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Isotope effects on intensities and excitation exchange interactions in the T1 state of crystalline naphthalene
Volume 42, number 3
CHEMCAL
1.5September 1976
PHYSICS LETTERS
ISOTOPE EFFECTS ON INTENSITIES AND EXCITATION EXCHANGE
1N THE T, STATE OF CRYSTALLINE
Teresa L. MUCHNICK, Robert E. TURNER Sterling Chemistry
L&oratory,
Ycle University,
LNTERACTIQNS
NAPHTHALENE and Steven D. COLSON
New Haven, Connecticut
065.20, US.4
Received 30 April 1976 Revised manuscript received 5 May 1976
We have observed that the naphthalenexI8 crystal shows 40% less net Davydov splitting than the naphthalene-ira crystal. Comparisons of isotope effects on splittings and intensities show vibronic contributions to both spin-orbit and excitation exchange interactions involving totally symmetric modes.
1. Introduction The concept of the “ideal mixed crystal” [l] has been useful in understanding many aspects of the spectroscopy of molecular crystals [2]. Isotopic mixed crystals have been considered “ideal”, provided that the only effect of isotopic substitution is on the zero order energies of the isolated molecules. All intermoleL:llar effects are presumed independent of isotopic substitution. However, experimental evidence exists which leads to a breakdown of these assumptions for some molecular crystals. In the case of benzene [3,4] a dependence of the static gas-to-crystal shift A of a guest molecule on the isotopic composition of the host has been observed. A similar effect has been observed in chemically mixed crystals [ 51. More recently Sheka and Terenetskaya (ST) 163 have reported dynamical isotope effects on the first singlet states S1 of crystalline naphthalene N-!lI, and NiZ,. They have measured a smaller value for the total resonance exchange interaction in N-d, than in N-izg while observing a 1.5 fold decrease in total vibronic intensity for N-d, compared to N-/r,. They further note that, while the Davydov splittings for the (O-O) transitions are equal in both molecules, splittings for the totally symmetric vibronic transitions are not directly proportional to their relative intensities as would be expected from a weak coupling model 171. 570
In past years, isotopic mixed crystals of naphthalene have been the subject of numerous experimental and theoreticai studies. Details of the phosphorescence [S, 91, fluorescence [9-l 11, singlet absorption [l] , and Raman [ 121 spectroscopy have been explained in the context of ideal mixed crystals. More recently, resonant pair interactions in heavily doped isotopic mixed crystals have been studied [13-181. Spectroscopic studies of the first triplet states T, of N-h, and N-d, presented in this paper show an isotope effect on the vibronic intensity and the magnitude of Davydov splitting similar to that observed by ST for the S, state. The intensities and splittings of various totally symmetric vibronic transitions are determined for the two isotopes. From these data, it can easily be observed that the magnitude of Davydov splitting is not a simple function of intensity, nor is it independent of isotope effects. Inter- and intramolecular mechanisms for these effects are explored with application to the T, of naphthalene and in general. In light of these results, a reevaluation of the strict ciassification of isotopic mixed crystals 3s ideal mixed crystals is required. For naphthalene, the effects are not large and can often be accounted for in light of these new data.
2. Experimental
results
The first triplet states of crystalline
naphthalene
CHEMICAL PHYSICS LETTERS
Volume 42, number 3
N-h, and N-d, have been studied by photoexcitation spectroscopy. Single crystals of zone refined N-fz, and N-d, with a small amount (< 1%) of P-bromonaphthalene trap [ 191 were grown from the melt and cooled by being slowly lowered into liquid nitrogen. The excitation source in these experiments was a Molectron DL 200 tunable dye Iaser pumped by a nitrogen laser constructed in this laboratory. To cover A&espectral range of interest the following laser dyes were used: 7-diethylamino-4-methylcoumarin (440478 nm); coumarin 120 (420-457 nm). The laser beam was directed through a collimator to the sample held at 15 K in an Air Products Displex cryogenic refrigerator fitted with an optical dewar [20]. Naphthalene absorption was observed by detecting trap emission as a function of laser wavelength. Zmitted light was focused on the entrance slit of a J/Y model H-20 monochromator set at 520 nm. This eliminated scattered laser light from the signal detection. A Centronix Q4249 BA photomultiplier tube was mounted at the exit slit of the monochromator. The laser repetition rate used was 7Hz. The resultant phosphorescence signal (lifetime x 40 ms) was averaged by an analog integrator and recorded on magnetic tape with a PDP-12 (D.E.C.) computer. The spectra obtained were normalized for the dye laser gain profile.measured with a Molectron 53-05 pyroelectric joulemeter. BeTable 1 Splittings and intensities
of the observed tot&
symmetric
frequency (cm-’ )
a)
bands in the So -+ Ti transition of crystalline
splitting b) (cm-’ )
0 498 712 1024
100 40
9.5 4.7 -
v1 * v2 v1+ v4
1564 1344 996 12iO 1522
40 20 10 4 4
vi f v5 VI +“7
1842 2062
20 15
frequency (cm-’ )
relative intensity
splitting (cm-’ )
0 479 584 776
1co 40 2 2
8.7 4.3 -
3.9 8.5 (1) -
1541 1292 959 1064 1255
20 20 10 4 2
:iY
4.0 (1)
1771 2020
10 10
(1) (1)
-___ "1 v2 v4
y5 “7 2Vl
naphthalene
Naphthalenwia relative intensity
030
1976
cause the dye laser output degrades in time and was not measured simultaneously with the taking of the spectrum, the accuracy of our intensity measurements is limited to + 10%. The frequencies and intensities of the totally symmetric fundamentals and combinations have been measured for the T, of H-h, and N-d, (table 1). The vibrational assignments for N-?z, follow those of Castro and Robinson i19]. Assignments for Nil, were made by correlation with the N-h, spectrum using isotope shifts obtained from ground state Raman frequencies [12,21]. Detailed vibrational analyses will be presented elsewhere 1221. Comparison of the results for N-h, and N-d, shows an isotope effect on the magnitude of Davydov splitting upon deuteration. An = 10% decrease in splitting has been measured for both rhe 0,O and v1 bands. In N-dg, splitting was merisureable in only one additional band y5, whereas a total of five bands exhibited splitting in N-hg. The detectability of splitting was limited by the laser linewidth to = 1.5 cm-‘. An estimate of the total splitting can be made by assuming as an upper bound a value of * 1 cm-’ for those modes of reasonab!e intensity p 10% of the 0,O) whose splittings were not measurable. This approximation gives 33 cm-’ as the total splitting in N-/z8 versus 19 cm- ’ in N-d,. In N-kg, the origin represents 30% of the total splitting c versus 50% in N-d,.
Naphthalene-Jzs Mode
1.5 September
a) Frequencies are measured from the mean of the doublets. 21299.4 and 21308.1 cm-’ for Nils [22]. b) Splittings in parentheses are estimated (see text).
The origin doublets are at: 21202.5
and 21212.0
(1) -
cm-’ for N-iza;
571
Volume 42, numbes 3
CHEMICAL PHYSICS LETTERS
Tinese results show a substantial effect of deuteration on the total splitting. in addition, for both N-lza and N-ds, measured splittings do not correlate with intensity even *though there exists a qualitatively consistent trend of decreasing splitting with decreasing relative intensity. Note that in N&8, vs does not follow this trend. Also ZJ~undergoes an unusually large reduction in splitting (8.5 cm-1 in Nh, to 1.8 cm-’ in N-d,) and a substantial reduction in relative intensity upon deuteration. hr contrast, ~7 exhibits a significant change only in its splitting. For the other symmetric bands, there are no appreciable changes in vibronic intensities relative to rhe origin. The 25% reduction in totally symmetric vibronic intensity in N-da is caused mostly by the change in ~5, and vs f Ye.
3. Theoretical considerations Two simple theoretical concepts are found to be inconsistent with our experimental observations. The “ideal mixed crystal theory” is inapplicable to the naphthalene T, state as a result of the observed isotope effect on the (Q,O) and net Davydov splittings. Furthermore, the normally expected correlation between Davydov splittings and intensities of vibronic transitions involving totally symmetric modes is not observed. At this point we would like to discuss some of the possible reasons for the breakdown of these theoretical expectations. The isotope effect on the Davydov splittings can result from either a structural or vibronic mechanism and the lack of correlation between splittings and intensities can arise from the coupling mechanism whereby a vibrpnic transition gains intensity. The Davydov splitting results from excitatron exchange interaction integrals of the form
(1) where *i is the total vibionic wavefunction for molecule a in state f. One usuahy makes the Born-Oppenheimer and Condon approximations, assuming Var, to be a pure electronic operator, resulting in
(2) where xi and *f are vibrational 572
and electronic
wave-
15 Septcmbar 1976
functions respectively. The vibrational functions include those of the lattice vibrational modes. In neat crystals, the a and b-type vibrational overlap integrals in eq. (2) are identical and give the usual conclusion that the total electronic splitting will be divided among the totally symmetric vibronic transitions in accordance with their intensities. (The vibrational overlap integrals squared are identical with the FranckCondon factors which determine the distribution of intensity in the totally symmetric progressions.) The net Davydov splitting is found by simply summing each individual splittin g. The concept of isotopic invariance involves a number of assumptions any or all of which could breakdown for a specific system. One might argue that isotopic substitution wiIl result in slight changes in the crystal structure [23,24]. If this were significant, then a change in gas-to-crystal shift as well as excitation exchange interactions might also be anticipated. However, vapor phase data on the phosphorescence 1251 and fluorescence [26,27] of N-Ii8 and N-d8 in conjunction with spectra taken of the lowest singlet [6] and triplet (see table 1) states of crystalline naphthalene demonstrate no appreciable change in the gas-to-crystal shift A of naphthaleneJz8 (A = 191 cm-l, for T, and A = 463 cm-‘, for S1) versus naphthalene-d8 (A = 19 1 cm-‘, for T, and A=467 cm-‘, for S1). Another possible reason for the breakdown of the theory is that the exchange interaction potential can be perturbed by molecular and/or lattice vibrations, and that this perturbation can show an isotope dependence. The intermolecular interaction potential Vab could then be expanded in the coordinates of vibration (QF) giving
where Vfr represents the unperturbed potential. This expansion will give additionat terms in the exchange integra! of the form
which will respond coordinates. These states where short electron-exchange for triplet states.
to isotopic changes in the normal terms will be more important for range, strongly distance dependent, type interactions dominate such as
Volume 42, nmnber 3
CHEMICAL PHYSICS LETXERS
It might also be argued that mixing of the exciton T, state with higher triplet exciton states will result in “borrowing” of exchange interaction from the higher triplet. This mixing might show a deuterium substitution effect (the mixing being due to vibronic coupling). However, it should be pointed out that triplet states do not generally have large exchange interactions. Thus, even if there were significant mixing of higher triplet states with the T, state there would not be a large contribution to exchange interaction in T, . Consequently, the observed isotope effect on the net Davydov splitting is most likely due to either a structural change or to a vibronic perturbation of the interaction potential var,. The intensity of a singlet-triplet transition can result from both direct or vibronic spin-orbit coupling_ Likewise, vibronic mixing can contribute to the intensity of a singlet-singlet transition. When one recognizes that totally symmetric vibrations can cause such vibronic mixing [28] (especially in solids where the molecular symmetry is reduced), it becomes apparent that Davydov splittings need not always be simply related to the intensity distribution in the totally symmetric progression in eiher isotope even if the net splitting is isotopically invariant. Vibronic mixing is expected to show an isotope effect f29] which is the best indication of its existence for totaliy symmetric modes. In addition, isotopic substitution is also expected to result in a mixing of the vibrational modes [30] (referred to as isotope dynamic mixing, IDM) which will result in a change in relative vibronic intensities. In that IDM merely causes a redistribution of the net intensity, it can be ~stinguished from an isotope effect on vibronic mixing which causes a change in the total intensity. In fact, IDM does not seem to be an important effect for the T1 totally symmetric vibronic states of naphthalene (vide infra).
4, Conclusions For the S, state of naphthalene, the isotope effect on the net measured Davydov splitting is = 10%. However, the complexity of the S, absorption spectrum [63 makes its quantitative evaluation difficult. In *&e solid, the origin and totally symmetric vibronic levels borrow intensity from the S, state [6]. The isotope effect on the vibronic intensities and the pacr correspondence between intensity and splitting suggest that
15 September 1976
this mixing is at ler& partially vibronic in nature. For the T1 state, the spectrum is basicaliy simpler and, consequently, the effects can be evaluated with more precision. We find a 40% reduction in the net Davydov splitting and a 25% reduction in the totally symmetric vibronic intensity upon deuteration. It is the transitions involving vs which show a significant change in relative intensity indicating that they are vibronically active. In addition, there is, at least qualitatively, for the entire S, + T, spectrum an = 50% decrease in total intensity for N_ds compared to N-Jr, [22]. This is consistent with the = 70% increase in radiative lifetime upon dcut&ation, predicted by the quantum yield measurements of Fisher and Lim [3 I ] . This is further ]28,32] evidence that isotope effects on triplet state lifetimes should not generally be equated solely to the expected [33] change in ~#~~-~~~j~~e decay processes. Furthermore, there is no evidence for intensity redistribution as would be predicted by IDM effects which must therefore be smaller than our w 10% experimental uncertainty. The isotope effect on the splitting of the (0,O) + v1 band follows that of the origin and its splitting is roughly proportional to its intensity indicating that there are no significant vibronic contributions to either the splitting or intensity of this band, i.e. eq. (2) would be a reasonable approximation. On the other hand, the splittings of bands involving ran and ~7 show much larger isotope effects and there is no simple relationship between splittings and intensities. While the vibronic contributions to the intensities of transitions involving v5 might explain the lack of a correlation between their splittings and intensities, they do not explain the large isotope effect on the splittings. (Vibronic spin--orbit coupling is not expected to have a large effect on triplet exciton splittings*‘.) Fu~ermore, splitting changes caused by isotope induced changes in the Iattice constants are not expected to be sensitive to the vibrational state of the excited molecules. Thus, we are left to conclude that * Spin-orbit couplin_ecan, in principle, result in the borrowing of Davvdov splitting from sin&et states. However, even in molecules containing heavy atoms, the triplet state lifetimes are orders of magnitude longer than those of typical singtet states, indicating that the amount of singlet character (and thus the amount of borrowed splitting) is small. For the case of naphthalene with a Tg state lifetime of several seconds, spin-orbit coupling ciearly makes a negligible contribution to the T1 state Davydov spiitting.
573
7lolume
42, number
3
CHCMICAL
PHYSICS LETTERS
there are vibronic contributions to the excitation exchange interactions involving t’s and v7 in the T, state of crystalline naphthalene. From the small isotope effect on their frequencies, it can be seen that these modes are basically C-C stretching vibrations. We find the magnitade of the effect on the v5 and ~7 splittings to be unexpectedly large. One possible alternate explanaticn would be that the lines attributed to the Davydov doublets were improperly assigned. However, these assignments were based upon polarization measurements [19] in N-tz, and there were no other reasonable assignments in the case of N-d,.
[lo]
H.K. Hong and R. Kopelman, J. Chem. Phys. 57 (1972) 3888. 1111H. Port and H.C. Wolf, Z. Naturforsch. 23a (1968) 3 15. 1121 P.N. Prasad and R. Kopelman, I. Chem. Phys 57 (1972)
856. t131 H.K. Hong and R Kopelman, Phys. Rev. Letters 25 (1970) 1030. [I41 H.K. Hong and R. Kopelman, J. Chem. Phys. 55 (1971) 724. lLS1 H.K. Hong and R. Kopelman, J. Chem. Phys. 55 (197 1) 5380.
1161 P-N. Prasad and R. Kopelman, [I71 tlB1
Acknowledgement
1191
Financial support from the National Science Foundation is gratefully acknowledged.
WI WI 1221
References E.R. Bernstein, S.D. Colson, R. Kopelman and G.W. Robinson, J. Chem. Phys. 48 (1968) 5596. Fiz. Tverd. Tela. 13 I21 E.F. Sheka and LP. Terenetskaya, (1971) 1071, [English transL Soviet Phys. Solid State
ill
13 (1971) 8891, and references therein.
1231 g; L WI (271
t31 S.D. Colson, J. Chem. Phys. 48 (1968) 3324. (41 S.D. Colson and T.L. NetzeI, Chcm. Phys. Letters 16
WI
(1972) 555. f51 J.M. van Pruyssen,
1291 f301 (311
F.B. Tudron and S.D. Colson, hfol. Phys. 31 (1976) 699. Chem. Phys. 8 (1975) 161 E.F. Sheka and I.P. Terenetskayn, 99. 171 W.T. Simpson and D.L. Peterson, J. Chem. Phys. 26 (1957) 588. ISI D.&f. Hanson, J. Chem. Phys. 51 (1969) 5063. t91 D.hf. Hanson, J. Chem. Phys. 52 (1970) 3409.
15 SeptemSer 1976
1321 [33]
J. Chem. Phys. 57 (1972) 863. R. Kopelman, E.Lf. hfonberg, F.W. Ochs and P.N. Prasad, Phys. Rev. Letters 34 (1975) 1506. R. Kopelman, E.M. Monberg, F.W. Ochs and P.N. Prasad, J. Chem. Phys. 62 (1975) 292. G. Castro and G.W. Robinson, J. Chem. Phys. 50 (1969) 1159. T.L. Netzel, Doctoral dissertation, Yale Univ. (1973) A. Bree and R.A. Kydd, Spectrochim. Acta 26A (1970) 1791. T.L. Muchnick, R.E. Turner and S.D. Colson, unpublished results. D.W.J. Cruickshank, Acta Cry% IO (1957) 504. G.S. Pawley and E.A. Yeats, Acta Cryst. B25 (1969) 2009. H. Gatterman and hf. Stockburger, J. Chem. Phys. 63 (1975) 4541. D.P. Craig, J.M. HoLlas, M.F. Redies and S.C. Waft, Phil. Trans. Roy. Sot. 253A (1961) 543. D.P. Craig and f.hf. Hollas, Phys. Trans. Roy. Sot. 253A (196 1) 569. P-hi. Johnson and L. Ziegler, I. Chem. Phys. 56 (1972) 2169. N. Kanamaru and E.C. Lii, Chem. Phys. 10 (1975) 141. G. Orr and G-3. Small, Chem. Phys. Letters 21 (1973) 395. S.F. Fischer and EC. Lim, Chem. Phys. Letters 14 (1972) 40. F.B. Tudron, J.hI. van Pruyssen and S.D. Colson, 3. Chem. Phys. 63 (1975) 2086. G.W. Robinson and R.P. Frosch, 3. Chem. Phys. 37 (1962) 1962.
CHEMCAL
1.5September 1976
PHYSICS LETTERS
ISOTOPE EFFECTS ON INTENSITIES AND EXCITATION EXCHANGE
1N THE T, STATE OF CRYSTALLINE
Teresa L. MUCHNICK, Robert E. TURNER Sterling Chemistry
L&oratory,
Ycle University,
LNTERACTIQNS
NAPHTHALENE and Steven D. COLSON
New Haven, Connecticut
065.20, US.4
Received 30 April 1976 Revised manuscript received 5 May 1976
We have observed that the naphthalenexI8 crystal shows 40% less net Davydov splitting than the naphthalene-ira crystal. Comparisons of isotope effects on splittings and intensities show vibronic contributions to both spin-orbit and excitation exchange interactions involving totally symmetric modes.
1. Introduction The concept of the “ideal mixed crystal” [l] has been useful in understanding many aspects of the spectroscopy of molecular crystals [2]. Isotopic mixed crystals have been considered “ideal”, provided that the only effect of isotopic substitution is on the zero order energies of the isolated molecules. All intermoleL:llar effects are presumed independent of isotopic substitution. However, experimental evidence exists which leads to a breakdown of these assumptions for some molecular crystals. In the case of benzene [3,4] a dependence of the static gas-to-crystal shift A of a guest molecule on the isotopic composition of the host has been observed. A similar effect has been observed in chemically mixed crystals [ 51. More recently Sheka and Terenetskaya (ST) 163 have reported dynamical isotope effects on the first singlet states S1 of crystalline naphthalene N-!lI, and NiZ,. They have measured a smaller value for the total resonance exchange interaction in N-d, than in N-izg while observing a 1.5 fold decrease in total vibronic intensity for N-d, compared to N-/r,. They further note that, while the Davydov splittings for the (O-O) transitions are equal in both molecules, splittings for the totally symmetric vibronic transitions are not directly proportional to their relative intensities as would be expected from a weak coupling model 171. 570
In past years, isotopic mixed crystals of naphthalene have been the subject of numerous experimental and theoreticai studies. Details of the phosphorescence [S, 91, fluorescence [9-l 11, singlet absorption [l] , and Raman [ 121 spectroscopy have been explained in the context of ideal mixed crystals. More recently, resonant pair interactions in heavily doped isotopic mixed crystals have been studied [13-181. Spectroscopic studies of the first triplet states T, of N-h, and N-d, presented in this paper show an isotope effect on the vibronic intensity and the magnitude of Davydov splitting similar to that observed by ST for the S, state. The intensities and splittings of various totally symmetric vibronic transitions are determined for the two isotopes. From these data, it can easily be observed that the magnitude of Davydov splitting is not a simple function of intensity, nor is it independent of isotope effects. Inter- and intramolecular mechanisms for these effects are explored with application to the T, of naphthalene and in general. In light of these results, a reevaluation of the strict ciassification of isotopic mixed crystals 3s ideal mixed crystals is required. For naphthalene, the effects are not large and can often be accounted for in light of these new data.
2. Experimental
results
The first triplet states of crystalline
naphthalene
CHEMICAL PHYSICS LETTERS
Volume 42, number 3
N-h, and N-d, have been studied by photoexcitation spectroscopy. Single crystals of zone refined N-fz, and N-d, with a small amount (< 1%) of P-bromonaphthalene trap [ 191 were grown from the melt and cooled by being slowly lowered into liquid nitrogen. The excitation source in these experiments was a Molectron DL 200 tunable dye Iaser pumped by a nitrogen laser constructed in this laboratory. To cover A&espectral range of interest the following laser dyes were used: 7-diethylamino-4-methylcoumarin (440478 nm); coumarin 120 (420-457 nm). The laser beam was directed through a collimator to the sample held at 15 K in an Air Products Displex cryogenic refrigerator fitted with an optical dewar [20]. Naphthalene absorption was observed by detecting trap emission as a function of laser wavelength. Zmitted light was focused on the entrance slit of a J/Y model H-20 monochromator set at 520 nm. This eliminated scattered laser light from the signal detection. A Centronix Q4249 BA photomultiplier tube was mounted at the exit slit of the monochromator. The laser repetition rate used was 7Hz. The resultant phosphorescence signal (lifetime x 40 ms) was averaged by an analog integrator and recorded on magnetic tape with a PDP-12 (D.E.C.) computer. The spectra obtained were normalized for the dye laser gain profile.measured with a Molectron 53-05 pyroelectric joulemeter. BeTable 1 Splittings and intensities
of the observed tot&
symmetric
frequency (cm-’ )
a)
bands in the So -+ Ti transition of crystalline
splitting b) (cm-’ )
0 498 712 1024
100 40
9.5 4.7 -
v1 * v2 v1+ v4
1564 1344 996 12iO 1522
40 20 10 4 4
vi f v5 VI +“7
1842 2062
20 15
frequency (cm-’ )
relative intensity
splitting (cm-’ )
0 479 584 776
1co 40 2 2
8.7 4.3 -
3.9 8.5 (1) -
1541 1292 959 1064 1255
20 20 10 4 2
:iY
4.0 (1)
1771 2020
10 10
(1) (1)
-___ "1 v2 v4
y5 “7 2Vl
naphthalene
Naphthalenwia relative intensity
030
1976
cause the dye laser output degrades in time and was not measured simultaneously with the taking of the spectrum, the accuracy of our intensity measurements is limited to + 10%. The frequencies and intensities of the totally symmetric fundamentals and combinations have been measured for the T, of H-h, and N-d, (table 1). The vibrational assignments for N-?z, follow those of Castro and Robinson i19]. Assignments for Nil, were made by correlation with the N-h, spectrum using isotope shifts obtained from ground state Raman frequencies [12,21]. Detailed vibrational analyses will be presented elsewhere 1221. Comparison of the results for N-h, and N-d, shows an isotope effect on the magnitude of Davydov splitting upon deuteration. An = 10% decrease in splitting has been measured for both rhe 0,O and v1 bands. In N-dg, splitting was merisureable in only one additional band y5, whereas a total of five bands exhibited splitting in N-hg. The detectability of splitting was limited by the laser linewidth to = 1.5 cm-‘. An estimate of the total splitting can be made by assuming as an upper bound a value of * 1 cm-’ for those modes of reasonab!e intensity p 10% of the 0,O) whose splittings were not measurable. This approximation gives 33 cm-’ as the total splitting in N-/z8 versus 19 cm- ’ in N-d,. In N-kg, the origin represents 30% of the total splitting c versus 50% in N-d,.
Naphthalene-Jzs Mode
1.5 September
a) Frequencies are measured from the mean of the doublets. 21299.4 and 21308.1 cm-’ for Nils [22]. b) Splittings in parentheses are estimated (see text).
The origin doublets are at: 21202.5
and 21212.0
(1) -
cm-’ for N-iza;
571
Volume 42, numbes 3
CHEMICAL PHYSICS LETTERS
Tinese results show a substantial effect of deuteration on the total splitting. in addition, for both N-lza and N-ds, measured splittings do not correlate with intensity even *though there exists a qualitatively consistent trend of decreasing splitting with decreasing relative intensity. Note that in N&8, vs does not follow this trend. Also ZJ~undergoes an unusually large reduction in splitting (8.5 cm-1 in Nh, to 1.8 cm-’ in N-d,) and a substantial reduction in relative intensity upon deuteration. hr contrast, ~7 exhibits a significant change only in its splitting. For the other symmetric bands, there are no appreciable changes in vibronic intensities relative to rhe origin. The 25% reduction in totally symmetric vibronic intensity in N-da is caused mostly by the change in ~5, and vs f Ye.
3. Theoretical considerations Two simple theoretical concepts are found to be inconsistent with our experimental observations. The “ideal mixed crystal theory” is inapplicable to the naphthalene T, state as a result of the observed isotope effect on the (Q,O) and net Davydov splittings. Furthermore, the normally expected correlation between Davydov splittings and intensities of vibronic transitions involving totally symmetric modes is not observed. At this point we would like to discuss some of the possible reasons for the breakdown of these theoretical expectations. The isotope effect on the Davydov splittings can result from either a structural or vibronic mechanism and the lack of correlation between splittings and intensities can arise from the coupling mechanism whereby a vibrpnic transition gains intensity. The Davydov splitting results from excitatron exchange interaction integrals of the form
(1) where *i is the total vibionic wavefunction for molecule a in state f. One usuahy makes the Born-Oppenheimer and Condon approximations, assuming Var, to be a pure electronic operator, resulting in
(2) where xi and *f are vibrational 572
and electronic
wave-
15 Septcmbar 1976
functions respectively. The vibrational functions include those of the lattice vibrational modes. In neat crystals, the a and b-type vibrational overlap integrals in eq. (2) are identical and give the usual conclusion that the total electronic splitting will be divided among the totally symmetric vibronic transitions in accordance with their intensities. (The vibrational overlap integrals squared are identical with the FranckCondon factors which determine the distribution of intensity in the totally symmetric progressions.) The net Davydov splitting is found by simply summing each individual splittin g. The concept of isotopic invariance involves a number of assumptions any or all of which could breakdown for a specific system. One might argue that isotopic substitution wiIl result in slight changes in the crystal structure [23,24]. If this were significant, then a change in gas-to-crystal shift as well as excitation exchange interactions might also be anticipated. However, vapor phase data on the phosphorescence 1251 and fluorescence [26,27] of N-Ii8 and N-d8 in conjunction with spectra taken of the lowest singlet [6] and triplet (see table 1) states of crystalline naphthalene demonstrate no appreciable change in the gas-to-crystal shift A of naphthaleneJz8 (A = 191 cm-l, for T, and A = 463 cm-‘, for S1) versus naphthalene-d8 (A = 19 1 cm-‘, for T, and A=467 cm-‘, for S1). Another possible reason for the breakdown of the theory is that the exchange interaction potential can be perturbed by molecular and/or lattice vibrations, and that this perturbation can show an isotope dependence. The intermolecular interaction potential Vab could then be expanded in the coordinates of vibration (QF) giving
where Vfr represents the unperturbed potential. This expansion will give additionat terms in the exchange integra! of the form
which will respond coordinates. These states where short electron-exchange for triplet states.
to isotopic changes in the normal terms will be more important for range, strongly distance dependent, type interactions dominate such as
Volume 42, nmnber 3
CHEMICAL PHYSICS LETXERS
It might also be argued that mixing of the exciton T, state with higher triplet exciton states will result in “borrowing” of exchange interaction from the higher triplet. This mixing might show a deuterium substitution effect (the mixing being due to vibronic coupling). However, it should be pointed out that triplet states do not generally have large exchange interactions. Thus, even if there were significant mixing of higher triplet states with the T, state there would not be a large contribution to exchange interaction in T, . Consequently, the observed isotope effect on the net Davydov splitting is most likely due to either a structural change or to a vibronic perturbation of the interaction potential var,. The intensity of a singlet-triplet transition can result from both direct or vibronic spin-orbit coupling_ Likewise, vibronic mixing can contribute to the intensity of a singlet-singlet transition. When one recognizes that totally symmetric vibrations can cause such vibronic mixing [28] (especially in solids where the molecular symmetry is reduced), it becomes apparent that Davydov splittings need not always be simply related to the intensity distribution in the totally symmetric progression in eiher isotope even if the net splitting is isotopically invariant. Vibronic mixing is expected to show an isotope effect f29] which is the best indication of its existence for totaliy symmetric modes. In addition, isotopic substitution is also expected to result in a mixing of the vibrational modes [30] (referred to as isotope dynamic mixing, IDM) which will result in a change in relative vibronic intensities. In that IDM merely causes a redistribution of the net intensity, it can be ~stinguished from an isotope effect on vibronic mixing which causes a change in the total intensity. In fact, IDM does not seem to be an important effect for the T1 totally symmetric vibronic states of naphthalene (vide infra).
4, Conclusions For the S, state of naphthalene, the isotope effect on the net measured Davydov splitting is = 10%. However, the complexity of the S, absorption spectrum [63 makes its quantitative evaluation difficult. In *&e solid, the origin and totally symmetric vibronic levels borrow intensity from the S, state [6]. The isotope effect on the vibronic intensities and the pacr correspondence between intensity and splitting suggest that
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this mixing is at ler& partially vibronic in nature. For the T1 state, the spectrum is basicaliy simpler and, consequently, the effects can be evaluated with more precision. We find a 40% reduction in the net Davydov splitting and a 25% reduction in the totally symmetric vibronic intensity upon deuteration. It is the transitions involving vs which show a significant change in relative intensity indicating that they are vibronically active. In addition, there is, at least qualitatively, for the entire S, + T, spectrum an = 50% decrease in total intensity for N_ds compared to N-Jr, [22]. This is consistent with the = 70% increase in radiative lifetime upon dcut&ation, predicted by the quantum yield measurements of Fisher and Lim [3 I ] . This is further ]28,32] evidence that isotope effects on triplet state lifetimes should not generally be equated solely to the expected [33] change in ~#~~-~~~j~~e decay processes. Furthermore, there is no evidence for intensity redistribution as would be predicted by IDM effects which must therefore be smaller than our w 10% experimental uncertainty. The isotope effect on the splitting of the (0,O) + v1 band follows that of the origin and its splitting is roughly proportional to its intensity indicating that there are no significant vibronic contributions to either the splitting or intensity of this band, i.e. eq. (2) would be a reasonable approximation. On the other hand, the splittings of bands involving ran and ~7 show much larger isotope effects and there is no simple relationship between splittings and intensities. While the vibronic contributions to the intensities of transitions involving v5 might explain the lack of a correlation between their splittings and intensities, they do not explain the large isotope effect on the splittings. (Vibronic spin--orbit coupling is not expected to have a large effect on triplet exciton splittings*‘.) Fu~ermore, splitting changes caused by isotope induced changes in the Iattice constants are not expected to be sensitive to the vibrational state of the excited molecules. Thus, we are left to conclude that * Spin-orbit couplin_ecan, in principle, result in the borrowing of Davvdov splitting from sin&et states. However, even in molecules containing heavy atoms, the triplet state lifetimes are orders of magnitude longer than those of typical singtet states, indicating that the amount of singlet character (and thus the amount of borrowed splitting) is small. For the case of naphthalene with a Tg state lifetime of several seconds, spin-orbit coupling ciearly makes a negligible contribution to the T1 state Davydov spiitting.
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CHCMICAL
PHYSICS LETTERS
there are vibronic contributions to the excitation exchange interactions involving t’s and v7 in the T, state of crystalline naphthalene. From the small isotope effect on their frequencies, it can be seen that these modes are basically C-C stretching vibrations. We find the magnitade of the effect on the v5 and ~7 splittings to be unexpectedly large. One possible alternate explanaticn would be that the lines attributed to the Davydov doublets were improperly assigned. However, these assignments were based upon polarization measurements [19] in N-tz, and there were no other reasonable assignments in the case of N-d,.
[lo]
H.K. Hong and R. Kopelman, J. Chem. Phys. 57 (1972) 3888. 1111H. Port and H.C. Wolf, Z. Naturforsch. 23a (1968) 3 15. 1121 P.N. Prasad and R. Kopelman, I. Chem. Phys 57 (1972)
856. t131 H.K. Hong and R Kopelman, Phys. Rev. Letters 25 (1970) 1030. [I41 H.K. Hong and R. Kopelman, J. Chem. Phys. 55 (1971) 724. lLS1 H.K. Hong and R. Kopelman, J. Chem. Phys. 55 (197 1) 5380.
1161 P-N. Prasad and R. Kopelman, [I71 tlB1
Acknowledgement
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Financial support from the National Science Foundation is gratefully acknowledged.
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References E.R. Bernstein, S.D. Colson, R. Kopelman and G.W. Robinson, J. Chem. Phys. 48 (1968) 5596. Fiz. Tverd. Tela. 13 I21 E.F. Sheka and LP. Terenetskaya, (1971) 1071, [English transL Soviet Phys. Solid State
ill
13 (1971) 8891, and references therein.
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t31 S.D. Colson, J. Chem. Phys. 48 (1968) 3324. (41 S.D. Colson and T.L. NetzeI, Chcm. Phys. Letters 16
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F.B. Tudron and S.D. Colson, hfol. Phys. 31 (1976) 699. Chem. Phys. 8 (1975) 161 E.F. Sheka and I.P. Terenetskayn, 99. 171 W.T. Simpson and D.L. Peterson, J. Chem. Phys. 26 (1957) 588. ISI D.&f. Hanson, J. Chem. Phys. 51 (1969) 5063. t91 D.hf. Hanson, J. Chem. Phys. 52 (1970) 3409.
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