How Methylation Modifies the Photophysics of the Native All-

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How Methylation Modifies the Photophysics of the Native All-Trans Retinal Protonated Schiff Base: A CASPT2/MD Study in Gas Phase and in Methanol Rute Barata-Morgado, M. Luz Sánchez, Aurora Muñoz-Losa, M. Elena Martín, Francisco J. Olivares del Valle, and Manuel Ángel Aguilar J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b00773 • Publication Date (Web): 28 Feb 2018 Downloaded from http://pubs.acs.org on March 3, 2018

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The Journal of Physical Chemistry

How Methylation Modifies the Photophysics of the Native all-trans Retinal Protonated Schiff Base: a CASPT2/MD Study in Gas Phase and in Methanol Rute Barata-Morgado1, M. Luz Sánchez1, Aurora Muñoz-Losa2, M. Elena Martín1, Francisco J. Olivares del Valle1, Manuel A. Aguilar1,* Correspondence to: M.A. Aguilar (e-mail: [email protected]) 1

Área de Química Física, University of Extremadura, Avda. Elvas s/n, Edif. José Mª

Viguera Lobo 3ª, planta, Badajoz, 06006, (Spain) 2

Dpto. Didáctica de las Ciencias Experimentales y Matemáticas, Facultad de Formación del Profesorado, University of Extremadura, Avda. Universidad s/n, Cáceres, 10003, (Spain)

Abstract A comparison between the free-energy surfaces of the all-trans Retinal Protonated Schiff Base (RPSB) and its 10-methylated derivative in gas phase and methanol solution is performed at CASSCF//CASSCF and CASPT2//CASSCF levels. Solvent effects were included using the average solvent electrostatic potential from molecular dynamics method. This is a QM/MM (Quantum Mechanics/Molecular Mechanics) method that makes use of the mean field approximation. It is found that the methyl group bonded to C10 produces noticeable changes in the in solution free-energy profile of the S1 excited state, mainly in the relative stability of the MECIs with respect to the FC point. The conical intersections yielding to the 9-cis and 11-cis isomers are stabilized while that yielding to 13-cis isomer is destabilized, in fact, it becomes not accessible by excitation to S1. Furthermore, the planar S1 minimum is not present in the methylated compound. The solvent notably stabilizes the S2 excited state at the FC geometry. Therefore, if the S2 state has an effect on the photoisomerization dynamics it must be because it permits to the RPSB population to branch around the FC. All these changes combine to speed up the photoisomerization in the 10-methylated compound with respect to the native compound.

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1. INTRODUCTION The photoisomerization of the retinal protonated Schiff base (RPSB) has been profusely studied both from a theoretical1–15 and an experimental16–29 point of view. Studies inside the protein25,26,30–35 and in solution28,36–38 have been performed in order to elucidate the role played by the protein in accelerating the cis/trans photoisomerization and increasing its quantum yield. It has been proposed that, in polar solvents, after the absorption of a photon of the adequate energy, the excited state population branches in the neighborhood of the absorption S1 Franck-Condon (FC) geometry into a reactive and a non-reactive channel. The initial relaxation on the S1 reactive channel originates a reduction of the Bond Length Alternation (BLA) and the torsion of one or more double bonds. These torsions are associated with S0/S1 conical intersections (CI). At the CIs, the population could branch again between those molecules that isomerize and those that return to the initial geometry. It is well known that the solvent modifies the population ratios, in fact, the quantum yield decreases noticeably when one passes from the protein (0.64) to polar solvents (0.16).26,39 On the contrary, the time constants increases in solution,25,40 they are almost one order of magnitude larger in methanol (4 ps) than in the protein (0.15-0.5 ps). Most of proteins associated with RPSB can be classified into two great groups24,41 attending to the nature of the chromophore, the 11-cis-retinal or the all-trans retinal. Even though both isomers share the basic scheme introduced above, they show some differences in their behavior. Thus, the 11-cis isomer transforms in the all-trans isomer both inside the protein and in polar solvents. However, the all-trans-retinal isomerizes to the 13-cis-retinal inside the protein but to the 9-cis and 11-cis isomers in methanol solution. Another difference between them is that the photoisomerization of the 11-cisretinal seems to be a barrier-less process42, both in solution and in the protein, while a small barrier (about 1 kcal/mol) has been proposed10,43 in the photoisomerization of the all-trans-retinal. Additional information about the de-excitation dynamics can been obtained by introducing small structural modifications1,2,21,30,44 in the RPSB. Recently, Kukura and co-workers42,45 have shown that the addition of a methyl group at the C10 position (see Figure 1) of RPSB accelerates the electronic decay in methanol solution for both the cis and all-trans isomers and results in protein-like photophysics. The dynamics for 10methyl RPSB differ from the non-methylated compound, being the excited state lifetime reduced from 4 ps to only 0.7 ps. These authors suggest that “this accelerate excited state decay … demands a lower barrier toward the CI”. In a previous paper,10 we compared the free energy excited state surface of several simplified models of the 11-cis RPSB in the gas phase and in methanol solution. It was found that in methanol, at the Franck-Condon geometry, the S1 and S2 states are almost degenerated; consequently, the S1 surface has a region of ionic character (1Bu-like) and another one with a covalent character (2Ag-like), which is similar in nature to the ground state. In covalent states the positive charge is mainly located on the nitrogen atom at the iminium end, while in the ionic state the charge is spread out over the C-tail of the retinal molecule. It was also suggested that, in solution, the emission from the covalent minimum originates the high-frequency part of the fluorescent band, while emission

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from the ionic minimum is responsible for the low-frequency part. The ionic minimum is separated from the conical intersection by an energy barrier of about 0.7 kcal/mol. In methanol, the photoisomerization of retinal follows a three states model, being the S2 state involved only in the initial stages of the process (in the FC region). This is in clear contrast with the behavior in the gas phase or inside the protein where only two states are involved. Two very interesting QM/MM studies about this subject have been recently published. The two studies highlight the importance that the S1/S2 energy gap has in determining the evolution of the excited state.46,47All these facts draw a complex scenario where small modifications in the structure of the chromophore or in the surrounding medium produce important changes in the photodynamic of the system. In the present paper, we compare free energy surfaces of the complete all-trans RPSB molecule with that of the 10-methyl derivative (see Figure 1), trying to find the reasons that explain the different decay dynamics of these two compounds. (Figure 1: near here) The rest of the paper is organized as follows: In section 2 the main features of the method used in the localization of the main critical points (FC, minima, CI, etc.) are explained and the computational aspects are detailed. In Section 3, the free energy surfaces of the two molecules are compared, both in the gas phase and in methanol solution. Finally, the main conclusions are reported in Section 4.

2. METHODS AND COMPUTATIONAL DETAILS Ground state geometries where optimized both at CASSCF and MP2 levels. Excited states geometries where optimized only at CASSCF level. Electronic states were described using SA-CASSCF of three roots assuming equal weights for all of them. All electrons of the π skeleton were included in the active space, that is, 12 valence π electrons in 12 orbitals (12e, 12o). Transition energies and relative free energies of the different structures were calculated at CASPT248 level; i.e., they include the electron dynamics correlation energy. For all the multiconfigurational calculations we employed MOLCAS 7.449. The split-valence 6-31G(d) basis set was used to facilitate comparison with previous studies. We did all the calculations with no IPEA50,51 (ionization potential-electron affinity) shift. An additional imaginary level shift52 of 0.1i Eh was included in order to minimize the appearance of intruder states. Solvent effects were determined using the ASEP/MD method53 developed in our laboratory. This is a QM/MM (Quantum Mechanics/Molecular Mechanics) method that makes use of the mean field approximation. Its main characteristics have been described elsewhere.54,55 Here, we shall detail only those points pertinent to the current study. Minima were optimized56 both in the ground and excited states assuming equilibrium solvation. ASEP/MD alternates high-level quantum calculations and molecular dynamics (MD) simulations in an iterative procedure that uses a stepwise strategy. During the MD simulation, the geometry and charge distribution of the solute and solvent molecules are taken as fixed. From the MD data one obtains the averaged solvent electrostatic potential (ASEP) that is introduced as a perturbation into the solute molecular

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Hamiltonian. By solving the associated Schrödinger equation, a new solute point charges distribution is obtained that serves as input for a new MD calculation. The process finishes when convergence in the solute point charges and in the solute energy is reached. The basis scheme is displayed in Figure 2. With respect to other QM/MM methods ASEP/MD neglects the Stark component of the solute-solvent interaction energy. In previous paper we have shown that this approximation introduce only small errors on the quantities calculated. Thus, our results would agree with the provided by other QM/MM methods. The main advantage of ASEP/MD is that, because of its lower computational cost, it permits to combine a high-level quantum description of the solute with a detailed (microscopic) description of the solvent and an adequate description of thermal effects (a very large number of solvent configurations can be easily included). During the ASEP/MD cycle, solute atomic charges were computed from the quantum calculations through a least-squares fit to the electrostatic potential at the points where the solvent atoms are located. To optimize the geometry of the molecule in solution we used a technique described in a previous paper56 based on the use of the free-energy gradient method (FEG)57–59, where the solute geometry is optimized in presence of the averaged force generated by the solvent. In the searching for the Minimum Energy Conical Intersections, MECIs, we use a modification of the Martinez et al.60 algorithm where the solvent contribution to the gradient difference vector is also calculated with the FEG method. (Figure 2: near here) Once determined the geometry and charge distribution of the minima, and according to the Franck-Condon principle, vertical transition energies were calculated assuming frozen solvent conditions, that is, the solvent distribution used to determine the solute wave-function of the final state is the solvent distribution in equilibrium with the wave-function of the solute initial state. Displayed values for geometries, charges and energies were obtained as the average of the last five ASEP/MD cycles. Fluctuations are related to the limited size of the molecular simulations. All the displayed energies were calculated at CASPT2/CASSCF level. It can be interesting to compare the computational cost of ASEP/MD and other methods. The ASEP/MD cost is clearly lower than that of traditional QM/MM methods that do not use the mean fiend approximation, as this approximation permits to reduce the number of quantum calculations from several thousands to a few tens. Consequently, an upper level calculation can be used in the description of the chromophore. However, its cost is several tens of times larger than continuum models (it is necessary to perform a larger number of quantum-mechanic calculations and several Molecular Dynamics simulations). The main advantage of ASEP/MD is that it permits to properly account for specific interactions and thermal effects. MECIs were calculated61 using both equilibrium and non-equilibrium solvation. In the case of equilibrium solvation (Eq-MECI), it is assumed that the solvent structure is in equilibrium with the charge distribution of the upper state. Because of the searching procedure is restricted to a subset of configurations of the solvent (those that are in equilibrium with the upper state) the Eq-MECI is an upper limit to the true MECI. In order to relax this restriction, also non-equilibrium calculations were performed (Neq-MECI). To this end, we introduce a generalized solvent coordinate. Following Malhado and Hynes11, two diabatic states, denoted 1 and 2, were defined. In the first diabatic state the charge distribution, {q(1)}, correspond to that of the ground state, i.e.,

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the positive charge of the molecule is mainly located on the iminium moiety. In the second one, {q(2)}, the charge is mainly placed at the opposite end of the alkyl chain. An auxiliary solute charge distribution is then defined as the linear combination of the solute charges associated to the two diabatic states: {qaux}(λ) = λ{q(1)} + (1-λ){q(2)}

(1)

The dimensionless quantity λ is the generalized solvent coordinate. Next, the averaged solvent potentials, VNeq (λ), associated with the auxiliary charge distributions {qaux}(λ) were calculated using the ASEP/MD methodology and introduced into the chromophore molecular Hamiltonian. The Neq-MECIs were then calculated for different λ values. If a linear response is assumed for the solvent, then the solvent polarization associated with {qaux}(λ) can be written in the usual way: VNeq= λVeq(1) + (λ-1)Veq(2). However, we prefer Eq (1) as it is also valid for non-linear response. Once the critical points on the free-energy surface have been located, (MECIs, Franck– Condon points, minima, etc.), free energy differences between them were estimated making use of a dual method, where the solute contributions are quantum mechanically calculated but the solute–solvent interaction contributions are classical. With this approximation the free-energy difference between two species or states, I and J, in solution, ΔGIJ, reads: ΔGIJ = ΔEIJ + ΔGint IJ + ΔVIJ

(2)

where ΔEIJ is the internal quantum energy difference between the two species or states I and J and ΔGint is the solute–solvent interaction free-energy difference, which is calculated classically using the free-energy perturbation (FEP) method.62 In calculating this term the solute geometry was assumed to be rigid and a function of the perturbation parameter ζ. When ζ = 0, the solute geometry and charges correspond to the initial state (the chromophore ground state, for instance). When ζ = 1, the charges and geometry correspond to the final state (the critical points on the chromophore excited state surface). Charges and geometries of the initial and final states are those obtained using ASEP/MD. A linear interpolation is applied for intermediate values. A value of Δζ = 0.05 was used. That means a total of 40 separate molecular dynamics simulations were carried out to determine the solute-solvent interaction free-energy difference. The final value is obtained as the arithmetic mean of the backward and forward values. It is convenient to split the ΔGint term into others two terms, ΔEint and ΔGdist. The ΔEint term is the solute-solvent interaction energy difference between the two states (I and J) and it is always calculated using the real solute charge distribution. The second term, ΔGdist, is the solvent distortion energy, i.e., the energy spent in to polarize the solvent from the situation I to J. In equilibrium solvation this term is calculated using the real charge distribution; however, in non-equilibrium solvation it is estimated by using the auxiliary charge distribution ΔVIJ is a term that includes the solute zero-point energy difference and the solute entropic contribution between the two states. This term, ΔVIJ, can be evaluated by applying the harmonic oscillator and rigid rotor approximations to the vibrational and rotational modes of the solute in solution, and it needs the information provided by the Hessian matrix, something that makes its calculation difficult in solution systems. In previous papers63 it has been verified that this term is not noteworthy and given its large

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computational cost its contribution has been neglected. Consequently, final results do not include the ΔVIJ term. All the in solution calculations were performed with the ASEP/MD program, using the data provided by MOLCAS 7.449 and Moldy64. The number of methanol molecules was 630. No counterion was included. Previous studies of Muñoz-Losa et al9., Röhrig et al65., and Rajamani and Gao66 using chloride as counterion found that, because of the large dielectric screening effect of methanol, the effect of the counterion on the structure and spectrum of the solute is minimal. This fact has been corroborated by experiments showing that the position of the chromophore absorption band in polar solvents is not affected by the nature of the counterion.38 During the MD simulation all molecules were described by combining Lennard-Jones interatomic interactions with electrostatic interactions at fixed intramolecular geometry. The solvent and solute molecules were represented using AMBER non-bonded parameters67. Periodic boundary conditions were applied, and spherical cutoffs were used to truncate the molecular interactions at 9.0 Å. A time step of 0.5 fs was used. The electrostatic interaction was calculated with the Ewald68 method and the temperature was fixed at 298 K by using a Nosé-Hoover69,70 thermostat. Each MD simulation was run at constant volume for 75 ps (25 ps equilibration, 50 ps production). The total number of ASEP/MD cycles was, at least, 10 and the ASEP at each cycle was calculated from the data of 1000 configurations evenly distributed along the simulation. In solution final results were obtained by averaging the last five ASEP/MD cycles and therefore they represent an effective simulation time of 250 ps.

3. RESULTS AND DISCUSSIONS A priori any double bond of the alkyl moiety of the all-trans RPSB molecule could undergo photo-isomerization71. However, whereas in bacteriorhodopsin only the 13-cis product is found, in polar solvents the 9-cis and the 11-cis products are preferred. A special attention will be dedicated to these isomers. The absorption and emission bands will be first analyzed, and then we will discuss the non-radiative de-excitation paths. As it has been already indicated, the S1 energy surface has a complicate topology: part of the energy surface has an ionic character while other part is covalent. The reactive channel is related to the ionic S1 region, while the covalent region seems to be related to the non-reactive channel. Recent studies by Valsson and Filippi72, and Martinez and coworkers3 on RPSB models with three double bonds have shown that CASSCF optimizations tend to overestimate the number of critical points (minima and CIs) on the potential energy surface in gas phase. Most of these critical points disappear when geometries are optimized at CASPT2 level. Unfortunately, the high computational cost of CASPT2 optimizations makes unfeasible its application to the study of RPSB. Polar solvents have a similar effect10 on the free energy surfaces: they reduce the number of minima on S1. Thus, and waiting for more accurate calculations, CASPT2/CASSCF in methanol solution calculations are expected to provide a good approximation to the S1 free-energy surface.

3.1 Gas Phase

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Table 1 displays absorption transition energies in gas phase of the main critical points (minima, FC, CI, etc.) involved in the photochemistry of the methylated and nonmethylated (native) all-trans-RPSB at several calculation levels. The maximum of the absorption energy obtained at CASPT2//MP2 level for the native all-trans-RPSB is placed at 1.97 eV, in a very good agreement with the experiment73 (2.03 eV). At this computational level the BLA at the ground state minimum is 0.274 Å. The ground state minimum is almost flat, except by the torsion of the β-iononic ring with respect to the linear chain, see Table 2. Thus, the C5C4C9C10 dihedral angle, φ, takes a value of -42.5º. The value of this angle is important because a larger torsion results in a larger deconjugation of the ring double bond with the rest of the chain and consequently in an increase of the vertical transition energy. When the geometry is optimized at CASSCF level, the BLA increases until 0.568 Å and the torsion angle to -68.6º. As a consequence, the absorption vertical transition increases to 2.35 eV. The introduction of a methyl group at position C10 does not have an appreciable effect on the dihedral angle nor on the BLA of the ground state. Therefore, the vertical absorption energy is almost identical to that found in the non-methylated compound (1.95 eV vs 1.97 eV at CASPT2//MP2 and 2.35 vs 2.34 eV at CASPT2//CASSCF). Due to the difficulty of performing geometry optimization of excited state using CASPT2 method, the remaining critical points on S1 will be described at CASSCF//CASSCF and CASPT2//CASSCF methods. (Table 1: near here) As for the emission spectrum of the native compound, a minimum (confirmed by frequency calculations) was located on the ionic region of the S1 state. This minimum is placed 0.6-0.8 eV below the FC point, see Figure 3, and, like the ground state, the alkyl chain remains essentially flat. However, there are notably differences in the bond lengths. In agreement with previous results on a five double bond model, the S1 minimum has a single and double bond distribution opposite to that displayed by the ground state. Formal double bonds elongate while formal single bonds become shorter. During the evolution of the RPSB molecule from the FC point to the minimum, the BLA decreases taking a value of -0.10 Å (the minus sign is a consequence of the change in the single and double bond character). The emission from this minimum appears at 1.51 eV when calculated at CASPT2//CASSCF. Both at the minimum and at the absorption FC geometry the S2 state is placed at very high energy above the S1 state (between 1.3 eV and 0.8 eV depending on the calculation level). (Table 2: near here) (Figures 3a and 3b: near here)

MECIs associated to the rotation around C9C10, C11C12 and C13C14 double bonds have been located on S1. These structures will be denoted as MECI-9, MECI-11 and MECI-13, respectively. In all cases, the double bonds involved in the CI rotate until to reach a value close to 90º, and simultaneously their length increases until 1.47-1.48 Å, losing the π character. This fact eases the torsion and permits the internal rotation of the molecule. Both at CASSCF and CASPT2 levels the three CIs are below the absorption FC point, see Fig. 3. The two MECIs with lower energies are MECI-9 and MECI-11. The MECI-13 is almost 0.2 eV above the MECI-9 and the MECI-11. At all the MECI

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geometries, the S2 state is also well separated (1.1 eV in the MECI-9 and for more than 2 eV for the other two MECIs). It can be concluded that the S2 state does not play any role in the evolution of the excited state in gas phase. The S1 surface seems to be very flat around the S1 minimum and it is separated from the conical intersections (MECI-9 and MECI-11) by a barrier lower than 1 kcal/mol. Olivucci and co-workers74 have suggested that the multiexponential decay displayed by this system is related to this flatness of the energy surface joints to different amounts of kinetic energy in the reactive torsional mode. Table 3 and Figure 4 display the charge distribution at the main critical points for native and methylated all-trans-RPSB. In order to ease the charge analysis a bipolar distribution is shown. To this end the molecule was divided into two moieties, placing the separation surface at the middle point of the C11=C12 bond. We denote these moieties as the alkyl and the iminium parts. In the ground state the positive charge of the molecule is localized around the nitrogen atom, i.e., in the iminium part of the molecule. During the transition part of this charge is transferred to the alkyl moiety. Consequently, the charge at the FC point spreads out over the whole molecule. However, in the MECIs the positive charge concentrates on the alkyl moiety. This inversion in the charge distribution suggests the use of two diabatic states to represent the photoisomerization process, one with the positive charge placed close to the nitrogen atom, the other one with the charge mainly placed on the alkyl moiety. These two states will be used in the study of non-equilibrium solvation in the following subsection. (Table 3: near Here) As for the 10-methyl derivate, its S1 potential-energy surface presents noticeable differences with respect to that of the native compound, see Figure 3. Thus, we did not success in localizing on the S1 free energy surface a minimum equivalent to that found in the native chromophore. The path that connects the absorption FC point with the MECIs seems to be a barrier-less process. Furthermore, the stability of MECI-9 and MECI-11 is increased in about 0.2 eV with respect to the FC point. The relative stability of MECI-13 is not affected. In sum, an important effect of the methylation at C10 is to favor the rotation of the two double bonds contiguous to that carbon atom. This increase, in turn, the slope of the de-excitation path, something that could increase the decay speed. (Figure 4: near here) Finally, it can be highlighted some other points about the methylated and the native RPSB in gas phase. On the one hand, the geometries of both derivatives (Table S1) are very similar, only it is possible to appreciate small differences in the close neighborhood of C10. On the other hand, the absolute charge values on the atoms close to the C10 methyl group decrease, especially in atoms C9, C10 and C11. Finally, it is worthy of note that for the 10-methyl derivative the S2 state is also well separated from S1 at the FC and MECIs structures and it seems not to play any role in the decay dynamics of the S1 state in the gas phase. 3.2 Methanol solution

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Before discussing about the relative stabilities of the different structures in solution it is interesting to analyze the changes introduced by the solvent in the geometries (Table 2) and charge distributions (Table 3). In each and every one of the studied critical points the absolute atomic charge values increase in going from gas phase to solution. This increase can be notable in some atoms (see for instance charges on C9 and C10 in Figure 4a). As it has already been indicated, in the ground state the positive charge concentrates in the iminium part. During the electron transition there is a flux of positive charge from the iminium to the alkyl moiety that results in an ionic state where the charge is evenly distributed between the two moieties (at the S1 minimum geometry). As on the one hand S1 displays, in general, a less localized charge than S0 and on the other hand polar solvent like methanol favor charge separation, it results that the S1 state is worse solvated than the ground state and it is, as a whole, destabilized. At the MECIs the flux of positive charge toward the alkyl moiety further increases and there is an inversion of the charge distribution with respect to the ground state. As for the geometry, the solvent decreases the BLA values and increases the value of the φ dihedral angle. Part of the blue solvent shift (see below) is a geometric effect associated to the increase of φ. In the native compound, the absorption vertical energy transitions S0S1 are 3.04 and 3.54 eV at CASPT2//MP2 and CASPT2//CASSCF levels. Even if the difference in the transition energy is almost 0.5 eV the solvent shift is in both cases similar, about 1.1 eV. This value overestimates the experimental27 value (δ=0.77 eV) in about 0.3-0.4 eV. Part of this discrepancy could be related to the neglecting of the electronic polarization of the solvent. It is well known that the use of non-polarizable fixed charges to represent the solvent overestimates the solute-solvent interaction energy. Since the S0 state solvates better than S1, this overestimation produces an increase of the absorption transition energy. At CASSCF//CASSCF level a minimum on S1 was located at 3.52 eV over the ground state minimum, which represents 1.03 eV below the FC point. When the dynamic correlation is included the S1 minimum is de-stabilized and its energy becomes similar to that of the FC point. The in methanol emission energy from this minimum is estimated between 1.54-1.72 eV (experimental value38 is 1.72 eV). The calculated solvent shift is lower than 0.1 eV. In agreement with experiment the solvent shift on the emission transition energy is negligible. Solvation has a very large effect on the absorption spectra but hardly modify the emission bands position. The differences observed in the solvent effects on the absorption and the emission spectra can be explained by the large differences in the solvent molecule distributions around the S0 (covalent) and the S1 (ionic) minima. In the ground state the positive charge is located on the nitrogen atom. This charge is strongly solvated by methanol molecules, i.e., the solvent is very structured around the nitrogen atom, see rdfs in Figure 5. The rest of the molecule (that is in essence neutral) is worse solvated and there is not a well-defined solvent structure around it. When the molecule is excited, part of the charge is transferred from the nitrogen atom to the alkyl moiety, a region where the solvent molecules do not have the adequate orientation to stabilize the charge and, consequently, there is an important decrease of the solute-solvent interaction energy with respect to the initial situation, which, in turns, originates an important solvent shift. On the contrary, in the ionic S1 minimum, the charge is distributed over the entire molecule and there are molecules solvating both the alkyl chain and the nitrogen atom. When the emission takes place, the charge concentrates again on the iminium part, but

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in this region there are already solvent molecules oriented in the correct direction. Therefore, the solvent can stabilize the increased charge on the nitrogen atom and the solute solvent interaction energy between the initial and the final state is very similar, from here the small solvent shift. (Figure 5: near here) The energy gap between S2 and S1 at the absorption FC geometry is considerable in gas phase but it reduces in solution (from 0.8 eV to 0.15 eV for the native all-trans-RPSB at CASPT2//CASSCF level). Consequently, transitions from S0 to S1 and S2 overlap. In agreement with experiments, two well-defined bands are expected in the absorption spectra in gas phase but only one in solution. The proximity of the two bands at the FC point could affect the decay dynamics as population transfer between the two states becomes now possible. Similar effects have been recently documented.46,47 The three MECIs (MECI-9, -11 and -13) display higher energies than the S1 minimum at CASSCF//CASSCF level. At CASPT2//CASSCF the MECIs are stabilized with respect to the minimum, see Figure 3. The relative stability follows the order MECI-9 > MECI-11 > MECI-13. Only MECI-9 and MECI-11 have energies lower or similar than the absorption FC point. MECI-13 is clearly above the FC point, i.e., it is non-accessible from excitation to S1. In agreement with the experiments only 9-cis and 11-cis isomers are accessible from S1 excitation. In sum, solvation causes important modifications in the relative stability of the critical points. The presence of a methyl group bonded to C10 also produces noticeable changes in the in solution free-energy profile of the S1 excited state, mainly in the relative stability of the MECIs with respect to the FC point. On the contrary, the S0/FC energy gap is not affected; therefore, the absorption transition energy does not change (3.47 and 3.54 eV for the native and methylated all-trans-RPSB at CASPT2//CASSCF level). Similar to that found in gas phase we do not success in localizing a minimum on S1; hence, the in solution dynamic from the FC to the MECI geometries seems to be also a barrier-less process. It is worthy of note that the introduction of the methyl group decreases the MECI energies in about 0.3-0.5 eV. This value is more than twice the in gas phase value; consequently, the decay process in solution is characterized by a very large slope. These two factors (lack of a minimum and increase of the decay path slope) permit to explain the different decay dynamics found in the native and 10-methyl all-trans-RPSB. Until now we have assumed equilibrium solvation. It is expected that if this restriction were relaxed, permitting non-equilibrium solvation, the position of the MECIs would be shifted to lower energies (with respect to the FC point). However, we find that the variations are very small. Thus, for instance, for MECI-9, the Neq-MECI is only 0.1 eV more stable then the Eq-MECI. Furthermore, the chromophore geometry is only slightly affected by the new solvent structure. The generalized solvent coordinate, λ, (see Eq. (1)) takes values close to 0.8. These small changes do not modify the main conclusions about the retinal photochemistry and consequently will not be further discussed. (Figure 6: near here) The S2 state, at the FC absorption geometry, is close to the S1 (0.27 eV). On the contrary, at the MECIs, the S2 state is well separated from S1 and S0. Therefore, if the S2

10


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state has an effect on the photoisomerization dynamics it must be because it permits to the RPSB population to branch around the FC. The mechanism proposed for the photodynamics of the native and the 10-methyl all-trans- RPSB is displayed at Figure 6. This mechanism is similar to the suggested for Kukura and co-workers42,45 with two small differences: 1) the small energy barrier on S1 has been completely suppressed for the methylated compound and 2) the S2 state have been added in order to highlight its possible role on the non-reactive decay path.

4. CONCLUSIONS Despite the fact that RPSB is one of the more studied photochemical systems, there is some controversy about the details of the photoisomerization dynamics in polar solvents. Recent studies by Kukura and co-workers have shown that the methylation at the C10 position originates important changes in the reaction dynamics. In this paper we have compared the S1 free-energy surface of the native and methylated compound both in gas phase and in methanol solution. We find that the introduction of a methyl group modifies the S1 free-energy profile in two aspects: 1) The small barrier that separates the S1 minimum from the MECI in the native chromophore disappears when the alltrans-RPSB is methylated at C10 and, therefore, the photoisomerization becomes a nonactivated process 2) MECI-9 and MECI-11 geometries become stabilized with respect to the FC point and the other MECIs. These two effects combine to speed up the photoisomerization. The solvent increases further the relative stability of these two MECIs, hence, the slope of the free-energy surface increases. Moreover, the interaction with the solvent brings closer the S1 and the S2 energy levels at the absorption FC geometry, permitting the branching of the population between the reactive and nonreactive channels. These conclusions are not modified by the consideration of nonequilibrium solvation. Supporting Information: Selected geometrical parameters for diverse structures of the methylated and native RPSB molecules in solution are available in the Supporting Information." Acknowledges This work was supported by the GR15169 project from the Consejería de Economía, Comercio e Innovación of the Gobierno de Extremadura.

11



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S0→S1 S0→S2 R=H CASSCF//CASSCF 3.40 4.41 CASPT2//CASSCF 2.35 3.62 CASSCF//MP2 2.87 3.61 CASPT2//MP2 1.97 2.94 CASSCF//CASSCF(2roots) 3.33 CASPT2//CASSCF(2roots) 2.37 4 Expt. 2.00 3.44

S0→S1 S0→S2 R = CH3 CASSCF//CASSCF 3.37 4.44 CASPT2//CASSCF 2.34 3.61 CASSCF//MP2 2.81 3.53 CASPT2//MP2 1.95 2.88 CASSCF//CASSCF(2roots) 3.30 CASPT2//CASSCF(2roots) 2.35 Expt. -

Table 1: Absorption transition energies (in eV) for native and methylated all-transRPSB in gas phase

17



R: H

CASSCF Gas phase MeOH

Page 18 of 27

MP2 Gas phase MeOH

C— C

1.451

1.458

1.424

1.440

C= C

1.346

1.341

1.369

1.356

C14 — C15

1.427

1.443

1.397

1.416

C15 = N16

1.292

1.283

1.323

1.306

N16 — C17

1.467

1.460

1.461

1.460

N16 — H18 BLA ϕ

1.004 0.568 -68.5

1.015 0.624 -68.3

1.018 0.274 -42.5

1.033 0.419 -45.4

R: CH3 C—C

CASSCF Gas phase MeOH 1.465 1.464

MP2 Gas phase MeOH 1.426 1.443

C=C

1.348

1.343

1.374

1.359

C14 — C15

1.427

1.444

1.396

1.416

C15 = N16

1.292

1.283

1.324

1.306

N16 — C17

1.467

1.460

1.461

1.460

N16 — H18 BLA ϕ

1.004 0.579 -69.5

1.016 0.639 -69.5

1.018 0.259 -42.4

1.032 0.422 -47.8

Table 2: Selected geometrical parameters (distances in Ångström angles in grades) for ground state minimum of the methylated RPSB in gas phase and in methanol solution. a) Native compound b) Methylated compound

18


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φ

Geometry State Gas phase R=H MeOH Gas phase R = CH3 MeOH

S0 0.273 0.727 0.141 0.859 0.237 0.763 0.080 0.920

S1 0.625 0.375 0.463 0.537 0.592 0.408 0.407 0.593

MECI-9 S0 S1 0.171 0.942 0.829 0.058 0.238 0.963 0.762 0.037 0.925 0.139 0.075 0.861 0.211 0.903 0.789 0.097

MECI-11 S0 S1 0.017 1.082 0.983 -0.082 0.115 0.477 0.885 0.523 -0.025 1.031 1.025 -0.031 0.099 1.173 0.901 -0.173

MECI-13 S0 S1 0.133 0.772 0.867 0.228 0.267 0.693 0.733 0.307 0.096 0.779 0.904 0.221 0.182 0.89 0.818 0.11

Table 3: Charge distribution for diverse structures of the methylated RPSB in solution. Values with grey background corresponds to the alkyl moiety, in white to the iminium moiety

19



TOC GRAPHIC

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All-‐trans RPSB



HºΨº = EºΨº

MD calculation [HQM + HQM/MM]Ψ = E Ψ New geometry and solute charge distribution

Gradient, charge distribution

NO

Converged

YES

Solute properties


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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46


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How Methylation Modifies the Photophysics of the Native All-

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