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Vibrational relaxation in molecular crystalsby four-wave mixing: naphthalene
Volume 72, number
1
VIBRATIONAL BY FOUR-WAVE
CHEMICAL
RELAXATION MIXING:
PHYSICS
lN MOLECULAR
LETTERS
15
iWiy 1980
CRYSTALS
NAPHTHALENE*
P.L. DECOLA, R.M. HOCHSTRASSER Department of Chemistry and Laboratory for Research on the Structure of Matter. Unwenrty Phikzdelphirr. Pennsylwtua 19104. USA
of lWwzsylrank
and
H.P. TROMMSDORFF kboMtoUe de SpectromPme Physrque. Luboratoue de Phynque GPnkale, UnirversztP Sclennfique et Meduxte de Grenoble. 38 Grenoble&we Ceder S3, France Received
12 Apnl 1980
Four-wa\e miGng with two narrow-band lasers (WI and ~2) was used to investigate the hnneshape of a vibrational transition of the naphthalene crystal at 1 6 K. The dispexs~on of the coherent enussion at 2~1 -wz ws measured by vxying ~2 with wt -w2 m the regon of the 1385 cm-’ totally symmetnc mode. The dispersion IS well-fitted by a lorentzian OWZFthe complete signal range of 7 decades, the dampmg parameter was 0 03 f 0.005 cm-‘. Thus the nbrational relaxation time of the rrenkel-type exaton exceeds 88 (-15) ps
1. Introduction In this paper we present measurements of the homogeneous lineshape for a vibrational transItIon of the naphthalene crystal at 1.6 K. We beheve these are the first very high resolution spectra of Raman transltions m molecular solids. The experiments provide new mformation about vibrational relaxation. Vibrational relaxation in molecular crystals 1s still not well understood. Neither the timescales nor the pathways of the relaxation of excited vlbratlonal states towards thermal equtibnum were yet elucidated by experiments. By contrast there have appeared recently a number of experimental stu&es of the vibrational rekation in mixed molecular crystals Cl-3 J _ In mixed crystals the guest vlbrational relaxation may occur by energy transfer to other vibrational and lattice modes * Tlus research was supported by the Army Research Office (Durham), and 111part by the NSF-MRL program under grant DMR76-80994, and by a NATO grant SA 5-2-05-B (1258) The mstrumentatlon was made avtiable by the Regonal Laser Laboratones (NSF-RIF Uruwxsrty of Pennsylvama)
just as for neat solids. However, the guest moIecule modifies the lattice spectrum so that mechanisms and tunescales for vlbrahor.al relaxation of a particular guest level will not usually be the same in different hosts [4]. In the neat crystal one has in addition the delocalization of the initial vibrational excitation so that differences in relaxation between neat solids and impurity centers are again expected in an ensemble of two level systems. The lmewidth cf 2 spectral transition provides a lower limit on the homogeneous dephasmg time (T )_ In the low-temperature limit, for which 227’ = Tr 2- m 2 homogeneous system, the observed linewidth in a real solid may still yield only 2 lower limit for the popuIatlon decay time (T,) because of the inhomogeneous nature of the system. In mixed crystals this problem can be overcome by holebuming [2] and echo technique [S] _ In neat crystals the energy transfer (&) mighE occur faster than the frequency width of the inhomogeneous distribution (0) so that the spectral line is not inhomogeneous and cannot be holebumed in the usual sense. In any case in the presence of energy transfer occumng in an inhomogeneous system the spectral L
Volume
72. number
1
CHEMICAL
PHYSICS
lineshapes are not expected to be lorentzum, the zerotemperature dephasmg of the vibrational exclton IS not characterized by a smgle T2, nor is the decay of the state euponentlal [6-81. There are lumtmg cases where a hnewrdth measurement m a crystal would yield the population decay If /3,/O $ 1 the spectral lmes ~111 be very much narrower than D, thus if l/T1 > D?/& the he wll be appro.timately lorentzian havmg a width 1/2T,. Thus is a much less restnctlve mequahty than the l/T, > D requirement for mL\ed crystal transltlons. Thus the narrowmg of spectral lines by energy transfer m crystals substantially lengthens the range of vibratIona relrtvatlon tunes that can be studied m the frequency domam In the present work four-wave mcung (CARS) with Its associated large dynanuc range IS used to deternune the linewidths of vibrational transitions in the naphthalene crystal at 1.6 K. Previous coherent Raman studies on thn system [9] were carried out with rather broadband lasers but nevertheless exposed vIbrational states havmg widths less than 0.3 cm-l. The bandwdths used in tills work are ~0 03 cm-l thereby allowing the measurement of coherence damping parameters to an accuracy of =90 MHz.
2,. Experimental The naphthalene crystal was prepared as follows: The startmg matenal (Aldrich, gold label, scmaation grade) was recrystalhzed from ethanol (200 proof) treated with potassmm metal, subhmed and subsequently zone refined. The crystal was grown m a Bndgman furnace at the speed of 1 mm/h and was cooled to room temperature over one day and removed from the tube by HF etchmg The sample, a plate of about 2 mm thickness was prepared by cleaving the crystal along the ab plane, and the dIrection of the axes was determined concscopically. This sample was attached loosly to a holder ad lowered over a penod of about 4 h mto the optical cryostat filled with liquid hehum. The onentatlon of the crystal was adjusted by observmg the back reflection of the laser beams from the crystal surface. The measurements were made at 1.6 K. The general expenmental arrangement was the same as described previously [9]. Ln the present experunent,
15 hlay 1980
LETTERS
the spectra were recorded by keepmg w1 fiied while scanmng w2 _The signal at w3 = 20, - 02 was divided by the intensity of the beam of the laser at 02. Molectron DL 300/400 and DL II dye lasers, pumped sunultaneously by a Molectron UV 1000 nitrogen laser were used. The former, operated with an intracavlty etaIon, delivered the beam at wl, the latter, delivering w2, was operated wthout etalon when scanned over a large frequency Interval, and was pressure scanned with an mtracavlty etalon over the region of the peak of the CARS resonance. The absolute frequencies of the lasers were measured to 20.2 cm-l accuracy. The Raman spectrum m the 1380 cm-l regon of naphthalene at 1.6 K was recorded using 4880 A excitatlon and a Spex-Ramalog mstrument The crystal ab face was irradiated with hght polanzed along the b ~JUS and the spectrum was obtained for scattered l&t polarized parallel and perpendlcuiar to b.
3. Results Fig. 1 shows spectra obtained at me&urn and high resolution. The polanzatlon of all beams was parallel to the crystal a axis. The small penodtc Intensity vanatlons in the medium-resolution scan probably reflect the change of overlap in the sample of the beam at wl wth the different modes of the broad band beam at w2 (wdth 0.5 cm-*), they do not slgruficantly mcrease the uncertamtles in the evaluation of the data. The strong resonance at 1385.3 cm-l corresponds to the A.JS) mode of naphthalene and the weak resonance at 138 1.2 cm-l corresponds to a combination band, these two resonances were not resolved III prev~ous Raman work [9]. w1 was f&ed at 16994.0 cm-l, correspondmg to a two-photon energy of about 2430 cm-l above the origm of the first singlet-singlet transition, but away from any strong two-photon transitlon [9] - The fwhm of the resonance at 1385.3 cm-l m the tigh-resolution scan was 0.11 f 0.05 cm-1 and contams contnbufions from the wrdth of the lasers and from homogeneous and mhomogeneous broadening processes. Solid curve 2 m fig. 1 represents I x(3)/x&12 wth x(3) =
xck
+ ~+Jk+
and the set of parameters
-(w1-w2)+‘qJ giver.
(1)
m table 1. A more de-
Volume
72, number
1
CHEMICAL
PHYSICS
loa 103. 2. i’\
:“,1./+_/
‘,
,,
1 SCAN
10-l.
(a)
lo-2. NAPHTHALENE 2 wxYnYo~
laI
1380
1390
1410
1400 01-02
I
(cm-‘]
Fig l_ Four-wave nuung spectra of a naphthalene crystal. The tntenstty of the beam at ws = 2wt - wt (open ctrcles) was measured as wa was scanned. The frequency of wr was kept tiled at 16994 0 cm-‘. The directions of propagatton of all beams v.ere nearly perpendicular to the ab cleavage plane and all polanzations were parallel to the = aus The continuous trace represents I x(~)/&&I calculated accordmg to formula (1) and using the parameters gtven m table 1 Q,R = lxNRl X(1-~~)~th~=O05mcurvc(l)ande=Omcurre(2) In scan (a) the laser dehvering wa \\as operated wtth an mtrauvtty etalon and was pressure scanned The strong resonance to the mode A (5) Whereas the at 1385 3 cm-t corresponds weak resonance at 138 1.2 cm-r correspon % to a combmatron band. possrbly bzg(l 3) + bag(16).
tailed fit of the h&-resolution scan (fig. la) was accomphshed by using a gaussran drstnbutron of resonances for the ag(S) mode only of the form A,(no2)-~l2
15 May 1980
homogeneous broadenmg of a lorentzian line or the fume gaussian frequency bandwidth of the lasers. Both the lorentzian and Voigt bneshapes yield fits that are good to withm 15% with rR parameters differing by 25%. Curve 2 in fig. 1 was calculated from (1) assuming that x$ IS real, and the fit is seen to be poor near the tnterference mirumum. Curve 1 was a best tit and corresponds to J& = I x$kl(l0 05%). The smail imaginary contnbution is of the proper magnitude to arise from the small two-photon absorption [IO] of the crystal at ol, but it is drfticult to distinguish this from a laser spectral impurity of = 1 : IO8 at 6 cm-l from the line center. Thus 0.05 Ix$kl should be regarded as the upper hmit for im {x(3)) at this frequency. The same Raman resonance region was observed in the previous study with wt at 16630 cm-t using a l---2 cm-t laser bandwidth [V] and the value of ]AR/ J&I = 6.5 + 0.5 cm-l compares well with the sum of the amplitudes of the two resonances exposed in the present work. The Raman spectrum of the 1380 cm-t region displayed a strong A, band at 1384.6 cm-t and a Bg band at 1384.2 cm-t_ This splittmg of 0.4 C 0.1 cm-t is interpreted as factor-group sphtting of the 1385 cm-1 band not reported m previous work [I I] _The polar+ zation condition of the four-wave mixing experiment was such that only the A, Raman bands could be seen.
4. Discussion / dA exp(-AZ/o?)
wrth the parameters I?, = 0.030 f 0.005 cm-l, u= 0.022 f 0.007 cm-f being the only other modificatrons from the values in table 1. This tit allows for inTable 1 Non-hnear
LETTERS
parameters
for naphthafene
Mode (R)
mmbinaton band
052-003
040=003
1381.2
= 0.2
ag(5 )
6 07 f 0.0
0040~0006
1385.3~02
The states under study here are Frenkel excitonsIn the case of the 1385 cm-l band, the molecular vibrational state corresponding to the carbon-ring stretch sphts m the crystal into two optrcally accessrble states separated by 0.4 cm-l_ The K = O($) state of the band is at higher energy so interband scattering can contribute to the observed linebroadening of the Raman transition occurring with oI and w2 polarized on the same crystal principal axis. If the observed dampmg of 0.03 cm-l were caused by only population relaxation then the appropriate value for T, wodd be 88 f 15 ps. Stnctly the observed width provides only an upper limit for this relaxation time but there are sound reasons to conclude that in this case the dominant contnbution to the width is likely to be population decay. Close to the absolute zero of tem3
Volume
72. number
CHEMICAL
1
PHYSICS
perature the addrtronal contnbutron would be from the inhomogeneous drstnbutron appropnately narrowed by the excrton motion. It IS hkely that the values of D for vrbrational and electromc transrtrons be roughly in the ratro of gas-to-crystal shifts for the two types of transrtions. Electronic D values are * 1 cm-l, the required ratio is ==O.OS-0.01, so that D2/fl for the vrbratronal transrtron IS expected to be m the range 4 x IO-3-9 -. 5 x IO-’ cm-l. Such contributions to the wrdth are negligrble compared wrth the observed value of 4 X lo-’ cm-l. The Nl crystal drsplays an exciton band for the u = 1 level that 1s also about 0.4 cm-t wade [12]. In that case T, process can be neglected and the coherence decay although non-exponenual occurs predommantly m the nanosecond tme-
LETTERS
15 May 1980
vibrations of the naphthalene crystal. In the case D were to be greater than fl the excitation would be effectively localized and the result would be freed from band scattenng contnbutrons.
Acknowledgement
We are grateful to A C. McGhie and C. Nyr for the preparatron of the crystals, to the Alexander von Humboldt Foundation for the award of a fellow&up (to RMH), and to Professor Herbert Waltber of the Uruversrty of Munich for lus hosprtality to RMH durmg the completion of thrs work.
scale [S].
However the detarled structure of the Iineshape is interpreted our results indrcate that the vrbratronal relaxation of the 1385 cm-l mode of naphthalene occurs with a hfetrme m excess of 88 ps. Consrdenng the large size of naphthalene compared wrrh many of the smaller systems studied by Karser and Lautereau 1121 rt rs remarkable that the populatron relaxatron IS so long III the naphthalene case. Although naphthalene has 48 normal modes perhaps rt IS mamly those levels havmg total a, symmetry in the free molecule that wu be involved m the relaxation, and that of these the most important ones wrll be located withm the onephonon
ener~-~~
re&m.In
fzctthereare
only
References
fire
[ 131 for which less than + 150 cm- 1 energy mismatch occurs and they are all bmary combinatrons of modes II and ttz that could couple to aJ5) through terms m the molecular potential having form $zrnQ5 X QnQm where E(3) 1s the cubic anharmomcrty. Obviously this rather simple srtuatron wrLl not persist as the temperature of the crystal is Increased and many more levels become accessrble. One way to deduce the parameters &rrn would be from the intensitres of forbidden Raman lmes nearby to a (5). The Raman results presente d here are not III agreement wrth the theoretrcal predctions of Pawley and Cyvin [ 141 who calculated that ag(5) would have the smallest exciton bandwrdth (0.04 cm-l) of all the such modes
112 [I3 t14
K-ii Rebanc and P. Saan. J Lummescence 12 (1976) 23. S Voelker and R M Mxfarlane, Chem Phys. Letters 61 (1979)421. R hl Hochstrasser and C. Nyl. J Chem. Phys. 70 (1979) 1112. R M. Hochstrasser and P N Prasad, III. Excited states, ed E-C hm (Audcnuc Press. New York, 1973) p 120. W H Hesselmk and D A Wiersma. Chem Phys Letters 44 (1976) 76. R J. ElIlot, J A. Krumhansl zmd P L Leath, Rev- Mod Phvs 46 (1974) 465. J. Nafter and Jl Jortncr. J. Chem. Phys. 68 (1978) 1513. I1 Abram, R h¶ Hochst.rasser. J I: Kohl, M C. Semack and D White. J. Chem Phys. 71 (1979) 153; I I Abram&d R M Hoch&.&, J. &em. whys., to be pubbshed. R M Hochstrasser. G R Meredrth and H P Trommsdorff, J Chem Phys . to be pubbhed R Bl Hochstrasser and H N. Sung, J Chem. Phys. 66 (1977) 3276. D.M Hansen and A R. Gee, J. Chem Phys. 51 (1969) 5052 A. Laubereau and W. tier, Rev hlod. Phys 50 (1978) 607. R. SculJy and D H. Whlffen. Spectrochim. Acta 16 (1960) 1409 G S Pawley and S J Cynn. J. Chem. Phys. 52 (1970) 4073.
1
VIBRATIONAL BY FOUR-WAVE
CHEMICAL
RELAXATION MIXING:
PHYSICS
lN MOLECULAR
LETTERS
15
iWiy 1980
CRYSTALS
NAPHTHALENE*
P.L. DECOLA, R.M. HOCHSTRASSER Department of Chemistry and Laboratory for Research on the Structure of Matter. Unwenrty Phikzdelphirr. Pennsylwtua 19104. USA
of lWwzsylrank
and
H.P. TROMMSDORFF kboMtoUe de SpectromPme Physrque. Luboratoue de Phynque GPnkale, UnirversztP Sclennfique et Meduxte de Grenoble. 38 Grenoble&we Ceder S3, France Received
12 Apnl 1980
Four-wa\e miGng with two narrow-band lasers (WI and ~2) was used to investigate the hnneshape of a vibrational transition of the naphthalene crystal at 1 6 K. The dispexs~on of the coherent enussion at 2~1 -wz ws measured by vxying ~2 with wt -w2 m the regon of the 1385 cm-’ totally symmetnc mode. The dispersion IS well-fitted by a lorentzian OWZFthe complete signal range of 7 decades, the dampmg parameter was 0 03 f 0.005 cm-‘. Thus the nbrational relaxation time of the rrenkel-type exaton exceeds 88 (-15) ps
1. Introduction In this paper we present measurements of the homogeneous lineshape for a vibrational transItIon of the naphthalene crystal at 1.6 K. We beheve these are the first very high resolution spectra of Raman transltions m molecular solids. The experiments provide new mformation about vibrational relaxation. Vibrational relaxation in molecular crystals 1s still not well understood. Neither the timescales nor the pathways of the relaxation of excited vlbratlonal states towards thermal equtibnum were yet elucidated by experiments. By contrast there have appeared recently a number of experimental stu&es of the vibrational rekation in mixed molecular crystals Cl-3 J _ In mixed crystals the guest vlbrational relaxation may occur by energy transfer to other vibrational and lattice modes * Tlus research was supported by the Army Research Office (Durham), and 111part by the NSF-MRL program under grant DMR76-80994, and by a NATO grant SA 5-2-05-B (1258) The mstrumentatlon was made avtiable by the Regonal Laser Laboratones (NSF-RIF Uruwxsrty of Pennsylvama)
just as for neat solids. However, the guest moIecule modifies the lattice spectrum so that mechanisms and tunescales for vlbrahor.al relaxation of a particular guest level will not usually be the same in different hosts [4]. In the neat crystal one has in addition the delocalization of the initial vibrational excitation so that differences in relaxation between neat solids and impurity centers are again expected in an ensemble of two level systems. The lmewidth cf 2 spectral transition provides a lower limit on the homogeneous dephasmg time (T )_ In the low-temperature limit, for which 227’ = Tr 2- m 2 homogeneous system, the observed linewidth in a real solid may still yield only 2 lower limit for the popuIatlon decay time (T,) because of the inhomogeneous nature of the system. In mixed crystals this problem can be overcome by holebuming [2] and echo technique [S] _ In neat crystals the energy transfer (&) mighE occur faster than the frequency width of the inhomogeneous distribution (0) so that the spectral line is not inhomogeneous and cannot be holebumed in the usual sense. In any case in the presence of energy transfer occumng in an inhomogeneous system the spectral L
Volume
72. number
1
CHEMICAL
PHYSICS
lineshapes are not expected to be lorentzum, the zerotemperature dephasmg of the vibrational exclton IS not characterized by a smgle T2, nor is the decay of the state euponentlal [6-81. There are lumtmg cases where a hnewrdth measurement m a crystal would yield the population decay If /3,/O $ 1 the spectral lmes ~111 be very much narrower than D, thus if l/T1 > D?/& the he wll be appro.timately lorentzian havmg a width 1/2T,. Thus is a much less restnctlve mequahty than the l/T, > D requirement for mL\ed crystal transltlons. Thus the narrowmg of spectral lines by energy transfer m crystals substantially lengthens the range of vibratIona relrtvatlon tunes that can be studied m the frequency domam In the present work four-wave mcung (CARS) with Its associated large dynanuc range IS used to deternune the linewidths of vibrational transitions in the naphthalene crystal at 1.6 K. Previous coherent Raman studies on thn system [9] were carried out with rather broadband lasers but nevertheless exposed vIbrational states havmg widths less than 0.3 cm-l. The bandwdths used in tills work are ~0 03 cm-l thereby allowing the measurement of coherence damping parameters to an accuracy of =90 MHz.
2,. Experimental The naphthalene crystal was prepared as follows: The startmg matenal (Aldrich, gold label, scmaation grade) was recrystalhzed from ethanol (200 proof) treated with potassmm metal, subhmed and subsequently zone refined. The crystal was grown m a Bndgman furnace at the speed of 1 mm/h and was cooled to room temperature over one day and removed from the tube by HF etchmg The sample, a plate of about 2 mm thickness was prepared by cleaving the crystal along the ab plane, and the dIrection of the axes was determined concscopically. This sample was attached loosly to a holder ad lowered over a penod of about 4 h mto the optical cryostat filled with liquid hehum. The onentatlon of the crystal was adjusted by observmg the back reflection of the laser beams from the crystal surface. The measurements were made at 1.6 K. The general expenmental arrangement was the same as described previously [9]. Ln the present experunent,
15 hlay 1980
LETTERS
the spectra were recorded by keepmg w1 fiied while scanmng w2 _The signal at w3 = 20, - 02 was divided by the intensity of the beam of the laser at 02. Molectron DL 300/400 and DL II dye lasers, pumped sunultaneously by a Molectron UV 1000 nitrogen laser were used. The former, operated with an intracavlty etaIon, delivered the beam at wl, the latter, delivering w2, was operated wthout etalon when scanned over a large frequency Interval, and was pressure scanned with an mtracavlty etalon over the region of the peak of the CARS resonance. The absolute frequencies of the lasers were measured to 20.2 cm-l accuracy. The Raman spectrum m the 1380 cm-l regon of naphthalene at 1.6 K was recorded using 4880 A excitatlon and a Spex-Ramalog mstrument The crystal ab face was irradiated with hght polanzed along the b ~JUS and the spectrum was obtained for scattered l&t polarized parallel and perpendlcuiar to b.
3. Results Fig. 1 shows spectra obtained at me&urn and high resolution. The polanzatlon of all beams was parallel to the crystal a axis. The small penodtc Intensity vanatlons in the medium-resolution scan probably reflect the change of overlap in the sample of the beam at wl wth the different modes of the broad band beam at w2 (wdth 0.5 cm-*), they do not slgruficantly mcrease the uncertamtles in the evaluation of the data. The strong resonance at 1385.3 cm-l corresponds to the A.JS) mode of naphthalene and the weak resonance at 138 1.2 cm-l corresponds to a combination band, these two resonances were not resolved III prev~ous Raman work [9]. w1 was f&ed at 16994.0 cm-l, correspondmg to a two-photon energy of about 2430 cm-l above the origm of the first singlet-singlet transition, but away from any strong two-photon transitlon [9] - The fwhm of the resonance at 1385.3 cm-l m the tigh-resolution scan was 0.11 f 0.05 cm-1 and contams contnbufions from the wrdth of the lasers and from homogeneous and mhomogeneous broadening processes. Solid curve 2 m fig. 1 represents I x(3)/x&12 wth x(3) =
xck
+ ~+Jk+
and the set of parameters
-(w1-w2)+‘qJ giver.
(1)
m table 1. A more de-
Volume
72, number
1
CHEMICAL
PHYSICS
loa 103. 2. i’\
:“,1./+_/
‘,
,,
1 SCAN
10-l.
(a)
lo-2. NAPHTHALENE 2 wxYnYo~
laI
1380
1390
1410
1400 01-02
I
(cm-‘]
Fig l_ Four-wave nuung spectra of a naphthalene crystal. The tntenstty of the beam at ws = 2wt - wt (open ctrcles) was measured as wa was scanned. The frequency of wr was kept tiled at 16994 0 cm-‘. The directions of propagatton of all beams v.ere nearly perpendicular to the ab cleavage plane and all polanzations were parallel to the = aus The continuous trace represents I x(~)/&&I calculated accordmg to formula (1) and using the parameters gtven m table 1 Q,R = lxNRl X(1-~~)~th~=O05mcurvc(l)ande=Omcurre(2) In scan (a) the laser dehvering wa \\as operated wtth an mtrauvtty etalon and was pressure scanned The strong resonance to the mode A (5) Whereas the at 1385 3 cm-t corresponds weak resonance at 138 1.2 cm-r correspon % to a combmatron band. possrbly bzg(l 3) + bag(16).
tailed fit of the h&-resolution scan (fig. la) was accomphshed by using a gaussran drstnbutron of resonances for the ag(S) mode only of the form A,(no2)-~l2
15 May 1980
homogeneous broadenmg of a lorentzian line or the fume gaussian frequency bandwidth of the lasers. Both the lorentzian and Voigt bneshapes yield fits that are good to withm 15% with rR parameters differing by 25%. Curve 2 in fig. 1 was calculated from (1) assuming that x$ IS real, and the fit is seen to be poor near the tnterference mirumum. Curve 1 was a best tit and corresponds to J& = I x$kl(l0 05%). The smail imaginary contnbution is of the proper magnitude to arise from the small two-photon absorption [IO] of the crystal at ol, but it is drfticult to distinguish this from a laser spectral impurity of = 1 : IO8 at 6 cm-l from the line center. Thus 0.05 Ix$kl should be regarded as the upper hmit for im {x(3)) at this frequency. The same Raman resonance region was observed in the previous study with wt at 16630 cm-t using a l---2 cm-t laser bandwidth [V] and the value of ]AR/ J&I = 6.5 + 0.5 cm-l compares well with the sum of the amplitudes of the two resonances exposed in the present work. The Raman spectrum of the 1380 cm-t region displayed a strong A, band at 1384.6 cm-t and a Bg band at 1384.2 cm-t_ This splittmg of 0.4 C 0.1 cm-t is interpreted as factor-group sphtting of the 1385 cm-1 band not reported m previous work [I I] _The polar+ zation condition of the four-wave mixing experiment was such that only the A, Raman bands could be seen.
4. Discussion / dA exp(-AZ/o?)
wrth the parameters I?, = 0.030 f 0.005 cm-l, u= 0.022 f 0.007 cm-f being the only other modificatrons from the values in table 1. This tit allows for inTable 1 Non-hnear
LETTERS
parameters
for naphthafene
Mode (R)
mmbinaton band
052-003
040=003
1381.2
= 0.2
ag(5 )
6 07 f 0.0
0040~0006
1385.3~02
The states under study here are Frenkel excitonsIn the case of the 1385 cm-l band, the molecular vibrational state corresponding to the carbon-ring stretch sphts m the crystal into two optrcally accessrble states separated by 0.4 cm-l_ The K = O($) state of the band is at higher energy so interband scattering can contribute to the observed linebroadening of the Raman transition occurring with oI and w2 polarized on the same crystal principal axis. If the observed dampmg of 0.03 cm-l were caused by only population relaxation then the appropriate value for T, wodd be 88 f 15 ps. Stnctly the observed width provides only an upper limit for this relaxation time but there are sound reasons to conclude that in this case the dominant contnbution to the width is likely to be population decay. Close to the absolute zero of tem3
Volume
72. number
CHEMICAL
1
PHYSICS
perature the addrtronal contnbutron would be from the inhomogeneous drstnbutron appropnately narrowed by the excrton motion. It IS hkely that the values of D for vrbrational and electromc transrtrons be roughly in the ratro of gas-to-crystal shifts for the two types of transrtions. Electronic D values are * 1 cm-l, the required ratio is ==O.OS-0.01, so that D2/fl for the vrbratronal transrtron IS expected to be m the range 4 x IO-3-9 -. 5 x IO-’ cm-l. Such contributions to the wrdth are negligrble compared wrth the observed value of 4 X lo-’ cm-l. The Nl crystal drsplays an exciton band for the u = 1 level that 1s also about 0.4 cm-t wade [12]. In that case T, process can be neglected and the coherence decay although non-exponenual occurs predommantly m the nanosecond tme-
LETTERS
15 May 1980
vibrations of the naphthalene crystal. In the case D were to be greater than fl the excitation would be effectively localized and the result would be freed from band scattenng contnbutrons.
Acknowledgement
We are grateful to A C. McGhie and C. Nyr for the preparatron of the crystals, to the Alexander von Humboldt Foundation for the award of a fellow&up (to RMH), and to Professor Herbert Waltber of the Uruversrty of Munich for lus hosprtality to RMH durmg the completion of thrs work.
scale [S].
However the detarled structure of the Iineshape is interpreted our results indrcate that the vrbratronal relaxation of the 1385 cm-l mode of naphthalene occurs with a hfetrme m excess of 88 ps. Consrdenng the large size of naphthalene compared wrrh many of the smaller systems studied by Karser and Lautereau 1121 rt rs remarkable that the populatron relaxatron IS so long III the naphthalene case. Although naphthalene has 48 normal modes perhaps rt IS mamly those levels havmg total a, symmetry in the free molecule that wu be involved m the relaxation, and that of these the most important ones wrll be located withm the onephonon
ener~-~~
re&m.In
fzctthereare
only
References
fire
[ 131 for which less than + 150 cm- 1 energy mismatch occurs and they are all bmary combinatrons of modes II and ttz that could couple to aJ5) through terms m the molecular potential having form $zrnQ5 X QnQm where E(3) 1s the cubic anharmomcrty. Obviously this rather simple srtuatron wrLl not persist as the temperature of the crystal is Increased and many more levels become accessrble. One way to deduce the parameters &rrn would be from the intensitres of forbidden Raman lmes nearby to a (5). The Raman results presente d here are not III agreement wrth the theoretrcal predctions of Pawley and Cyvin [ 141 who calculated that ag(5) would have the smallest exciton bandwrdth (0.04 cm-l) of all the such modes
112 [I3 t14
K-ii Rebanc and P. Saan. J Lummescence 12 (1976) 23. S Voelker and R M Mxfarlane, Chem Phys. Letters 61 (1979)421. R hl Hochstrasser and C. Nyl. J Chem. Phys. 70 (1979) 1112. R M. Hochstrasser and P N Prasad, III. Excited states, ed E-C hm (Audcnuc Press. New York, 1973) p 120. W H Hesselmk and D A Wiersma. Chem Phys Letters 44 (1976) 76. R J. ElIlot, J A. Krumhansl zmd P L Leath, Rev- Mod Phvs 46 (1974) 465. J. Nafter and Jl Jortncr. J. Chem. Phys. 68 (1978) 1513. I1 Abram, R h¶ Hochst.rasser. J I: Kohl, M C. Semack and D White. J. Chem Phys. 71 (1979) 153; I I Abram&d R M Hoch&.&, J. &em. whys., to be pubbshed. R M Hochstrasser. G R Meredrth and H P Trommsdorff, J Chem Phys . to be pubbhed R Bl Hochstrasser and H N. Sung, J Chem. Phys. 66 (1977) 3276. D.M Hansen and A R. Gee, J. Chem Phys. 51 (1969) 5052 A. Laubereau and W. tier, Rev hlod. Phys 50 (1978) 607. R. SculJy and D H. Whlffen. Spectrochim. Acta 16 (1960) 1409 G S Pawley and S J Cynn. J. Chem. Phys. 52 (1970) 4073.