Tracking the excited-state time evolution of the visual pigment with multiconfigurational quantum chemistry

Abstract

The primary event that initiates vision is the photoinduced isomerization of retinal in the visual pigment rhodopsin (Rh). Here, we use a scaled quantum mechanics/molecular mechanics potential that reproduces the isomerization path determined with multiconfigurational perturbation theory to follow the excited-state evolution of bovine Rh. The analysis of a 140-fs trajectory provides a description of the electronic and geometrical changes that prepare the system for decay to the ground state. The data uncover a complex 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. It is shown that the twisted structure achieved at decay features a momentum that provides a natural route toward the photoRh structure recently resolved by using femtosecond-stimulated Raman spectroscopy.

The visual pigment rhodopsin (Rh) (1, 2) is a G protein-coupled receptor containing a 11-cis retinal chromophore (PSB11) bounded to a lysine residue (Lys-296) via a protonated Schiff base linkage (see Fig. 1). While the biological activity of Rh is triggered by the light-induced 11-cis all-trans isomerization of PSB11, this reaction owes its efficiency (e.g., short time scale and high quantum yields) to the protein cavity (1). Recently, the mechanism of the isomerization of retinal in Rh has been investigated by using femtosecond-stimulated Raman spectroscopy (FSRS) (3). Kukura et al. (3) have reported on experimentally derived structures of photoRh and bathoRh, namely the first and second ground-state intermediates of the Rh photocycle.

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.

While such progress has provided information on the structural changes achieved 200 fs after light absorption, the faster structural changes prompting the excited-state decay of PSB11 (i.e., the central event of the isomerization mechanism) remain to be established. Indeed, it has been suggested that such decay may occur on a 60-fs time scale through fast hydrogen out-of-plane (HOOP) motion (3), whereas the traditional view points to a slower ≈150-fs decay driven by cis–trans isomerization motion (4). In principle, molecular dynamics simulations featuring a quantum chemical description of the chromophore can be used to address such issues. This fact was shown by Warshel (5) using semiempirical quantum chemistry to describe PSB11 and geometrical constraints to account for the protein environment. Later, Birge and Hubbard (6) reported a different semiempirical study of an explicit chromophore–counterion pair evolving along a single coordinate. While the first simulation of the retinal photoisomerization using a full atomic-level protein model (7) was reported for the related receptor bacterio-Rh (bR), attempts to simulate the PSB11 excited-state motion in a complete 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-state force field for PSB11 in Rh.

The ab initio (i.e., first-principles) complete-active-space self-consistent-field (CASSCF) method (11) is a multiconfigurational method offering maximum flexibility for the unbiased description of the electronic and equilibrium structure of a molecule (i.e., with no empirically derived parameters and avoiding single-reference wavefunctions). Furthermore, the CASSCF wavefunction can be used for subsequent multiconfigurational second-order perturbation theory (CASPT2) (12) computations of the dynamic correlation energy of each state, ultimately leading to a quantitative evaluation of the excitation energies and excited-state energy differences. Recently, we (13) have implemented the ab initio CASPT2//CASSCF protocol (where equilibrium geometries and electronic energies are determined at the CASSCF and CASPT2 levels, respectively) in a quantum mechanics/molecular mechanics scheme allowing for the evaluation of the excitation energy of different chromophores (treated quantum mechanically) embedded in protein and solution environments (described by the AMBER force field) with a few kcal·mol⁻¹ errors (14) [see supporting information (SI) Appendix].

Because of their prohibitive computational cost, CASPT2 potential energy surfaces cannot be presently used for even a single trajectory computation on systems as large as PSB11. On the other hand, although the CASSCF potential energy could be used, this level of theory is known to overestimate both the excitation energy and gradient of PSB11 (14). To overcome these difficulties, we adopt a scaled-CASSCF/AMBER potential that reproduces the CASPT2//CASSCF/AMBER profile of the Rh isomerization path with a 0.75 kcal·mol⁻¹ standard deviation. This potential is used to compute a 140-fs adiabatic trajectory along the spectroscopic (S₁) state of Rh starting at the vertical excitation (i.e., Franck-Condon) point with zero initial velocities.

We show that our scaled-CASSCF/AMBER trajectory provides a description of the S₁ evolution of PSB11 in Rh. This evolution is found to involve a complex space-saving motion of the –C9C10–C11C12–C13C14- moiety that goes beyond the previously proposed bicycle-pedal, one-bond-flip, and hula-twist models (15). We found that, after 60-fs evolution, up to 50% of the kinetic energy flows along a mode involving the flipping of the C10–C11 unit and pointing to a conical intersection. Evolution along this mode leads to a sharp increase in decay probability that reaches a maximum after 110 fs when the reactive -C11C12- bond is ≈80° twisted.

Results and Discussion

Trajectory Computation and Analysis.

The high cost of numerical CASPT2 gradients makes the evaluation of a classical trajectory impossible for the retinal chromophore. Such calculation, when limited to a few hundred femtoseconds, could be achieved at the CASSCF level. However, CASSCF energies not only do not reproduce the observed spectral properties of Rh but yield a too steep energy profile (i.e., too large forces). To solve this problem and evaluate a realistic trajectory we noticed that scaling the CASSCF isomerization energy profile yields a curve overlapping with the corresponding CASPT2 curve (see Fig. 2A). Therefore a scaled-CASSCF potential may provide an excited-state force field with near CASPT2 accuracy. Accordingly, for our Rh model, the following relationship holds:

where α = 0.795 is a constant. We now seek the solution of the classic equations of motion [i.e., the trajectory x̄(t)] using the CASSCF/6–31G∗/AMBER gradient multiplied by α. This computation (see SI Appendix) is equivalent to solving the equations of motion by using the unscaled CASSCF gradients but scaling the time according to the relationship:

t is the unphysical CASSCF time, and t′ is the physical CASPT2 time. We use the CASSCF/6–31G∗/AMBER gradient and the above time relationship to generate a 140-fs classical trajectory that approximate a trajectory driven by the CASPT2 potential. Such a computation is performed under the following conditions: (i) we keep fixed the protein structure at the crystallographic geometry but release the full retinal chromophore, the Lys-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. Condition i is related to the assumption that the x-ray structure provides a representation of the average conformation of the protein cavity (with respect to the many sampled at room temperature) that does not change within the observed 200-fs reaction time (16) (the effects of protein motion are discussed in ref. 7 that investigate the dependence of the dynamics on the shape of the excited state potential). This condition is consistent with the observation that the isomerization coordinate is coupled mainly to the vibrational modes of retinal (17). Condition ii, which is in line with the fact that the production of the first isolable intermediate bathoRh takes place even at 5 K (18) and with temperature-independent quantum efficiency (19), implies that such a trajectory provides information on the motion and decay time of the center of the vibrational wavepacket produced by laser pulse excitation of the chromophore. As detailed in SI Appendix, the validity of this assumption is probed in two ways: (i) the stability of the computed time scale (within 10 fs) and mechanism of the excited-state motion with respect to the change of initial torsional deformation, is supported computing eight different trajectories (± 5° about the C12–C13, C11–C12, C10–C11, and C9–C10 bonds) using a computationally more affordable CASSCF/3–21G*/AMBER gradient; this result is consistent with previous trajectory calculations (that included protein structure sampling) on bR (20) and shows that the results from different trajectories are qualitatively similar. (ii) Using a parametrized 2D analytic model of the S₁ energy surface we show that a trajectory released from the S₀ equilibrium geometry with no initial momentum closely follows the motion of the center of a vibrational wavepacket simulated with 1,000 trajectories. The conditions are consistent with the observation of ground-state coherent vibrational motion immediately after S₁ decay (17).

Fig. 2.

The excited-state trajectory. (A) α·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 and CASPT2 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 of the H–C1₁–C1₂–H dihedral from the C10–C11–C12–C13 dihedral value.

Fig. 2B shows the S₁ potential energy along the computed trajectory. Seven single-point CASPT2/CASSCF/6–31G*/AMBER computations have been performed to validate the scaled energy profile and compute the correct S₁–S₀ energy gap. It is apparent that the scaled-CASSCF energies remain close to the CASPT2 energies all along the trajectory, supporting the accuracy of our procedure. Within 10 fs the S₁ system undergoes a ≈8 kcal·mol⁻¹ energy decrease. After such an event the potential energy decreases slowly and monotonically until a region of degeneracy, located ≈15 kcal·mol⁻¹ below the Franck-Condon point, is reached after 110 fs. Because, consistently with the S₁ forces (see Methods: Validation of the Rh Model and Excited-State Description), the initial motion is dominated by simultaneous double-bond expansion and single-bond contraction, 8 kcal·mol⁻¹ vibrational energy must be initially located along such mode. Indeed, as shown in Fig. 2C, the -C11C12- double bond expands in 20 fs to 1.53 Å. This expansion reflects the complete inversion of the double-bond, single-bond character occurring, mainly, in the –C9C10–C11C12–C13C14- moiety.

Fig. 2D shows the time evolution of the coordinates describing the torsional deformation about the reactive -C11C12- bond and of the out-of-phase HOOP motion (see Fig. 2 legend for the definition of the HOOP coordinate) of the -C11C12- hydrogens. It is remarkable that after only 10-fs evolution the torsional deformation starts to increase. A similar behavior is seen for the HOOP mode that must be obviously coupled to the corresponding torsion. However, notice that while the torsional coordinate displays a constant decrease (i.e., a counterclockwise twist) motion along the trajectory, the HOOP mode oscillates about a 0 value, indicating that the average geometry of the C11 and C12 centers is not pyramidalized.

Fig. 2D shows that the isomerization motion is interrupted by a partial oscillation at ≈60-fs delay. (A related event is also seen in the stretching as shown in Fig. 2C.) Interestingly, as apparent from Fig. 2B, such oscillation appears to match a change in the evolution of the S₁–S₀ energy gap that remains nearly constant in the 55- to 75-fs time range and then starts to decrease rapidly toward a degeneracy achieved at 110-fs delay. After the degeneracy is achieved the trajectory evolves in the region of a S₁–S₀ intersection that, as recently documented (21, 22), spans the bottom of the S₁ energy surface.

The changes of the retinal conformation along the trajectory are crucial for the understanding of the Rh space-saving 11-cis → all-trans photoisomerization mechanism. A correct description of this motion requires the mapping of the torsional deformation of all bonds in the PSB11 backbone (Fig. 3A). It is found that after photoexcitation different bonds begin to twist reaching a maximum deformation at ≈60 fs and then partially, or completely, go back toward their initial conformation. For instance, the -C6C7- bond controlling the β-ionone ring orientation undergoes an ≈20° positive (i.e., clockwise) rotation that is partially recovered after a 90-fs delay.

Fig. 3.

Time evolution of the Rh structure. (A) Values of the PSB11 backbone dihedral angles along the S₁ trajectory of Rh. (B) Pictorial illustration of the S₁ structural evolution of PSB11 in Rh. (C) Linear momentum vector and crankshaft torsional parameters at 110-fs delay. The experimentally derived (3) parameters of photoRh are given in square brackets.

There is a striking exception to such a behavior: the twist about the -C9C10- bond adjacent to the reactive -C11C12- bond. This bond remains untwisted until 60-fs delay and then undergoes a 40° change that is never recovered. Notice that the time scale for the activation of the -C9C10- twisting corresponds to the oscillation seen along the reactive -C11C12- torsion (see Fig. 2D), suggesting that this motion is associated with a steric constraint imposed by the protein environment and, in turn, to a change in the isomerization coordinate. This constraint appears to be associated to the energy maximum (i.e., a transition state featuring a 40° twisted -C11C12- bond) located along the reaction path after the S₁-Rh minimum (see Fig. 3A) as indicated from a comparison of such a structure with the 55-fs snapshot structures (see SI Appendix).

Visualization and analysis of the entire 140-fs S₁ trajectory, together with the backbone deformation described above, point to a space-saving isomerization mechanism that includes the previously 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, on average, the -C7C8–C9C10–C11 segment of PSB11 twists with respect to the two remaining fragments (the –NHC15–C14C13–C12 and β-ionone) and does so up to 60- to 70-fs delay. Such motion is characterized mainly by a negative twist of the reactive -C11C12- 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 -C9C10- bond adjacent to the reactive -C11C12- bond starts to twist in the positive direction. In other words, the C10–C11 fragment rotates with respect to the backbone, leading to a 80° twisted -C11C12- bond and to a moderately twisted (≈30°) -C9C10- bond at 110-fs delay. Such isomerization mode can be described as an asynchronous (in the sense that the extent of twisting of the –C9C10- and -C11C12- bonds is different) bicycle-pedal coordinate. Remarkably, the coupling between these double bonds and reaction time scale were reported in early semiempirical studies (5, 23). However, notice that, because C10 and C11 are the only centers to move, the term asynchronous crankshaft coordinate is more appropriate. The nature of this motion is confirmed by plotting the linear momentum vectors in the 65- to 110-fs region. Fig. 3C shows that at 110-fs delay the momentum is consistent with an almost net crankshaft motion (a coupled component describes the motion of the methyl group at C12 and a stretch of the C15–C14C13–C12 fragment).

Electronic Structure Evolution.

The change in the electronic structure of PSB11 as a function of time is an important issue that, to our knowledge, has not been explored by using ab initio multiconfigurational quantum chemistry (early semiempirical studies are reported in refs. 5 and 6). This fact is remarkable given the importance of the wavefunction change for the S₁ → S₀ decay process (e.g., the derivative coupling <ψ₁|∂/∂_q|ψ₂) contributing to the Massey parameter) and the need to rationalize the time-resolved fluorescence data (4, 24). Furthermore, recent spectral studies on bR demonstrate an ultrafast change of the charge distribution during the excited-state evolution of the vibrational wavepacket (25). For these reasons, we now describe the changes in the distribution of the PSB11-positive charge and relate them to the change of the S₁ wavefunction.

As a prerequisite for the interpretation of our data we recall that in Rh (26) the S₁ state of PSB11 has a dominant charge transfer character as originally proposed by Michl, Bonacic-Koutecky, and coworkers (27, 28). Upon S₀ → S₁ excitation, the positive charge, initially located on the -NC15- moiety, moves away along the σ-skeleton, leading to the observed large values of Δμ and f. The charge distributions of the S₀ and S₁ states reflect the different nature of the corresponding wavefunctions that, with respect to the C11C12 bond, can be associated with resonance formula displaying a charge in the -NC15- half or β-ionone half of the retinal backbone. Accordingly, a convenient way to describe the wavefunction evolution along the trajectory is to report the value of the charge residing on the β-ionone half as defined by the structure in Fig. 4A.

Fig. 4.

Property time evolution. (A) Excited-state evolution of the charge residing on the β-ionone fragment of PSB11. (B) Evolution of the S₀–S₁ oscillator strength (•) and energy difference (○) evaluated at the CASPT2 level. (C) Evolution of the S₁ total kinetic energy (○) and the kinetic energy fraction (□) associated to the linear momentum projected, at each time step, on the crankshaft mode defined in the Inset.

At time 0 (i.e., at the Franck-Condon point) the S₀ wavefunction can be associated with a charge almost completely located on the -NHC15-containing fragment. In contrast, the S₁ wavefunction is associated with a 57% positive charge on the β-ionone fragment. This charge increases during the first 10 fs and decreases to a value slightly below 50% after 20 fs. During the following 50 fs the system maintains, on the β-ionone fragment, an average charge fraction above 50% consistently with a S₁ character.

However, after 70-fs evolution the charge undergoes large oscillations with a ≈20-fs period indicating a periodic change in the electronic structure. The large decrease at 110 fs indicates that, suddenly, the excited-state wavefunction acquires an S₀ character. This finding is explained by considering that after 80 fs the S₁–S₀ energy gap decreases rapidly (see Fig. 4B) until a S₁–S₀ conical intersection is reached at 110 fs. Because along a loop centered on a conical intersection the S₁ and S₀ wavefunctions exchange their characters twice (29), a trajectory passing or oscillating in the intersection vicinity will display significant wavefunction changes. Consistent with Fig. 4A, the change increases in magnitude as the distance between the trajectory and the intersection decreases (21).

The PSB11 electronic structure evolution is expected to determine the change of molecular properties such as f and, in turn, the emission spectrum. Fig. 4B shows f computed at the CASPT2/CASSCF/6–31G*/AMBER level for the set of evenly spaced time windows seen in Fig. 2B. It is apparent that f increases, reaches a maximum at ≈35 fs, and then constantly decreases. At this nonstationary point the predicted fluorescence λ_max^f would be of 704 nm. Remarkably, this value compares well with the excitation wavelength-dependent λ_max^f (705–650 nm) observed by Kochendoerfer and Mathies (30) for Rh when a 560- to 510-nm excitation wavelength is used.

Excited-State Decay.

The computed trajectory intersects the first point of S₁–S₀ degeneracy on a 110-fs time scale and then remains in the intersection space. Although a classical trajectory is obviously unphysical in such region, here we use a semiclassical model to estimate the change in S₁ → S₀ decay probability as a function of time. Accordingly, we compute the Landau-Zener decay probabilities (31) P = exp[−(π/4)ξ] by evaluating the Massey parameter ξ:

along the trajectory (see SI Appendix). It is found that P remains < 0.1 up to 110 fs and then increases to 0.9 in correspondence of the conical intersection. This intersection point shows a geometrical displacement consistent with those of the reported CI-Rh intersection (14). The computed high crossing probability is also consistent with previous studies including the related system bR (5, 6, 20).

According to the result above the linear momentum of Fig. 4C is expected to play a fundamental role in prompting the production of the primary photoproduct photoRh. In particular, as indicated by Warshel (5) and suggested by Mathies and coworkers (17) on the basis of the time-resolved absorption data, to allow for a high photoisomerization quantum yield the momentum shall (i) point toward the photoproduct and (ii) have a large magnitude. It is apparent that the computed vector relates the −80° and 30° twisted C11C12 and C9C10 bonds of our 110-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 relaxation resides on the crankshaft-like isomerization mode (the lack of momentum at time 0 makes it easy to follow the flow of the available 17.3 kcal·mol⁻¹ energy along the PSB11 modes). Fig. 4C shows the evolution of the kinetic energy of the crankshaft coordinate. It is apparent that the energy content of the mode increases regularly, reaching a maximum value at 110 fs. Such behavior indicates the presence of a mechanism driving almost half of the available kinetic energy in the reactive molecular mode. In other words, despite the flat excited-state energy surface (see Fig. 2A), only a limited quantity of the Rh S₁ excess vibrational energy gets redistributed among the many degrees of freedom of PSB11. (Because, the protein is frozen, the computed total amount of PSB11 kinetic energy may be overestimated.)

Conclusions and Further Comparison with the Experiments

Although FSRS provides information on the structure of retinal immediately after the S₁ → S₀ decay (3), an experimentally derived atomic-level description of its S₁ evolution in Rh is not accessible. We have shown that a multiconfigurational quantum chemical model of Rh provides such information, enlightening the way in which biological evolution has crafted one of the most efficient photochemical reactions in nature.

It is found that the S₁ isomerization motion involves two conformational changes occurring after the initial 20-fs stretching relaxation. The first falls in the 20- to 60-fs time window and involves a ≈35° twisting of the C11C12 bond accompanied by a more limited, but cooperative, twisting of a portion of the retinal backbone. The second occurs in the 60- to 110-fs window and involves a 35° twisting of the reactive bond coupled with a ≈30° reverse-twisting of the adjacent C9–C10 bond to yield a crankshaft motion. While, to our knowledge, such a mechanism is new, the analysis, via Fourier transform of the optical absorption spectra, of deuterium substitution effects for the C11 and C12 hydrogens (32), points to the existence of different phases in the excited-state evolution. The first is characterized by a lack of the deuterium effect and ends after 20 fs. The second involves a 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 the deuterium substitution effect that becomes complex in the 120- to 170-fs range. Assuming that the magnitude of the deuterium substitution effect provides information on the progress along the isomerization coordinate the observed phases seem to parallel 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 basic information on the excited-state dynamics. Time-resolved fluorescence emission study on Rh demonstrates that although the decay process is nonexponential and the observed lifetime is excitation wavelength-dependent the major component of the signal (80–60%) has an ultrashort lifetime in the 100- to 300-fs range (4) and, thus, significantly longer than 60-fs lifetime estimated on the basis of stationary measurements. According to our trajectory the excited-state lifetime cannot be <110 fs. Thus, although the trajectory only describes the center of the wavepacket, 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 S₁ lifetimes and emission properties in agreement with the experiment. Both FSRS experiments and computations carried out with our model (see Fig. 5) and recent crystallographic data (33) point to a bathoRh characterized by a distorted all-trans chromophore. It is thus clear that the stereochemistry of the isomerization is consistent with a one-bond-flip event. However, in Rh this motion is not associated with an excited-state one-bond-flip motion. 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 to S₀. Notice that although a complete crankshaft isomerization has been shown to operate in the photoactive yellow protein chromophore (34), in Rh this motion must be quenched during the picosecond conversion of photoRh to bathoRh. Indeed, as indicated by the FSRS data (3), whereas the C11C12 bond of photoRh twists further to reach the −140° value of bathoRh, the C9C10 bond twists back to a smaller 30° value. (This change in the nature of the relaxation coordinate is likely caused by the S₀ force field imposing the reconstitution of the double bond character at C11C12 and C9C10.) It is therefore natural to propose that the relatively slow photoRh → bathoRh conversion is caused by the need to populate a reaction coordinate that is orthogonal to the one impulsively populated upon excited-state decay.

Fig. 5.

Validation of the Rh model. (A) CASSCF/6–31G∗/AMBER-optimized structures for Rh (S₀-Rh) and bathoRh compared with the available NMR (38) and FSRS (values in square brackets). (B) Comparison between computed and observed (39) stationary resonance Raman spectra of Rh. See SI Appendix for details.

Methods: Validation of the Rh Model and Excited-State Description

For our Rh model (for the quantum mechanics/molecular mechanics method and resonance Raman spectra evaluation see SI Appendix) the CASPT2/CASSCF/AMBER protocol (14) yields S₀ → S₁ and S₀ → S₂ λ_max^a values (478 and 327 nm) only 3 kcal·mol⁻¹ off the experimental values (498 and 340 nm) (35), a computed 14.6 D change in dipole moment (Δμ) that falls within the observed 13–15 D range (36) and a S₀ → S₁ f value (0.8) that compares well with the experimental quantity (1.0) (35). Similarly, the computed λ_max^a and photon energy storage of bathoRh are 5 kcal·mol⁻¹ off the observed values. The method has also been used to evaluate the λ_max^a of PSB11 in methanol, yielding an opsin shift 2 kcal·mol⁻¹ off the experimental value (14). We found that the S₀ → S₁ λ_max^a computed with the ANO-S (C,N[4s3p1d]/H[2S]) correlated basis set yields a reduced 10-nm red-shifted error. However, because of its excessive computational cost, such a basis could not be adopted.

Fig. 5A shows the structural parameters of S₀-Rh and the primary isolable photoproduct bathoRh recently resolved by FSRS (3). It is apparent that S₀-Rh has a chromophore conformation close to the one observed in bovine Rh (37, 38). Most remarkably, the predicted structure is very close to the FSRS-derived structure. To further estimate the quality of the computed S₁ force field we have simulated the resonance Raman spectra of Rh by using the lower CASSCF/3–21G*/AMBER level. It is apparent (see Fig. 5B) that the qualitative features of the observed spectra (39) are reproduced, including the presence of 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).

Abbreviations

Rh

rhodopsin

bR

bacterio-Rh

FSRS

femtosecond-stimulated Raman spectroscopy

HOOP

hydrogen out-of-plane

CASSCF

complete-active-space self-consistent-field

CASPT2

multiconfigurational second-order perturbation theory.