J. Phys. Chem. 1992, 96,9643-9650 nor any of several possible procedures for contracting the total grid extent required for the propagation. Although grid shortening methods also exist for FFT-based procedures, they cannot be used simply with nonuniform grids. The second important aspect for implementation on massively parallel supercomputers is that of communications. The communication time for an FFT on the hypercube is 2(ts tmmmn/p)log, p , and that for the DAF algorithm is 2(t, t,,,b/2). Here, t, is the start-up time, t,,, is the communication time for a word, n is the length of the input vector (I grid size), p is the number of prwessors, and b is the band width of the DAF class matrix propagator. For given tsand t,,,, the FFT has the term 24 log, p compared to the DAF 24, the difference being (log, p - 1)2t,. For 128 processors, this would be 124 longer for the FFT. For the second term, one compares (2t,,,n/p) log, p for the FFT, with t,,,b for the DAF, so the extremes (with 10 I 6 I20 and 512 In I32768) are 56t,,, to 3584t,,, for the FFT and lOt,,, to 20t” for the DAF. It is clear that the DAF is extremely well suited to implementation on massively parallel supercomputers. On the basis of these results, we are optimistic that other versions of the DAF formalism will also be successful and provide useful new tools for real time quantum dynamics.’+ We are carrying out many such computational studies now, with particular emphasis on the Gaussian biased sampling-Monte Carlo evaluation of the DAF path integral scattering amplitude6 and the quadrature (DDAF) and Monte Carlo (CDAF) evaluation of real time dynamics.
+
+
Acknowledgment. The authors gratefully acknowledge helpful
9643
suggestions and comments on this work by Dr. J. Gustafson.
References and Notes (1) Hoffman, D. K.; Nayar, N.; Sharafeddin, 0. A.; Kouri, D. J. J . Phys. Chem. 1991,95, 8299. (2) Hoffman, D. K.; Kouri, D. J. J. Phys. Chem. 1992, 96. 1179. (3) Kouri, D. J.; Zhu, W.; Ma, X.;Pettitt, B. M.; Hoffman, D. K. J. Phys. Chem., companion paper in this issue. (4) Kouri, D. J.; Hoffman, D. K. J. Phys. Chem., companion paper in this issue. (5) Hoffman, D. K.; Arnold, M.; Kouri, D. J. J . Phys. Chem. 1992, 96, 6539. (6) Hoffman, D. K.; Arnold, M.; Zhu, W.; Kouri, D. J. J. Chem. Phys.,
submitted for publication. (7) Makri, N. Chem. Phys. Lerr. 1989, 159, 489. Makri’s effective prop agator is based on introducing a sharp cutoff, Pmax,into the Fourier integral evaluation of the free particle propagator. The resulting effective free prop agator processes a structure which decays with the distance propagated, (x - x’), as sin [Pmnr(x- x’)]/(x - x’), which is much weaker than the Gaussian decay of the DAF class free propagator. (8) Hoffman, D. K.; Sharafeddin, 0. A.; Kouri, D. J.; Carter, M.;Nayar, N.; Gustafson, J. Theor. Chem. Acru 1991, 79, 297. (9) Judson, R. S.;McGarrah, D. B.; Sharafeddin, 0. A.; Kouri, D. J.; Hoffman. D. K. J. Chem. Phvs. 1990. 94. 3577. (10) Sharafeddin, 0. A.; Kouri, D.’J.; Judson, R. S.;Hoffman, D. K. J . Chem. Phys. 1992, 96, 5039. (1 1) Feit, M. D.; Fleck, J. A. J . Chem. Phys. 1982, 78, 301; 1983, 79, 302; 1984,80, 2578. (12) Devries, P. NATO AS1 Series. 1988 8171, 113. (13) Kosloff, D.; Kosloff, R. J . Comput. Phys. 1983, 52, 35. (14) Kosloff, R.;Kosloff, D. J . Chem. Phys. 1983, 79, 1823. (15) Kouri, D. J.; Hoffman, D. K. Chem. Phys. Lorr. 1991, 186, 91. (16) Truong, T. N.; McCammon, J. A.; Kouri, D. J.; Hoffman, D. K.J . Chem. Phys. 1992, 96, 8136. (1 7) Luscomb, J. H.; Frensley, W. R. Nanorech. 1990, 1, 13 1.
Photophysics of Donor-Acceptor Substituted Stilbenes. A Time-Resolved Fluorescence Study Using Selectively Bridged Dimethylamino Cyano Model Compounds R e d Lapouyade,*.t Konstantin Czeschka; Wilfried Majenz,*Wolfgang Rettig,*gt Eric Gilabert,s and Claude Rullibe*v* Photophysique et Photochimie Moleculaire, URA du CNRS No. 348, Univ. de Bordeaux I, 351, cours de la LibPration, F-33405 Talence, France, I. N. Stranski-Institute, Techn. Univ. Berlin, Strasse des 17. Juni 112, 0-IO00 Berlin 12, FRG, and Centre de Physique MolCculaire Optique et Hertrienne, U.A. du CNRS No. 283, Univ. de Bordeaux I, 351, cours de la LibCration, F-33405 Talence, France (Received: December 16, 1991; In Final Form: August 17, 1992) Several selectively bridged 4-(dimethylamino)-4’-cyanostilbenesare investigated. All of them show strongly red-shifted fluorescence spectra connected with a considerable dynamical Stokes shift in polar solvents. Bridging, however, affects the photophysics (fluorescence quantum yields and lifetimes) dramatically. Blocking of the double bond twist by a sufficiently rigid bridge ( 10" mol/L) and high laser excitation energy. From these results?6 it appears that concentration effects, by solvent temp ("C) DCS MPQB complex formation, may stabilize the TICT state and, at the same propylene carbonate -25 4 0 h 10 60* 10 time, slow down its rate of formation: an activation barrier appears propylene carbonate -50 200 10 160 h 40 between DE and TICT state. For these particular experimental propylene carbonate -7 5 580 i 30 560 30 conditions, the classical dual-luminescence of both the DE and n-butanol 20 120 30 90* 25 the TICT states as well as a precursor-successor relationship between the populations of these two states is observed.30 This The polar solvent cage relaxes around a highly polar ICT state suddenly created by photoexcition. As already e ~ p l a i n e d , ~it' . ~ ~ specific aspect is developed in a separate paper,36since this more is possible, from the time-dependent shift of the emission maxicomplex situation deserves a detailed and precise discussion. A mum, to deduce the time T , characteristic for the relaxation of key observation is that for identical high concentration/high excitation intensity conditions, all the compounds able to twist the solvent cage. In Table IV,we present the corresponding T, values of DCS around the single bond connecting the ethylene double bond to deduced from our measurements in different experimental conthe anilino moiety (DCS, DCS-B34, DCS-B34a) exhibit similar ditions and the T , values for a model compound (MPQB) used precursorsuccessordual fluorescence behavior, whereas DCS-B24, as a standard for the studies of pure solvent cage effects.34 As unable to relax along this reaction coordinate, shows only one band. we may observe from Table IV, a good correlation exists between An example of such picosecond time-resolved fluorescence spectra T , values of DCS and of the model compound. This shows that is given in Figure 5. the spectral evolution observed for DCS has to be related to the Discussion solvation process occurring in the emitting excited state. But we cannot conclude on the exact nature of this emitting state: The results of fluorescence spectra, quantum yields and k,, Whether it is a TICT state or not is not contradictory with these values as a function of solvent polarity and molecular structure results. It is well possible, for example, that the TICT state is can either be discussed within the conventional kinetic scheme formed without an activation barrier from the DE state. This involving only E* and P* states and the quenching reaction kEP should explain why the rate constant of formation is essentially (mechanism A, Scheme Ia) or within the three-state model controlled by the solvent cage which has to change continuously presented above (mechanism B, Scheme Ib). and at each time to match the newly created TICT state. Also Regarding the spectra alone, the absence of well visible dual it is well possible and already indicated by the similar solvatofluorescence seems to speak against the more complicated chromic behavior of DCS and DCS-B24 (Figure 3) that the threestate model, and the similarity of the spectra for the various E*(DE) and A*(TICT) states have nearly the same dipole momodel compounds would seem to indicate only one emitting specics ment which explains why we do not observe a strongly different E* or very similar emission spectra for species E* and A*. The behavior between DCS, DCS-B24, and DCS-B34 for the timekinetic results, however, are more sensitive, and the following resolved solvatochromism. The small difference found between analysis establishes that at least three excited states (model B) DCS and DCS-B24, however, namely a somewhat smaller redare photophysically relevant and that these differ in the twisting shift for DCS-B24 for the fully relaxed spectrum as compared of single and/or double bonds. to the initial one, is consistent with the assumption of a further The decreasing k,, values with increasing solvent polarity are relaxation step for DCS (E* A*) as compared to DCS-B24. interpreted within both models as indicating a significantly reduced The above results cannot unequivocally answer the question dipole moment of P*as compared to A* or E*, in accordance with as to the formation of a TICT state in DCS and related molecules. previous interpretations.I0 The difference between the k,, values TABLE I V Fluorescence Spectral Relaxation Times 7 , (p)of DCS and the Model Compound MpQB3*in Propylene Carbonate and n-Butanol at Different Temperatures
* *
-
*
Lapouyade et al.
9648 The Journal of Physical Chemistry, Vol. 96, No. 24, 1992
for DCS-B24 and DCS (ratio -80) and the observation of a lifetime maximum, however, is difficult to explain using model A. Although it is known that stiff stilbene (the unsubstituted analogue of DCS-B24) has about a 6-fold higher k,, rate in alkane solvents as compared to stilbene,37this behavior is not yet well understood. 90° stilbene
A It clearly points to the importance of single bond rotations for the double bond twisting process in unsubstituted stilbene. Quantum chemical calculations indicate that the twist angle of the phenyl groups can generally strongly modify the activation barrier from E* to P* as well as the energy of these state^.^^,^^ A possible interpretation of the kinetic difference involves the In reaction along a reaction path of higher the case of DCS this kinetic difference between bridged and unbridged compounds is strongly increased (factor = 60-90, Table 11) as compared to stilbene (factor of 6 in alkanes3’), and this suggests the assignment of a physical entity to explain this multidimensional twisting problem, namely a real intermediate A* reached from E* by barrierless relaxation through twisting of the ethylene-aniline single bond (mechanism B). The difference in k, rates for DCS and DCS-B24 is interpreted in mechanism B by a relatively slow transition across a barrier from the relaxed species A* toward P*, either “directly” by simultaneous twisting of single and double bonds or indirectly via activated return to E* and subsequent reaction E* P*. The relaxation possibility E* A* therefore acts as a trap preventing the excited E* molecules from the fast photoreaction toward P* and thus immediate fluorescence quenching. In polar solvents, where r # ~is~ high, A* is populated efficiently, and we can conclude that its formation rate k E A has to compete efficiently with the direct nonradiative transition kEp. The latter, however, is measurable in the model compound DCS-B24, where only relaxation toward P* is possible, and where the fast fluorescence decay times (Tf 5 20 ps) indicate k,, = kEP1 5 X 1O1Os-I at room t e m p e r a t ~ r e .A~ ~cautious evaluation of kEA in DCS will thus come up with k E A > 5 X 10” s-l. As judged from fluorescence decay times and quantum yields in polar solvents (Tables I and I1 andlo), the A* state of DCS is highly emissive (kf= 4 X los s-l) and therefore has unusual properties for a TICT state. The forbidden nature of the classical TICT emission is, however, linked closely to the perpendicularity of the TICT conformation. Deviations from this idealized geometry through thermal motion cause vibronic coupling with allowed states and lead to the usual increase of kf(T1CT) with increasing temperat~re.4~ The highly allowed TICT emission in the case of DCS may therefore be indicative of a very strong coupling between TICT and allowed states and of large deviations from perpendicularity. As already explained above, further support for the involvement of a real intermediate A* comes from the ps time-resolved dual fluorescence spectra of DCS and model compounds at higher c o n c e n t r a t i ~which n ~ ~ ~show ~ ~ the precursomuccessor relationship characteristic for TICT formation. In the low-concentration conditions studied for the lifetime and time-resolved red-shift measurements, the activation barrier for A*(TICT) formation is probably very small,36and TICT formation (kEA)may occur at T > T, in a few picoseconds within the excitation pulsewidth used. The present model compounds pinpoint which of the several flexible single bonds in DCS is the one leading to A*. Already several years ago, a bridged derivative of DCS has been studied where the rotation of the dimethylamino group was b10cked.~ From the identical solvatochromic and quantum yield behavior of the two compounds, it was concluded that a TICT state was not populated. With the present model compounds a t hand, we
-
-
,
ii;z
9 O ” X push-pull-stilbene
n
-&f
LUMO HOMO Figure 6. Biradicaloid states accessible by twisting the central double bond in stilbene and a push-pull stilbene. In both cases,the excited state
has an energy minimum, and the ground state has an energy maximum for the perpendicular conformation. This arises from the energetic repulsion between these two states for twist angles #90°, regardless of the electronic nature of S, (‘hole pair” or ‘dot-d~t”’~-’~). For twisted stilbene, the subunit molecular frontier orbitals are made up by the nonbonding orbital of a phenylmethylene radical and are degenerate. For symmetric twisted stilbene, the frontier orbitals are a symmetrical linear combination of HOMO and LUMO depicted. Upon perturbation, especially by donor (D) and acceptor (A) substituents,HOMO and LUMO localize as shown schematically (disregarding the orbital changes due to the substituents). D shifts one localized orbital upwards (LUMO); A lowers the other one (HOMO). The two odd high-lying r-electrons can be placed into these frontier orbitals in two different ways: For degenerate frontier orbitals, electronic repulsion makes the ‘hole-pair” configuration (‘hp”) energetically less favorable than the “dot-dot” configuration (“dd”). The latter thus becomes So (nonpolar); “hp” is highly polar and SI. Push-pull substituentsopen an energy gap 6 in the frontier orbitals, and for sufficiently large 8, ”hp” is more stable than ‘dd” with the consequence of a highly polar twisted ground and a weakly polar twisted excited state P*. may add that this holds only for TICT formation through N(CH,)*-twisting, whereas twisting one of the other single bonds leads to a TICT state for both compounds. In DCS-B34, not only is double bond twisting blocked but also twisting around the single bond connecting the ethylene and benzonitrile moiety. Yet this compound is TICT-emissive in highly polar solvents and establishes that the rotation around the other single bond connecting ethylene to the anilino group leads to a TICT state. It still remains possible, that for DCS both single bond twist coordinates are TICT pathways. Studies of the DCS-B34 isomer, where the bridge is toward the aniline ring blocking the other single bond, may reveal that in the future. From the similar behavior of DCS-B34a and DCS-B134a, dialkylamino group rotation is shown to be a much less important pathway. There are only a few examples in the literature on other bridged push-pull stilbenes, but they are also compatible with TICT formation. For example, Katzenellenbogen et al.44studied the donor-acceptor nitromethoxyphenylindenes and found dual fluorescence which could, however, not be reproduced in our labor at or^.^^ The extremely Stokes-shifted TICT fluorescence of I was shown to be linked to a solvent-polarity dependent nonradiative process.44 Nikolov et al.46used an ester bridge in I1 which, a t the same time, acts as ortho-acceptor substituent. For good donor groups X (push-pull stilbene derivatives), e.&, amino or methoxy, high fluorescence quantum yields are observed, compatible with the results here. For less good donors like H and CH3, the quantum yields drop dramatically indicating that an intermediate A* state is not reached because it is energetically not low enough. Recently, a study on the dialkylaminonitrostilbena I11 and IV and the compound with the bridged dimethylamino group behaved similarly as the unbridged one in parallel to the case of DCS (ref 9 and present results). But for the dialkylaminonitrostilbenes, an additional nonradiative pathway seems to be possible for high solvent polarities, which was tentatively
The Journal of Physical Chemistry, Vol. 96, No. 24, 1992 9649
Donor-Acceptor Substituted Stilbenes O-CH,
/
V
I
Q $ - o x C I1
0 X=N(CH )
3 2,
NO-L
NH
2,
OCH
3)
CH
3,
H, C1, CN,
I1
assigned to NO2rotation?’ Further experiments on bridged nitro compounds are needed, similar to the ones described here, to assess the question whether a TICT formation similar to that for DCS is possible in the nitro analogues.
Me
R = H, CH 3 IV Charged stilbazolium dyes like V also exhibit a nonradiative decay channel via a P* state (twisted double bond).* Interestingly, triplet formation could be shown to be negligible at room temperature such that the defect = (1 - 4,-1$~~-4~,)= 0.5 in photophysical quantum yields (& = 0.006, = 0, 4t* = 0.5 in alcohols at room temperature*) has to be linked to an additional nontadiative decay channel in the singlet state. By bnventional reasoning, this would be assigned to internal conversion. In the light of the present study, another possibility is photochemistry to an A* state with nonemitting properties (either due to a very small krrate or due to a small So- Si energy gap: a photochemical funnelig). Recent data on VI in fact could identify such a nonemitting A*(TICT) state (reached by single bond rotation).49 In the corresponding ortho isomer VII, this A* state seems to be emissive and leads to a lifetime maximum very similar to that observed for DCS in the present s t ~ d y . ~ ~ , ~ ~ Related systems are aminobenzoxazinones VI11 and IX which possess a larger acceptor group. They have been used in the development of ion sensing fluorescence probes.52 A recent study of the solvatochromic properties of VI11 and IX and the comparison to that of X yield clear evidence for the involvement of TICT states.53 Similarly as for DCS/DCS-B134a and III/IV, there is no principle difference between VI11 and the aminobridged model compound IX supporting the notion that rotation around the other bonds is more important.
X
U
The solvatokinetic results in Table I1 indicate that the intramolecular fluorescence “quenching” rate constant k,,, Le., the transition rate constant from either A* or E* toward P* decreases with increasing solvent polarity. From this,an increased activation barrier for polar solvents can be concluded. From this follows that the precursor state (E* or A*) is more strongly stabilized by the polar solvent, hence more polar, than the quenching state PI. The latter thus has to be of weakly polar nature. As outlined in the introduction, the solvatokinetic behavior is opposite for unsubstituted stilbene, hence P* is more polar than E* in the stilbene case. This switching between polar and nonpolar character of P* is predicted by CNDO/S calculationsi0~5iand understandable within the theory of biradicaloid charge-transfer statesioJ2-i4~i6-i9 and may be visualized as shown in Figure 6. The fluorescence lifetime maximum at low temperature is less well developed for DCS-B34 than for the other compounds, especially in weakly polar solvents.29This can also be seen by the increase of the qEfvalues with solvent polarity (Table II), contrary to the case of DCS. We conclude, that for DCS-B34 the fluorescenceis a mixture of E* and A* fluorescence,with the A* component being the major one only in strongly polar solvents. When the double bond is bridged into a six-membered ring, the flexibility of the molecule is high enough to allow, in principle, the formation of a trans double bond in the ground state, as exemplified in 1-phenylcycl~hexene.~~ Therefore, relaxation in the excited state to the perpendicular P* state is also expected not to be hindered and consequently DCS-B34a behaves rather
9650 The Journal of Physical Chemistry, Vol. 96, No. 24, 1992
similarly to DCS (Table 11). Its deactivation behavior indicates that there is virtually no hindrance to reach the double bond twisted P* state in spite of the bridge. The six-membered ringbridged unsubstituted stilbene 3-phenyl-l,2-dihydronaphthalene was recently found to behave alike and to show nearly exclusively 'internal conversion" similar to stilbene, whereas in the corresponding five-membered ring compound, the latter is strongly reduced .55
Acknowledgment. This work has been supported by the Bundesministeriumfiir Forschung and Technologie (project 05314 FAIS) and by the EC-Large Scale Installations Program (GE 1-0018-D(B)).W.R. thanks the Deutsche Forschungsgemeinschaft for a Heisenberg Fellowship. We thank Dr.H. GBrner for critical discussions.
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