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J. Phys. Chem. B 2008, 112, 414-423
How the Environment Controls Absorption and Fluorescence Spectra of PRODAN: A Quantum-Mechanical Study in Homogeneous and Heterogeneous Media† Benedetta Mennucci,*,‡ Marco Caricato,§,⊥ Francesca Ingrosso,# Chiara Cappelli,‡ Roberto Cammi,∇ Jacopo Tomasi,*,‡ Giovanni Scalmani,⊥ and Michael J. Frisch⊥ Dipartimento di Chimica e Chimica Industriale, UniVersita` di Pisa, Via Risorgimento 35, 56126 Pisa, Italy, Department of Chemistry, Yale UniVersity, 225 Prospect Street, New HaVen, Connecticut 06520-8107, Gaussian, Inc., Wallingford, Connecticut 06492, Ecole Normale Supe´ rieure, De´ partement de Chimie, UMR 8640, 24 rue Lhomond, 75231 Paris Cedex 05, France, and Dipartimento di Chimica, UniVersita` di Parma, Viale delle Scienze 17/A, 43100 Parma, Italy ReceiVed: August 1, 2007; In Final Form: September 21, 2007
The spectroscopic behavior of 6-propionyl-2-(N,N-dimethyl)aminonaphthalene (PRODAN) is investigated in different environments, ranging from homogeneous solutions of different polarities to diffuse interfaces mimicking membranes. The variety of experimental data as well as computational results present in the literature still do not clarify the nature of the emission process; in particular, it is not well-established whether fluorescence in such a molecule occurs from a planar or from a twisted intramolecular charge transfer state. The first part of the work is thus devoted to better understand how the electronic transition processes occur in homogeneous solvents. The effect of the medium polarity as well as the hydrogen bond formation are studied. In the second part of the paper, a first attempt to interpret the experimental results of PRODAN in unilamellar vesicles is carried out. The complexity of the still-open questions about the photophysics of PRODAN has prompted us to base the study on quantum-mechanical calculations performed at various levels of theory, namely, DFT, TDDFT, CIS, and SAC-CI, and to include the effects of the environment in a self-consistent way. This is achieved by using the integral equation formalism version of the polarizable continuum model (IEFPCM). IEFPCM is a quite versatile approach, being able to treat equilibrium and nonequilibrium solvation in both homogeneous and heterogeneous media.
1. Introduction 6-Propionyl-2-(N,N-dimethyl)aminonaphthalene (PRODAN) has widely been used as a fluorescence probe since it was introduced by Weber and Farris.1 The effect of polar solvent on its absorption and, more effectively, on its fluorescence spectra is large, leading to significant shifts of the main bands: the experimental solvatochromic shift passing from cyclohexane to water is 1260 cm-1 for absorption and 6620 cm-1 for emission. Because of this large sensitivity to solvation, PRODAN has also been employed to probe the microenvironment in experiments on biomembranes, vesicles, and reverse micelles.2-5 In refs 2 and 3, the authors performed experiments on large unilamellar phospholipid vesicles. They found that the emission maxima of PRODAN in the bilayer depended on the phase state of the medium, emitting in the blue portion of the spectrum when the medium is a gel and in the green portion when the medium is a liquid crystal. From the temperature dependence of the PRODAN emission spectrum, it has been concluded that, in the liquid crystalline phase, there is an influence due to dielectric relaxation of the medium that is absent in the more †
Part of the “James T. (Casey) Hynes Festschrift”. * Corresponding author. E-mail:
[email protected] (B.M.); tomasi@ dcci.unipi.it (J.T.). ‡ Universita ` di Pisa. § Yale University. ⊥ Gaussian, Inc. # Ecole Normale Supe ´ rieure. 3 Universita ` di Parma.
packed gel phase. The red-shift does not depend on the polar head residue or on the charge, but on the presence of water molecules at the level of the glycerol backbone. More recently, investigations on large unilamellar vesicles4 led to the observation of a partition process of PRODAN between the bulk and the bilayer, in which, however, PRODAN is mostly found in the lipidic phase. The microenvironment probed by PRODAN is formed by two distinct regions: one polar at the interface and one less polar between phospholipid tails. This leads to the observation of two bands in the emission spectra and of two different fluorescence lifetimes. Experimental studies of PRODAN at a polar/nonpolar interface were extended to anionic and cationic reverse micelles.5 Experiments were carried out at a fixed water concentration, varying the surfactant concentration, and at a fixed surfactant concentration, varying the water content. When the surfactant concentration varied but not the content of water, bathochromic shift and an increase in the emission intensity were observed for the anionic case. On the other hand, by varying the water concentration, a new band at lower energy was also observed. The two bands were interpreted as the emission from two different excited states of PRODAN located at the interface. The large sensitivity of absorption and fluorescence of PRODAN to the local (or micro) environment can be explained by considering the nature of the electronic state giving rise to the spectroscopic signal; this can be in fact described as a photoinduced intramolecular charge transfer (ICT) state, as it is commonly found in organic molecules having an electron donor and an electron-acceptor group usually separated by
10.1021/jp076138m CCC: $40.75 © 2008 American Chemical Society Published on Web 11/16/2007
Environmental Influence on Spectroscopy of PRODAN aromatic rings. The phenomenon is of great interest because of the possible applications to study energy conversion in chemical and biological systems.6 Some ICT molecules give rise to dual fluorescence, with two fluorescence bands observed, which correspond to a local excited state and to the ICT state. The nature of emission from electronic excited states in PRODAN has been studied at the experimental and the computational levels.2-5,7-16 However, it is still not clear whether fluorescence in such a molecule occurs from a planar (P) or from a twisted (T) state. Both the donor (dimethylamino group) and the acceptor (propionyl group) can twist, with an increase of the molecular dipole moment. Early theoretical studies in vacuo were conducted on the basis of semiempirical calculations.9 Such studies reported that PRODAN has a planar ground-state geometry, but that fluorescence is due to emission from a highly polar excited state with a twisted geometry. Successive studies11-13 performed at different levels of the theory, namely, configuration interaction of single excitations (CIS),11 density functional theory approach combined with single configuration interaction (DFT/SCI),12 and semiempirical levels,12,13 concluded that emission from a twisted charge-transfer excited state is stabilized by polar solvents. The effect of the solvent polarity was taken into account by using a self-consistent reaction field (SCRF) approach, and discussed in terms of a Lippert-Mataga plot of the Stokes shift.13 A more extensive experimental study4 of the behavior of PRODAN absorption and emission band as a function of solvent polarity has shown, by using the Kamlet-Taft approach,17 that not only the solvent polarity, but also the possibility of solutesolvent hydrogen bond formation and solute aggregation (in water) have to be taken into account. Recently, Abelt and collaborators published two papers15,16 in which the fluorescence spectra of two systems similar to PRODAN were studied. In these two systems, the amino group is forced to be planar or twisted. From the comparison between the spectra of these two systems with the spectrum of PRODAN, the authors concluded that the emission occurs from the planar geometry in the excited state. They also confirmed their experimental results by configuration interaction (CI) calculations with the semiempirical Hamiltonian AM1 within the COSMO18 approach. The authors showed that, in the (constrained) twisted PRODAN derivatives, the stability of the T-ICT state versus the P-ICT state in solution depends on the choice of the solvent polarity (a higher polarity stabilizing the T-ICT), whereas the (constrained) planar derivatives have the same photophysical behavior as PRODAN.16 From this brief summary of the literature, it is clear that the absorption and, even more, fluorescence properties of PRODAN are still not completely clarified, as well as their dependence on the characteristics of the homogeneity, polarity, and acidity of the (micro)environment. The goal of the present work is thus twofold: On one hand, we try to better clarify the nature of the absorbing and emitting excited states in homogeneous media using different quantum-mechanical (QM) approaches. In this part, we address the problem of what state is at the origin of the emission process. We consider different environments, starting from the vacuum toward media of increasing polarity. We also take into account specific solute-solvent interactions, such as hydrogen bonds, which can play an important role in determining the spectroscopic properties of PRODAN. The study of the excited state of PRODAN is done computing the absorption and emission energies. The P-ICT versus T-ICT models are compared considering both planar and twisted
J. Phys. Chem. B, Vol. 112, No. 2, 2008 415 excited-state geometries. In the latter case, we focus on the twisting of the amino group with respect to the plane of the aromatic rings. On the other hand, we provide an estimate of the effect that a heterogeneous environment has on the transition energies; in this second part of the study, heterogeneous media are also studied. In particular, to mimic PRODAN in unilamellar vesicles, a model system made by a diffuse interface presenting the limit dielectric properties of water and cyclohexane is introduced. For this system, orientational and position effects are analyzed in terms of changes in the absorption and fluorescence energies. The paper is organized as follows: In section 2, we analyze the absorption and emission properties of PRODAN in homogeneous media with different polarities as well as the hydrogen bond properties. In section 3, the spectroscopic behavior of PRODAN at an interface between different media is reported and analyzed. Concluding remarks are summarized in section 4. 2. Homogeneous Media This section collects the data computed for the gas phase and for homogeneous media of different polarities (cyclohexane, acetonitrile, and water). A comparison with the experimental data available in the literature is also discussed. Calculations in different environments will be performed using density functional theory and its time-dependent extension (TDDFT). Ab initio calculations will be also performed in order to provide a comparison with the DFT results, namely, CIS excited-state optimizations, as well as single-point excitation energy calculation with the symmetry-adapted cluster/configuration interaction (SAC-CI)19 method (in gas phase only). The environment effect is taken into account by using the polarizable continuum model,20-22 in its integral equation formalism version (IEFPCM).23,24 All TDDFT transition energies in solution (either homogeneous or heterogeneous) will be calculated by using the correction to the linear response approximation (cLR) we recently proposed.25 Such an approach uses the excited-state relaxed density matrix to correct the time-dependent DFT excitation energies, and it introduces a state-specific solvent response. All the calculations were performed with the 6-311+G(d,p) basis set, and the calculations in solution were run using a cavity made of interlocking spheres with the following sphere radii, scaled by a factor of 1.2: 1.7 Å for C, 1.9 Å for CH, 2.0 Å for CHn (n ) 2, 3), 1.52 Å for O, and 1.6 Å for N. All calculations in the gas phase and in solution were done using a developing version of the Gaussian code,26 in which TDDFT gradients have recently been implemented with the inclusion of solvent effects.27 2.1. Absorbing and Emitting States. We start by discussing the data obtained in the gas phase using the B3LYP28 hybrid functional. Geometry optimization for the electronic ground state (S0) resulted in a planar minimum structure.29 The corresponding absorption energies for the first three excited states are reported in Table 1 together with the oscillatory strengths and dipole moments (µ). At the TDB3LYP level, the first vertical excited state, S1, has the highest oscillatory strength, and it is well separated from the S2 and S3 states, which are very close in energy and have null or small oscillatory strengths. These findings together with the good agreement with the experimental absorption energy (measured in cyclohexane; in the gas-phase data are not available) seem to show that the experimentally observed band
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TABLE 1: Absorption Data for the First Three Excited States In Vacuo Computed at the TDB3LYP Levela exptl S1 S2 S3 b
absorption
µ(Sn)
osc. strength
3.62b 3.48 3.75 3.76
10.2c 12.8 2.0 10.2
0.304 0.000 0.043
a Transition energies are in eV, and dipole moments are in debye. Cyclohexane solution (ref 4). c Benzene solution (ref 14).
TABLE 2: Emission Data for the First Excited State In Vacuo Computed at the TDDFT/B3LYP Level for the Planar and Twisted Optimized Structuresa exptl planar twisted
emission
µ
Stokes shift
3.15b-3.18c 3.19 2.37
10.2d 12.4 19.3
3904b-3540c 2340 (2400)
a Transition energies are in eV, dipole moments are in debye, and Stokes shifts are in cm-1. b Solution in cyclohexane (ref 10). c Solution in cyclohexane (ref 4). d Solution in benzene (ref 14).
at lowest energy and highest intensity corresponds to the transition to the S1 state. The calculated dipole for S1 seems to confirm what is observed in the most recent experiments,14 while it is in contrast with older studies, which estimated much larger values (with changes with respect to the ground state of ca. 20 D).1 Our findings are finally compared with the results obtained by Parusel et al. using the DFT/CIS approach.12 We note that a similar character was found for the S1 state (similar f and µ) but with the excitation energy red-shifted by 0.14 eV with respect to the present one. Still keeping the same level of calculation, we have performed geometry optimization of the S1 state and calculated the corresponding emission energy. As the main issue to investigate in order to clarify the nature of the fluorescent excited-state is whether its geometry is twisted, we also performed geometry optimization of S1 by starting from a structure in which the amino group was twisted by 90° with respect to the plane of the aromatic rings. The results obtained are reported in Table 2. According to the TDB3LYP calculations, the twisted geometry results in a more stable minimum than the planar one by ∼19 kcal/mol. As a result, the excitation energy for the twisted conformation is small and in worse agreement with the experimental value than the corresponding value for the planar geometry. A possible explanation for this is that the minimum excited-state configuration having a twisted geometry is an artifact due to the use of the B3LYP functional for describing charge-transfer states. In order to provide some insight into the artificial stability of the twisted state induced by the use of the B3LYP functional, let us discuss it in terms of the orbitals involved in the electronic transition for the planar and twisted geometries. The electronic transition mainly involves the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), both in the planar and in the twisted configuration. In both cases, the LUMO is a π* orbital with the electron density mainly located on the naphthalene ring and the carbonyl group. On the other hand, the HOMO for the planar structure is a very delocalized π orbital, whereas this delocalization is broken in the twisted conformation, for which the HOMO is very close to an atomic p orbital on the N atom. The transition is therefore quite different for the two geometries: a π f π* transition for the planar geometry, and an n f π* transition for the twisted one.
Figure 1. B3LYP/TDB3LYP and HF/CIS S0-S1 changes in the main geometrical parameters (in Å).
TABLE 3: Absorption and Emission Data In Vacuo Computed at the SAC-CI Level for the Structures Optimized at the TDB3LYP Levela S0 f S1 S1 f S0 (pl) S1 f S0 (tw) a
energy
osc. strength
Stokes shift
3.62 3.21 3.83
0.3854 0.2859 0.1984
3319
Transition energies are in eV, and Stokes shifts are in cm-1.
These results confirm the well-known difficulties of the B3LYP functional in describing long-range charge interactions;31 such difficulties can thus lead to an incorrect description of the charge density and of the geometry.32 To further investigate possible consequences on the analysis of PRODAN excited states, two other QM methods were tested, namely, CIS and SAC-CI. The CIS optimizations for the S1 excited state confirmed that the twisted geometry is not a minimum geometry, but it collapses in a planar one. For the planar case, on the contrary, B3LYP and CIS give a generally similar description as represented in Figure 1 in which the ground-to-excited changes in the main geometrical parameters are reported at both the B3LYP/TDB3LYP and HF/CIS levels. As it can be seen, calculated geometrical changes moving from the ground to the S1 state show a similar qualitative trend at the DFT and CIS levels (being that the CIS changes are generally larger, especially for C5C6 and C7N bonds). As a further test on the reliability of the B3LYP geometries, SAC-CI calculations of absorption and emission energies were also performed. The resulting transition energies are reported in Table 3. For the twisted structure, SAC-CI gives a significantly larger value than that calculated for the planar one, showing that, at this level of calculation, the twisted structure does not represent the absolute minimum in the S1 potential energy surface (PES), as instead found using a TDB3LYP description. Moving to the comparison with experiments, SAC-CI results give a very good agreement both for absorption and emission energies (if the planar structure is used), while the comparison with TDB3LYP results reported in Tables 1-2 shows that TDB3LYP underes-
Environmental Influence on Spectroscopy of PRODAN
J. Phys. Chem. B, Vol. 112, No. 2, 2008 417 TABLE 4: S0 and S1 Dipole Moments (Debye) in the Gas Phase and in the Various Solvents exptla gas phase cyclohexane acetonitrile water a
Figure 2. B3LYP gas-to-solution changes in S0 bond lengths (a). S0S1 changes are also reported (b). All values are in Å.
timates the absorption energy of ca. 0.15 eV, but, surprisingly, it correctly describes emission energies in the planar S1 state. This analysis seems to further confirm that the TDB3LYP description of planar geometries is correct, as well as transition energies for planar structures, while for the twisted structure, it leads to an unphysical stabilized state. In conclusion, both CIS and SAC-CI checks seem to show the existence of an S1 state whose nature does not change from the initial (or FranckCondon) region to the final relaxed structure, in which geometry changes mostly involve the modification of single and double bonds, but the donor and acceptor groups are still on the same plane. Following these indications, we move on now to analyze the effects of the environment. We repeated geometry optimizations of the electronic states in three different solvents (cyclohexane, acetonitrile, and water) using B3LYP for the ground state and both the TDB3LYP and CIS levels for the excited states. As found for the isolated molecules, also in the different solvents, TDB3LYP leads to two minima corresponding to a planar and a twisted structure, with the latter being the lowest one. Once again, this twisted minimum collapses into the planar one if a CIS level is used. This correspondence between solvated and isolated PRODAN confirms the gas-phase conclusion of the existence of an S1 state whose nature does not change upon relaxation also in the presence of a polar solvent. The change in the environment only affects the single- and double-bond lengths in the initial and final state as shown in Figure 2 in which the gas-to-solution changes in S0 bond lengths (graph a) and S0-S1 changes are reported. To conclude the analysis of the absorbing and emitting states, in Table 4 we report the dipole moments of the S0 and the vertical and relaxed S1 states in the various solvents (to have a
S0
S1 (vertical)
S1 (relaxed)
5.2 6.1 7.7 9.3 9.4
12.8 15.3 16.9 17.0
10.2 12.4 15.0 19.1 19.4
The reported experimental data refer to benzene solution (ref 14).
more direct comparison, gas-phase data already reported in Tables 1-2 are repeated here). In the relaxed S1 both geometry and dielectric relaxation have been taken into account. From the results reported in the table, it appears evident that the absorbing (or vertical) and emitting (or relaxed) states have the same nature: they both show a dipole moment that is almost double the S0 dipole in all media. In polar solvents, a further increase is found moving from the vertical to the relaxed S1. This increase of the dipole, however, is not induced by geometry effects but by the dielectric relaxation of the solvent (no increase is in fact found in the gas-phase or in cyclohexane). In polar solvents, in fact, we have to introduce two different solvation regimes for the vertical and the relaxed states; in the vertical state, the solvent response is determined by the optical dielectric constant (ca. 1.5 for both acetonitrile and water), as the rest of the response (corresponding to orientational motions of the solvent molecules) can be considered frozen during the vertical transition from S0 to S1. This partial response is generally indicated as nonequilibrium solvation. Only by assuming that the excited-state lifetime is long enough for the solvent molecules to reorient according to the excited-state charge distribution can we apply the complete response of the solvent in terms of its static dielectric constant: this is what we have assumed in order to get the relaxed S1 dipole moment. Summarizing the results obtained so far, we can conclude that the transitions of PRODAN, both in absorption and in emission, have a π f π* nature, involving the HOMO-LUMO orbitals, in which the charge density moves from the amino group toward the propionyl group, involving the whole central naphthalene structure. Irrespective of the presence of a polar solvent, the absorbing and emitting states are both planar with a dipole moment almost twice that of the ground state, in agreement with recent experimental studies.10,15,16 If such a planar S1 state is considered, the TDB3LYP level provides results in sufficiently good agreement with the experiments and with more accurate QM methods. TDB3LYP, however, leads to a second fictitious minimum for the S1 state characterized by a twisted geometry, which collapses to the planar one if we shift to a CIS description. Following these indications, we move on now to analyze the effects of the environment on absorption and emission energies, by considering only B3LYP/TDB3LYP results for the planar ground and excited states. 2.2. Polarity and Hydrogen-Bonding. In Table 5, we report the absorption data for the first three excited states in cyclohexane, acetonitrile, and water computed at the TDB3LYP level. All values have been obtained reoptimizing the geometries in each solvent and performing single-point calculations by using the cLR formalism recently proposed.25 Moreover, we remind the reader that, for polar solvents, the transition energy was calculated assuming a nonequilibrium solvation in the vertical S1. The results show a picture similar to what is found for the isolated molecule, with the difference being that, in all solvents,
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TABLE 5: Absorption Energies (eV) and Corresponding Oscillatory Strengths Calculated at the TD/B3LYP Level in Cyclohexane, Acetonitrile, and Water cyclohexane exptlb S1 S2 S3 a
acetonitrile
water
absorption
osc. strength
absorptiona
osc. strength
absorptiona
osc. strength
3.62 3.35 3.70 3.78
0.447 0.061 0.000
3.51 (-0.11) 3.26 (-0.09) 3.64 (-0.06) 3.90 (0.12)
0.484 0.046 0.000
3.46 (-0.16) 3.26 (-0.09) 3.64 (-0.06) 3.87 (0.09)
0.485 0.045 0.000
Shifts with respect to cyclohexane are also reported in parentheses. b The reported experimental data are taken from ref 4.
TABLE 6: Emission Energies (in eV) and Stokes Shifts (cm-1) for the S1 State in Cyclohexane, Acetonitrile, and Water, Computed at the TDB3LYP Level for the Planar Geometry emission
a
Stokes shift
exptl calcd
cyclohexane 3.15a-3.18b 3.09
exptl calcd
acetonitrile 2.71b 2.79
6500b 3800
exptl calcd
water 2.36b 2.77
8900b 3950
3904a-3540b 2097
From ref 10. b From ref 4.
there is a shift between the S2 and S3 states. In all cases, however, the S1 state remains well separated and with the largest oscillatory strengths. We therefore observe a trend that is similar to what was found in the gas phase. As observed in the experiments, moving from cyclohexane to acetonitrile and to water leads to a red-shift of the absorption energies. This can be related to the character of the S1 state, which presents a larger dipole moment than the ground state and, in a polar solvent, will be more stabilized than the ground state with respect to an apolar solvent (see below for a more detailed analysis). A very similar picture was found in a previous QM study by Lobo and Abelt15 where AM1/CISD calculations using a COSMO model to describe solvent effects gave absorption energies of 3.36 and 3.30 eV passing from cyclohexane to acetonitrile. A general comment about the PCM data is that they correctly reproduce the observed red-shift; the agreement is quantitative in the case of acetonitrile, for which the calculated shift with respect to cyclohexane is ca. 0.1 eV (exactly as measured experimentally), while, for water, the calculated shift underestimates the measured one. It has to be noted that calculations in acetonitrile and in water give very similar results, while experiments show a further red-shift moving from the first to the second: this can be explained in terms of a missing effect (e.g., hydrogen bonding) in the PCM description of water, which will be analyzed below. In Table 6 we report the same analysis for the emission energies: in all cases, the initial state is the planar S1 optimized at the B3LYP level in the different solvents. As was observed for absorption, PCM provides a correct description of the red-shift for emission. The calculated shift for acetonitrile (0.30 eV) correlates well with experiments (0.43 eV), even though the agreement is worse than that for absorption. A similar underestimation of the red-shift passing from cyclohexane to acetonitrile was also found in the previous AM1/ CISD/COSMO study,15 in which emission energies of 2.99 and 2.75 eV were calculated for the two solvents. The different quality in the description of absorption and emission energies explains the error in the calculated Stokes
Figure 3. Optimized structures of PRODAN with two water molecules H-bonded to the carbonyl oxygen both in the gas phase and with PCM. Selected bond distances are reported (in Å). B3LYP/6-311+G(d,p) was used for the ground state, and TDB3LYP/6-311+G(d,p) was used for the excited state.
shift, which is always smaller than that in the experiments. This can be related to the lower accuracy of TDDFT in describing excited states with respect to DFT in describing ground states. For water, the error with respect to experiments becomes significantly larger. The calculated shift is less than half of the observed one (0.32 versus 0.82 eV). Once again, PCM behavior in water can be related to an intrinsic limit of continuum methods when strong specific solute-solvent effects are present. PRODAN can, in fact, form H-bonds with water molecules. In order to get an estimate of such a specific effect, we have introduced a supermolecule approach considering PRODAN with two water molecules H-bonded to the carbonyl oxygen. This cluster has been optimized both in the gas phase and using a mixed discrete/PCM (or solvated supermolecule) description. For the ground state, we used a B3LYP/6-311+G(d,p) description, while for the excited state, the clusters were optimized at the TDB3LYP/6-311+G(d,p) level starting from a planar PRODAN. The resulting structures are reported in Figure 3. It is to be noted that, in the gas phase, the optimized S0 maintains only one water H-bonded to the PRODAN oxygen atom; in contrast, in the presence of PCM, the two water molecules both remain H-bonded to PRODAN, even if with H-bonding distances larger than those in the gas phase. For S1, both the gas phase and PCM give a similar structure, with PCM giving slightly longer H-bonds; in both phases, H-bonds are strengthened moving from S0 to S1, as it can be seen from the significantly shorter (C)O‚‚‚H(OH) distances. The results obtained for absorption and emission with the isolated and the solvated supermolecules are reported in Table 7. The first result to comment on is the evidently different description obtained for the isolated and the solvated supermolecules. In absorption, the result obtained in the isolated supermolecule is even blue-shifted with respect to that of cyclohexane, while, in emission, the red-shift is recovered but is very small; adding also the effect of the bulk with the PCM, a far better behavior
Environmental Influence on Spectroscopy of PRODAN TABLE 7: Absorption and Emission Data of PRODAN+2 Water in the Gas Phase and Bulk Watera exptlc gas PCM
exptlc gas PCM
absorptionb
µ
3.46 (-0.16) 3.39 (+0.04) 3.13 (-0.22)
9.75 13.21
emissionb
µ
Stokes shift (cm-1)
2.36 (-0.82) 3.02 (-0.07) 2.61 (-0.48)
15.97 22.41
8900 2984 4194
a Transition energies are in eV. Dipole moments of the S and S 0 1 states are also reported (in debye) together with the values (in cm-1) of the Stokes shifts. b The shift with respect to the cyclohexane is shown in parentheses. cThe experimental emission energies and Stokes shifts are from ref 4.
is obtained with a net red-shift both in absorption and emission. The isolated supermolecule can also be used to get an estimate of the pure H-bond effects both on absorption and emission: to do that we have to compare its transition energies (and dipole moments) with the results reported in Tables 1 and 2 for the gas-phase PRODAN. By doing this comparison, we get an explicit H-bonding shift of -0.09 eV for absorption and -0.17 eV for emission. In both cases, a net increase of the dipole moment of ca. 3 D for both S0 and S1 is found, indicating a contribution to the charge-transfer process due to H-bonding. Turning our attention to PCM results in absorption, the inclusion of two explicit water molecules in the QM part of the system seems to worsen the agreement with experiments, compared to the continuum-only picture (see Table 5). The transition energy is in fact too small. This observation, however, is not entirely correct. By looking at the cyclohexane and acetonitrile solvents, when compared to experiments, the PCM/ TDB3LYP results always lead to an ∼0.26 eV underestimation of the excitation energy; thus, if we consider this as the average intrinsic error of our model (PCM/TDB3LYP), the effective absorption energy in water should be 3.39 instead of 3.13 eV, which is reasonably close to experiments. In addition, we also need to take into account that the picture emerging from a supermolecule calculation where all H-bonding sites are saturated is a static one, which does not correctly reproduce the dynamics of H-bond interactions of PRODAN in liquid water. Too large a solvent effect is thus expected from this kind of analysis. Moving to the emission, the behavior is somehow opposite: the intrinsic error of the PCM/TDDFT model extracted from cyclohexane and acetonitrile calculations is small and erratic ((0.06 eV), while the PCM/TDB3LYP model gives an evident overestimation of the emission energy in water with respect to experiments, which is improved by considering the effect of the two H-bonded waters. This correction, however, is not sufficient to get a real quantitative agreement with the experiments. Once again, a possible source of inaccuracy is the TDB3LYP description of the excited-state geometry, which is here complicated by the presence of the H-bonded water molecules. We finish the analysis of the effects of homogeneous media on the absorption and emission properties of PRODAN by giving a short numerical explanation of the reasons why emission energies are far more sensitive to the environment than absorption energies (the experimental solvatochromic shift passing from cyclohexane to water is 1260 cm-1 for absorption and 6620 cm-1 for emission). 2.3. Absorption versus Fluorescence. In Figure 4, we report a graphical representation of the excitation and emission process
J. Phys. Chem. B, Vol. 112, No. 2, 2008 419 of PRODAN in an apolar (cyclohexane) and a polar solvent (water for which effects of H-bonds are neglected). For simplicity’s sake, in both graphs, only the solvation coordinate is explicitly shown, while the effects of relaxation of the geometrical internal coordinates of PRODAN are implicitly taken into account in the minima of the curves. In this picture, we have thus assumed that the dielectric relaxation of the solvent is faster than or as fast as the internal geometry changes from the ground state to the excited state. The main difference between apolar and polar solvents is that, in the first case, the dielectric response is immediate in the time scale of electronic transitions, while, in the latter, a delay (or nonequilibrium) induced by the slower part of the polarization (namely, the part related to orientational processes in the solvation shells) is present in a vertical absorption or emission. In the graphs, these different solvation responses are represented in gray-scale for the fast or electronic part (the only part present in cyclohexane) and in rotating ellipses for water molecules (here represented as small dipoles). A simplistic but qualitatively correct picture can be obtained in terms of the different dipole moments of the electronic states involved (reported in the graphs in debye units). The ground state (S0) will be differently stabilized by the apolar and the polar solvent (the difference in the free energy ∆∆GS0 is ca. 6 kcal/mol). Upon excitation, a large dipole moment appears as a result of the charge-transfer character of the S1 state, and this should induce a larger stabilization in the polar solvent with respect to the apolar one. However, this effect is reduced because of the nonequilibrium solvation in the polar solvent (the energy difference in the two final states is larger than in the S0, but not as much as expected on the basis of the dipole change). The net effect is a red-shift of the absorption energy of about 2 kcal/mol. Only when we let the polar solvent completely relax do the different stabilizations of S1 in the two solvents become evident and the difference in free energy ∆∆GS1 between cyclohexane and water becomes ca. 11 kcal/mol. The energy change from the vertical nonequilibrium S1 states and the completely relaxed 1 ; in water, such one is the so-called reorganization energy λSreor a quantity is about 6 kcal/mol (of which two-thirds is due to dielectric orientational relaxation). It is in this new equilibrium situation that the emission takes place; immediately after the transition, however, only in the case of cyclohexane, we have completely recovered the initial picture, while, in water, a new nonequilibrium (this time on the S0 PES) is reached. The combination of the different solvations in the equilibrated S1 and the vertical S0 in cyclohexane and in water gives origin to the calculated red-shift in the emission energy of about 7.5 kcal/ mol, i.e., more than three times what is found in the absorption. 0 It is to be noted that, for S0, the reorganization energy λSreor in water is ca. 5 kcal/mol. 3. Water Interface We consider now the changes in PRODAN absorption and emission energies when immersed in heterogeneous environments such as unilamellar vesicles and other membranes’ mimickers. This analysis is obtained using the extension of the IEFPCM to gas-liquid and liquid-liquid interfaces developed in our group.33 Within this framework, the interface is modeled in terms of static (and dynamic) permittivity, varying smoothly in the interfacial region. The use of such a diffuse region, whose width can be tuned, allows the method to better mimic the
420 J. Phys. Chem. B, Vol. 112, No. 2, 2008
Mennucci et al.
Figure 5. Pictorial view of PRODAN at the interface with the three different orientations (A, B, and C) exploited in the calculations.
TABLE 8: Absorption and Emission Energies (eV), Dipole Moments (Debye), and Stokes Shifts (cm-1) for the S1 State at the Interface for the Three Orientations (A, B, and C) and the Two Possible Directions (D1 and D2)a absorption Figure 4. Graphical representation of the excitation and emission process in apolar (cyclohexane) and polar solvent (water). Only the solvation coordinate is explicitly shown, while the effects of relaxation of the geometrical internal coordinates are implicitly taken into account in the minima of the curves.
changes in the dielectric properties of the bilayer representing the unilamellar vesicles. The operative expression used to represent the positiondependent permittivity is33
(z) )
( )
1 + 2 1 - 2 z - z0 + tanh 2 2 D
(1)
where 1 and 2 are the bulk permittivities of phases 1 and 2, respectively, and z indicates the direction perpendicular to the boundary surface. D in eq 1 is an adjustable parameter that defines the width of the interface. Far from z0, this function is almost constant and equal either to the bulk permittivity 1 or 2. In the interface region, the permittivity changes smoothly between these two values. We remark that, in the following, we shall test two different interface widths defined in terms of the parameter W (W ) 6D). Simulations seem to show that interfaces between water and a nonpolar solvent (or vacuum) are locally fairly sharp with an identifiable boundary between the two media, but this boundary, on the time scales of the simulations, fluctuates producing, on average, a smooth density profile that has an extension ranging from 4-5 to 10-15 Å. We have thus checked two different models: the first one uses W ) 7 Å, which has been chosen to effectively include the averaging found in the simulations at the interface,34 and the second one describes a sharp interface (W ) 2.77 Å, i.e., the hard sphere diameter of water), as it is locally. In the calculations of absorption and emission energies, we need both the static and the dynamic permittivity profiles. Here, we shall assume that both can be represented by a form of the type given in eq 1, with the same z0 and W parameters; the bulk permittivities used to represent the partition of PRODAN between vesicles and water are those of cyclohexane and water. The molecular geometry of PRODAN (for both the S0 and S1 states) has been optimized in bulk water at the B3LYP/6311+G(d,p) level of calculation, and the geometry has been kept fixed for all the subsequent calculations. Only the planar excited state has been considered for this part of the study. All calculations at the interface have been done using a locally modified version of the G03.35 A parameter to fix in the calculation at interfaces is the molecular orientation and position with respect to the interface.
emission
µ (S1)
Stokes shift
A B C
3.30 3.31 3.29
D1 2.92 2.97 2.95
18.05 17.27 17.30
3066 2762 2743
A B C
3.22 3.30 3.32
D2 2.78 2.87 2.89
19.24 17.95 17.63
3551 3467 3428
a For absorption calculations, the geometry is that of the ground state optimized at the B3LYP level in water, whereas the geometry of the S1 state is optimized at the TDDFT/B3LYP level in water. In all cases, the interface width is W ) 7.0 Å.
Here, three different orientations (indicated as A, B, and C, see Figure 5) have been tested. However, for this analysis, a single position with respect to the interface has been used, namely, that with the interface passing through the ring carbon atom linked to the carbonyl; this choice will be further tested in the following. For all orientations, two different directions have been considered, namely, that with water as solvent 1 (from now on indicated as direction D1), and the opposite one (direction D2). Before turning to present absorption and emission energies, we briefly comment on the relative stability of the different orientations/directions (for this analysis, the W ) 7 diffuse interface is used). Of the three different orientations, A is the most stable one (in both directions), with the other two being quite similar and both ca. 1 kcal/mol higher in energy. Differences between the two directions are almost negligible for orientation C, whereas they increase to 0.4 kcal/mol for B (with D1 being more stable) and to 0.7 kcal/mol for A (with D2 being more stable). The higher stability of orientation A can be explained, noting that it is the only one in which both polar heads of the molecule are within the diffuse region, while its higher sensitivity to different directions is explained by the vicinity of the propionyl group to the interface. Apparently D1 should always be more stable than D2 because, in the former case, the more polar propionyl group is within water, but for orientation A, the vicinity of this group to the interface makes its solvation almost equivalent in the two directions, while the other polar group is more efficiently solvated only in orientation D2.36 Now we analyze the effects of the interface on absorption and emission energies. In Table 8 we report absorption and emission energies together with the values of the dipole moment of the S1 excited state and the Stokes shift calculated for the three orientations (A, B, and C) and the two directions (D1 and D2) using a diffuse interface with width W ) 7.0 Å. Parallel calculations were
Environmental Influence on Spectroscopy of PRODAN repeated by using W ) 2.77 Å, and the results obtained show a very low sensitivity to this parameter, thus they are not reported here (see Supporting Information). As it can be seen from the table, the different orientations lead to non-negligible differences in the absorption energies (with the largest difference, ca. 0.1 eV, between orientations A(D2) and C(D2)). In contrast, the effects of assuming PRODAN oriented either with the acceptor (propionyl, D1) or the donor (dimethylamino, D2) pointing toward the aqueous phase does not lead to important changes (only for orientation A is a significant change found, i.e., 0.08 eV). In all cases, almost null effects are found by changing the width of the interface. Moving on to the comparison with respect to the bulk solutions (cyclohexane and water), all calculations lead to transition energies between those found in the corresponding bulk solutions (3.36 eV in cyclohexane and 3.26 in bulk water). Only orientation A(D2) presents an absorption energy that is even more red-shifted than bulk water. This result is unexpected, as the energy of both initial S0 and vertical S1 are higher than in bulk water (as expected, being that the interface is a medium with dielectric properties that are intermediate between the two bulk solvents), but they are differently destabilized, and, as a result, we get an absorption energy lower than that in water. For emission, the transition energies in the three orientations (and the two directions) are all intermediate between bulk cyclohexane (3.09 eV) and bulk water (2.77 eV), with orientation A(D2) being very close to that of the bulk aqueous solution. This can be explained observing that, in this location, PRODAN is almost completely immersed in the higher-permittivity region (explicitly with the dimethylamino group, which is in the waterside of the interface, but also with the propionyl group, which is within the diffuse region).37 Also, for the two other orientations, direction D2 gives the most red-shifted emission energy: this result correlates well with the dipole moments, which, in D2, are larger than in D1, showing that a larger charge transfer is present when the D2 direction is considered. These results correctly reproduce what is expected from simple considerations based on dielectric properties of the interface with respect to the two pure liquids; a confirmation, however, also comes from experimental data. In a recent paper by Moyano et al.,4 the emission spectra of PRODAN in large unilamellar vesicles (LUVs) of the phospholipid 1,2-di-oleoyl-sn-glycero-3-phosphatidylcholine (DOPC) was reported. In such a study, the emission spectra were measured by increasing the concentration of DOPC; with respect to PRODAN in water, a shift in the band toward higher energies was found, together with the appearance of a shoulder at ca. 2.90 eV. These two changes were explained in terms of the pseudophase model38 according to which only two solubilization sites have to be considered, that is, the water and the vesicle interface (i.e., all of the DOPC molecules). Within this model, the shift of the band was assigned to PRODAN moving from bulk water toward the interface near the water and the shoulder to PRODAN in a less polar environment more inside the phospholipid tails. The results reported in Table 8 for PRODAN at the interface seem to be in agreement with this analysis; in fact, all the different orientations give rise to transition energies close to that experimentally observed for PRODAN in the less polar region. In order to quantify how the calculated emission energies are sensitive to the position of PRODAN with respect to the interface, we have selected the most stable orientation A(D2)
J. Phys. Chem. B, Vol. 112, No. 2, 2008 421
Figure 6. Dependence of calculated emission energies on the position of PRODAN with respect to the interface (in orientation A). z is the coordinate perpendicular to the interface and the limit values (z f (∞) refer to bulk cyclohexane and bulk water; in the latter case, the result obtained for the solvated supermolecule is also reported (in red). The position-dependent values of the dielectric constant used to mimic the diffuse interface are also reported.
and repeated the calculations at different locations. The results are reported in Figure 6, in which z is the coordinate perpendicular to the interface (the position of PRODAN shown in Figure 5 corresponds to z ) 1.5). The limit values (z f (∞) refer to bulk cyclohexane and bulk water; in the latter case, the result obtained for the solvated supermolecule is also reported (in red). In the same graph, we also report the position-dependent value of the dielectric constant used to mimic the diffuse interface. Experimentally, the positions of PRODAN in LUVs that give origin to the observed shoulder is not known. According to what is suggested in the above-quoted paper,4 this should correspond to PRODAN located in the less polar region formed by the phospholipid tails. As can be seen from the graph, such a value in the emission energy is obtained at z ) -1.5: this indeed corresponds to PRODAN almost completely inside the ) 2 region corresponding to a dielectric with an effective permittivity of 7.5. This result agrees well with the analysis reported in that paper in terms of the well-known polarity parameter ET(30);39 for the band that corresponds to PRODAN in the less polar part of the bilayer, the ET(30) value found is similar to those in homogeneous tetrahydrofuran, that is, a solvent with a permittivity around 7. The agreement between calculated and experimental energies is, by far, less satisfactory for the shift of the main band (which, at high concentrations of DOPC, is measured at 2.53 eV instead of 2.36 as in water); this should correspond to PRODAN moving from bulk water to a still polar region in the interface near the water. Our calculations predict a fast convergence to the water bulk limit upon going to positive values of z (see graph). However, as the calculated bulk limit is significantly higher than what is experimentally found, such z-dependence cannot reproduce the observed shift. As discussed in the previous
422 J. Phys. Chem. B, Vol. 112, No. 2, 2008 section, this behavior is expected, as PRODAN and water are two strongly interacting systems that cannot be accurately described by a continuum approach. A better behavior could be obtained by taking into explicit account the water molecules that more strongly interact with the hydrogen-bonding sites of PRODAN. This has been done above for bulk water for which the emission of the PRODAN + 2 water supermolecule has been calculated (the obtained result is reported in the graph as a red square); repeating a similar analysis here, unfortunately, is much more difficult because now dynamic processes allowing the breaking and formation of H-bonds cannot be neglected as PRODAN crosses the interface. 4. Conclusions In this work, we presented a QM investigation of electronic properties of PRODAN, with particular attention to its absorption and emission spectra in homogeneous media with different polarity/H-bonding properties, and in heterogeneous environments (e.g., diffuse interfaces) mimicking membranes. As anticipated at the beginning, this study turned out to be quite complex, and for this reason it is advisable to review here the most important aspects regarding both the photophysics of the system and the methodological issues. About the photophysics, the first result to recall here is that the PRODAN excited state involved in the experimentally observed emission process appears to be planar both in the gas phase and in solution (including polar solvents and interfaces). The assignment of the planar S1 as the emitting state is confirmed by the good agreement with experimental data both in apolar and polar solvents. The corresponding change of the dipole moment passing from S0 to the planar S1 is here quantified in almost a doubling in all media, thus confirming the recent measurements and refuting the older values estimated from solvatochromic parameters. A twisted minimum energy conformation is also found, but the combined use of different QM methods univocally indicates that such a structure is an artifact of TDB3LYP. We have paid attention to the analysis of this defect, which turns out to be that found in preceding investigations on other problems. To overcome it would be sufficient to pass to higher levels of the QM theory, but this has a considerable computational cost. It would be better to find a functional not exhibiting this artifact: this search is in progress. Another interesting aspect in the photophysics of PRODAN is the large difference in the absorption/emission solvatochromic shifts (a factor of about 3) in polar solvents. The computational procedures we have used permit a dissection of the total solvent shifts: essentially, the different effect that a polar solvent has on absorption and emission processes may be explained in terms of different reorganization energies due to slow orientational rearrangements of solvent molecules around the solute ground and excited states, respectively. To quantify this differential solvation with discrete descriptions of the solvent molecules is a rather exacting computational task: there is in fact the need of accurate dynamic simulations. An efficient continuum model (such as IEFPCM) gives a reliable description of this phenomenon with minimal computational effort. Another important advantage of IEFPCM is its large versatility: this has been exploited here to study in a coherent way both homogeneous and heterogeneous media of different complexities. We remark that, on the whole, the computed quantities exhibit good agreement with the experimental ones, and, even more important, a detailed analysis of the electronic
Mennucci et al. aspects as well as of the physics of the involved processes can be achieved. The method, however, also has weak points. The most important one (which IEFPCM shares with the other continuum models) regards the neglecting of some solute-solvent specific interaction effects. For a general discussion on this point, see the recent book edited by Mennucci and Cammi.40 In our case, this limitation of continuum models is evident in water solution. The recipe to amend the effects of this limitation that we have adopted is the usual one, which has been successfully used in preceding studies: namely, to add a few water molecules in the quantum-mechanically treated “solute” and solvating this “supermolecule” with a continuum to include bulk effects. Acknowledgment. In occasion of this special issue in honor of J.T. Hynes, B.M. would like to thank him for the great period she had in his group in Boulder at the beginning of her scientific career: the extremely stimulating discussions on solvation and related processes she had with him significantly contributed to orient her future research interests. R.C. also takes this occasion to deeply recognize the pioneering work of J.T. Hynes in the developments of nonequilibrium QM solvation models; this work, done at the beginning of the 90’s, has been a landmark reference for all the successive evolutions in this field. Supporting Information Available: Pictures of the HOMO and LUMO orbitals involved in the electronic transition for the planar and twisted geometries. Picture of the difference between planar excited-state and ground-state electron densities. Table with absorption energies (eV) at the interface for the three orientations (A, B, and C) and the two directions (D1 and D2) obtained using W ) 2.77 Å as the width of the diffuse interface. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Weber, G.; Farris, J. F. Biochemistry 1979, 18, 3075. (2) Parasassi, T.; Krasnowska, E. K.; Bagatolli, L.; Gratton, E. J. Fluoresc. 1998, 8, 365. (3) Krasnowska, E. K.; Gratton, E.; Parasassi, T. Biophys. J. 1998, 74, 1984. (4) Moyano, F.; Biasutti, M. A.; Silber, J. J.; Correa, N. M. J. Phys. Chem. B 2006, 110, 11838. (5) Novaira, M.; Biasutti, M. A.; Silber J. J.; Correa N. M. J. Phys. Chem. B 2007, 111, 748. (6) (a) Valeur, B. Molecular Fluorescence: Principles and Applications; Wiley-VCH: Weinheim, Germany, 2002. (b) May, V.; Kuhn, O. Charge and Energy Transfer Dynamics in Molecular Systems; WileyVCH: Weinheim, Germany, 2004. (7) Heisel, F.; Miehe´, J. A.; Szemik, A. W. Chem. Phys. Lett. 1987, 128, 321. (8) Balter, A.; Nowak, W.; Pawelkiewicz, W.; Kowalczyk, A. Chem. Phys. Lett. 1988, 143, 565. (9) Ilich, P.; Prendergast, F. G. J. Phys. Chem. 1989, 93, 4441. (10) Catalan, J.; Perez, P.; Laynez, J.; Garcia Blanco, F. J. Fluoresc. 1991, 1, 215. (11) Parusel, A. B. J.; Schneider, F. W.; Ko¨ler, G. J. Mol. Struct. (THEOCHEM) 1997, 398/399, 341. (12) Parusel, A. B. J.; Nowak, W.; Grimme, S.; Kohler, G. J. Phys. Chem. A 1998, 102, 7149. (13) Parusel, A. B. J. J. Chem. Soc., Faraday Trans. 1998, 94, 2923. (14) Samanta, A.; Fessenden, R. W. J. Phys. Chem. A 2000, 104, 8972. (15) Lobo, B. C.; Abelt, C. J. J. Phys. Chem. A 2003, 107, 10938. (16) Davis, B. N.; Abelt, C. J. J. Phys. Chem. A 2005, 109, 1295. (17) Kamlet, M.; Abboud, J. L. M.; Abraham, M. H.; Taft, R. W. J. J. Org. Chem. 1983, 48, 2877. (18) Klamt, A.; Schu¨u¨rmann, G. J. Chem. Soc., Perkin Trans. 2 1993, 799. (19) Nakatsuji, H. Chem. Phys. Lett. 1978, 59, 362. (20) Tomasi, J.; Mennucci, B.; Cammi, R. Chem. ReV. 2005, 105, 2999. (21) Miertus, S.; Scrocco, E.; Tomasi, J. J. Chem. Phys. 1981, 55, 117. (22) Cammi, R.; Tomasi, J. J. Comput. Chem. 1995, 16, 1449.
Environmental Influence on Spectroscopy of PRODAN (23) Cance`s, E.; Mennucci, B.; Tomasi, J. J. Chem. Phys. 1997, 107, 3032. (24) Cance`s, E.; Mennucci, B.; Tomasi, J. J. Phys. Chem. B 1997, 101, 10506. (25) Caricato, M.; Mennucci, B.; Tomasi, J.; Ingrosso, F.; Cammi, R.; Corni, S.; Scalmani, G. J. Chem. Phys. 2006, 124, 124520. (26) Frisch. M. J.; Trucks, G. W.; Schlegel, H. B. et al. Gaussian, development version; Gaussian, Inc.: Pittsburgh, PA, 2007. (27) Scalmani, G.; Frisch, M. J.; Mennucci, B.; Tomasi, J.; Cammi, R.; Barone, V. J. Chem. Phys. 2006, 124, 094107. (28) (a) Becke, A. J. Chem. Phys. 1993, 98, 5648. (b) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785. (29) Two different conformers are possible for PRODAN, depending on the dihedral angle (0° and 180°) between the propionyl group and the naphthalene plane. At B3LYP/6-311+G(d,p), the two conformers are quite close in energy, both in the gas phase and in solution. In this study, all data refer to the conformer where the dihedral angle C11-C2-C1dO is 180°: at the present level of calculation, this conformer is slightly more stable than the other. In any case, as already observed in ref 15, the characteristics of the excited states are exactly equivalent in the two conformers, and the differences in their absorption and emission energies remain less than 1% in all environments. The consideration of either a single conformer or an average between the two will thus lead to the same conclusions both from a qualitative and a quantitative point of view. (30) Yamashita, M.; Kikuma, S.; Murakami, H.; Morita, R.; Shigekawa, H.; Appl. Phys. Lett. 1999, 75, 28. (31) Dreuw, A.; Head-Gordon, M. C. J. J. Am. Chem. Soc. 2004, 126, 4007. (32) Chiba, M; Tsuneda, T.; Hirao, K. J. Chem. Phys. 2006, 124, 144106. (33) (a) Frediani, L.; Cammi, R.; Corni, S.; Tomasi, J. J. Chem. Phys. 2004, 120, 3893. (b) Frediani, L.; Mennucci, B.; Cammi, R. J. Phys. Chem. B 2004, 108, 13796. (c) Bondesson, L.; Frediani, L.; Ågren, H.; Mennucci, B. J. Phys. Chem. B 2006, 110, 11361. (d) Curutchet, C.; Cammi, R.; Mennucci, B.; Corni, S. J. Chem. Phys. 2006, 125, 054710. (34) Michael, D.; Benjamin, I. J. Phys. Chem. B 1998, 102, 5145. (35) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.;
J. Phys. Chem. B, Vol. 112, No. 2, 2008 423 Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (36) It is interesting to check whether the anisotropy of the interface can lead to significant changes in the relative stability of the two conformers of PRODAN, which, in homogeneous environments, presented completely equivalent behaviors (see ref 29). These changes are expected to be largest in the A orientation, being that orientations B and C are practically insensitive. We have thus repeated the calculations for the equivalent of orientation A for the second conformer (let’s call it A′). The results obtained indicate that the original A(D2) system remains the most stable, followed by the new A′(D1), while the other A′(D2) becomes quite high in energy. This opposite behavior shown by A and A′ with respect to D1 and D2 environments can be explained by observing that, in the two conformers, the polar propionyl group points in the opposite direction with respect to the other polar group (the dimethylamino), and thus their relative stabilization will be different when solvent 1 is water or cyclohexane. (37) We note that, for orientation A′, emission energies in the two D1 and D2 environments are very similar (2.86 and 2.88 eV, respectively) and between the two values obtained for orientation A. (38) (a) Abuin, E.; Lissi, E.; Duarte, R.; Silber, J. J.; Biasutti, M. A. Langmuir 2002, 18, 8340. (b) Falcone, R. D.; Correa, N. M.; Biasutti, M. A.; Silber, J. J. J. Colloid. Interface Sci. 2006, 296, 356. (39) Reichardt, C. SolVents and SolVent Effects in Organic Chemistry; Wiley-VCH: Weinheim, Germany, 1990. (40) Mennucci, B., Cammi, R., Eds. Continuum SolVation Models in Chemical Physics: Theory and Applications; Wiley-VCH: Weinheim, Germany, 2007.
