CASSCF/6–31G*/AMBER energy profiles along the S1

isomerization path of Rh. (B) Scaled-CASSCF S1 and S0 energy profiles andCASPT2 points along the S1 trajectory of Rh. (C) C11–C12 stretch along the S1

trajectory of Rh. (D) C10–C11–C12–C13 dihedral angle (�) and HOOP wagging(�) along the S1 trajectory of Rh. The HOOP mode is defined as a deviation ofthe H–C11–C12–H dihedral from the C10–C11–C12–C13 dihedral value.

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ref. 7 that investigate the dependence of the dynamics on theshape of the excited state potential). This condition is consistentwith the observation that the isomerization coordinate is cou-pled mainly to the vibrational modes of retinal (17). Conditionii, which is in line with the fact that the production of the firstisolable intermediate bathoRh takes place even at 5 K (18) andwith temperature-independent quantum efficiency (19), impliesthat such a trajectory provides information on the motion anddecay time of the center of the vibrational wavepacket producedby laser pulse excitation of the chromophore. As detailed in SIAppendix, the validity of this assumption is probed in two ways:(i) the stability of the computed time scale (within 10 fs) andmechanism of the excited-state motion with respect to thechange of initial torsional deformation, is supported computingeight different trajectories (� 5° about the C12–C13, C11–C12,C10–C11, and C9–C10 bonds) using a computationally moreaffordable CASSCF/3–21G*/AMBER gradient; this result isconsistent with previous trajectory calculations (that includedprotein structure sampling) on bR (20) and shows that the resultsfrom different trajectories are qualitatively similar. (ii) Using aparametrized 2D analytic model of the S1 energy surface weshow that a trajectory released from the S0 equilibrium geometrywith no initial momentum closely follows the motion of thecenter of a vibrational wavepacket simulated with 1,000 trajec-tories. The conditions are consistent with the observation ofground-state coherent vibrational motion immediately after S1decay (17).

Fig. 2B shows the S1 potential energy along the computedtrajectory. Seven single-point CASPT2/CASSCF/6–31G*/AMBER computations have been performed to validate thescaled energy profile and compute the correct S1–S0 energy gap.It is apparent that the scaled-CASSCF energies remain close tothe CASPT2 energies all along the trajectory, supporting theaccuracy of our procedure. Within 10 fs the S1 system undergoesa �8 kcal�mol�1 energy decrease. After such an event thepotential energy decreases slowly and monotonically until aregion of degeneracy, located �15 kcal�mol�1 below the Franck-Condon point, is reached after 110 fs. Because, consistently withthe S1 forces (see Methods: Validation of the Rh Model andExcited-State Description), the initial motion is dominated bysimultaneous double-bond expansion and single-bond contrac-tion, 8 kcal�mol�1 vibrational energy must be initially locatedalong such mode. Indeed, as shown in Fig. 2C, the -C11AC12-double bond expands in 20 fs to 1.53 Å. This expansion reflectsthe complete inversion of the double-bond, single-bond charac-ter occurring, mainly, in the –C9AC10–C11AC12–C13AC14-moiety.

Fig. 2D shows the time evolution of the coordinates describingthe torsional deformation about the reactive -C11AC12- bondand of the out-of-phase HOOP motion (see Fig. 2 legend for thedefinition of the HOOP coordinate) of the -C11AC12- hydro-gens. It is remarkable that after only 10-fs evolution the torsionaldeformation starts to increase. A similar behavior is seen for theHOOP mode that must be obviously coupled to the correspond-ing torsion. However, notice that while the torsional coordinatedisplays a constant decrease (i.e., a counterclockwise twist)motion along the trajectory, the HOOP mode oscillates about a0 value, indicating that the average geometry of the C11 and C12centers is not pyramidalized.

Fig. 2D shows that the isomerization motion is interrupted bya partial oscillation at �60-fs delay. (A related event is also seenin the stretching as shown in Fig. 2C.) Interestingly, as apparentfrom Fig. 2B, such oscillation appears to match a change in theevolution of the S1–S0 energy gap that remains nearly constantin the 55- to 75-fs time range and then starts to decrease rapidlytoward a degeneracy achieved at 110-fs delay. After the degen-eracy is achieved the trajectory evolves in the region of a S1–S0

intersection that, as recently documented (21, 22), spans thebottom of the S1 energy surface.

The changes of the retinal conformation along the trajectory arecrucial for the understanding of the Rh space-saving 11-cis 3all-trans photoisomerization mechanism. A correct description ofthis motion requires the mapping of the torsional deformation of allbonds in the PSB11 backbone (Fig. 3A). It is found that afterphotoexcitation different bonds begin to twist reaching a maximumdeformation at �60 fs and then partially, or completely, go backtoward their initial conformation. For instance, the -C6OC7- bondcontrolling the �-ionone ring orientation undergoes an �20° pos-itive (i.e., clockwise) rotation that is partially recovered after a 90-fsdelay.

There is a striking exception to such a behavior: the twistabout the -C9AC10- bond adjacent to the reactive -C11AC12-bond. This bond remains untwisted until 60-fs delay and thenundergoes a 40° change that is never recovered. Notice that thetime scale for the activation of the -C9AC10- twisting corre-sponds to the oscillation seen along the reactive -C11AC12-torsion (see Fig. 2D), suggesting that this motion is associatedwith a steric constraint imposed by the protein environment and,in turn, to a change in the isomerization coordinate. Thisconstraint appears to be associated to the energy maximum (i.e.,

Fig. 3. Time evolution of the Rh structure. (A) Values of the PSB11 backbonedihedral angles along the S1 trajectory of Rh. (B) Pictorial illustration of the S1

structural evolution of PSB11 in Rh. (C) Linear momentum vector and crank-shaft torsional parameters at 110-fs delay. The experimentally derived (3)parameters of photoRh are given in square brackets.

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a transition state featuring a 40° twisted -C11AC12- bond)located along the reaction path after the S1-Rh minimum (seeFig. 3A) as indicated from a comparison of such a structure withthe 55-fs snapshot structures (see SI Appendix).

Visualization and analysis of the entire 140-fs S1 trajectory,together with the backbone deformation described above, pointto a space-saving isomerization mechanism that includes thepreviously proposed bicycle-pedal (5) (or crankshaft) coordinate(illustrated in Fig. 3B). After the initial stretching expansion(data not shown) that occurs on a time scale of �10 fs, onaverage, the -C7AC8–C9AC10–C11A segment of PSB11 twistswith respect to the two remaining fragments (the –NHAC15–C14AC13–C12A and �-ionone) and does so up to 60- to 70-fsdelay. Such motion is characterized mainly by a negative twist ofthe reactive -C11AC12- bond and a positive twist of the -C6–C7-bond. At the critical 60-fs delay the nature of the motion changes.The -C6–C7- twist stops and the -C9AC10- bond adjacent to thereactive -C11AC12- bond starts to twist in the positive direction.In other words, theAC10–C11A fragment rotates with respectto the backbone, leading to a 80° twisted -C11AC12- bond andto a moderately twisted (�30°) -C9AC10- bond at 110-fs delay.Such isomerization mode can be described as an asynchronous(in the sense that the extent of twisting of the –C9AC10- and-C11AC12- bonds is different) bicycle-pedal coordinate. Re-markably, the coupling between these double bonds and reactiontime scale were reported in early semiempirical studies (5, 23).However, notice that, because C10 and C11 are the only centersto move, the term asynchronous crankshaft coordinate is moreappropriate. The nature of this motion is confirmed by plottingthe linear momentum vectors in the 65- to 110-fs region. Fig. 3Cshows that at 110-fs delay the momentum is consistent with analmost net crankshaft motion (a coupled component describesthe motion of the methyl group at C12 and a stretch ofthe AC15–C14AC13–C12A fragment).

Electronic Structure Evolution. The change in the electronic struc-ture of PSB11 as a function of time is an important issue that, toour knowledge, has not been explored by using ab initio multi-configurational quantum chemistry (early semiempirical studiesare reported in refs. 5 and 6). This fact is remarkable given theimportance of the wavefunction change for the S1 3 S0 decayprocess (e.g., the derivative coupling ��1�/�q�2� contributing tothe Massey parameter) and the need to rationalize the time-resolved fluorescence data (4, 24). Furthermore, recent spectralstudies on bR demonstrate an ultrafast change of the chargedistribution during the excited-state evolution of the vibrationalwavepacket (25). For these reasons, we now describe the changesin the distribution of the PSB11-positive charge and relate themto the change of the S1 wavefunction.

As a prerequisite for the interpretation of our data we recallthat in Rh (26) the S1 state of PSB11 has a dominant chargetransfer character as originally proposed by Michl, Bonacic-Koutecky, and coworkers (27, 28). Upon S03 S1 excitation, thepositive charge, initially located on the -NAC15- moiety, movesaway along the �-skeleton, leading to the observed large valuesof � and f. The charge distributions of the S0 and S1 statesreflect the different nature of the corresponding wavefunctionsthat, with respect to the C11AC12 bond, can be associated withresonance formula displaying a charge in the -NAC15- half or�-ionone half of the retinal backbone. Accordingly, a convenientway to describe the wavefunction evolution along the trajectoryis to report the value of the charge residing on the �-ionone halfas defined by the structure in Fig. 4A.

At time 0 (i.e., at the Franck-Condon point) the S0 wavefunc-tion can be associated with a charge almost completely locatedon the -NHAC15-containing fragment. In contrast, the S1wavefunction is associated with a 57% positive charge on the�-ionone fragment. This charge increases during the first 10 fs

and decreases to a value slightly below 50% after 20 fs. Duringthe following 50 fs the system maintains, on the �-iononefragment, an average charge fraction above 50% consistentlywith a S1 character.

However, after 70-fs evolution the charge undergoes largeoscillations with a �20-fs period indicating a periodic change inthe electronic structure. The large decrease at 110 fs indicatesthat, suddenly, the excited-state wavefunction acquires an S0

character. This finding is explained by considering that after 80fs the S1–S0 energy gap decreases rapidly (see Fig. 4B) until aS1–S0 conical intersection is reached at 110 fs. Because along aloop centered on a conical intersection the S1 and S0 wavefunc-tions exchange their characters twice (29), a trajectory passing or

Fig. 4. Property time evolution. (A) Excited-state evolution of the chargeresiding on the �-ionone fragment of PSB11. (B) Evolution of the S0–S1

oscillator strength (●) and energy difference ( E) evaluated at the CASPT2level. (C) Evolution of the S1 total kinetic energy (E) and the kinetic energyfraction (�) associated to the linear momentum projected, at each time step,on the crankshaft mode defined in the Inset.

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oscillating in the intersection vicinity will display significantwavefunction changes. Consistent with Fig. 4A, the changeincreases in magnitude as the distance between the trajectoryand the intersection decreases (21).

The PSB11 electronic structure evolution is expected todetermine the change of molecular properties such as f and, inturn, the emission spectrum. Fig. 4B shows f computed at theCASPT2/CASSCF/6–31G*/AMBER level for the set of evenlyspaced time windows seen in Fig. 2B. It is apparent that fincreases, reaches a maximum at �35 fs, and then constantlydecreases. At this nonstationary point the predicted fluores-cence �max

f would be of 704 nm. Remarkably, this value compareswell with the excitation wavelength-dependent �max

f (705–650nm) observed by Kochendoerfer and Mathies (30) for Rh whena 560- to 510-nm excitation wavelength is used.

Excited-State Decay. The computed trajectory intersects the firstpoint of S1–S0 degeneracy on a 110-fs time scale and thenremains in the intersection space. Although a classical trajectoryis obviously unphysical in such region, here we use a semiclassicalmodel to estimate the change in S1 3 S0 decay probability as afunction of time. Accordingly, we compute the Landau-Zenerdecay probabilities (31) P � exp[�(/4)] by evaluating theMassey parameter :

�E�q�

��q�t ��1� �

�q��2

along the trajectory (see SI Appendix). It is found that Premains � 0.1 up to 110 fs and then increases to 0.9 incorrespondence of the conical intersection. This intersectionpoint shows a geometrical displacement consistent with those ofthe reported CI-Rh intersection (14). The computed high cross-ing probability is also consistent with previous studies includingthe related system bR (5, 6, 20).

According to the result above the linear momentum of Fig. 4Cis expected to play a fundamental role in prompting the pro-duction of the primary photoproduct photoRh. In particular, asindicated by Warshel (5) and suggested by Mathies and cowork-ers (17) on the basis of the time-resolved absorption data, toallow for a high photoisomerization quantum yield the momen-tum shall (i) point toward the photoproduct and (ii) have a largemagnitude. It is apparent that the computed vector relates the�80° and 30° twisted C11AC12 and C9AC10 bonds of our110-fs structure to the experimentally derived �110° and 45°values of photoRh (3). It is also remarkable that, at decay, 45%of the total kinetic energy gained during excited-state relaxationresides on the crankshaft-like isomerization mode (the lack ofmomentum at time 0 makes it easy to follow the flow of theavailable 17.3 kcal�mol�1 energy along the PSB11 modes). Fig.4C shows the evolution of the kinetic energy of the crankshaftcoordinate. It is apparent that the energy content of the modeincreases regularly, reaching a maximum value at 110 fs. Suchbehavior indicates the presence of a mechanism driving almosthalf of the available kinetic energy in the reactive molecularmode. In other words, despite the flat excited-state energysurface (see Fig. 2 A), only a limited quantity of the Rh S1 excessvibrational energy gets redistributed among the many degrees offreedom of PSB11. (Because, the protein is frozen, the computedtotal amount of PSB11 kinetic energy may be overestimated.)

Conclusions and Further Comparison with the ExperimentsAlthough FSRS provides information on the structure of retinalimmediately after the S1 3 S0 decay (3), an experimentallyderived atomic-level description of its S1 evolution in Rh is notaccessible. We have shown that a multiconfigurational quantum

chemical model of Rh provides such information, enlighteningthe way in which biological evolution has crafted one of the mostefficient photochemical reactions in nature.

It is found that the S1 isomerization motion involves twoconformational changes occurring after the initial 20-fs stretch-ing relaxation. The first falls in the 20- to 60-fs time window andinvolves a �35° twisting of the C11AC12 bond accompanied bya more limited, but cooperative, twisting of a portion of theretinal backbone. The second occurs in the 60- to 110-fs windowand involves a 35° twisting of the reactive bond coupled with a�30° reverse-twisting of the adjacent C9–C10 bond to yield acrankshaft motion. While, to our knowledge, such a mechanismis new, the analysis, via Fourier transform of the optical absorp-tion spectra, of deuterium substitution effects for the C11 andC12 hydrogens (32), points to the existence of different phasesin the excited-state evolution. The first is characterized by a lackof the deuterium effect and ends after 20 fs. The second involvesa moderate effect and occurs in the 20- to 60-fs time range.Finally, in a 70- to 110-fs phase there is an enhancement of thedeuterium substitution effect that becomes complex in the 120-to 170-fs range. Assuming that the magnitude of the deuteriumsubstitution effect provides information on the progress alongthe isomerization coordinate the observed phases seem toparallel the stretching relaxation (0–20 fs), preparatory motion(20–60 fs), and asynchronous crankshaft motion (60–110 fs)seen in our simulation.

The spontaneous emission spectrum provides the most basicinformation on the excited-state dynamics. Time-resolved fluo-rescence emission study on Rh demonstrates that although thedecay process is nonexponential and the observed lifetime isexcitation wavelength-dependent the major component of thesignal (80–60%) has an ultrashort lifetime in the 100- to 300-fsrange (4) and, thus, significantly longer than 60-fs lifetimeestimated on the basis of stationary measurements. According to

Fig. 5. Validation of the Rh model. (A) CASSCF/6–31G*/AMBER-optimizedstructures for Rh (S0-Rh) and bathoRh compared with the available NMR (38)and FSRS (values in square brackets). (B) Comparison between computed andobserved (39) stationary resonance Raman spectra of Rh. See SI Appendix fordetails.

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our trajectory the excited-state lifetime cannot be �110 fs. Thus,although the trajectory only describes the center of the wave-packet, the predicted lifetime falls within the observed quantities.

Our Rh model is not only consistent with the reactant (Rh)and product (bathoRh) spectral properties but also predicts S1lifetimes and emission properties in agreement with the exper-iment. Both FSRS experiments and computations carried outwith our model (see Fig. 5) and recent crystallographic data (33)point to a bathoRh characterized by a distorted all-trans chro-mophore. It is thus clear that the stereochemistry of the isomer-ization is consistent with a one-bond-flip event. However, in Rhthis motion is not associated with an excited-state one-bond-flipmotion. In fact, the described asynchronous crankshaft mode,capable of collecting up to 50% of the available kinetic energy(i.e., �6 kcal�mol�1) before decay, not only provides a space-saving coordinate but gives access to Landau-Zener tunneling toS0. Notice that although a complete crankshaft isomerization hasbeen shown to operate in the photoactive yellow protein chro-mophore (34), in Rh this motion must be quenched during thepicosecond conversion of photoRh to bathoRh. Indeed, asindicated by the FSRS data (3), whereas the C11AC12 bond ofphotoRh twists further to reach the �140° value of bathoRh, theC9AC10 bond twists back to a smaller 30° value. (This changein the nature of the relaxation coordinate is likely caused by theS0 force field imposing the reconstitution of the double bondcharacter at C11AC12 and C9AC10.) It is therefore natural topropose that the relatively slow photoRh3 bathoRh conversionis caused by the need to populate a reaction coordinate that isorthogonal to the one impulsively populated upon excited-statedecay.

Methods: Validation of the Rh Model andExcited-State DescriptionFor our Rh model (for the quantum mechanics/molecular me-chanics method and resonance Raman spectra evaluation see SI

Appendix) the CASPT2/CASSCF/AMBER protocol (14) yieldsS0 3 S1 and S0 3 S2 �max

a values (478 and 327 nm) only 3kcal�mol�1 off the experimental values (498 and 340 nm) (35), acomputed 14.6 D change in dipole moment (�) that falls withinthe observed 13–15 D range (36) and a S03 S1 f value (0.8) thatcompares well with the experimental quantity (1.0) (35). Simi-larly, the computed �max

a and photon energy storage of bathoRhare 5 kcal�mol�1 off the observed values. The method has alsobeen used to evaluate the �max

a of PSB11 in methanol, yielding anopsin shift 2 kcal�mol�1 off the experimental value (14). Wefound that the S0 3 S1 �max

a computed with the ANO-S(C,N[4s3p1d]/H[2S]) correlated basis set yields a reduced 10-nmred-shifted error. However, because of its excessive computa-tional cost, such a basis could not be adopted.

Fig. 5A shows the structural parameters of S0-Rh and theprimary isolable photoproduct bathoRh recently resolved byFSRS (3). It is apparent that S0-Rh has a chromophore confor-mation close to the one observed in bovine Rh (37, 38). Mostremarkably, the predicted structure is very close to the FSRS-derived structure. To further estimate the quality of the com-puted S1 force field we have simulated the resonance Ramanspectra of Rh by using the lower CASSCF/3–21G*/AMBERlevel. It is apparent (see Fig. 5B) that the qualitative features ofthe observed spectra (39) are reproduced, including the presenceof the ethylenic band (1,500–1,600 cm�1), fingerprint region(1,100–1,350 cm�1), and HOOP activity (900–1,100 cm�1).

We thank Centro Interuniversitario Per Il Calcold Automatico ItaliaNord-Orientale for granted calculation time. This work was supported bythe Universita di Siena (Progetto di Ateneo 02/04) and FondazioneMonte Del Paschi. N.F. was supported by Marie Curie FellowshipHPMF-CT-2001-01769, and T.A. was supported by Marie Curie Fellow-ship HPMF-CT-2002-01769. L.M.F. was supported by Spanish Ministryof Education and Science Postdoctoral Grant EX 27-04-2005 M.O.thanks Bowling Green State University for start-up funding.

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