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Redistribution of vibrational energy in naphthalene and anthracene studied in liquid solution
Volume 101, number 4.5
CHEMICAL
PHYSICS
LETTERS
18 October
1983
REDISTRIBUTION OF VIBRATIONAL ENERGY IN NAPHTHALENE AND ANTHRACENE STUDIED IN LIQUID SOLUTION N.H. GOTTFRIED and W. KAISER B&k Department El I dw Technischen Univers-tzt hfiinchen. Munich. West Germnn_v Received 11 August 1983
The temporal build-up and the decay of vibrational excess population in the electronic ground state is investigated_ CHstretching modes are fast resonantly excited by a picosecond IR pulse and the subsequent flow of energy into several totally symmetric vibrational modes is observed by spontaneous anti-Stokes Raman scattering. Estimated occupation numbers of the monitored modes suggest that the excess energy is redistributed over the many vibrational modes within 5 to 10 ps.
1_ Introduction
The redistribution of vibrational energy in the electronic ground state of polyatomic molecules is a topic of considerable current interest. In the liquid phase our knowledge of collision-induced intramolecular vibrational relaxation (IVR) and intermolecular energy dissipation is very limited in spite of important practical implications in chemistry and biology. The main reason for the lack of information is the strong interaction of molecules in the liquid phase and the resulting short time constants, which are of the order of 1O-l* s. With the advent of ultrashort laser pulses it became possible to start experimental investigations in this very short time domain. Previous time-resolved measurements using anti-Stokes Raman scattering [l--.5] suggested very rapid intramolecular interactions of vibrational energy in polyatomic molecules in liquids. In a series of papers [5] we have investigated the population lifetime of individual vibrational modes in small molecules by resonance excitation of CH-stretching modes and by subsequent studies of the transient population via anti-Stokes Raman scattering. Of major interest are the following observations: (i) There exists rapid vibrational energy exchange between similar modes of nearby energy states. For instance, energy is rapidly transferred from the primary excited CH-stretching modes to a neighboring Raman active CH-stretching mode during the excitation time of a few picoseconds. 0 009-2614/83/0000-0000/S
03.00 0 1983 North-Holland
(ii) The decay of vibrational energy proceeds via anharmonic coupling with neighboring overtones and combination modes. As an example we point to the favorable energy transfer in certain molecules from the CH-stretching modes at =ZOOO cm-l to the overtones of the corresponding bending modes at approximately 1500 cm-l. (iii) The degree of interaction between the fundamentals and the overtones and combination modes may be inferred from an inspection of the types of modes involved and from the investigation of the Fermi resonance between the modes of interest_ The quantitative study of infrared and Raman spectra has allowed us to estimate transfer rates for vibrational ener,gy in fair agreement with experimental observations. (iv) In small molecules with a few normal modes the possible decay routes are quite limited. The individual population lifetimes may vary drastically within the same molecule_ In acetylene, for instance, we found for the CH-stretching mode (3265 cm-l) and the mstretching mode (1968 cm-l) lifetimes of 2 ps and 24G ps, respectively. In this paper we are concerned with two mediwnsize molecules, naphthalene (C,,H,) and anthracene (C,,H,,), where the mode densities are quite large around the primarily excited CH-stretching modes (i7= 3050 cm-l). In this case, Fermi resonance cannot be readily deduced from infrared and Raman spectra. We investigate several energy states of the same molecule and follow the redistribution of vibrational energy 331
Volurue 10 1. number 4.5
CHEMICAL PHYSICS LETTERS
iron1 the excited CH-stretching modes at -3050 cm-l to lower lying states. In particular, we study for the different vibrational modes: (i) the rise and the delayed masimum of the population, (ii) the decay time. and - for the first time - (iii) the absolute change in population. Naphthalene and anthracene are simple aromatic molecules which are well suited for IVR studies: in recent years they have been studied in a series of papers [6]_ Our experimental data suggest that the vibrationdl energy supplied to these molecules via CH-stretch1s distributed over the ing modes at 3050 c*W1 _ rapidly many vibrdtionai modes.
28 October 1983
the average over a50 shots. In the experiments with anthracene a photomultipIier containing a GaAs photocathode was used. The samples were prepared from naphthalene (Merck, scintillation grade) and anthracene (Koch Light Ind.. zone-refined) crystals using C,Cl, (Merck, spectroscopy grade) as a solvent. The concentrations were chosentobec=8X IOq2Mandc=2X 10-2Mfor naphthalene and anthracene. respectively. All experiments were performed at room temperature.
3. Results and discussion
of time constants
2. Experimental Our mode-Iocked Nd : glass laser system produces single pulses of 6 ps duration (fwhm) and 50 mJ energy. Prcosecond light pulses of frequency near 3000 cmWi were obtained by pumping a parametric generatoramplifier configuration consistiug of two LiNbO, ctyst&. The bandwidth of the generated IR pulses amounted to 20 cm-t and the pulse duration to 5 ps. The second harmonic of the laser pulse at 18976 cm -t \\as used for probing the naphthalene solution. The polarisations of the IR excitstion and Raman probe pulse were chosen to be perpendicular to each other in order to mininiize coherent interactions
in the
sample. Both pulses were focused collinearly into the sample volume by af= 25 mm lens. The delay between the excitation and the probe pulse was adjusted by an optical d&y line. Authracene was investigated with the laser pulse at X = 1.053pni setving directly as a R.mlan probe_ In this way, disturbmg fluorescence was elinlindted.
The temporal resolution of our esperimental system was checked simultaneously for each experiment mczztring the correlation functiort of the esciting and probing pulses. The broken cutves in figs. 1 and 2 represent experbnentaf correlation cumes: their nmsima mark the zero point on the time scale. The scattered
.mti-Stokes signals were measured with the help of a monochromator and/or several interference filters in ~ofljuxlction with a pIioto~~lultiplier_ Since Raman cross seciiolts of-vibrational modes are very small (o = IO-2g cm?) we had to couut single photons for each laser shot. Each data point shown in figs. 1 and 2 represents
The IR absorption spectrum of naphthalene shows t\\o overlapping bands at p= 3064 cm-l andir= 3048 cm-l in the frequency range of CH-stretching modes f7]_ Both bands were excited by IR pulses of a frequency of i; = 3055 cm-t_ The transient change of the population of the three strong Raman transitions at Ft = 3058 cm-1 (CH-stretching mode), 2s = 1380 cm-1 (ring deformation mode), and Fg = 765 cm-l (skeleton mode) was investigated_ In a first step the energy transfer from the initially pumped IR-active CH-stretching modes to the totally symmetric CH-stretching mode vt @‘t = 3058 cm-t) was studied. In fig. Ia the anti-Stokes Raman intensity of it is shown versus delay time. The Raman signal rises sharply for negative delay times, which indicates the rapid energy transfer from the excited modes. The maximum of the Raman signal is delayed compared to the maximum of the correlation curve (i.e. to the excitation pulse) by I .5 ps. The scattered intensity decays more gradually than the correiation curve_ The solid curve in fig. la was calculated from a system of rate equations. The population of the it mode was determined by the rate of energy redistribution within the set of eight CH-stretching modes and by the decay time of these modes. One readily infers from this model that the energy of the initially pumped mode is rapidly (t d 0.5 ps) transferred to the Raman-active CH-stretching mode it _The decay time of the coupled set of CHstretching modes was found to be 2 2 OS ps. In fig. lb we show results obtained by monitoring the transfer of vibrational energy from CH-stretching modes to the ns mode @s = 1380 cm-t). The Raman
CHEMICAL
Volume 101, number 4,s Delay Time
PHYSICS
tJps3
Fig. 1. Redistribution of vibrational energy in naphthalene. (a) Anti-Stokes Raman signal of the mode v1 (3058 cni’). Rapid transfer of vibrational energy from the initially pumped IR-active CH-stretching mode to the monitored Raman-active CHstretching mode. The correlation curve is shown far comparison(broken line). (b) Anti-Stokes Raman signal ofv~ (1380 cm-‘). This ring deformation mode is poptdated by the decaying CHstretching modes. (c) Anti-Stokes Raman signal of pg 065 cm-‘). This ^‘breath-mg** type mode is not directly populated by the CH-stretching modes.
LETTERS
28 October
1983
signal of the u5 mode rises more slowly than the ~1 mode and reaches a delayed maximum at approximately 5 ps. The signal than decays with a time constant of 7s = 9 F 4 ps. The time dependence of the population of the _vsmode suggests that the “5 mode was populated by the decay of the CH-stretching modes. The solid line through the data points of fig. lb was calculated from the appropriate rate equations taking a time constant of 9 ps for the decay of the v5 mode. We note that the absolute value of the population of the p5 mode is quite small (see below)_ Only a fraction of the excited CH-stretching modes decays via the us mode. Next. the change of the population of the us mode fj58 = 765 Cr&) was monitored. At room temperature, this low-lying mode has a substantial thermal population of n = 2.6 X 1O-2. As a result we find an antiStokes Raman signal without exciting our sample_ The excitation of the CT-i-stretching modes generates an excess population in the v8 mode. In fig. Ic we observe a slow build-up of the excess population, a delayed maximum after approximately 10 ps, and a decay of population with a time constant of 7s = 7 13 ps. The relatively late build-up of population of the v8 mode in fig. lc suggests that vibrational energy was not transferred directly from the CH-stretching modes to this low-energy state. Obviously, intermediate vibrational levels - not observed in our investigations - are involved in populating the ps mode. This finding differs from the situation of the vs mode and suggests mode specific effects in the decay process, i-e_ a non-statistical energy redistribution.
A C&stretching mode at the frequency F= 3050 cm-i dominates the IR absorption spectrum of anthracene in the vicinity of 3000 cm-l [7]_ This mode was resonantIy excited by our IR pulses- The Raman spectrum of anthracene contains several lines between 3000 and 3 100 cm-l, but these Raman transitions have not yet been assigned to specific CH-stretching modes [8]. The spectral resolution of our detection system was =lOO cm-1 (fwhm); thus all Raman transitions around 3050 cm-1 were detected by our photomultiplier. First we studied the energy transfer from the excited IR-active CH-stretching vibration to the group of Raman-active CH-stretching modes. The anti-Stokes 333
Volume
CHEMICAL
101. number 4.5
PHYSICS
28 October
LElTERS
1983
signal is depicted in fig. 2a. The Raman signal rises rapidly with excitation to a slightly delayed maximum. The transient population of the Raman modes decays somewhat slower than the correlation curve. A deconvolution of the Raman signal with the correlation curve gives an estimated rapid decay of TcH = 1 f 0.5 ps. Next. the transfer of vibrational energy from the CH-stretching modes to the ring deformation mode y6 (1403 cm-l) was studied. The result is presented in fig. 2b. The statistical error of this measurement is high due to the reduced quantum efficiency of the IR photomultiplier at 9488 + 1403 cm-l. The maximum Raman signal of v6 is seen to occur at a delay time of -5 ps and the Raman signal decays with a time constant of approximately 10 +- 5 ps_ From the time dependence of the build-up we infer that this mode was populated as a result of the decay of the CH-stretching modes. The various time constants found for naphthalene and anthracene are summarized in table l_
4. Transient I
(
Q
Delay
1
I
,
10
Ttme
toCpsJ
population
of vibrational
modes
,
20
Of special interest for the interpretation of our results are the transient occupation numbers of the various monitored modes. The average excess population of the vs mode (765 CI~-~) of naphthalene was readily calculated by comparing the maximum Raman signal with the room-temperature thermal background signal of
I‘@. 2. Redistribution of vibr.ttional energy in anthracene. (a) Anti-Stokes Rdman signal for iT = 3050 cue1 _The monitored Rdm.m-active CH-stretching modes rapidly couple to the initially excited IR-xtive Cl1stretching modes_ The broken line indicates the correlation curve. (b) Anti-Stokes Rnman signal of ~6 (1403 cni’). Ilnerg of the dec.+ns CH-stretching modes is transferred to this ring deformation mode.
Table 1 Summ~ of experiment.d data: Frequencies of the monitored modes, relative Raman cross sections [ 71, delay times of the maGmum R.mlan signal, and observed decay times. In the last two cohmms we list estimates of the ehperimentai excess population and, fur compxison, occupation numbers calculated for temperatures T* equal to 537 and 477 K, for naphthalene and anthncene, respecrh ely Mode
I‘requency (CIII~’ )
Raman cross
Delay time of
Decay time
section (au)
ma_Guum
(ps)
(ps)
Excess population J*exp
ncalc (T*)
ndphth&nr =I
3055
1.5
3 * 0.5
0.1
2.7 x 10-4
y5
1380
35
5
954
0.01
0.024
“8
765
16
10
7+3
0.1
O-12
9
anthracene “l.“t.Y3
v.s
334
53050 1403
4
1
-I7
5
1 f 0.5 10 f 5
(O-1)
1.0 x lo+
(0.03)
0.014
Volume 101, number4,5
CHEMICALfHYSiCS LEXTEFS
the same mode. The population per excited molecule (the occupation number) was then de&mined from the fraction of molecules in the scattering volume which were excited by one IR photon. Knowing-the relative Raman cross sections of the monitored modes of naphthalene (see table 1) and taking into account spectrometer transmissions and photomuliplier sensitivities, the population of the v1 and v5 modes was calculated from the corresponding Raman signals. For the short-lived CH-stretching mode y1 a correction (factor two) was introduced to account for the duration of our pulses. The final values for the occupation numbers are shown in table l_ The data are believed to be accurate within a factor of two. In naphthalene, there are eight CH-stretching modes. Assuming rapid equilibrium among these modes, one absorbed IR photon corresponds to a population of 0.12 for each CH-stretching mode. This valce is in good agreement with our observed value of II = O-1_ The population of the p5 mode (JZ= O-01) is rather weak, while the low-energy mode v8 is populated considerably more strongly (JZ= 0.1). Obviously, vibrational energy was transferred to the vS mode without passing through the v5 state. In the case of anthracene it was not possible to detect Raman signals due to room-temperature occupation. Nevertheless, an estimate of the population of the v6 mode of anthracene is possible by assuming rapid equilibrium among the CH-stretchiig modes. Taking a population of l/l0 per CH-stretching mode and considering the short lifetime of these modes we estimate from our maximum Raman signals a value of 12= 0.3 for the population of the v6 mode- This value, unfortunately, is subject to a considerable error of possibly a factor of four. The density of vibrational states in the energy range of the CH-stretching modes was calculated to be 5 X IO* and 1 X lo4 per cm-l for naphthalene and anthracene, respectively- These large numbers suggest for both molecules the consideration of intramolecular energy relaxation in terms of statistical energy randomization. It is convenient to compare our data with model canonical distributions- At a given temperature T, the ensemble average of the vibrational energy of molecules consisting ofN atoms has the form:
28 October 1983
oi are the frequencies of the different vibrational modes. Formally, we may evaluate a vibrational temperature T* for those molecules which have absorbea one quantum of 3050 cm-l according to E(T*) = E-(300 K) + kc X 3050 cm-‘.
121
From eqs. (1) and (2) vaIues of T* of 537 and 477 K are calculated for naphthalene and anthracene, respectively. Calculated occupation numbers corresponding to T* are given in table 1. We point to the fact that the observed population of the ~2~and ps modes of naphthalene compares favorabIy with the occupation numbers calculated from _T*. We therefore believe that the vibrational excess energy is redistributed over most vibrational modes after IO ps. This picture is also consistent with our fmdings for anthracene. In this case, a statistical model for the energy redistribution may be more appropriate on account of the increased mode density in anthracene compared to that of naphthalene. We point to recent independent investigations of anthracene 191, where the transient vibrational population was monitored by a W probe pulse generating a fluorescence signal of the S, s&e_ A few picaseconds after IR excitation we find an excess population of lOa to 10-S for vibrational combination modes in the vicinity of 3000 cm-l. This estimate is in fair agreement with the population of 1 X 10d, calculated from T* (compare table 1). Up to this point we were concerned exclusively with intramolecular vibrational processes. In the liquid phase one expects fast intermolecular interactions with solvent molecules. We feel that the decay times of the modes vS and vs in naphthalene and of the mode v6 in anthracene reflect the loss of the excess vibrational enery of the molecule to the surroundings. Certainly, the energy dissipates to the solvent by vibration-translation (VT) interactions involving low-energy vibrational mode: 5. Conclusion Collision-induced intramolecular redistribution of vibrational energy was directly observed in solution by a dynamic and mode selective experiment. The following picture emerges. During the excitation of CH-stretching modes energy is rapidly distributed over all C&stretching modes. This first step of in-
Volume 101, number 4.5
CHEMICAL
PHYSICS
tramolecular vibrational relaxation takes place on a time scale of less than 0.5 ps. From these energy states vibrational energy is then transferred to a large number of neighboring combination modes. This energy transfer
was observed by the build-up of population of vibratinal modes at lower energy. Data are presented for the v5 mode (13S0 cm-l) and “8 mode (765 cm-l) of naphthalene and the v6 mode (1403 cm-l) of anthracene. Additionally we estimate occupation numbers for the various monitored modes. These findings suggest that the vibrational excess energy is - approximately - randomized after 5-10 ps. A careful analysis of our data, however, indicates thar mode specific processes esist during the redistribution of vibrational energy_ The observed remarkably short times are of interest for the consideration of state-selective reactive processes_
Acknowledgement The authors are indebted to Drs. A. Seilmeier W. Zintb for numerous valuable discussions_
and
References [ 11 A. Laubereau and W. Kaiser. Rev. Mod. Phys. 50 (1978) 607.
[ 21 R-R. Alfano and S.L. Shapiro, Phys. Rev. Letters 29 (1972)
336
1655.
LETTERS
28 October
1983
[3] EJ. Heilweil, FE. Doany, R. Moore and R.hf. Hochstrasser, J. Chem. Phys. 76 (1982) 5632. [4] H. Graener and A. Laubereau, Appl. Phys. B29 (1982) 213. (51 A. Fendt, S-F. Fischer and W. Kaiser. Chem. Phys. 57 (1981) 55; Chem. Phys. Letters 82 (1981) 350; C. Kohneder, W. Zinth and W. Kaiser, Chem_ Phys. Letters 91 (1982) 323; W. Zinth, C. Kohneder, B. Benna, A. Irgens-Defregger, SF. Fischer and W. Kaiser, J. Chem. Phys. 78 (1983) 3916. 16 ] SM. Beck, DE. Powers. J-B. Hopkins and R-E. Smalley, J. Chem. Phys. 74 (1981) 43;
FM Behlen, D.B. McDonald, V. Sathuraman and S.A. Rice, J. Chem. Phys. 75 (1981) 5685; R.M. Hochstrasser and JE. Wessel, Chem- Phys. 6 (1974) 19; 1Vm.R. Lambert, P-M. Felker and A.H. Zewail, 1. Chem. Phys. 75 (1981) 5958; T. Tamm and P. Saari, Chem. Phys. 40 (1979) 311; R.W. Anderson, in: Picosecond phenomena II. Springer Series in Chemical Physics, Vol. 14, eds. R-M. Hochstrasser, W. Kaiser and C.V. Shank (Springer, Berlin, 1980); P-L. Decola, Rdl. Hochstrasser and H.P. Trommsdorff. Chem. Phys. Letters 72 (1980) 1; B.H. Hesp and D.A. Wiersma, Chem. Phys. Letters 75 (1980) 423. 171 B. Schrader and W. Meier, eds., Raman/IR atlas of organic compounds (Verlag Chemie. Weinheim. 1978). 181 J. R%&en, 1~. Stenman and E. Penttinen, Spectrachim. Acta 29A (1973) 395. 191 N.H. Gottfried, A. Seilmeier and W. Kaiser. to be published.
CHEMICAL
PHYSICS
LETTERS
18 October
1983
REDISTRIBUTION OF VIBRATIONAL ENERGY IN NAPHTHALENE AND ANTHRACENE STUDIED IN LIQUID SOLUTION N.H. GOTTFRIED and W. KAISER B&k Department El I dw Technischen Univers-tzt hfiinchen. Munich. West Germnn_v Received 11 August 1983
The temporal build-up and the decay of vibrational excess population in the electronic ground state is investigated_ CHstretching modes are fast resonantly excited by a picosecond IR pulse and the subsequent flow of energy into several totally symmetric vibrational modes is observed by spontaneous anti-Stokes Raman scattering. Estimated occupation numbers of the monitored modes suggest that the excess energy is redistributed over the many vibrational modes within 5 to 10 ps.
1_ Introduction
The redistribution of vibrational energy in the electronic ground state of polyatomic molecules is a topic of considerable current interest. In the liquid phase our knowledge of collision-induced intramolecular vibrational relaxation (IVR) and intermolecular energy dissipation is very limited in spite of important practical implications in chemistry and biology. The main reason for the lack of information is the strong interaction of molecules in the liquid phase and the resulting short time constants, which are of the order of 1O-l* s. With the advent of ultrashort laser pulses it became possible to start experimental investigations in this very short time domain. Previous time-resolved measurements using anti-Stokes Raman scattering [l--.5] suggested very rapid intramolecular interactions of vibrational energy in polyatomic molecules in liquids. In a series of papers [5] we have investigated the population lifetime of individual vibrational modes in small molecules by resonance excitation of CH-stretching modes and by subsequent studies of the transient population via anti-Stokes Raman scattering. Of major interest are the following observations: (i) There exists rapid vibrational energy exchange between similar modes of nearby energy states. For instance, energy is rapidly transferred from the primary excited CH-stretching modes to a neighboring Raman active CH-stretching mode during the excitation time of a few picoseconds. 0 009-2614/83/0000-0000/S
03.00 0 1983 North-Holland
(ii) The decay of vibrational energy proceeds via anharmonic coupling with neighboring overtones and combination modes. As an example we point to the favorable energy transfer in certain molecules from the CH-stretching modes at =ZOOO cm-l to the overtones of the corresponding bending modes at approximately 1500 cm-l. (iii) The degree of interaction between the fundamentals and the overtones and combination modes may be inferred from an inspection of the types of modes involved and from the investigation of the Fermi resonance between the modes of interest_ The quantitative study of infrared and Raman spectra has allowed us to estimate transfer rates for vibrational ener,gy in fair agreement with experimental observations. (iv) In small molecules with a few normal modes the possible decay routes are quite limited. The individual population lifetimes may vary drastically within the same molecule_ In acetylene, for instance, we found for the CH-stretching mode (3265 cm-l) and the mstretching mode (1968 cm-l) lifetimes of 2 ps and 24G ps, respectively. In this paper we are concerned with two mediwnsize molecules, naphthalene (C,,H,) and anthracene (C,,H,,), where the mode densities are quite large around the primarily excited CH-stretching modes (i7= 3050 cm-l). In this case, Fermi resonance cannot be readily deduced from infrared and Raman spectra. We investigate several energy states of the same molecule and follow the redistribution of vibrational energy 331
Volurue 10 1. number 4.5
CHEMICAL PHYSICS LETTERS
iron1 the excited CH-stretching modes at -3050 cm-l to lower lying states. In particular, we study for the different vibrational modes: (i) the rise and the delayed masimum of the population, (ii) the decay time. and - for the first time - (iii) the absolute change in population. Naphthalene and anthracene are simple aromatic molecules which are well suited for IVR studies: in recent years they have been studied in a series of papers [6]_ Our experimental data suggest that the vibrationdl energy supplied to these molecules via CH-stretch1s distributed over the ing modes at 3050 c*W1 _ rapidly many vibrdtionai modes.
28 October 1983
the average over a50 shots. In the experiments with anthracene a photomultipIier containing a GaAs photocathode was used. The samples were prepared from naphthalene (Merck, scintillation grade) and anthracene (Koch Light Ind.. zone-refined) crystals using C,Cl, (Merck, spectroscopy grade) as a solvent. The concentrations were chosentobec=8X IOq2Mandc=2X 10-2Mfor naphthalene and anthracene. respectively. All experiments were performed at room temperature.
3. Results and discussion
of time constants
2. Experimental Our mode-Iocked Nd : glass laser system produces single pulses of 6 ps duration (fwhm) and 50 mJ energy. Prcosecond light pulses of frequency near 3000 cmWi were obtained by pumping a parametric generatoramplifier configuration consistiug of two LiNbO, ctyst&. The bandwidth of the generated IR pulses amounted to 20 cm-t and the pulse duration to 5 ps. The second harmonic of the laser pulse at 18976 cm -t \\as used for probing the naphthalene solution. The polarisations of the IR excitstion and Raman probe pulse were chosen to be perpendicular to each other in order to mininiize coherent interactions
in the
sample. Both pulses were focused collinearly into the sample volume by af= 25 mm lens. The delay between the excitation and the probe pulse was adjusted by an optical d&y line. Authracene was investigated with the laser pulse at X = 1.053pni setving directly as a R.mlan probe_ In this way, disturbmg fluorescence was elinlindted.
The temporal resolution of our esperimental system was checked simultaneously for each experiment mczztring the correlation functiort of the esciting and probing pulses. The broken cutves in figs. 1 and 2 represent experbnentaf correlation cumes: their nmsima mark the zero point on the time scale. The scattered
.mti-Stokes signals were measured with the help of a monochromator and/or several interference filters in ~ofljuxlction with a pIioto~~lultiplier_ Since Raman cross seciiolts of-vibrational modes are very small (o = IO-2g cm?) we had to couut single photons for each laser shot. Each data point shown in figs. 1 and 2 represents
The IR absorption spectrum of naphthalene shows t\\o overlapping bands at p= 3064 cm-l andir= 3048 cm-l in the frequency range of CH-stretching modes f7]_ Both bands were excited by IR pulses of a frequency of i; = 3055 cm-t_ The transient change of the population of the three strong Raman transitions at Ft = 3058 cm-1 (CH-stretching mode), 2s = 1380 cm-1 (ring deformation mode), and Fg = 765 cm-l (skeleton mode) was investigated_ In a first step the energy transfer from the initially pumped IR-active CH-stretching modes to the totally symmetric CH-stretching mode vt @‘t = 3058 cm-t) was studied. In fig. Ia the anti-Stokes Raman intensity of it is shown versus delay time. The Raman signal rises sharply for negative delay times, which indicates the rapid energy transfer from the excited modes. The maximum of the Raman signal is delayed compared to the maximum of the correlation curve (i.e. to the excitation pulse) by I .5 ps. The scattered intensity decays more gradually than the correiation curve_ The solid curve in fig. la was calculated from a system of rate equations. The population of the it mode was determined by the rate of energy redistribution within the set of eight CH-stretching modes and by the decay time of these modes. One readily infers from this model that the energy of the initially pumped mode is rapidly (t d 0.5 ps) transferred to the Raman-active CH-stretching mode it _The decay time of the coupled set of CHstretching modes was found to be 2 2 OS ps. In fig. lb we show results obtained by monitoring the transfer of vibrational energy from CH-stretching modes to the ns mode @s = 1380 cm-t). The Raman
CHEMICAL
Volume 101, number 4,s Delay Time
PHYSICS
tJps3
Fig. 1. Redistribution of vibrational energy in naphthalene. (a) Anti-Stokes Raman signal of the mode v1 (3058 cni’). Rapid transfer of vibrational energy from the initially pumped IR-active CH-stretching mode to the monitored Raman-active CHstretching mode. The correlation curve is shown far comparison(broken line). (b) Anti-Stokes Raman signal ofv~ (1380 cm-‘). This ring deformation mode is poptdated by the decaying CHstretching modes. (c) Anti-Stokes Raman signal of pg 065 cm-‘). This ^‘breath-mg** type mode is not directly populated by the CH-stretching modes.
LETTERS
28 October
1983
signal of the u5 mode rises more slowly than the ~1 mode and reaches a delayed maximum at approximately 5 ps. The signal than decays with a time constant of 7s = 9 F 4 ps. The time dependence of the population of the _vsmode suggests that the “5 mode was populated by the decay of the CH-stretching modes. The solid line through the data points of fig. lb was calculated from the appropriate rate equations taking a time constant of 9 ps for the decay of the v5 mode. We note that the absolute value of the population of the p5 mode is quite small (see below)_ Only a fraction of the excited CH-stretching modes decays via the us mode. Next. the change of the population of the us mode fj58 = 765 Cr&) was monitored. At room temperature, this low-lying mode has a substantial thermal population of n = 2.6 X 1O-2. As a result we find an antiStokes Raman signal without exciting our sample_ The excitation of the CT-i-stretching modes generates an excess population in the v8 mode. In fig. Ic we observe a slow build-up of the excess population, a delayed maximum after approximately 10 ps, and a decay of population with a time constant of 7s = 7 13 ps. The relatively late build-up of population of the v8 mode in fig. lc suggests that vibrational energy was not transferred directly from the CH-stretching modes to this low-energy state. Obviously, intermediate vibrational levels - not observed in our investigations - are involved in populating the ps mode. This finding differs from the situation of the vs mode and suggests mode specific effects in the decay process, i-e_ a non-statistical energy redistribution.
A C&stretching mode at the frequency F= 3050 cm-i dominates the IR absorption spectrum of anthracene in the vicinity of 3000 cm-l [7]_ This mode was resonantIy excited by our IR pulses- The Raman spectrum of anthracene contains several lines between 3000 and 3 100 cm-l, but these Raman transitions have not yet been assigned to specific CH-stretching modes [8]. The spectral resolution of our detection system was =lOO cm-1 (fwhm); thus all Raman transitions around 3050 cm-1 were detected by our photomultiplier. First we studied the energy transfer from the excited IR-active CH-stretching vibration to the group of Raman-active CH-stretching modes. The anti-Stokes 333
Volume
CHEMICAL
101. number 4.5
PHYSICS
28 October
LElTERS
1983
signal is depicted in fig. 2a. The Raman signal rises rapidly with excitation to a slightly delayed maximum. The transient population of the Raman modes decays somewhat slower than the correlation curve. A deconvolution of the Raman signal with the correlation curve gives an estimated rapid decay of TcH = 1 f 0.5 ps. Next. the transfer of vibrational energy from the CH-stretching modes to the ring deformation mode y6 (1403 cm-l) was studied. The result is presented in fig. 2b. The statistical error of this measurement is high due to the reduced quantum efficiency of the IR photomultiplier at 9488 + 1403 cm-l. The maximum Raman signal of v6 is seen to occur at a delay time of -5 ps and the Raman signal decays with a time constant of approximately 10 +- 5 ps_ From the time dependence of the build-up we infer that this mode was populated as a result of the decay of the CH-stretching modes. The various time constants found for naphthalene and anthracene are summarized in table l_
4. Transient I
(
Q
Delay
1
I
,
10
Ttme
toCpsJ
population
of vibrational
modes
,
20
Of special interest for the interpretation of our results are the transient occupation numbers of the various monitored modes. The average excess population of the vs mode (765 CI~-~) of naphthalene was readily calculated by comparing the maximum Raman signal with the room-temperature thermal background signal of
I‘@. 2. Redistribution of vibr.ttional energy in anthracene. (a) Anti-Stokes Rdman signal for iT = 3050 cue1 _The monitored Rdm.m-active CH-stretching modes rapidly couple to the initially excited IR-xtive Cl1stretching modes_ The broken line indicates the correlation curve. (b) Anti-Stokes Rnman signal of ~6 (1403 cni’). Ilnerg of the dec.+ns CH-stretching modes is transferred to this ring deformation mode.
Table 1 Summ~ of experiment.d data: Frequencies of the monitored modes, relative Raman cross sections [ 71, delay times of the maGmum R.mlan signal, and observed decay times. In the last two cohmms we list estimates of the ehperimentai excess population and, fur compxison, occupation numbers calculated for temperatures T* equal to 537 and 477 K, for naphthalene and anthncene, respecrh ely Mode
I‘requency (CIII~’ )
Raman cross
Delay time of
Decay time
section (au)
ma_Guum
(ps)
(ps)
Excess population J*exp
ncalc (T*)
ndphth&nr =I
3055
1.5
3 * 0.5
0.1
2.7 x 10-4
y5
1380
35
5
954
0.01
0.024
“8
765
16
10
7+3
0.1
O-12
9
anthracene “l.“t.Y3
v.s
334
53050 1403
4
1
-I7
5
1 f 0.5 10 f 5
(O-1)
1.0 x lo+
(0.03)
0.014
Volume 101, number4,5
CHEMICALfHYSiCS LEXTEFS
the same mode. The population per excited molecule (the occupation number) was then de&mined from the fraction of molecules in the scattering volume which were excited by one IR photon. Knowing-the relative Raman cross sections of the monitored modes of naphthalene (see table 1) and taking into account spectrometer transmissions and photomuliplier sensitivities, the population of the v1 and v5 modes was calculated from the corresponding Raman signals. For the short-lived CH-stretching mode y1 a correction (factor two) was introduced to account for the duration of our pulses. The final values for the occupation numbers are shown in table l_ The data are believed to be accurate within a factor of two. In naphthalene, there are eight CH-stretching modes. Assuming rapid equilibrium among these modes, one absorbed IR photon corresponds to a population of 0.12 for each CH-stretching mode. This valce is in good agreement with our observed value of II = O-1_ The population of the p5 mode (JZ= O-01) is rather weak, while the low-energy mode v8 is populated considerably more strongly (JZ= 0.1). Obviously, vibrational energy was transferred to the vS mode without passing through the v5 state. In the case of anthracene it was not possible to detect Raman signals due to room-temperature occupation. Nevertheless, an estimate of the population of the v6 mode of anthracene is possible by assuming rapid equilibrium among the CH-stretchiig modes. Taking a population of l/l0 per CH-stretching mode and considering the short lifetime of these modes we estimate from our maximum Raman signals a value of 12= 0.3 for the population of the v6 mode- This value, unfortunately, is subject to a considerable error of possibly a factor of four. The density of vibrational states in the energy range of the CH-stretching modes was calculated to be 5 X IO* and 1 X lo4 per cm-l for naphthalene and anthracene, respectively- These large numbers suggest for both molecules the consideration of intramolecular energy relaxation in terms of statistical energy randomization. It is convenient to compare our data with model canonical distributions- At a given temperature T, the ensemble average of the vibrational energy of molecules consisting ofN atoms has the form:
28 October 1983
oi are the frequencies of the different vibrational modes. Formally, we may evaluate a vibrational temperature T* for those molecules which have absorbea one quantum of 3050 cm-l according to E(T*) = E-(300 K) + kc X 3050 cm-‘.
121
From eqs. (1) and (2) vaIues of T* of 537 and 477 K are calculated for naphthalene and anthracene, respectively. Calculated occupation numbers corresponding to T* are given in table 1. We point to the fact that the observed population of the ~2~and ps modes of naphthalene compares favorabIy with the occupation numbers calculated from _T*. We therefore believe that the vibrational excess energy is redistributed over most vibrational modes after IO ps. This picture is also consistent with our fmdings for anthracene. In this case, a statistical model for the energy redistribution may be more appropriate on account of the increased mode density in anthracene compared to that of naphthalene. We point to recent independent investigations of anthracene 191, where the transient vibrational population was monitored by a W probe pulse generating a fluorescence signal of the S, s&e_ A few picaseconds after IR excitation we find an excess population of lOa to 10-S for vibrational combination modes in the vicinity of 3000 cm-l. This estimate is in fair agreement with the population of 1 X 10d, calculated from T* (compare table 1). Up to this point we were concerned exclusively with intramolecular vibrational processes. In the liquid phase one expects fast intermolecular interactions with solvent molecules. We feel that the decay times of the modes vS and vs in naphthalene and of the mode v6 in anthracene reflect the loss of the excess vibrational enery of the molecule to the surroundings. Certainly, the energy dissipates to the solvent by vibration-translation (VT) interactions involving low-energy vibrational mode: 5. Conclusion Collision-induced intramolecular redistribution of vibrational energy was directly observed in solution by a dynamic and mode selective experiment. The following picture emerges. During the excitation of CH-stretching modes energy is rapidly distributed over all C&stretching modes. This first step of in-
Volume 101, number 4.5
CHEMICAL
PHYSICS
tramolecular vibrational relaxation takes place on a time scale of less than 0.5 ps. From these energy states vibrational energy is then transferred to a large number of neighboring combination modes. This energy transfer
was observed by the build-up of population of vibratinal modes at lower energy. Data are presented for the v5 mode (13S0 cm-l) and “8 mode (765 cm-l) of naphthalene and the v6 mode (1403 cm-l) of anthracene. Additionally we estimate occupation numbers for the various monitored modes. These findings suggest that the vibrational excess energy is - approximately - randomized after 5-10 ps. A careful analysis of our data, however, indicates thar mode specific processes esist during the redistribution of vibrational energy_ The observed remarkably short times are of interest for the consideration of state-selective reactive processes_
Acknowledgement The authors are indebted to Drs. A. Seilmeier W. Zintb for numerous valuable discussions_
and
References [ 11 A. Laubereau and W. Kaiser. Rev. Mod. Phys. 50 (1978) 607.
[ 21 R-R. Alfano and S.L. Shapiro, Phys. Rev. Letters 29 (1972)
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LETTERS
28 October
1983
[3] EJ. Heilweil, FE. Doany, R. Moore and R.hf. Hochstrasser, J. Chem. Phys. 76 (1982) 5632. [4] H. Graener and A. Laubereau, Appl. Phys. B29 (1982) 213. (51 A. Fendt, S-F. Fischer and W. Kaiser. Chem. Phys. 57 (1981) 55; Chem. Phys. Letters 82 (1981) 350; C. Kohneder, W. Zinth and W. Kaiser, Chem_ Phys. Letters 91 (1982) 323; W. Zinth, C. Kohneder, B. Benna, A. Irgens-Defregger, SF. Fischer and W. Kaiser, J. Chem. Phys. 78 (1983) 3916. 16 ] SM. Beck, DE. Powers. J-B. Hopkins and R-E. Smalley, J. Chem. Phys. 74 (1981) 43;
FM Behlen, D.B. McDonald, V. Sathuraman and S.A. Rice, J. Chem. Phys. 75 (1981) 5685; R.M. Hochstrasser and JE. Wessel, Chem- Phys. 6 (1974) 19; 1Vm.R. Lambert, P-M. Felker and A.H. Zewail, 1. Chem. Phys. 75 (1981) 5958; T. Tamm and P. Saari, Chem. Phys. 40 (1979) 311; R.W. Anderson, in: Picosecond phenomena II. Springer Series in Chemical Physics, Vol. 14, eds. R-M. Hochstrasser, W. Kaiser and C.V. Shank (Springer, Berlin, 1980); P-L. Decola, Rdl. Hochstrasser and H.P. Trommsdorff. Chem. Phys. Letters 72 (1980) 1; B.H. Hesp and D.A. Wiersma, Chem. Phys. Letters 75 (1980) 423. 171 B. Schrader and W. Meier, eds., Raman/IR atlas of organic compounds (Verlag Chemie. Weinheim. 1978). 181 J. R%&en, 1~. Stenman and E. Penttinen, Spectrachim. Acta 29A (1973) 395. 191 N.H. Gottfried, A. Seilmeier and W. Kaiser. to be published.