J . Phys. Chem. 1993,97, 13046-13051
13046
Electronic Energy Transfer: Density of States Mita Chattoraj, Basil Paulson, Yan Shi, G. L. CIOSS,~ and Donald H. Levy' The Department of Chemistry and the James Franck Institute, The University of Chicago, Chicago, Illinois 60637 Received: June 3, 1993'
Intramolecular electronic energy transfer has been observed in one isomer of the bichromophoric molecule
D-SpA where the donor (D)is naphthalene, the spacer (Sp) is cyclohexane, and the acceptor (A)is dimethylaniline (DMA).Because the emission spectra of both the donor and acceptor overlap, the emission wavelength could not be used as a diagnostic for energy transfer. However, the donor and acceptor have very different fluorescencelifetimes, and large changes in the fluorescencelifetimes of the vibronic states of naphthalene due to the presence of DMA could be used as a measure of the mixing and energy transfer between the two chromophores. The methyl groups of DMA cause the density of states to rise very rapidly at energies close to the zero-point level, and in the cis isomer this leads to energy transfer from naphthalene vibronic levels that are only slightly above the zero-point level of DMA. The energy-transfer rate was measured as a function of the excited vibronic-state energy. The onset of energy transfer in cis isomers occurs at a lower energy than in the trans isomer, corresponding to a lower density of states.
Introduction Energy transfer between two chromophores in a donor-acceptor system is a classic example of a radiationless process.2 The properties of such donor-acceptor systems are different from those of the isolated donor or acceptor since each chromophore is perturbed by the other. It is often convenient to discuss energy transfer in terms of zero-order states which are the eigenfunctions of the Hamiltonian describing the system for infinite separation of the chromophores. The isolated donor can undergo an electric dipole allowed transition to a donor excited state. Isoenergetic with this donor excited state are acceptor excited states which cannot be excited from its ground state due to unfavorable FranckCondon factors. Hence, the absorption spectrum of the bichromophore is characteristic of the donor. However, the electrostatic interactions between the chromophores cause these zero-order states to be nonstationary. By exciting the donor-acceptor system and measuring the time evolution of the emission spectrum in terms of the fluorescence of the donor and the acceptor, it is possible to obtain a measure of this interaction.3.4 The intensity of donor-like emission decreases, and there is a simultaneousrise in the acceptor-like emission as the nonstationary state evolves, i.e., as the energy transfers. The steady-state properties of a bichromophore also provide a measure of the interaction between the two chromophores. For example, after the initially excited nonstationary donor state has evolved into the molecular eigenstates, the mixed nature of the eigenstate produces an emission spectrum that is part donor-like and part acceptor-like. The relative amounts of these emissions are a measure of the interaction between the zero-order donor and acceptor states.5 In the present work, the fluorescencelifetime of one of the chromophores is substantially longer than the other. Their interaction is investigated by determining the lifetime of the bichromophore and analyzing it in terms of the individual donor and acceptor fluorescence lifetimes. The system studied in this paper is of the type D S p A , where D is naphthalene (NPT) and A is N,N-dimethylaniline (DMA) rigidly separated by a spacer, Sp. The origin transitions for the first excited singlet states of the chromophores are within 600 cm-*of each other, and the emission spectra of both chromophores are in the same wavelength region. This means that the emission spectra are not clearly separated, and we are not able to use the *Abstract published in Advance ACS Abstrucrs, November 15, 1993.
0022-365419312097- 13046$04.00/0
relative intensities of the emission spectra to measure the extent of mixing. Since the two chromophores have different lifetimes, we were able to use the fluorescence lifetime as a measure of state mixing. Although the origin of DMA is at a somewhat higher energy than that of NPT, the low-frequency modes associated with the methyl groups cause the density of DMA states to rise very rapidly as a function of energy. The SIstate of naphthalene is long lived (383 ns at its origin transition), and 2-methylnaphthalene has a quantum yield of -0.3 at the origin6 DMA has a relatively short lifetime (2.35 ns) and lower fluorescence quantum yield (0.1 8 f O.O2).' The extent of mixing of the states of the two chromophores can be estimated by measuring the change in the lifetime of (or the quenching of) the naphthalenelike transitions in the presence of DMA. In studying radiationless transitions in single chromophores,C1o only the mixed eigenstates can be probed. The advantage of investigatingenergy transfer in bichromophores is that it is possible to switch off the perturbing interaction by isolating the chromophores.
Experimental Section The compounds were synthesizedby standard methods." The two isomers of the bichromophore 1-(2-naphthy1)-4-(NINdimethylanilin-4-y1)cyclohexane (NPT-CCDMA) were completely separated into the cis (equatorial-axial, ea) and trans (equatorial-equatorial,ee) isomers. Spectra presented here were recorded using fluorescenceexcitation and dispersed fluorescence techinques. The basic experimentalapparatus has been described elsewhere,12and only a brief description will be given here. The molecules were heated to attain sufficient vapor pressure; 85 O C for (N,N-dimethylanilin-4-yl)cyclohexane(C6-DMA), 99 OC for 2-naphthylcyclohexane (NPT-C6), and 190 OC for the cis and trans isomers of NPT-CgDMA. They were seeded into helium gas at 13-14 atm stagnation pressure, and the mixture was expanded into a vacuum chamber through a 0.050-mm-diameter pinhole. Mass-selected photoionization was recorded for all samples. The ionization experiments were performed by skimming the freejet expansion. The resultant molecular beam was then probed by the frequency-doubled output of an Nd-YAG pumped dye laser between the ion extraction grids of a time of flight mass spectrometer. The ion signal was recorded as a function of excitation wavelength. The appearance of a single mass signal 0 1993 American Chemical Society
Electronic Energy Transfer
The Journal of Physical Chemistry, Vol. 97, No. 50, 1993 13047 1
a a
b I
3
00
.'
32000
32400
32800
33200
WAVENUMBER (CM-')
Figure 1. Fluorescence excitation spectra of (a) (NJV-dimethylanilin3000 32000 31000 30000 29000 4-y1)cyclohexane(C6-DMA),(b) 2-naphthylcyclohexane(NPT-C6),(c) W A VEN UMBER (CM-' ) trans- 1-(2-naphthyl)-4-(NJV-dimethylanilin-4-yl)cyclohexane(NPT-C6DMA), (d) cis- 1-(2-naphthyl)-4-(N,~-dimethylanilin-4-yl)cyc~ohexane Figure 2. Emission spectra of the origin transitions of NPT-C6 and (NPTC6-DMA). C6-DMA. The intensity scale is different for each of the plots. The resolution is 50 cm-I. (a) 2-Naphthylcyclohexane ("46) excited at 3 1 784 cm-l. (b) (N,N-dimethylanilin-4-yl)cyclohexane (C6-DMA) at the expected time indicated that decomposition was not excited at 32383 cm-I. The signal at the resonant wavenumber is occurring at the oven temperature. exclusively due to scattered light. In the fluorescence experiments the mass spectrometer was replaced with fluorescence collection optics and a photomultiplier lowest energy transition is at 32 312 cm-I. The intensity pattern tube. The excitation spectra were measured by monitoring the of the peaks did not vary as a function of the helium backing intensity of the undifferentiated fluorescenceas a function of the pressure, indicating that the features are not due to the presence wavelength of the incident light. An optimized SR640-DCM of hot bands. There is an 8-member 24-cm-1 progression dye mixture was used. The primary purpose in obtaining the characteristic of methyl rotor vibrations. The intensity pattern excitation spectra was to locate peaks for the measurement of suggests a change in the equilibriumgeometry between theground fluorescence lifetime, and the peak positions are more accurate and excited states. The spectral congestionand intensity increases than their relative intensities. Every effort was made to avoid with excitation energy, and within 500 cm-l of the first transition power saturation. All the fluorescence excitation spectra were it become impossible to identify individual peaks in the spectrum. normalized to the excitation laser intensity. The excitation spectrum of NPT-C6 near its SI SOorigin Fluorescence emission from the jet was also dispersed with an is shown in Figure lb. At low temperatures NPT-C6 is expected f/3.8 0.275-m monochrometer and detected with a proximity to exist in two conformations. There are two transitions at 31694 focused microchannel plate intensified diode array (EGCG and 3 1784 cm-l, which we identify as the conformer origins. The Princeton Applied Research, 1455B-700-HQ). identificationof these peaks as conformer origins and not members Time-resolved studies of the fluorescence emission were of a vibrational progression has been confirmed by us using holeobtained by routing the output of the photomultiplier tube (RCA burning16J7and power-saturation'* experiments. The vibronic 8575) to the input of a Tetronix 2232-3db 100-MHz interleaving structure closely resembles that of 2-meth~lnaphtha1ene.I~Cordigital storage oscilloscope which was interfaced with the data relating the vibrational features of NPT-C6 with the modes that acquisition computer by means of a GPIB board. The duration apear most prominently in the 2-methylnaphthalene spectrum, of the excitation light pulse was 4 ns. The rise time of the we find that, similar to other 2-substituted naphthalenes,"J the photomultiplier tube was 2.5 X le9s. The data set contained a, type transistions which couple the S3 state are relatively intensity readings at intervals of 500 ps. enhanced compared to bl, type transitions. Thus the transition Deta Fitting Procedure. The fluorescenceprofile was modeled at 717 cm-' may be correlated to the 8; and the 969 cm-i by transition to the 7; transitions of naphthalene of ar symmetry. Unfortunately any further assignments remain tentative since h(t - to) = Ag(t) B~0'e4"t')"g(t') dt'+ C (1) most prominent transitions in naphthalene do not have straightforward analogues in NPT-C6 due to mode mixing in the Si The first term is the contribution of the scattered laser light, the state.19 second is the convolution13 of a single exponential with the The excitation spectra of the trans and cis isomers of the measured instrument function, g(r), C is the detector pedestal, bichromophore, NPT-C6-DMA, are shown in parts c and d, and to is the time offset between the instrument function and respectively, of Figure 1. Both spectra are a combination of the fluorescence profile measurements. After estimating the initial spectra of the isolated chromophores NPT and DMA. However, values of the parameters, a simplex routine" is used to iteratively the intensity of the transitions characteristic of DMA are more fit themodel function using x2 minimization as the fitting criterion. intense in the spectrum of the cis isomer. The DMA contribution The best values of the parameters from the simplex fit are used to the spectrum of the trans isomer is visible only on careful as the initial guess for a zero-gradient fit routine.ls inspection of the baseline. Dispersed Emission Studies. Figure 2a shows the dispersed Results emissionspectrumof NPT-C6excitedat 31 784cm-I (theorigin). The spectrum closely resembles that of 2-methy1na~hthalene.l~ Figure l a shows the fluorescence excitation spectrum of C6There are characteristic transitions at 532,767, and 1392 cm-I. DMA. The spectrum is extremely complex and congested. The
-
+
Chattoraj et al.
13048 The Journal of Physical Chemistry, Vol. 97, No, 50, 1993
II
TABLE I: Fluorescence Lifetimes and Miof Trans NPT-CBDMA a
d
Coefficients
trans NPT-C6-DMA NPT-C6 mix. c a f ~ , ns b energy: cm-1 ~ , no b 02 x 104 d energy,"cm-1 -92' 90.6 f 4.2 -90, 95.8 f 0.7 14f 12 0 382.7 f 2.4 0 1.7 f 0.6 372.8 f 2.6 619 136.9 f 0.9 - 6 7 f 16 221 f 33 623 717 170.6 f 0.4 -18.3 3.1 716 196.3 f 5.0 146.9 i 4.3 144.8 f 1.2 -2.4 f 4.9 914 912 155.0 f 4.7 139.4 f 1.1 -17.2 i 4.8 969 968 1164 128.4 f 1.1 -5.1 i 7.3 139.9 f 5.2 1161 135.1 f 0.6 24f 18 1400 119f 1 1 1399
*
a The transitions are listed relative to the SI origin of the trans isomerofNPT-C6-DMAat31 773cm-I. Theerror barsareonestandard deviation evaluated from the scatter among several independent measurements at each energy. e The transitions are listed relative to the SI +SO origin of C6-NPT at 31 784 cm-l. The error bars reflect only the error caused by the uncertainty in the measured lifetimes. This peak at 3 1 68 1 cm-l is a conformer origin. /This peak at 3 1 694 cm-1 is an NPTC6 conformer origin. +
33000
32000
31000
30000
TABLE Ik Fluorescence Lifetimes and Mixing Coefficients of Cis NPT-C6DMA
29000
-
WAVE NUMBER (CM-I ) Figure 3. Emission spectra of the 1 164-cm-1vibration of NPT-C6 and NPT-C6-DMA. The intensity scale is different in each plot. The signal at the resonant wavenumber in each of these spectra is exclusively due to scattered laser light. The resolution is 50 cm-l. (a) Spectrum of 2-naphthylcyclohexane (N?T-C6) excited at 32 945 cm-I (1 164 cm-I above the more intense origin transition). (b) Spectrum of ?ram-142naphthyl)-4-(NJV-dimethylanilin-4-yl)cyclohexane (NPT-C6-DMA)excited at 32 934 cm-1 (1161 cm-1 above the more intense origin). (c) Spectrumof cis-1-(2-naphthyl)-4-(N,N-dimethylanilin-4-yl)cyclohexane (NPT-C6-DMA) excited at 32 940 cm-I (1163 cm-1 above the higher energy origin transition).
The emission spectrum of C6-DMA excited at 32 383 cm-l is shown in Figure 2b. Because the spectrum is weak, the sensitivity has been increased relative to Figure 2a. The emission is in the same wavenumber region as naphthalene and is extremely broad with weak transitions extending from 32 000 to 29 000 cm-', with few distinguishing characteristics. This broad, red-shifted emission indicates a geometry change between the ground and excited states of the chromophore producing one or more active normal modes. The emission spectra of the bichromophores were also studied. The DMA contributions to the excitation spectra (Figure lc,d) were extremely weak in intensity and could not be distinguished, so only the naphthalene vibronic transitions were excited, and the emission spectrum was inspected for evidence of DMA character. Figure 3 shows the dispersed emission spectra of NPT-C6 and the trans and cis isomers of the bichromophore all excited at the 1162 cm-1 vibration of naphthalene. The emission spectrum of NFT-C6 is dominated by broad features with linewdithsof 150 cm-I on top of a developing background, due to the onset of intramolecularvibrational energy redistribution (IVR)processes.*O The emission spectra of both the trans and cis isomers of the bichromophore are almost indistinguishablefrom that of NPTC6. In this wavenumber region there is a high density of DMA excited states, and it was hoped that the interaction between the chromophores would be evident in the spectra of the bichromophores. However, theextremely weakand broadly distributed peaks of DMA are not discernable. Lifetime Studies. Fluorescence lifetimes of NPT-C6 and the cis and trans isomers of NPT-C6-DMA were measured (Tables I and 11). The lifetimes of the two NPT-C6 conformer origins, 95.8 and 382.7 ns, are very different. The fluorescence lifetimes for the transitions of this molecule decrease with increasing excitation energy, although there are some fluctuations about this general trend. The lifetimes of the naphthalene-like transitions in NPT-C6-DMA also show a similar decrease with increasing energy. The time constants for the fluorescence decay
-
cis NPT-C6-DMA NPT-C6 energy,"cm-1 7.b ns energy,f -_- cm-1 1.6ns -106' 128.4 f 3.5 -90, 95.8 f 0.7 -958 273.6 f 6.2 394.8 f 9.4 0 0 382.7 f 2.4 265.1 f 38.7 215 226 332.0 f 2.3 488 160.6 f 6.6 479 217.6 f 0.8 121.9 i 2.2 628 619 136.9 f 0.9 717 153.6 f 4.5 716 170.6 f 0.4 914 144.8 1.2 105.6 f 2.9 916 96.9 f 1.8 968 969 139.4 f 1.1 1164 70.9 f 3.1 1163 128.4 f 1.1 67.3 f 2.4 1351 131.0 f 0.5 1346 60.1 i 2.4 1396 1400 135.1 f 0.6
*
mix. coef a2
x 104 d
-1.9 i 1.5 18 f 13 38.8 f 6.1 21.5 i 3.7 15.5 f 4.6 61.4 i 6.5 75.4 4.8 151 f 15 173 f 13 221 f 16
The transitionsare listed relative to the origin transitionof cis NPTC6-DMA at 31 777 cm-I. b The error bars are one standard deviation evaluated from the scatter among several independent measurementsat each energy. The transitions are listed relative to the origin transition of C6-NFT at 3 1 784 cm-I. d The error bars reflect only the error caused by the uncertaintyin the measured lifetimes. e This peak at 31 671 cm-I is a conformer origin. Since the corresponding NPT-C6 transition is unknown,noanalysisisattempted.fThispeakat 31 694cm-IisanNPTC6 conformer origin. 8 Same as c, except at 31 682 cm-1.
of theorigin transition of the naphthalenechromophorearesimilar for NPT-C6 and the cis and trans isomers of NPT-C6-DMA. However, in the cis conformer, the fluorescencelifetime decreases more steeply with energy than in NPT-C6 or in the trans isomer of the bichromophore. Figures 4-6 show the fluorescence decay profiles of "426 and the trans and cis isomers of the bichromophore excited at energies 1392, 1399, and 1396 cm-* above their respective origin transitions. The best fits to the data set are also shown.
Discussion For molecules with conformationalflexibility, spectral activity reflects the existenceof vibrational progressions as well as multiple conformers. Interconversion between conformers separated by a barrier of sufficient energy will not occur in a molecular beam. In NPT-C6, the naphthalene will exist in two equatorial conformationson thecyclohexane ring. In theexcitationspectrum (Figure lb), two conformer origins are found. MMX type molecular mechanics calculations21predict two conformers for the trans (ee) and three conformers for the cis isomer of NPTC6-DMA (see Figure 7). Two conformer origins are found for the trans isomer (Figure IC) and are assigned to the two orientations of the naphthalene chromophorewith respect to the cyclohexane ring. In the cis isomer it is energeticallyfeasible for
The Journal of Physical Chemistry, Vol. 97, No. 50, 1993 13049
1500
ii
i
;
E '
1500k
1000
1000
500
500
-I
;
3
0
0 0
100
200
300 Time ( n s )
400
500
Figure4. Fluorescencedecay of NPT-C6 excited at 1392cm-I above the origin. The points are the experimental data, and the line is the best fit to the data.
i
0
100
300 Time (ns)
200
400
500
Figure 6. Fluorescencedecay of cis NPT-C6-DMAexcited at 1396 cm-I above the origin. The points are the experimental data, and the line is the best fit to the data. ee 1
3
ae 1
ea 1
ee2
0
100
200
300
400
500
ea2
Time (ns) Figure 5. Fluorescence decay of trans NPT-C6-DMA excited at 1399
cm-I above the origin. The points are the experimentaldata, and the line is the best fit to the data.
the individual chromophoresto be in the equatorial-axial or axialequatorial positions on the cyclohexane ring. The configuration with the naphthalene in the equatorial position would again possess two conformers. Three conformer origins are observed in the excitation spectrum of the cis isomer (Figure Id). Intersystem crossing is mostly responsible for the nonradiative depletion of the low-lying vibrational states of the first excited singlet state of naphthalene. There are at least two and possibly as many as four triplet manifolds in naphthalene with origins lower thantheoriginoftheS1state.22 Since the& +Sotransition is allowed in the substituted naphthalenes, it may be assumed that all the SIlevels studied have the same radiative rate. Hence the variation in lifetime observed in the vibrational levels of NPTC6 may be attributed to the variation in the rates of intersystem crossing. Thedifference in the lifetime of the two origin transitions of NPT-C6 corresponds to a factor of 8 difference in the rate of intersystem crossing (where we have used k, = 1.6 X lo6, the
Figure 7. MMX-optimizedgeometries of cis and trans NPT-C6-DMA.
radiative rate of 2-methylnaphthalene).Io This difference in the spin-orbit coupling constant is due to the change in the microenvironment of the chromophore in the two conformers. The measured lifetime of gas-phase DMA near its first ns, and the fluorescence observable transition is 2.35 X quantum yield is 0.174 in this energy region.' For this molecule the intersystemcrossing rate and the quantum yield remain nearly constant for -2500 cm-I above the first observable transition. Substitution of the amino nitrogen of aniline with bulky methyl groups results in distortion of the molecule due to steric interaction between the methyl groups and the ortho hydrogens of the aromatic ring. As a result, the lone-pair *-orbital is no longer parallel to the *-orbitals of the ring. Kasha23 has shown that for
Chattotaj et al.
13050 The Journal of Physical Chemistry, Vol. 97, No. 50, 1993
molecules of this type the matrix element for spin-orbit interaction is a maximum when the inclination between the two sets of *-orbitals is 4S0, as in DMA. This is the reason for the poor fluorescence quantum yield of this chromophore compared to aniline. The first observable transitions in the SI SOspectrum of C6-DMA are -600 cm-I higher in energy than the origin transition of NPT-C6. The density of states of naphthalene character in this energy region is relatively low. The excitation spectrum of DMA, however, becomes congested almost immediately above its first transition, due to the presence of lowfrequencymodes. Thus naphthalene states with vibrational energy in excess of 600 cm-l will be perturbed by DMA. As the density of DMA-like states increases, degeneracies between levels of the two chromophoreswill become more likely, and the effects of the perturbation will become more pronounced. The emission spectra of both chromophores are in the same wavelength region. The extremely weak and relatively featureless emission spectrum of DMA makes it impossible to distinguish its presence in the presence of the intense naphthalene emission. In order to measure the extent of the interaction between the chromophores, we analyzed the variation of the fluorescence lifetime of the vibrations of naphthalene due to the presence of DMA. The two commuting zero-order Hamiltonians flNPT and pDMA describe the vibronic eigenstates of unperturbed naphthalene and DMA, respectively. By adding a perturbation term H’,the eigenfunctionsof the perturbed SIstate may be described by linear combinationsof naphthalene and DMA zero-order states, where the coefficient a is obtained from the diagonalization of the complete Hamiltonian.
-
NPT-CB-DMA EE 0.030
0.026 0.022 r’
fj 0.018
.*
$
0.014
8 U
0.010
.*
0.002 -
a
4
0.008 -0.002 -0.006 -
’
-0.010 -100
T~~
(1 - a 2 ) T~~
+- a2 TDMA
(3)
I 1500
1180
NPT-CB-DMA EA
0.026 -
8
0.022 0.018 -
$
0.014 -
8
0.010 -
r’
.I
U
a
2
0.006
I I
i
-
I
.I
0.002 -0.002 -
f
*
=
I
-0.006 -
-100
1 -=-
540 860 Wavenumber (em-’)
Figure 8. Mixing coefficient (a2)trans NPT-CCDMA as a function of the excitation energy in excess of the naphthalene origin.
-0.010
The matter is further complicated by the fact that the zerothorder wavefunctions of naphthalene and DMA contain contributions from triplet states. It is these contributions that cause intersystem crossing and radiationless decay of the SIstates. At low excitation energy, the radiationless decay rates of methylnaphthalenevary from level to level, and the rate is not a monotonic function of excitation energy. At higher excitation energy, the scatter in radiationless lifetime disappears and the lifetime becomes a smooth function of energy. The scatter in the lifetimes of methylnaphthalene is very well illustrated in Figures 3e and 4e of ref 10. A model was proposed to account for the energy dependence of the lifetimes in the smooth region. However, in the region where the dependence is erratic, the lifetime depends on the details of the coupling between the singlet and triplet states, and no quantitative understanding of the lifetime was possible. lo Any perturbation that has an effect on the level structure will also have an effect on the radiationless decay rate. In the region of low excitation energy where the energy dependence of the rates are erratic, the perturbation could increase or decrease the rate. In trying todeterminethecoupling ofthe twochromophores, we will have to be concerned with the fact that the addition of DMA not only changes the lifetime because of energy transfer, but also because of changes in the intersystem crossing rate. Our data indicate that the effect on the intersystem crossing rate is small and random while the effect of energy transfer is large and monotonic once there is a sufficient density of DMA levels, Therefore we can, at least qualitatively, separate the two effects on the lifetime. If the intersystem crossing rate of naphthalene was not affected by the addition of DMA, then the fluroescence lifetime of the bichromophore, TDA would be given by
220
’
I
220
540 860 Wavenumber (em-’)
1180
1500
Figure 9. Mixing coefficient (a2)of cis NPT-CCDMA as a function of the excitation energy in excess of the naphthalene origin.
and the square of the mixing coefficient would be given by,
’
’
a= = ~ / T D A -~ / T N P T /‘DMA
-
(4)
/‘NPT
We have evalulated the quantity a2for severalvibrational levels of both isomers using eq 4, the measured fluorescence lifetimes of NPT-C6 and the bichromophores, and the lifetime of DMA from ref 7. The values of a* obtained in this way are listed in Tables I and I1 and plotted in Figures 8 and 9. The error bars given in the tables and figures are those due to experimental uncertainty in the measured lifetime. They do not reflect the deficiency in the model caused by changes in the intersystem crossing rate. For both isomers, the values of a2 are small for low-energy vibrational levels. There is some variation in the small values of a2, and many of the values are negative. We interpret this as being due to changes in the intersystem crossing rate which are left out of eq 4. If these changes produced by the addition of DMA are such as to decrease the intersystem crossing rate and lengthen the fluorescence lifetime, the derived value of a2 will be negative. For the cis isomer starting at about 800 cm-I above the origin, the value of a2 increases sharply and monotonically. We interpret this as the point where the density of DMA levels is sufficiently high to allow energy transfer from naphthalene to DMA. Assuming that the density of sites is roughly the same in both isomers, the small value of a2 for the trans isomer out to 1400 cm-l indicates that the coupling is weaker in the trans isomer. A larger perturbative matrix element in the cis isomer would compensate for a lower density of states and more mismatch in
Electronic Energy Transfer
The Journal of Physical Chemistry, Vol. 97,No.50, 1993 13051
energy levels. This would explain why energy transfer is seen at a lower excitation energy in the cis isomer. At some excitation energy, the density of states should become high enough to produce energy transfer and a monotonic shortening of the lifetime in the trans isomer, but this has not happened in the energy range we investigated. The greater interaction between the chromophores in the cis isomer is also observed in the fluorescence excitation spectrum where the intensity of the broad background of DMA-like transitions is larger than that in the trans isomer. In a study of the difference in the rates of energy transfer between cis and trans isomers of 1-(4-anisyl)-4-(N,N-dimethylanilin-4-yl)cyclohexane5 we have seen a similar increase in rate for the equatorialaxial (cis) isomers over the diequatorial (trans) ones. Although the trans isomer containstwo conformers, the relative intensity of their origin peaks lead us to assume that the vibrations we are exciting are for the more abundant conformer. In the cis isomer, however, there is a more even distribution of groundstate conformers. However, since the transitions we have measured are within a few wavenumbers of a transition of similar intensity in NPT-C6, the lifetimes are presumablyrepresentative of the conformationwhose origin transition is 3 1 777 cm-', close to the 31 780 cm-1 origin transition of NPT-C6. Only for the lifetime measured at 628 cm-1 is there a possibility of confusion, since this peakcould equally well be described as a transition 723 cm-1 above the origin at 31 682 cm-1 with a corresponding a2 value of (5.60 f 0.36) X le3.This does not affect our general conclusions.
Conclusion By measuring the fluorescence lifetime of the naphthalene chromophorein the presence and absence of DMA, we are able to obtain a measure of the mixing coefficient between their first excited singlet states. Once a threshold is reached, the extent of mixing increases with the density of states. The interaction between the chromophores is different in the cis and trans isomers. This dependence of the intramolecular electronic coupling on nuclear geometry is a topic of current interest in intramolecular electron t r a n ~ f e r and ~ ~ 2photodissociation ~ dynamics on multidimensional potential energy surfaces.30 Acknowledgment. This work was supported by the NSF under Grants CHE 8818321 and CHE 8520326. We would also like to acknowledge Aseet Mukherjee for his help with the fitting routines.
References and Notes (1) Deceased May 1992. (2) Robinson, G. W.; Frosch, R. P. J. Chem. Phys. 1%3,38, 1187. (3) Felker, P. M.; Syage, J. A.; Lambert, W. R.; &wail, A. H. Chem. Phys. Lett. 1982, 92, 1. (4) Ernsting, N. P.; Kaschke, M.; Kleinschmidt, J.; Drexhage, K. H.; Huth, V. Chem. Phys. 1988, 122, 431. (5) Chattoraj, M.; Bal, B.; Closs, G. L.; Levy, D.H. J. Phys. Chem. 1991, 95, 9666. (6) Ichimura, T.; Auty, A. R.; Jones,A. C.; Phillips, D. Bull. Chem.Soc. Jpn. 1985, 58, 2407. (7) Kraus, F.; Gregorek, E.;Weyssenhoff, H. V. Zeit. Physik. Chem. 1972, 82, 139. (8) Phillips, L. A.; Levy, D. H. J. Chem. Phys. 1986, 85, 1327. (9) Wessel, J. Degenerate Vibronic Interference in Naphthalene. Ph.D. Thesis, University of Chicago, 1970. (IO) Jacobson, B. A.; Guest, J. A,; Novak, F. A.; Rice, S. A. J. Chem. Phys. 1987.87, 269. (11) Sigman, M. E.; Closs, G. L. J . Phys. Chem. 1991.95, 5012. (12) Sharfin, W.; Johnson, K. E.; Wharton, L.; Levy, D. H. J. Chem. Phys. 1979, 71, 1292. (13) Chang, M. C.; Courtney, S. H.; Cross, A. J.; Gulotty, R. J.; Petrich, J. W.; Fleming, G. R. Anal. Instrum. 1985,14,433. (14) Kuester, J. L.; Mize, J. H. In Uptimiration Techniques with Fortran; McGraw-Hill: New York, 1973; p 298. Modified for use with Fortran-77. (1 5) Brun, R.; Lienart, D.HBUUK User Guide; CERN Program Library
Y250. Subroutine HFIT used. (16) Wittemeyer, S. A.; Topp, M. R. Chem. Phys. Lor?.1989,163,261. (17) Lipert, R. J.; Colson, S. D.Chem. Phys. Lett. 1989, 161, 303. (18) Rizzo, T.; Park, Y. D.;Peteanu, L. A.; Levy, D.H. J. Chem. Phys. 1985, 84, 2534. (19) Warren, J. A.; Hayes, J. M.; Small, G. J. J . Chem. Phys. 1984,80, 1786. (20) Beck, S. M.; Hopkins, J. B.; Powers, D.E.; Smalley, R. E. J. Chem. Phys. 1981, 74, 43. (21) Serena Software, using methods similar to Allinger, N. L.; Hindman, D.;Helmut, H. J. Am. Chem. Soc. 1977, 99, 3282. (22) Stockburger, M.; Gattermann, H.; Klusmann, W. J . Chem. Phys. 1975,63,4529. (23) Kasha, M. Photochem. Photobiol. 1968, 7, 561. (24) Closs, G. L.; Miller, J. R. Science 1988, 240, 440. (25) Larsson, S. Chem. Phys. Lett. 1982,90, 136. (26) Osuka,A.; Maruyama, K.; Mataga, N.; Asahi, T.; Yamazaki, T.; Tamai, N. J. Am. Chem. SOC.1990, 112,4958. (27) Osuka,A,; Maruyama, K.; Mataga, N.; Asahi, T.; Yamazaki, T.; Tamai, N.; Nishimura, Y. Chem. Phys. Lett. 1991, 181, 413. (28) Pasman, P.; Verhoeven, J. W.;deBoer, T. J. Chem. Phys. Lett. 1978, 59, 381. (29) Helms, A,; Heiler, D.;McLendon, G. J . Am. Chem. Soc. 1991,113, 4325. (30) Pierson, M. D.;Kash, P. W.; Butler, L. J. J. Chem. Phys. 1992, 97, 355.
