Consequences of Strong Coupling between Solvation and Electronic

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J. Phys. Chem. B 2008, 112, 11353–11360

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Consequences of Strong Coupling between Solvation and Electronic Structure in the Excited State of a Betaine Dye Tateki Ishida*,† and Peter J. Rossky*,‡ Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan, and Center for Computational Molecular Science, Institute for Computational Engineering and Sciences, and Department of Chemistry and Biochemistry, UniVersity of Texas at Austin, Austin, Texas 78712 ReceiVed: February 26, 2008; ReVised Manuscript ReceiVed: June 24, 2008

The electronic ground and excited-state structures of the betaine dye molecule pyridinium-N-phenoxide [4-(1pyridinio)phenolate] are investigated both in the gas phase and in aqueous solution, using the reference interaction site model self-consistent-field (RISM-SCF) procedure within a CASSCF framework. We obtain the total free energy profiles in both the ground and excited states with respect to variation in the torsion angle between the phenoxide and pyridinium rings. We analyze the effect of solvent on the variation of the solute dipole moment and on the charge transfer character in the excited state. In the gas phase, it is shown that the potential energy profile in the excited-state decreases monotonically toward a perpendicular ring orientation and the dipole moment decreases along with decreasing charge localization. In water, the free energy surface for twisting is better characterized as nearly flat along the same coordinate for sterically accessible angles. These results are analyzed in terms of contributions of the solvation free energy, the solute electronic energy, and their coupling. Correspondingly, the dependence of the charge transfer character on solute geometry and solvation are analyzed, and the important roles in the excitation and subsequent relaxation processes for the betaine dye are discussed. It is found that there is considerable solute electronic reorganization associated with the evolution of solvation in the excited state, and it is suggested that this reorganization may contribute significantly to the early time evolution of transient spectra following photoexcitation. 1. Introduction Excited state properties in the condensed phase are practically important in underlying our understanding of photochemistry while, at the same time, these properties remain relatively challenging to address theoretically. In contrast, experimental approaches to detect fast dynamics in solution are highly developed and the observation of time-dependent spectral changes linked to excited-state electronic changes and to solvatochromic effects has been accessible for some time.1-9 Among the many substances which show a sizable solvatochromic effect, the dye betaine-30 (Reichardt’s dye)10 is very susceptible to solvent polarities. It is well-known for its sizable blue shift in polar solvents, increasing with increasing polarity, indicating a relatively large change in charge-transfer (CT) character in the excitation, with the greater charge separation in the ground state. This feature implies that intramolecular electron transfer occurs by photoexcitation, and that the relaxation of the excited-state therefore also serves as a model of photoinitiated electron transfer.11-16 In all condensed phase transient spectral experiments, a key challenge is the interpretation of spectral changes in terms of solvation and solute contributions. The most common assumption underlying such analysis8,17 assumes that the ground and excited states have different charge distributions, but that these * Authors to whom correspondence should be addressed. E-mail: (T.I.) [email protected]; (P.J.R.) [email protected]. † Department of Theoretical and Computational Molecular Science, Institute for Molecular Science. ‡ Center for Computational Molecular Science, Institute for Computational Engineering and Sciences, and Department of Chemistry and Biochemistry, University of Texas at Austin.

molecular charge distributions are independent of solvent and of dynamical changes in solvation state. While this assumption can be reasonable if the solute is not too polarizable, there are indications that substantial quantitative contributions will result from coupling of electronic state and solvent structure,18-22 and one would expect that the role of such coupling could be particularly important in contexts capable of exhibiting considerable charge transfer. The case of betaine-30, where a considerable research effort has already been invested, is a good example where this can be effectively explored, both experimentally and theoretically.11,12,14,18,19,22-24 A relatively complex analysis of spectral dynamics was required for this case, as reported by Kovalenko et al.14 These researchers invoked multiple time scale solvation dynamics and intramolecular solute dynamics (with corresponding, geometry-dependent, oscillator strengths) in order to rationalize the data. A fundamental element in this analysis is the potential role of a twisted geometry for the central chromophore, which consists of the pyridinium and phenoxide rings.14,19,24 It is, of course, necessarily difficult to validate a relatively complex molecular interpretation of the spectral dynamics based on experimental data alone, and here, the interaction of theory and experiment can be exceptionally beneficial. The related twisted intramolecular charge transfer (TICT) for (p-dimethylamino)benzonitrile (DMABN) is well-known.25,26 In the TICT case, the solute has less charge separated character in the ground-state and CT occurs by photoexcitation, so that the solute dipole is enhanced with the twisting of the excited solute in polar solvents. For the interpretation of fluorescence measured in TICT, models have been proposed which invoke both solvent polarity and viscosity.27,28 In the case of DMABN, it is accepted

10.1021/jp801660b CCC: $40.75  2008 American Chemical Society Published on Web 08/15/2008

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Figure 1. Molecular geometry and site labels used for 4-(1-pyridinio)phenolate (PNP).

that the solute electronic structure is dramatically modified by both photoexcitation and relaxation of excited-state geometry.29-33 In particular, it is accepted that the torsional motion plays an important role in the CT process.32 In the present paper, we explore in detail, computationally, the coupled effects of solute geometry, solute electronic structure, and solvation, for a betaine dye. Rather than performing calculations for the very large betaine-30, with five pendant phenyl rings, it is desirable to focus on a smaller chromophore that will allow a higher level computation to be carried out. The central chromophore of betaine-30, pyridinium-N-phenoxide (denoted below as PNP), is the simplest betaine dye (see Figure 1), and the basic phenomenon of charge transfer discussed above is a property of this central moiety, although PNP has not been the subject of much experimental study to the best of our knowledge.34 In theoretical studies, PNP is often employed for comparison with other betaine dye molecules.23,35,36 For the ground-state in the gas phase, solute electronic structure calculations have been performed and it has been reported that even this simplest betaine has a somewhat twisted form;36 the torsion angle between the pyridinium and phenoxide rings was found to be 25-40°,23,35-37 as a result of steric conflicts between ring hydrogens, preventing the conjugation-promoted planarity of the ring pair. For solution phase, although one report of a calculation with a semiempirical quantum description and an approximate description of the solvent reported that the groundstate torsion angle of PNP was 90° in water, higher level calculations by us,37 applying the reference interaction site model self-consistent-field (RISM-SCF) approach found the torsion angle in water to be 46.7°in qualitative accord with previous theoretical and experimental results for betaine-30.18,24,38 For the excited-state in the gas phase, ab initio singles only configuration interaction (SCI) results calculated at a density functional theory (DFT) ground-state geometry yield a dipole moment drop (14.92 D f 9.50 D) and the vertical transition energy of 2.9 eV.36 For solution, it has been reported from semiempirical calculations39 that for the S1 excited-state in the gas phase and in water, the solute dipole moment decreases monotonically as the torsion angle tends to 90°. As in the TICT case, the CT process in a betaine dye in the excited-state should be correlated with the solute-solvent interaction. Solvation structure is influenced by the charge

Ishida and Rossky distribution of the molecular wave function, and the solvation free energy (excess chemical potential) strongly depends on this solvation structure. At the same time, the solute electronic energy is sensitive to the polarization of the solute wave function. Both factors will enter the free energy surface of betaine to some extent. Previously, it has been shown by the present authors that a molecular level description for PNP in polar solvents is essential to investigate the ground-state S0 free energy profile and the solute properties.37 Here, we apply a variation of the same approach, the RISMSCF method, to the same PNP system but in the first excitedstate S1. The RISM-SCF approach, described in the next section, has succeeded in describing many physical and chemical properties in solution at the molecular level for ground states,40-42 and some studies for excited states have been reported.43,44 Results for excited states of relatively large molecules such as betaine dyes have not been carried out previously. Going beyond any of the previous considerations, our method employs both a reasonably high level ab initio theory for the electronic structure calculations of the solute, and it uses an integral equation theory with a detailed molecular description of the solvent to describe solvation. Further, these two aspects are treated in a self-consistent manner, which could be particularly significant. Therefore, we can expect to obtain a reliable description of electronic structure changes of the solute molecule associated with solvation. It is anticipated that the description of the electronic structure engendered by solvent hydrogen bonding could be particularly notable, since, in the present approach, the charges on solute atomic sites are not only determined by the solute electronic state, but also by the average solvent state. In particular, we focus on the excited-state CT process for PNP in water. For describing adequately the qualitative modification of the PNP electronic structure between zwitterionic ground-state character and CT character in the S1 state, we employ a complete active space (CAS)SCF calculation.45 In the context of spectroscopic data, we note at the outset that the methods used here describe equilibrium solvation statistics, so that we are able to describe equilibrium initial and final electronic states, as well as states corresponding to vertical transitions in nuclear coordinates, but the approach cannot capture relaxation dynamics. Further, the method as currently formulated does not provide electronic responses to solvent fluctuations, so that contributions to lineshapes due to solventinduced inhomogeneous broadening18,19 are not addressed. This paper is organized as follows. In the next section, section 2, we present the theoretical methods employed for the processes of interest in PNP, and the details of the computation procedure are described. In section 3, the results for electronic structure obtained for PNP in the S1 state in the gas phase are reported first. The S1 free energy profile in water with respect to the central torsion angle between rings is then presented. We then examine the relationship between the behavior of those profiles and the S1 CT process, emphasizing the variation in solute charge distribution with conformation and solvation. The conclusions of this work are summarized in section 4. 2. Theoretical Methods In this section, we briefly describe the methods used to evaluate the electronic structure and solvation. 2.1. The RISM-SCF Method. We only briefly summarize the theoretical methods employed, as the details of the RISMSCF method can be found elsewhere.46-48 The free energy of the system can be defined within the RISM-SCF theory as

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G ) Esolute + ∆µu

(1)

where Esolute is the solute electronic energy computed with the molecular Born-Oppenheimer Hamiltonian from the electronic wave function and ∆µu is the excess chemical potential of this solute in solution. Variational conditions on the free energy yield the solute electronic structure and the atomic site-site correlation functions which describe the solvent distribution around the solute. These correlation functions are obtained by solving the extended RISM (XRISM) equations49-51 for the site-site correlation functions (with the hypernetted-chain closure relation):

huV ) ωu/cuV/ωV + Fωu/cuV/hVV

F 2β R∈u γ∈V

∑ ∑ ∫0

∞

2 4πr2 dr(hRγ - 2cRγ - hRγcRγ) (3)

where β ) 1/kBT (kB is the Boltzmann constant). The electrostatic potential originating in the solvent around the solute is then obtained from the following:

VR ) F

∑ qγ∫

γ∈V

gRγ(r) dr r

solventa

site

H2O

H O

soluteb C O N H a

q/e

σ/Å

ε/(kcal/mol)

0.41 -0.82

1.000 3.166

0.056 0.155

σ/Å

ε/(kcal/mol)

3.550 2.960 3.250 2.420

0.070 0.210 0.170 0.030

From ref 64. b From refs 62 and 63.

(2)

where h(r) ) g(r) -1 and c(r) are the total and direct site-site radial correlation functions, respectively, and labels u and V represent individual atomic sites on solute and solVent molecules, respectively. ω represents the set of intramolecular site-site correlation functions, and F is the solvent number density. The asterisk denotes the spatial convolution integral. With correlation functions obtained from the XRISM equations, the solute (u) excess chemical potential is given by

∆µu )

TABLE 1: Molecular Mechanics Parameters for Solvent and Solute

(4)

where qγ represents the partial charge on the solvent site γ, and gRγ(r) ) hRγ(r) + 1 is the site-site radial distribution function between the solute site R and the solvent site γ. After the solvated Fock operator was constructed including this electrostatic potential, the electronic structure calculation in the condensed phase is performed fully self-consistently. 2.2. Computational Details for the S1 State of PNP. In both the gas and solution phases, all of the ab initio calculations were carried out at the CASSCF level, with the (9s5p1d/4s1p)/ [3s2p1d/2s1p] basis set, which possesses valence double-ζ plus polarization (DZP) quality.52 For the excited-state calculations in the gas phase, the optimized structures from the RHF level in the ground-state were used. In the computation for the excitedstate in water, the ground-state optimized geometries in aqueous solution obtained by the RISM-SCF method at the RHF level were employed. Throughout all optimizations, both the pyridinium and the phenoxide ring were constrained to be planar with C2 symmetry in each ring. The active space used in the CASSCF calculation included 11 active orbitals (12 electrons), which is constructed from π and π* orbitals for the pyridinium and phenoxide ring moieties, respectively, 6 π-valence active orbitals, and the nonbonding (n) orbital on the oxygen. With the present active space set, we could not obtain convergence for the pure S1 state with an optimized geometry in C1 symmetry from the ground-state at the RHF level. Rather than pursue the much more time-consuming calculation with an even larger active space, we first confirmed that the state-averaged CASSCF wave function with both the C2 and C1 optimized geometries, under the condition without molecular orbital symmetry, included the same main configuration state function (CSF) for the S1 state. With this established, we carried out the calculation for the S1 excited-state under C1 symmetry, but using the molecular geometry optimized in C2 symmetry in the ground-

state at the RHF level. Since we focus only on the torsion angle parameter between the pyridinium and phenoxide rings in S1, this calculation appears to be a reasonable compromise between completeness and computational effort for the present purposes. In solution, the partial charges on the solute atomic sites needed for XRISM were calculated by least-squares-fitting of the electrostatic potential (usually termed ESP), which was evaluated at a number of grid points around the solute. It is important to discuss the grid generation used. We had previously noted that the symptom of using too few points was the appearance of nonsystematic “oscillation” in solute charges and solvation free energy profiles with changes in solute geometry.37 In addition, since a grid point distribution may not be uniformly optimal with varying molecular conformation, the ESP fitting can produce numerically unstable results.53,54 Therefore, it is desirable to introduce a well chosen grid distribution to handle these problems. As discussed in the literature,55 one profitable approach is the Lebedev grid method.56,57 Recently, this method has been applied in the field of density-functional theory (DFT) in the context of numerical integrations.58-60 With this grid method, it is possible to avoid biasing the grid points in certain angular directions and to provide a grid point distribution at a fixed distance from atomic centers. We implemented the Lebedev method, combining it with the grid generating procedure based on the Voronoi polyhedra.61 In the present case, we generated about 45000 grid points around the solute to evaluate solute ESP charges. This number of grid points is sufficient to respond to the large change of wave function between the ground and excited states and to avoid numerical inconsistencies with geometric alterations. 2.3. Molecular Mechanics Parameters for Solute and Solvent. For the RISM calculation, all the required additional parameters for both the solute and solvent molecules are adopted from standard sets used in computer simulation.62,63 These are summarized in Table 1. The simple point charge (SPC64) like model was used as a model of water solvent; SPC is supplemented by Lennard-Jones parameters for the H atom (σ ) 1.0 Å and ε ) 0.056 kcal · mol-1). All calculations were carried out at T ) 298.15 K. 3. Results and Discussion In this section, we describe the results of the calculations and discuss their origins. 3.1. Gas Phase Results. We consider first the results in the absence of solvent. 3.1.1. Torsional Energy Surface. From our investigation, it was found that the CASSCF wave function in the vertically excited S1 state was described mainly by a π f π*-like transition, from the phenoxide ring to the pyridinium ring. Figure 2 shows the charge transferred schematically for this transition.

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Ishida and Rossky

Figure 2. Representation of the transition between the two rings in 4-(1-pyridinio) phenolate in the S0 f S1 excitation using molecular orbitals from the gas phase calculation. Contours corresponding to orbitals from the major configurations contributing to S0 and S1 states are shown.

Figure 4. Dipole moment variation with the central torsion angle for the S0 and the S1 states in the gas phase and in water.

Figure 3. Gas phase energy profiles along the central torsion angle, relative to S0, χ ) 0°, for the S0 and the S1 states. The energy S1-S0 difference at χ ) 0° is 55.6 kcal/mol.

This figure indicates that the CASSCF wave function in the S1 state is represented by a dominant configuration corresponding to the direct charge transfer from orbitals on the phenoxide ring to orbitals on the pyridinium ring without a change in nuclear geometry. This is a very reasonable result since PNP has a charge-separated character in the ground state, with the phenoxide ring anionic and the pyridinium ring cationic. In the S1 excited state, charge separation is reduced. The wave function obtained indicates that it includes an n f π* character also, with a smaller weight. The vertical transition energy obtained was 2.26 eV. This is in very close agreement with the experimental estimate of Gonza´lez et al.34 for the transition energy of PNP in vacuum of 18509 cm-1 (2.29 eV). In Figure 3, the torsional potential energy surface in the gas phase is shown. The energy curve decreases monotonically with respect to the torsion angle, reaching a minimum at χ ) 90° with an energy difference between χ ) 0° and 90° of about 10.7 kcal mol-1. PNP favors a perpendicular conformation in the excited state, in contrast to about 40° in the ground state, in agreement with limited previous studies.39 In the ground state, the PNP wave function has strongly charge-separated character, but there is π-conjugation between the two rings.37 In the case of the excited state, the phase on each ring in the π* orbital becomes antibonding at the junction. One may expect that this twist can enhance the shift in CT character upon excitation, which we consider next. 3.1.2. Solute Dipole Moment. In Figure 4, the dipole moment results in the S0 and S1 states are displayed. The solvated case will be discussed in section 3.2.2, below. As shown in Figure 4, the dipole moment of the simplest betaine in the gas phase is largely reduced. At the vertical excitation angle (χ ) 40°), the dipole moment decreases dramatically (14.0 D f 1.62 D),

consistent with the expected charge transfer character. It is also seen that the dipole moment is further reduced as χ increases. The charge transfer associated to the excitation in PNP is “enhanced” in that, as the torsion angle increases, the originally localized electrons in the ground-state are increasingly delocalized in the excited state. As a result, the dipole moment decreases. This charge transfer behavior is exactly the reverse of the process occurring in the TICT case. 3.2. Results in Aqueous Solution. We now consider the impact of solvation by water. 3.2.1. Torsional Free Energy Profile in the S1 State. In Figure 5a, the total free energy profile in water is shown. We find the Vertical transition energy from S0 to S1 at the groundstate optimized torsion angle in water (χ ) 46.7°) to be 4.06 eV. It should be noted that this value is calculated for vertical excitation in solute and solvent, with the solVent electrostatic potential constrained to the ground-state values. We note that we do not include any polarizability in the solvent model, so that no relaxation of the solvent-induced potential is appropriate here. Gonza´lez et al.34 have reported about 3.3 eV in water as an experimental result. Our result is in qualitatively accord, with the transition energy in solution reflecting the expected substantial blue shift with respect to the gas phase value of 2.3 eV. As seen more clearly in the relative comparisons presented in Figure 5b, in contrast to the ground state,37 the free energy curve becomes nearly flat for angles larger than χ ) 46.7° (the optimal torsion angle in the S0 state in water). Compared to the energy surface in the S1 state in the gas phase, also shown in the figure, the difference in behavior for 40° e χ e 90° is remarkable. Parts a and b of Figure 5 indicate that the free energy profile with respect to the torsional motion in PNP is forced in the gas phase while being essentially flat as it approaches the perpendicular conformation in water. These would imply quite different torsional dynamics between gas and water cases and would imply, in particular, a nearly random walk in torsion angle following photoexcitation in solution. Hence, it is of particular interest to investigate the constituents of the total free energy. Figure 6 displays the torsional changes in the solvation free energy term separately from the electronic energy. The excess chemical potential increases toward χ ) 90°, balancing the decrease in electronic energy. Figure 7 shows the change in solvent radial distribution function (rdf) between the S0 and S1 states at χ ) 46.7°, the S0 optimized torsion angle in water. Figure 7 presents the rdf between the solute oxygen and the

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Figure 7. Radial site-site distribution function for O(solute)-H(solvent) in the S0 and in the S1 states, reflecting loss of hydrogen bonding in the excited state.

Figure 5. Solution free energy profile with respect to the central torsion angle in water, relative to S0, χ ) 0°. (a) Profiles in the S0 and S1 states. The free energy difference at χ ) 0° is 84.9 kcal/mol. (b) Profile for S1 in water, relative to χ ) 0° and on an expanded scale. For comparison, results in the gas phase are also shown. Lines are provided as a visual guide.

Figure 6. S1 state torsional profiles for the solute excess chemical potential ∆µu and solute electronic energy in water, relative to χ ) 0°.

water hydrogen site, which reflects most clearly the strength of solvent hydrogen bonding with solute sites. As seen in Figure 7, the height of the first peak decreases dramatically due to the transition from S0 to S1. Correspondingly, one finds that the solute O site charge decreases from -1.13 (S0) to -0.60 (S1). To quantify the implication from the rdf that hydrogen bonding effects are an important factor here for solvation, we calculated the formal contribution of solute oxygen-solvent interaction to the excess chemical potential (Eq. 3) at the S0 optimized torsion angle in the S0 and S1 states in water. (Of course, in the free energy, all contributions are coupled.) We obtained -96.05 (S0)

Figure 8. Solute dipole moment torsional profile in the S1 state in water, and, for comparison, in the gas phase.

and -13.82 (S1) kcal/mol. Thus, the change in hydrogen bonding between in the S0 and in the S1 states is quite important. Also, the O site charge in the excited-state decreases slightly (-0.60e f -0.59e) toward the perpendicular conformation. Therefore, the solvation energy will be reduced substantially by the excitation and also decreased gradually due to an increase in the torsion angle, in correspondence with the excess chemical potential profile in Figure 6. On the other hand, the solute electronic energy decreases as the torsional angle increases, as it does in the gas phase. While the difference between χ ) 0° and 90° is about 2 kcal/mol for the excess chemical potential, and about 8 kcal/mol for the solute electronic energy, in the sterically accessible region χ ) 40° f 90°, the changes in these properties are nearly the same in magnitude (about 2 kcal/mol). Therefore, the total free energy profile in the sterically accessible region of torsion angle is essentially flat. It is also interesting to note that the solvent-induced change in the solute electronic energy surface is comparable to, and of the same sign as, the solvation free energy (cf. S1 in gas in Figure 5b, and Esolute in Figure 6). We relate these features to electronic charge distribution below, and then discuss the spectroscopic significance in the context of the S1 state solvation process. 3.2.2. Solute Dipole Moment in Water. The solute dipole moment is displayed in Figure 8. The dipole moment decreases in the region from 0° to ∼47°. For larger angles, it exhibits a trend similar to that of the total free energy profile, with the slight positive deviation in the region between 60° and 90° being

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Figure 9. Net charges on the phenoxide and pyridinium rings in water as a function of torsion angle in the S0 and S1 states. The gas phase results are shown for comparison.

within numerical error. Compared to the excited-state dipole moment in the gas phase, the magnitude increases as a result of polar solvation. The solute dipole moment is, nevertheless, greatly reduced compared to that in the ground state. For example, the dipole moment decreases at the S0 optimal angle (χ ) 46.7°) from 27.1 D in S0 to 2.4 D in S1 (see Figure 4). Corresponding to the decrease of the solute O site charge previously discussed, the solute C(2) and C(3) site charges (see Figure 1) are enhanced from -0.26 (S0) to -0.60 (S1). Our results for the solute dipole moment parallel the features of the excess chemical potential shown in Figure 6. 3.3. Charge Transfer Character and Solvation Process in the S1 State. In order to characterize the charge transfer in the present system, one appropriate quantity for analysis is the total charge on each ring of PNP, obtained by summing the ESP charges, in both the S0 and S1 states. In Figure 9, the alteration of the total charge on each ring in water is indicated as a function of the torsion angle, and results in the gas phase are also shown for comparison. Corresponding to the enhancement of dipole moment in water, the magnitude of the total charge on each ring in the S0 state is considerably larger than that in the gas phase. However, in the relatively low polarity S1 state, the results are quite similar. These indicate that the wave function manifests charge transfer character both in the gas phase and in water, but that the solvent greatly enhances the difference. As seen in Figure 9, the total charge on the pyridinium and phenoxide rings are relatively large in the ground S0 state, as reported previously.37 On the other hand, in the S1 state; the magnitude of the charges is close to zero. These features are in agreement with expectations based on previous discussions for betaine30. In the physical excitation, the betaine dye is first excited vertically in the nuclear coordinates and then proceeds to a new equilibrium point, in general due to both solute structural relaxation and solvation dynamics. Therefore, it is of interest to specifically compare equilibrium excited-state solute properties to those at the vertically excited point in water. As noted earlier, this comparison is accessible with the current methods, although the dynamics of the relaxation is not. In the previous discussion, we considered the process of solvation only in regard to the shift in the vertical energy gap (from 2.26 eV in gas to 4.06 eV in water), evaluated by constraining the solvent distribution to be that in the ground S0 state and using the S0

Ishida and Rossky optimized solute geometry. We can then compare the constrained solvation with equilibrium solvation in S1 and obtain the initial and final states associated with solvation dynamics. The results obtained show that the solute dipole moment decreases from 27.1 to 10.7 D following vertical excitation. A relatively large further reduction to 2.4 D is associated with relaxation of solvation structure in the S1 state. One can, at this point, ask how this relaxation would be reflected in a spectroscopic signature. There are several aspects that are more or less accessible to us. First is the time scale. Although, as mentioned, we cannot access the dynamics here, we do know that for both water and acetonitrile19,65 solvation dynamics is predominantly a subpicosecond process. Significant torsional dynamics occurs in betaine-30 only on a longer time scale, at least in acetonitrile.19,65 Hence, processes occurring in the spectra at subpicosecond times14 are highly likely to be engendered by solvent dynamics or higher frequency intramolecular processes. The second aspect is the solvent-induced Stokes shift. The electronic reorganization associated with S1 solvation dynamics, reflected in the dipole moment change from 10.7 to 2.4 D, necessarily evolves on the same time scale as the solvation dynamics. In the present work, the energetics will not be directly comparable to those of betaine-30, since the solvent accessibility must be affected by the pendant phenyl rings in that case. However, for completeness, we note here that we find the S1 energy gap is 4.06 eV vertically (larger than in betaine-30) and exhibits a solvent-induced Stokes shift of 0.33 eV at equilibrium solvation. In addition, we have calculated the Stokes shifts for torsion angles between 60° and 90° and find a value near 0.38 eV, almost independent of torsion angle. The relative independence of Stokes shift from the torsional angle is consistent with the data shown in Figure 8, where one sees that the dipole moment does not change much with the change of torsion angle (toward 90°). The third aspect is oscillator strength. We can only roughly estimate oscillator strength variation, because CASSCF wave functions obtained in the S0 and S1 states are not orthogonal. Nevertheless, we evaluated the corresponding integral at three angular points around the optimized torsion angle in water (40°, 46.70° and 60°). We obtained oscillator strengths of 0.08, 0.07, and 0.07, corresponding to those torsion angles, suggesting that in this range that might be accessed at short times, there is not a strong dependence of oscillator strength on the geometry. To rationalize experimental transient spectra for betaine-30 in acetonitrile, Kovalenko et al.14 have argued that charge transfer must have less influence on the Stokes shift when occurring on very short time scales and that torsion is an important component. The present results, combined with earlier results,19,65 suggest that torsion does not play a key role in the complex early (subpicosecond) time evolution of the spectra. Rather, these results suggest that in this time regime, the transient spectra reflect an electronic relaxation on the solvation time scale, causing the excited-state spectrum to evolve. To demonstrate whether this view is correct would require the calculation of both the absorption and emission spectrum of S1, which is a task beyond the capacity of the present methods. 4. Conclusions The solvated excited-state properties of the simplest betaine dye, pyridinium-N-phenoxide (PNP) were investigated in water. We employed the coupled integral equation-electronic structure method RISM-SCF with a CASSCF wave function, and implemented the Lebedev grid approach to obtain stable ESP fitting results. The free energy profile and molecular charge

Consequences of Strong Coupling distribution have been evaluated with respect to the torsional inter-ring angle, in both the S0 ground-state and the S1 excited state. The same properties were studied in the gas phase for comparison purposes. The S1 wave function included primarily π f π* inter-ring excitation and also a smaller n f π* contribution; both were from the phenoxide ring to the pyridinium ring. The transition energy in vacuum of 2.26 eV is in good agreement with estimates based on experimental data. In water, the vertical transition energy was evaluated as 4.06 eV, in qualitative accord with the observed solvatochromic blue shift. While the gas phase torsional energy in S1 decreased significantly and monotonically with torsion angle to a minimum with perpendicular rings at χ ) 90°, at equilibrium in aqueous solution, the S1 free energy profile becomes nearly flat in the sterically accessible region from χ ∼ 45° to 90°, as a result of compensation between a less favorable solvation free energy and more favorable electronic energy. In a less polar solvent, such as acetonitrile, one would expect the same trend toward a flatter free energy surface compared to vacuum, but to retain some net driving force. The dipole moment of PNP in the gas phase was substantially reduced on vertical excitation (14.0 D f 1.62 D), decreasing slightly more upon twisting in the excited state, with increased decoupling of the ring π systems. In aqueous solution, the solute dipole moment is dramatically enhanced in the ground state37 to 27.1 D, so that the adiabatic excitation to S1 in the groundstate geometry leads to an even larger dipole moment shift of nearly 25 D (27.1 D f 2.4 D). It was found that these changes were consistent with calculated shifts in atomic and ring charges, with the charge transfer character being qualitatively similar in the gas and solution phases. Of particular interest, it was shown that upon vertical excitation in both solvent and solute coordinates, the PNP dipole moment changed from 27.1 to 10.7 D, with solvent relaxation leading to the final adiabatic value of 2.4 D. Thus, there is a substantial electronic reorganization accompanying solvation dynamics in S1. We propose that the electronic charge reorganization process associated with solvation dynamics may contribute significantly on the subpicosecond time scale in the detailed femtosecond-resolved optical spectra now accessible for the betaine system in polar solvents.14 However, estimates of the torsional dependence of the transition dipole and of the Stokes shift suggest that torsion should be at most weakly reflected in spectral features,14 at least at short times (less than ∼1 ps). It is of interest to determine the generality of these results for other molecular solutes, but it is clear from these results alone that for a molecular transition that has substantial charge transfer character and a large associated molecular polarizability, effects such as these can be expected. A theoretical analysis treating the time-dependence of these properties and a full account of molecular spectra is an important subject for future investigations. Acknowledgment. T.I. gratefully acknowledges research support by the Grant in Aid for Scientific Research (19029044, 20038047) on Priority Areas “Molecular Theory for Real Systems (No. 461)” from the Ministry of Education, Culture, Sports, Science, and Technology in Japan. P.J.R. is grateful for support of this research by a grant from the National Science Foundation (CHE-0615173). Additional support by the R. A. Welch Foundation (F-0019) is gratefully acknowledged.

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