J. Phys. Chem. 1996, 100, 10701-10706
10701
Optical Properties of Triarylpyrylium Dimers Isabelle Lampre and Dimitra Markovitsi* Laboratoire de Photophysique et Photochimie, CEA/Saclay, DRECAM, SCM, CNRS-URA 331, 91191 Gif-sur-YVette, France
Ce´ line Fiorini and Fabrice Charra Laboratoire de Physique Electronique des Mate´ riaux, CEA/Saclay, DEIN/LETI, 91191 Gif-sur-YVette, France
Miche` le Veber Laboratoire de Physique des Solides, UniVersite´ de Paris Sud, CNRS-URA 002, Baˆ t. 510, 91400 Orsay, France ReceiVed: January 30, 1996; In Final Form: March 26, 1996X
The present paper deals with ion-pair dimers (two chromophores and their counterions) formed by 2,6-diphenyl4-(4′-dialkylaminophenyl)pyrylium tetrafluoroborates in solution. They are studied at room temperature by electronic absorption and fluorescence spectroscopy and using a time-resolved nondegenerate six-wave mixing technique. Spectral analysis gives evidence that the excited states of the dimers are delocalized on both cationic chromophores. The properties (energy, oscillator strength, relative polarization) of the FranckCondon transitions are determined. It is found that the Franck-Condon transition that is lowest in energy is orthogonal to the transition corresponding to fluorescence, proving that relaxation results in a drastic change in the wave function of the lowest excited state. It is shown, for the first time, that dimers formed upon aggregation are capable of generating second harmonic in solution. This observation leads to the conclusion that the dimer geometry in the ground state is noncentrosymmetric and that excitation induces an important variation of the atomic charge distribution.
1. Introduction The photophysical properties of dimers formed upon aggregation of dye molecules can be, in general, easily determined.1-15 As a matter of fact, dimer formation is evidenced through the appearance of isosbestic points in the absorption spectra recorded as a function of concentration or temperature. The shift of the dimer spectrum with respect to that of the monomer is usually explained in terms of strong exciton coupling leading to delocalized excitation. According to the exciton theory, the dimer excited states are linear combinations of the excited states localized on each chromophore.16,17 Depending on the relative position of the monomer transition dipole moments, the oscillator strength may be concentrated on either the upper or the lower dimer transition. In particular, for parallel transition moments as defined in ref 17, the upper dimer transition is allowed while the lower one is forbidden. This type of arrangement is invoked to interpret the most frequently encountered hypsochromic shift of absorption spectra, always accompanied by a decrease in fluorescence quantum yield, or even a complete quenching of the fluorescence emission. Within this context, the behavior of the dimers formed by the 2,6-diphenyl-4-(4′-dialkylaminophenyl)pyrylium tetrafluoroborates shown in Figure 1 in fluid solutions is quite unique.18,19 In contrast to what is expected, dimerization leads to a hypsochromic shift of the absorption spectra while the fluorescence quantum yield increases by 2 orders of magnitude. Moreover, the dimer emission spectrum is extended in the nearinfrared resulting in a surprisingly high difference between absorption and fluorescence maxima (6000 cm-1). X
Abstract published in AdVance ACS Abstracts, May 15, 1996.
S0022-3654(96)00289-4 CCC: $12.00
Figure 1. Schematic representation of the studied 2,6-diphenyl-4-(4′dialkylaminophenyl)pyrylium tetrafluoroborates. P1-12+: R ) CH3, R′ ) C12H25. P12-12+: R ) R′ ) C12H25.
In order to obtain a better insight into the intriguing behavior of the dimers formed by {P1-12+, BF4-} and {P12-12+, BF4-}, we have undertaken a systematic study of these compounds. As a first step, we investigated the properties of the triarylpyrylium cations P1-12+, experimentally observed in polar solvents.20 We showed that the P1-12+ absorption spectrum in the visible region is characterized by a broad band related to two electronic transitions close in energy and perpendicular to each other. We also found that excitation of this band induces an important charge transfer, evidenced by second harmonic generation. A detailed investigation of the dimerization process19 revealed that each dimer consists of two cationic chromophores and their counterions: (P1-12+, BF4-)2 or (P12-12+, BF4-)2. The aim of the present work is to characterize experimentally the electronic transitions related to the absorption and fluorescence of the dimers. For this purpose, we use mainly two methods involving polarized light, thus allowing a photoselection © 1996 American Chemical Society
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of the electronic transitions. On the one hand, we perform fluorescence anisotropy measurements (section 3). On the other hand, we study second harmonic generation in solution by means of the recently developed nondegenerate six-wave mixing technique21,22 (section 4). 2. Materials and Apparatus The synthesis of {P1-12+, BF4-} and {P12-12+, BF4-} is reported elsewhere.18,19 It was shown previously that the spectroscopic properties of {P1-12+, BF4-} and {P12-12+, BF4-} are practically the same for both the dimer and the monomer, but the solubility of the latter compound in nonpolar solvents is much higher.19 For this reason, in our investigation, we use the more easily synthesized {P1-12+, BF4-}, except for nonlinear optical experiments requiring high concentration. Polystyrene films were prepared as described in ref 20. Corrected fluorescence spectra were recorded on a SPEX Fluorolog-2 spectrofluorimeter equipped with both a germanium detector (North Coast, EO-817) and a R928 photomultiplier tube. Two Glan-Thomson polarizers were used for the fluorescence anisotropy measurements. Fluorescence decays were recorded using a single photon-counting setup. The excitation source was a dye laser (rhodamine 6G) synchronously pumped by a mode-locked Nd:YAG laser. The detector was a microchannel plate (R1564U). The instrumental response function was 50 ps (fwhm). The experimental setup used for second harmonic generation is described in detail in ref 22. The light source was a Q-switched mode-locked Nd:YAG laser delivering 25 ps (fwhm) pulses at 1064 nm at repetition rate of 10 Hz. The energy of the laser pulses at the sample location was ca. 5 mJ and 50 µJ for the fundamental frequency (1064 nm) and the second harmonic (532 nm), respectively. The sample was contained in a quartz cell having a 1 mm optical path length; the absorbance at 532 nm was higher than 3. 3. Spectroscopic Study Figure 2 shows the monomer and dimer absorption spectra of {P1-12+, BF4-}. We should stress that the spectrum of the monomer ion pair (P1-12+, BF4-) (Figure 2a) is identical to that of the dissociated cationic chromophore.19 The spectrum of Figure 2a is fitted by the sum of two log-normal curves23 peaking at 17 900 and 19 300 cm-1. They correspond to oscillator strengths of 0.59 and 0.24 and transition moments of 8.4 and 5.1 D. Those values are in agreement with the values calculated quantum mechanically for the two lowest singlet transitions S0 f S1 and S0 f S2.20 The monomer spectrum can also be fitted by the sum of two Gaussian curves. The resulting maxima and oscillator strengths are similar to those obtained by the sum of two log-normal curves, but the fit is not as good, in particular in the blue side of the spectrum. As a matter of fact, log-normal curves allow us to take into account the asymmetry of structureless absorption bands related to electronic-vibrational interactions.24 The dimer spectrum (Figure 2b) consists of a main peak surrounded by lower intensity absorption bands and cannot be fitted by only two lognormal curves, proving that the number of transitions is larger than in the case of the monomer. In order to determine those transitions, we have performed fluorescence anisotropy measurements in polystyrene films. This photoselection method allows the determination of the average angle R formed between the transition dipoles corresponding to absorption and emission:25
r(λ) ) (3 cos2 R - 1)/5
(1)
Figure 2. Absorption spectra of {P1-12+, BF4-}: (a) monomer in chloroform (10-5 M), (b) dimer in toluene. The dimer absorption spectrum is deduced from the absorption spectra obtained for {P1-12+, BF4-} in toluene by subtracting the monomer spectrum. The experimental spectra (O) are fitted by the sum (s) of two (a) or four (b) log-normal curves23 (- - -). The arrow denotes the excitation energy corresponding to the writing process of the six-wave mixing experiment.
The fluorescence excitation and emission spectra of the dimer (P1-12+, BF4-)2 in polystyrene, peaking at 515 and 720 nm, respectively, are similar to those obtained in toluene. Likewise, the fluorescence lifetime τf (12.5 ns) is only slightly longer than that found in toluene (9.65 ns) but the fluorescence quantum yield φf is much higher (0.7 ( 0.3 instead of 0.02). The anisotropy is found to be constant all over the emission spectrum, showing that all the vibronic bands19 have the same polarization. This behavior is different from that of the Rhodamine B dimers for which the fluorescence polarization was found to be wavelength-dependent and vibronic interactions were invoked to interpret the dimer excited states.6 In contrast to emission, the excitation anisotropy is wavelengthdependent (Figure 3): in the red edge, it has a value of ca. -0.1; then it increases up to 0.3 and decreases down to 0.1 at the blue edge. This means that the absorption spectrum corresponds to transitions having different polarizations. The minimum number of log-normal curves23 necessary to obtain acceptable fits for both the excitation and the anisotropy spectra is four. The fit of the dimer spectra (Figure 3) with four bands (2 × 2) is quite reasonable because the monomer is characterized by two electronic transitions close in energy (Figure 2a). The fitting procedure is described in the Appendix. The energy, oscillator strengths, transition dipole moments, and anisotropy values associated with the four log-normal curves giving the best fit are listed in Table 1. On the basis of this finding, we have also fitted the absorption spectra of (P1-12+, BF4-)2 and (P12-12+, BF4-)2 in toluene with the sum of four log-normal curves (Figure 2b). The resulting maxima and oscillator strengths (Table 1) are close to those determined for the spectra of (P1-12+, BF4-)2 in polystyrene films. We remark that, as
Optical Properties of Triarylpyrylium Dimers
J. Phys. Chem., Vol. 100, No. 25, 1996 10703
Figure 3. Excitation spectra of (P1-12+, BF4-)2 in polystyrene films, λem ) 850 nm: (a) nonpolarized spectrum (O) fitted by the sum (s) of four log-normal curves23 (- - -), (b) anisotropy spectrum (O) fitted using the log-normal curves determined in (a).25
TABLE 1: Propertiesa of the Dimer Electronic Transitions Obtained by Fitting Excitation Spectra with Four log-normal Curves23 |0〉 f |1〉 |0〉 f |2〉 |0〉 f |3〉 |0〉 f |4〉 (P1-12+, BF4-)2 in polystyreneb
(cm-1)
E f µ (D) r ((0.02) (P1-12+, BF4-)2 in E (cm-1) toluene f µ (D) (P12-12+, BF4-)2 in E (cm-1) toluene f µ (D)
16 500 0.05 2.5 -0.20 16 800 0.04 2.1 16 500 0.03 2.0
17 950 0.37 6.6 0.13 18 400 0.23 5.2 18 050 0.25 5.4
19 290 0.93 10.1 0.30 19 650 1.06 10.7 19 350 0.89 9.9
20 700 0.22 4.8 0.11 20 900 0.24 4.9 20 600 0.21 4.7
a E ) energy, f ) oscillator strength, µ ) transition moment, and r ) fluorescence excitation anisotropy. b The molar extinction coefficient cannot be precisely measured for polystyrene films. Therefore, the oscillator strengths f and the transition moments µ are determined by assuming that the total oscillator strength of the dimer in polystyrene is the same as in toluene.
expected, the total oscillator strength associated to the dimer is practically twice that associated to the monomer. The four components of the dimer absorption spectrum may be related to excited states which are either localized on one of the two monomers or delocalized on both of them. We will try to elucidate this point by considering the oscillator strength found for the dimer transitions. If an excited state remains localized upon aggregation, its oscillator strength is not expected to change whereas no particular values are predicted for delocalized states as far as the dimer geometry is not known. The values listed in Table 1 for toluene solutions clearly show that the oscillator strengths corresponding to the states |1〉 and |3〉 are quite different from the monomer ones. Consequently, those states are delocalized. In contrast, the oscillator strengths associated with |2〉 and |4〉 are nearly identical to that corresponding to the S2 state of the monomer. If the two S2 states remain localized upon dimerization, the energy of the corresponding transitions, depending on interactions with the local environment, may become different due to nonequivalent positions of the two cations within the dimer. This effect was theoretically demonstrated in the case of columnar aggregates formed by discotic triarylpyrylium derivatives.26 In such a case,
the delocalized states |1〉 and |3〉 would be built only on the two S1 states. This means that the coupling between the two S0 f S1 transitions should be larger than their energy difference (∆E1). It is well-known that the more important the charge transfer character of a transition, the bigger the influence of the environment on its energy. Since the charge transfer character of the S0 f S1 transition is stronger than that of the S0 f S2 transition,20 ∆E1 is expected to be larger than the energy difference between the S0 f S2 transitions of two nonequivalent chromophores (2500 cm-1). According to this scheme, delocalization of the S1 states should require a coupling of several thousands wavenumbers. The latter value is surprisingly high, ruling out the hypothesis of localized S2 states. Consequently, we deduce that the dimer states are delocalized on both chromophores and each one may be a linear combination of both S1 and S2, as has been previously shown.26 For this reason, we cannot derive a dimer geometry based exclusively on the spectroscopic data. The anisotropy value determined for the lowest in energy dimer transition is -0.2. Usually, the anisotropy of the lowest in energy absorption band associated with a nondegenerate allowed transition is close to 0.4 corresponding to parallel transition moments in absorption and fluorescence. For example, a value of 0.37 was found for P1-12+ in a polymer matrix20 showing that relaxation in the lowest excited state does not induce a big change in polarization. The anisotropy found for the |0〉 f |1〉 transition of the (P1-12+, BF4-)2 dimers shows that the transition moments related to absorption and fluorescence are orthogonal. Consequently, we deduce that relaxation involves a drastic change in the wave function of the lowest excited state. This is corroborated by the energy difference, 2500 cm-1, between the maxima of the lowest absorption band and the fluorescence one. The latter value, although smaller than the observed Stokes shift (6000 cm-1), is higher by 1 order of magnitude than that observed for Rhodamine B dimers in solid matrices.6 The drastic change in the wave function of the lowest excited state of the triarylpyrylium dimers can be explained only if the dimer geometry provides certain degrees of freedom, even in a rigid environment. It has been suggested for dimers of other ionic dyes that the counterions are sandwiched between the two chromophores.1,11 Assuming that this geometrical arrangement is also valid for the examined triarylpyrylium dimers, we can speculate that relaxation involves a motion of the small and light anions in the space between the two much larger and heavier cations. As the position of the counterions is mainly defined by electrostatic interactions, it depends on the atomic charge distribution within the dimer. If the atomic charge distribution changes upon excitation, the counterions will move to reach a new equilibrium position. The counterion motion would affect the properties of the dimer states by changing the local environment. Our findings concerning the electronic states of the studied triarylpyrylium dimers are illustrated in the simplified diagram in Figure 4. These states are denoted either by |0〉, |1〉, |2〉, |3〉, and |4〉 in the Franck-Condon configuration, or by |0′〉, |1′〉, |2′〉, |3′〉, and |4′〉 in the configuration reached after relaxation. The dimer absorption spectrum is identical to the fluorescence excitation one. This proves that |1′〉 is formed with the same yield φ* upon excitation of anyone of the states |1〉, |2〉, |3〉, or |4〉. We remark that the transitions toward these states are all characterized by moments higher than 2D (Table 1) and, consequently, they are all allowed. The same conclusion can
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Figure 4. Simplified diagram of the electronic states of the studied dimers. φ* denotes the yield of |1′〉 formation and knr the nonradiative rate constant.
Figure 6. {P12-12+, BF4-} in toluene: amplitude of the second harmonic signal 4(2ω) as a function of time. The solid line corresponds to an exponential decay with a lifetime of 620 ps.
be drawn regarding the transition |0′〉 r |1′〉 on the basis of the radiative lifetime τrad which can be evaluated by the equation:
in which more than 90% of the compound is dimerized. During the pulse duration, an intense peak, called “coherent artifact” is observed; it is due to a coherent coupling between writing and reading beams. After this “coherent artifact”, the signal decays exponentially with a lifetime of 620 ps. Knowing that the signal generated by the monomer in solvents of low viscosity decays within the laser pulse duration,20 we attribute the longlived signal in Figure 6 to the dimer. The signal disappearance in the time-resolved six-wave mixing experiment is due to two phenomena. The photoinduced χ(2) grating is destroyed by rotational diffusion (Brownian motion) of the selectively excited molecules and/or it vanishes because the excited molecules return to their ground state. The rotational orientation time of an electric dipole can be evaluated through the Debye-Stokes-Einstein equation:
τrad ) τfφ*/φf
(2)
Taking into account that φ* e 1 and considering the τf and φf values determined for (P1-12+, BF4-)2 in polystyrene films, τrad is found to be smaller than 18 ns. The electronic structure, and consequently, τrad of the dimer fluorescent state in toluene should be quite similar to those in polystyrene, since the fluorescence maxima as well as τf are practically the same in the two solvents. Following this reasoning, the great difference found for φf (0.02 and 0.7 in toluene and in polystyrene, respectively) is attributed to different φ* (eq 2) due to competition between formation of |1′〉 from the Franck-Condon states and ground state recovery through nonradiative processes (knr in Figure 4). Our attribution is supported by the observation that deactivation of the monomer excited states in fluid solvents is governed by nonradiative processes which are seriously inhibited in solid matrices.20 Our scenario regarding the relaxation process leading to |1′〉 is based on the hypothesis of an important photoinduced change in the atomic charge distribution. This hypothesis may be experimentally confirmed by second harmonic generation. 4. Nonlinear Optical Properties Figure 5 shows the arrangement of the light beams involved in the nondegenerate six-wave mixing technique.21,22 Quantum interference of the writing beams 1(ω) and 3(2ω), originating from the same picosecond laser source of frequency ω, creates in the solution a second-order susceptibility χ(2) grating. During the lifetime of this induced χ(2) grating, a reading beam 2(ω) can be frequency doubled. The generated second harmonic signal 4(2ω) is the phase-conjugate signal of the writing beam 3(2ω). It propagates in a direction opposite to that of the beam 3(2ω).
Figure 5. Beam arrangement for phase conjugation by nondegenerate six-wave mixing. ω and 2ω denote the first and second harmonic of the same laser beam. Writing beams: 1(ω) and 3(2ω). Reading beam: 2(ω). Generated second harmonic signal: 4(2ω).
Figure 6 shows the time dependence of the amplitude of the signal 4(2ω) obtained with a {P12-12+, BF4-} toluene solution
τd ) 3ηV/kT
(3)
where η is the solvent viscosity, V the molecular volume, T the temperature, and k the Boltzmann constant. The volume V of the (P12-12+, BF4-)2 dimer, estimated from the van der Waals radii, is ca. 1500 Å3 and τd is found to be 650 ps in toluene at room temperature. The lifetime of the second harmonic signal is close the τd value but very different from the dimer fluorescence lifetime (9.85 ns), showing that the signal decays mainly because of rotational diffusion. It is worth noticing that, in the case of the monomer, the signal vanishes, not because of rotational diffusion but due to the extremely short lifetime of the excited state.20 At this point, we can draw two conclusions based on the fact that the examined dimers are capable of generating second harmonic. First, their geometry in the ground state is noncentrosymmetric. Such a picture is in contrast to what is intuitively believed for aggregated dimers for which an antiparallel arrangement of the ground state dipole moments is usually suggested. Therefore, unlike higher order aggregates,27 dimers have not been studied so far with respect to their second-order susceptibility. Second, excitation of the dimers induces an important charge transfer in the sense of a variation ∆µ of the electric dipole moment of the dimer. We see in Figure 2 that two different excited states, |2〉 and |3〉, can be reached under selective excitation by the beams 1(ω) and 3(2ω), corresponding to an energy of 18 800 cm-1. Consequently, at least one of the transitions |0〉 f |2〉 and |0〉 f |3〉 is active during the writing process. Conversely, outside the so-called “coherent artifact”, relaxation to the excited state |1′〉 has already taken place. Therefore, the reading process involves only the transition |0′〉 r |1′〉, related to a variation ∆µ′ of the electric dipole moment of the dimer. In order to determine the dimer excited state(s) active in our nonlinear optical experiment, we have studied the amplitude of the generated signal by changing the polarization of the various
Optical Properties of Triarylpyrylium Dimers
J. Phys. Chem., Vol. 100, No. 25, 1996 10705 characterized by an important intramolecular charge transfer and is active in second harmonic generation.20 5. Summary and Conclusions
Figure 7. {P12-12+, BF4-} in toluene: amplitude of the polarized 4(2ω) signal at 72 ps as a function of the angle φ formed between polarization of the beam 2(ω) and the vertical direction. (O) Beams 1 and 3 are vertically polarized (x direction) and the x component of 4(2ω) is detected. (4): Beam 1 is horizontally polarized (y direction), and beam 3 is vertically polarized and the x component of the signal is measured. (0) Beams 1 and 3 are vertically polarized and the y component of 4(2ω) is observed. The solid lines correspond to the functions E4,x ) cos2(φ) + 0.23 sin2(φ), E′4,x ) 0.26 cos2(φ) + 0.21 sin2(φ), E4,y ) 2 × 0.26 sin(φ) cos(φ).
light beams. Such an experiment may provide information about the relative orientation of the transition moments and the variations of the electric dipole moment related to the writing and the reading processes.21,22 Figure 7 shows the amplitude of the polarized 4(2ω) signal (E4), recorded outside the “coherent artifact”, as a function of the angle φ formed by the polarization of the beam 2(ω) and the vertical direction. The three experimental plots (E4,x, E′4,x, and E4,y) can be fitted by the functions {A cos2(φ) + B sin2(φ)}, {C cos2(φ) + D sin2(φ)} and {2E sin(φ) cos(φ)}, respectively. These functions correspond to the theoretical dependence of the polarized signal amplitude: (5) (5) 2 2 E4,x ∝ E12E22E* 3[χxxxxxx cos (φ) + χxyyxxx sin (φ)]
(4)
(5) (5) 2 2 E′4,x ∝ E12E22E* 3[χxxxyyx cos (φ) + χxyyyyx sin (φ)]
(5)
(5) E4,y ∝ E12E22E* 3[2χyxyxxx sin(φ) cos(φ)]
(6)
where Ei denotes the amplitude of the light electric vector of the ith beam and χ(5) is the fifth-order susceptibility. The best fits in Figure 7 are obtained for A ) 1, B ) 0.23, C ) 0.26, D ) 0.21, and E ) 0.26. The latter set of values is quite similar to that expected (1, 0.25, 0.25, 0.16, 0.25) for a chromophore in which the transition moments and the variations of the electric dipole moment ∆µ and ∆µ′ related to both the writing and the reading processes are all parallel. This agreement suggests that the electronic transitions of the dimer involved in the writing and reading processes are characterized by quasi-collinear transition moments. Among the transitions |0〉 f |2〉 and |0〉 f |3〉 induced by the writing beams, only the latter is polarized parallel to the |0′〉 r |1′〉 transition. Therefore, we deduce that the second harmonic signal should be mainly due to the |0〉 f |3〉 transition. Moreover, the ∆µ associated to the transition |0〉 f |3〉 should be parallel to ∆µ′ associated with |0′〉 r |1′〉 and also parallel to the considered transitions. Remarks. The |0〉 f |3〉 transition, active in second harmonic generation, is the one having the largest oscillator strength (Table 1). The state |3〉 is delocalized on the two cationic chromophores (section 3) and built, totally or partially, on the two states S1. The S0 f S1 transition of the free cation is
In the present work we have investigated the optical properties of ion-pair dimers (two cationic chromophores and their counterions) formed by 2,6-diphenyl-4-(4′-dialkylaminophenyl)pyrylium tetrafluoroborates. As a first step, we have focused on the properties of the dimer excited states for which we have obtained information through steady-state absorption and polarized fluorescence spectroscopy. Afterwards, we have studied the nonlinear optical properties by using a nondegenerate sixwave mixing technique with picosecond resolution. Our main findings are summarized as follows. The fluorescence excitation spectra of the dimers have been decomposed into four bands related to two electronic transitions, close in energy, per cationic chromophore. The energy, oscillator strength, and relative polarization of the corresponding Franck-Condon transitions have been determined. This analysis has provided evidence that the dimer excited states are delocalized on both cationic chromophores. We have also found that the energy and the polarization of the transition related to fluorescence are quite different from those of the lowest in energy Franck-Condon transition. This drastic change of the wave function corresponding to the lowest in energy dimer singlet state is not hindered in solid matrices proving that the dimer geometry provides certain degrees of freedom, even in a rigid environment. We have shown, for the first time, that the dimers formed upon aggregation are capable of generating second harmonic in solution. This property reveals that the ground state geometry of the examined dimers is noncentrosymmetric and that excitation induces an important variation of the electric dipole moment of the dimers. The polarization dependence of the second harmonic signal suggests that the transition toward the third Franck-Condon state, characterized by the largest oscillator strength, is active in second harmonic generation. Finally, we have interpreted the relaxation in the lowest excited state of the dimers in terms of counterion motion caused by the photoinduced variation of the atomic charge distribution. In order to get a better insight into the relaxation process, we have undertaken a theoretical investigation based on quantum chemistry methods and the exciton theory. Appendix We present hereafter the reasoning and the procedure followed to fit the fluorescence excitation and excitation anisotropy spectra of the dimers by using the same four log-normal curves. For an excitation spectrum corresponding to n transitions, the total intensity I(E) is given by n
I(E) ) ∑Ii(E)
(7)
i)1
where Ii(E) denotes the intensity of the ith transition at energy E. In the same way, the anisotropy rex(E) can be written: n
rex(E) ) ∑pi(E)ri
(8)
i)1
where ri represents the anisotropy of the ith transition and pi(E) the fractional contribution of the ith transition to the total excitation spectrum at energy E defined as
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pi(E) ) Ii(E)/I(E)
Lampre et al.
(9)
The fit is performed in an iterative way. A first fit of the excitation spectrum with the sum of n log-normal curves provides a set of pi(E) values (eq 9). Then, those values are used for the fit of the anisotropy spectrum (eq 8), ri being the fitting parameters. If no acceptable fit is obtained for the anisotropy, the excitation spectrum is fitted again by modifying the parameters of the log-normal curves. Acknowledgment. The authors thank Dr. P. Millie´ and Dr. J. M. Nunzi for helpful discussions. References and Notes (1) Leninson, G. S.; Simpson, W. T.; Curtis, W. J. Am. Chem. Soc. 1957, 79, 4314. (2) West, W.; Pearce, S. J. Phys. Chem. 1965, 69, 1894. (3) Rohatgi, K. K.; Mukhopadhyay, A. K. Photochem. Photobiol. 1971, 14, 551. (4) Selwyn, J. E.; Steinfeld, J. I. J. Phys. Chem. 1972, 76, 762. (5) Ga`l, M. E.; Kelly, G. R.; Kurucsev, T. J. Chem. Soc., Faraday Trans. 2 1973, 69, 395. (6) Chambers, R. W.; Kajiwara, T.; Kearns, D. R. J. Phys. Chem. 1974, 78, 380. (7) Obermueller, G.; Bojarski, C. Acta Phys. Polonica 1977, A52, 431. (8) Kopainsky, B.; Hallermeier, J. K.; Kaiser, W. Chem. Phys. Lett. 1981, 83, 498. (9) Lopez Arbeloa, I.; Ruiz Ojeda, P. Chem. Phys. Lett. 1982, 87, 556. (10) Hamada, K.; Kubota, H.; Ichimura, A.; Iijima, T.; Amiya, S. Ber. Bunsenges. Phys. Chem. 1985, 89, 859.
(11) Ishchenko, A. A.; Vasilenko, N. P.; Maidannik, A. G.; Balina, L. V. Dokl. Akad. Nauk. Ukr. SSR, Ser. B 1988, 46. (12) Valdes-Aguilera, O.; Neckers, D. C. J. Phys. Chem. 1988, 92, 4286. (13) Prishchepov, A. S.; Zaripov, B. D.; Astanov, S. Opt. Spektrosk. 1989, 66, 1311. (14) Yuzhakov, V. I. Usp. Khim. 1992, 61, 1114. (15) Rohatgi-Mukherjee, K. K. Indian J. Chem. 1992, 31A, 500. (16) Davydov, A. S. Theory of Molecular Excitons; Plenum Press: New York, 1972. (17) Kasha, M.; Rawls, H. R.; Ashraf El-Bayoumi, M. Pure Appl. Chem. 1965, 11, 371. (18) Markovitsi, D.; Jallabert, C.; Strzelecka, H.; Veber, M. J. Chem. Soc., Faraday Trans. 1990, 86, 2819. (19) Lampre, I.; Markovitsi, D.; Birlirakis, N.; Veber, M. Chem. Phys. 1996, 202, 107. (20) Markovitsi, D.; Sigal, H.; Ecoffet, C.; Millie´, P.; Charra, F.; Fiorini, C.; Nunzi, J. M.; Strzelecka, H.; Veber, M.; Jallabert, C. Chem. Phys. 1994, 182, 69. (21) Charra, F.; Devaux, F.; Nunzi, J. M.; Raimond, P. Phys. ReV. Lett. 1992, 68, 2440. (22) Fiorini, C.; Charra, F.; Nunzi, J. M. J. Opt. Soc. Am. B 1994, 11, 2347. (23) To fit the spectra, we have used the simplified log-normal function f(x) ) a exp{-b2[ln((x - c)/d]2}. (24) Siano, D. B.; Metzler, D. E. J. Chem. Phys. 1969, 51, 1856. (25) Lakowicz, J. R. Principles of Fluorescence Spectroscopy; Plenum Press: New York, 1983. (26) Ecoffet, C.; Markovitsi, D.; Millie´, P.; Lemaistre, J. P. Chem. Phys. 1993, 177, 629. (27) Wang, Y. Chem. Phys. Lett. 1986, 126, 209.
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