Real-time dynamics of vibrational predissociation in anthracene-Arn (n = 1, 2, 3)

ChemicalPhysics North-Holland

157 (1991)

231-250

Real-time dynamics of vibrational predissociation in anthracene-Ar, (n = 1,2,3 ) Ahmed

He&al,

Luis Bailares

‘, David

H. Semmes

* and Abmed

H. Zewail

Arthur Amos Noyes Laboratory of Chemical Physics 3, California institute of Technology, Pasadena, CA 91125, USA Received I3 May 199 1

This paper is contributed on a wonder@ occasion celebrating the contributions of Jan Kommandeur, a colleague andfiiend. Jan’s classic work on pyrazine (and others) is important to many of the problems discussed here. We wish him the best!.

The vibrational predissociation of van der Waals complexes of anthracene-Ar. (n= 1,2,3), isolated in a supersonic expansion, has been studied following excitation to single vibrational levels (12& lOA, 12& 6;) in S,. Using picosecond time-resolved fluorescence spectroscopy, the intramolecular vibrational-energy redistribution (IVR ) and the vibrational predissociation (VP) dynamics ate studied and related to the character of the mode and its energy. The IVR and VP rates are also discussed in relation to the cluster size.

1. Introduction The real-time dynamics of vibrational predissociation in stilbene-rare gas complexes has been studied before in this laboratory as an example of large molecular systems [ 11. The studies revealed the relative importance of intramolecular vibrational redistribution (IVR) and vibrational predissociation (VP), and the mode specificity of the dynamics. In this paper, we extend the study on vibrational predissociation to several anthracene-Ar complexes, providing analysis of the IVR process and the predissociation rates. Anthracene is interesting in comparison with stilbene because it has higher symmetry ( DZh) than planar stilbene ( C2,,), is more rigid and does not have large-amplitude low-frequency modes [ 2 1. Furthermore, the vibrational structure of the excitation spectrum of anthracene [ 3,4 J has several

Fulbright/Spanish Ministry of Education and Science Postdoctoral Fellow. ’ Present address: Rohm & Haas Co., 727 Norristown Road, Springhouse, PA 19477, USA. 3 Contribution no. 8432. 0301-0104/91/S

fundamental modes which are accessible with considerable intensity up to z 1400 cm- ’ and are well resolved from the other bands. Finally, anthracene has similar but inequivalent assignable [ 51 binding sites for the rare gas atoms so that geometrical isomers can be studied. This paper is structured as follows. Section 2 includes a description of the experimental set-up and the analysis method of the experimental data. The results and discussion for each complex excited to several vibrational bands are reported in section 3. In section 4 the main conclusions of the present work are presented.

2. Experimental 2. I. Apparatus The experimental set-up has been described in detail elsewhere [ 1,6 1. Briefly, anthracene-argon gas complexes were formed in a continuous supersonic jet expansion into a vacuum chamber held at less than 2 mTorr. Approximately 100 psi of a mixture of 1W

03.50 0 1991 Elsevier Science Publishers B.V. All rights resewed.

232

A. Heikal et al. / Vibrational predissociation in anthracene-Ar,,

of argon in helium was passed over anthracene heated ( x 160 “C) in a Pyrex tube and expanded through a x 80 u pinhole. This high backing pressure reduces the underlying emission from hot bands and low-energy sequence bands. Tunable UV picosecond laser pulses ( x 15 ps duration and z 5 cm- ’ energy width without etalons [ 61) were used to excite the complexes in the jet at a distance about thirty times the pinhole diameter, X/D= 30. These pulses were generated by doubling the output (using LiI03 crystal) of a cavity-dumped dyelaser(1.8X10-3MofLDS698ina15/18 (volume) mixture of propylene carbonate and ethylene glycol ) . The dye laser is synchronously pumped by a mode-locked Ar+ laser. The laser-induced fluorescence (LIF) from the complexes in the expansion was focused into the slit of a f m Spex monochromator, detected by a Hammamatsu R2287U microchannel plate photomultiplier tube (MCP-PMT) and then time-resolved by single photon counting electronics. The temporal system response function was measured by moving the molecular beam nozzle into the path of the laser beam to detect the scattered light. From this apparatus one can obtain a 40 ps response time [ 71, and for this study reported here typically the full width at half maximum (fwhm) is about 90 ps. 2.2. Analysis and data treatment The data analysis method has been extensively discussed elsewhere [ 1.1. Briefly, a nonlinear leastsquares method using Marquardt’s algorithm [ 8,9] was used to fit the experimental data to the most simple exponential form possible, convoluted with the measured system response function. Negative amplitudes in the fitting parameters reflect rise times and the positive amplitudes reflect decay times. The validity of the fit is based on the residual (the number of standard deviations each point is away from the fit), the reduced x: statistic, and the fact that the fluorescence of the resonantly excited bare anthracene can be tit well as a single exponential. Such decays were recorded and tit routinely during the course of this work as a control experiment with which we could compare with other temporal data to insure that the response function did not drift. Care was taken to measure the response function

accurately and to maintain reproducibility during the measurement of any fluorescence decay. Therefore, the system response function was monitored before and after each fluorescence decay, so that any drift or change in its shape can be recognized. From simulations [ 1 ] and by inspecting the residuals, with a 80 ps fwhm response function and about 3000 counts of signal (at the maximum of a data curve), risetimes in the temporal data as short as x 20 ps can be resolved. Our data were collected with high enough signal-to-noise ratio so that any additional such fast components could be distinguished. All decay rates were reproducible to z 10%.

3. Results and discussion 3.1. Preliminaries 3.1.1. Anthracene spectroscopy and dynamics The S,-So electronic transition in anthracene ( D2,, point group symmetry) is short-axis polarized and corresponds to a ‘B$,,(rtx*)-‘A; transition [lo]. Depending on the symmetry assignment, only a,, b, and bs, vibrational levels are expected to be active in absorption from the So vibrationless level and in emission from the S, vibrationless level. The strongest transition in the S, excitation spectrum is fully dipole-allowed ( Bzua&& [ 41. The excitation spectrum of jet-cooled anthracene has been studied [ 3,4] and most of the vibrational levels above the electronic origin ( 27695 cm- ’ ) have been assigned [ 3 1. The vibrational levels at 385 cm- ’ (12;), 755 cm-’ (lob), 766 cm-’ (12;) and 1380 cm- ’ (66 ) were assigned using the dispersed fluorescence spectrum (for low energy levels) and rotational band contour analysis [ 41. The levels at 385 and 755 cm- ’ were assigned as a, fundamentals and the 766 cm-’ band as an overtone of 385 cm-’ level with a, symmetry [4]. The rotational band contour analysis shows 2a, symmetry at 755 cm-’ and 1380 cm-’ [ 3,4]. These assignments indicate that each of these bands represents an overlap of two levels with a, symmetry; 754 and 756 cm-’ for the 755 cm-’ excitation, and 1379 and 1380 cm-’ for the 1380 cm-’ level. Lambert et al. [ 111 have measured the fluorescence lifetime in the S, state up to x 4000 cm-’ using

233

A. Heikal et al. / Vibrational predissociation in anthracene-Ar,,

time-resolved fluorescence spectroscopy. Below 1500 cm - ’ the lifetime varies non-monotonically between 28 and 6 ns due to a mode dependence in the intersystem crossing. Some model calculations involving IVR are now emerging [ 12 1. The dynamics of IVR have been studied extensively in bare anthracene by Felker et al. [ 6,131. Three regimes have been classified and they are now found in many other systems [ 141. No IVR was observed below 1290 cm- ‘, within the time resolution of the experiments. Modulated fluorescence decays show a restrictive IVR among a few vibrational levels in the intermediate energy regime ( 1300-l 5 14 cm- ’ ) . Dissipative IVR among approximately 10 or more levels was observed as biexponential decays (still with some modulations) from those levels above 1514 cm-‘. 3.2.1. Anthracene-Ar,, Henke et al. [ 51 have studied the fluorescence excitation spectrum for anthracene-argon complexes for the region up to 400 cm-’ to the red of the bare molecule origin. Bands are assigned as anthracene-Ar,, n = 1- 10, according to the spectral shift and the integrated peak intensities. The anthracene-Ar, band in the excitation spectra is shifted 43 cm-’ to the red of the electronic origin of anthracene and has a shoulder to the red which was attributed to a different isomer with less stability. A band at 98 cm-’ to the red was assigned as anthracene-Arz with two shoulders corresponding to different geometrical configurations A weak band at 137 cm- ’ to the red with intense background was assigned as anthracene-Ar,. Keelan [ 15 ] has measured the spectra up to 800 cm-’ in the anthracene S, state. The Og, as well as vibrational bands at 385, 755, 766 and 1380 cm-’ attributed to anthracene-Ar,, were observed 40 cm-’ to the red of the corresponding bands in the bare anthracene molecule. Bands assigned to the anthracene-Ar, complex were observed 97 cm-’ to the red of the origin and 385 cm-’ of the bare molecule. Only one unassigned band was observed in the vicinity of 766 or 755 cm-‘, however, at x 760 cm-‘. Considering that argon atoms in vdW clusters cause a slight perturbation on the potential energy of the bare molecule, we will assign, for simplicity, the vibrational levels of anthracene-Ar,, as those of the bare anthracene molecule.

3.2. Anthracene-Ar, 3.2. I. Experimental data Five of the excitation bands; the origin, 385, 755, 766 and 1380 cm-‘, have been studied in these experiments for anthracene-Ar,. These bands are shifted x43 cm-’ to the red of the corresponding transitions in the bare anthracene [ 51. For bare anthracene, the dispersed fluorescence spectrum and fluorescence decay of 08 transition are shown in fig. 1. In all cases below, we report the best fit ($ and residuals) of the fluorescence decays with the minimum number of exponential components. Such decays were repeated several times under different experimental conditions to guarantee the reproducibility of the results. The adequacy of two- and threeparameters fit follows the procedure outlined before

0:

Aatbracene

(a)

A

3600

3yY)

An,,.

._

37w

3800

Wavelength

a0

I

2.7

5.4

Time

_hB

39lo

4oca

(A)

8.1

10.8

13.4

(as)

Fig. I. (a) Dispersed fluorescence spectrum of the vibrationless bare anthracene with spectral resolution R = 1.6 A. (b) Fluorescence decay of the band at 3803.3 A fitted as a single exponential (z= 20.5 ns, x: ~0.940) convoluted with the system response function with full width at half maximum (fwhm) of 90 ps.

A. Heikal et al. / Vibrationalpredissociationin anthracene-Ar.

234

by Semmes et al. [ 11. In describing triple exponential tits, it should be noticed that one is a rise component and two are decay components (with one of them being the fluorescence lifetime). See below (section 3.2.2.2) for more discussion. 3.2.1.1. O$. The fluorescence spectrum of vibrationless S, anthracene-Ar, (fig. 2a) is similar to the fluorescence spectrum of the vibrationless state of the bare anthracene (fig. la), but with a 43 cm- ’ red shift. The fluorescence decay, shown in fig. 2b, is well fit by a single exponential with a lifetime of 12.7 ns. The electronic lifetime effect is induced by the “heavy” argon atom, as discussed by Jortner et al. 1161.

different conditions of excitation, i.e. on resonance and z 3 cm-’ to the red is shown in fig. 3. All of the major features in the dispersed fluorescence spectrum can be assigned as transitions from the initially prepared state, reflecting the absence of vibrational mixing. The fluorescence intensity decays in 12.0 ns without any additional component (fig. 4). The timeresolved data from the bare anthracene produced exciting to the red is fitted to a triexponential with a 1.39 ns risetime and 252 ps and 17.6 ns decay times (fig. 5). 3.2.1.3. 755 cm- ’ (lO$. The dispersed fluorescence spectrum is shown in fig. 6. The emission is similar to that from the bare anthracene but with 9

3.2.1.2. 385 cm-’ (126). The dispersed fluorescence spectrum of this band of the complex under

Anthracene-Arl

I

0:

Anthracene-Ar,

12:

1

Anthraccne

0:

Red -3 cm-l \

L

3ssO

m

3390

3710

3730

I

17

5.4

Time

8.1

LO.8

13.4

(as)

Fig. 2. (a) Dispersed fluorescence spectrum (R= 1.6 A) of the vibrationless S, anthracene-Ar,. (b) Fluorescence decay of the band at 3807.5 A from the vibrationless S, anthracene-Ar, fitted asa single exponential (T= 12.7 ns,X: =0.898, R=2.4A).

Wavelength

(A)

Fig. 3. Dispersed fluorescence spectrum (R= 1.6 A) of anthracene-Ar, 12; excited on resonance and z 3 cm-’ to the red.

A. Heikd et al. / Vibrational predissociation in anthracene-Ar.

Antbmceae-Arl

I

2.1

0.0

235

12:

1

I

I

5.3

1.9

10.6

t

13.2

Time (ns) Fig. 4. Single exponential fit (T= 12.0 ns, x: = 1.026, R= 3.2 A) of the fluorescence decay of the band at 3667.5 A from anthracene-Art 126.

53-

Antbrrcsac-Ar,

i

1;

‘. Biexponcntial

a 3 Tricxponctttirl

.

0.0

27

3.4

6.1

IO.8

13.4

Time (na) Fig. 5. Triple exponential tit (5, --252 ps, amplitude l/amplitude fluorescence=AI/Af=0.167, r,= 1.39 ns, AJAr= - 1.104, g= 17.6 ns, ,$ = I .060, R=2.4 A) of the time-resolved emission of the bare anthracene at 3610.5 A produced in the dissociation of anthracene-Ar, 126, exciting zz3 cm-’ to the red of the excitation band. The upper residual for the best biexponential fit with x: = 1.742.

A. He&al et al. / Vibrational predissociationin anthracene-Ar,,

236

Anthracenc-Art

IO, and

-25

-9

cm-l

3.2.1.4. 766 cm- I (12;). The data from this level is similar to that one of lOA.The band at 3568.1 A can be assigned as resonant emission [ 3 ] and the fluorescence decay of this band gives a double exponential lit: 1.36 ns and 4.11 ns fast decaying components (with low spectral resolution R= 6.4 A). The fluorescence decay of the origin-like band at 36 15.1 A fits a triexponential with lifetimes of 210 ps, 1.30 ns and 20.9 ns (fig. 8).

12:

em-1

Adi

3.2.1.5. 1380 cm- ’ (6;). At this level, the emission from the complex is broad origin-like fluorescence and depends on the precise excitation wavelength (fig. 9). For resonant excitation, the most intense band at 3622.6 A fits a triexponential with lifetimes of 527, 339 ps and 8.12 ns and a single exponential of 5.93 ns when exciting x 12 cm- ’ to the red (with low resolution R= 4.0 A) (fig. 10). On the other hand, the band at 36 15.1 A fits a biexponential with a rising component of 28 1 ps for resonant excitation and exciting x 12 cm- ’ to the red gives a best fit (with low signal-to-noise and R =.4.8 A) as a biexponential with rising component of 485 ps (fig. 11).

No argon

10:

I

3.2.2. Data analysis

*

3500

3600

3700

Wavelength

3mo

3900

4Qoo

(;6)

Fig. 6. Dispersed fluorescence spectra (R=2.4 A) of anthracene-Ar, 106 and 126. The emission from 128 without argon in the molecular beam is also shown. The uppermost trace is a highresolution spectrum (R= 1.6 A) of the main band of the 12; emission. The excitation band is contaminated with scattered laser light. The asterisk indicates the excitation wavelength.

and 25 cm-’ red shifts. The band at 3629.5 A can be assigned as resonant emission of the complex [ 31 and its fluorescence decay (with low resolution R= 4.8 A) tits a double exponential with a fast component of 1.52 ns. The time evolution of the origin-like band at 36 15.0 8, tits a triexponential with lifetimes of 47 1 ps, 1.35 ns and 17.9 ns (fig. 7). The relative intensity of the two origin-like bands in the fluorescence spectrum does not change when the excitation is shifted to the red.

As discussed elsewhere 3.2.2.1. Kinetic model. [ 1,14,17], the kinetic treatment is not necessarily correct for isolated molecular systems, but the experimental studies on dissipative IVR [ 17 ] verified the validity of the kinetic modelling of these processes provided that coherence effects are averaged out. All the temporal data presented in the last section fit well by single, double and triple exponentials and therefore, we use a kinetic model to interpret all these data. The simplest possible mechanisms correspond to parallel and sequential processes [ 1 ] that would give different results for the different intermediate and final species. We first consider the parallel scheme

k ,vR

A - ArLtiai /

A-Ar&,AA-Ar

A. Heikal et al. / Vibrational predissociationin anthracene_Ar,,

Anthracene-Ar,

237

10: Rise

Decay

0.0

2.1

5.4

8.1

10.8

13.4

Time (ns) Fig. 7. Temporal data (r, = 1.52 ns, A,/Af= 1.333, q=7.98 ns,xf’= 1.018,R=4.8 A) for thedecayofthe band at 3629.5 AofanthraceneAr, 10; and the triexponential tit (q ~471 ps, AI/Af=0.237, r2= 1.35 ns, AJAr= - 1.210, q= 17.9 ns, x: =0.959, R= 1.6 A) of the unassigned band at 36 15.0 A Anthracene-Ar,

I< Rise

Decay

0.0

2.1

5.3

1.9

10.6

13.2

Time (ns) rr=4.1 1 ns, x: = 1.080, R=6.4 A) for the decay of the anthracene-Ar, 12 detecting (r,=210ps,A,/A~=0.173,r~=1.30ns,A~/A~=-1.141,~~=20.9ns,~~=1.021,R=1.6~~ofthe

Fig. 8. Temporal data (T,= 1.36 ns, A,/A,=0.412, at3568.1

Aandthetriexponentialtit unassigned band at 36 15.1 A.

Aatbracene-Art

Hot

band

6’,

emission

Fig. 9. Dispersed fluorcwmce spectrum (R= 1.6 A) of authracene-Ar, 6& hot baud emission in the absence of argon in the =12cm-‘. molecular beam and the sDactnun excitiugtothered The asterisk marks the excitation wavele&h.

Time (ns) Fig. 10. Temporal data from the emission at 3622.6 A exciting on resonance (slower rise, TI= 527 ps, .41/&=0.903, TZ=339 ~,~~,~-1.280,~~~8.12ns,~~=1.118,R=3.2A)andexcitingtothered~ 12 cm-’ (faster rise, 5=5.93 ns,X: =0.954, R=4.0 A).

PS,

A. Heikul et al. / Vibrational predissociation in anthracene-Ar.

Anthracene-Ar.

Time

239

6:

(ns)

Fig. 1 I. Temporal data from the emission at 3615.1 A exciting on resonance fit as a biexponential with faster rise (q ~281 ps, A,/Ar= -0.834, ~~~8.69 ns, x: = 1.082, R= 3.2 A), but with slower rise when exciting z 12cm-‘tothered(r,=485ps,A,/Ar=-0.811, rr=lO.lns,~~=1.009,R=4.8A).

Here A represents the anthracene molecule and the asterisk indicates the vibronic excited state. The solution of the kinetic equations for this mechanism gives single exponential evolution for the initial state with the total decay rate (/&R+&), and biexponential with the same rate in the rise for each product [ 11. The amplitudes for each product are equal in magnitude and are functions of kIVR,kvp and k+ In contrast, if we consider the sequential process, A- AGitial- klVRA-A? ana,3

A*+ArL

A+Ar

the population of the product state will evolve as triexponential with a rise time equal to the slower of the IVR and VP rates and two decaying components with different amplitudes depending on the measured rates: kIVR,kvp and b. The emission of the redistributed state would be biexponential rising with the faster of klVRand kvp. A single exponential should fit the fluorescence decay of the initial state with the IVR rate. Combinations of these two simple schemes

with more parallel or sequential branches would give the same main features for the time evolution of different species [ 11. 3.2.2.2. Separation of IVR and VP. Most of the results reported for anthracene-Ar, can be interpreted using the simple sequential mechanism. For every excitation, except anthracene-Ar, 6;) triexponentials are accurately matched, supporting the kinetic scheme for a two-step dissociation in which IVR precedes VP. When triexponential decays are measured for a certain excitation band, it is not possible to determine which of the two short lifetimes is due to IVR and VP. However, by time-resolving the decay of other bands (other than nascent anthracene) we can identify VP and IVR. Fast decays identifying the IVR lifetime were measured only for resonant emission bands in anthracene-Ar, 10; and 12;. The fact that these decays are fit as biexponentials instead of single exponentials, as expected from the sequential kinetic

A. Heikal et al. / Vibrationalpredissociation in anthracene-Ar,,

240

model, could be due to contamination of these data with hot-band emission from the bare molecule decaying with the longer lifetime component. For anthracene-Ar, 12;) the data can be explained by considering the existence of isomers with less stability, shifted in the absorption wavelength only by a few wavenumbers to the red [ 5 1. The fact that a triexponential decay was measured by detecting the assigned bare anthracene as a product of the dissociation of this complex is consistent with this assumption. As in the excitation to the red, this was the case with resonant excitation due to the broad bandwidth of our laser. For the temporal data of anthracene-Ar, 66, probably the intense hot band emission (see fig. 9) is contaminating the data. In any case, double exponential decays were measured for the band at 36 15.1 A with rising components of 281 and 485 ps when exciting on-resonance and at % 12 cm- ’ to the red, respectively. The high density of vibrational states at this energy (see next section) suggests the possibility of unresolved fast component corresponding to dissipative IVR which is expected to occur on a very short time scale [ 131. The different rising components

could be explained considering the production of different redistributed states reflecting different rates of predissociation. For the same reason, the IVR would be in the decay of the triexponential data measured at 3622.6 A. Taking all these trends into consideration, IVR and VP lifetimes were distinguished and are listed in table 1. 3.2.2.3. I VR and the density of states in anthraceneTo understand the role of IVR in this complex, and particularly the role of the low energy levels in the vibrational redistribution, it is necessary to take into account the contribution of van der Waals modes to the total density of states in the complex [ 18 1. The symmetry reduction in the complex, compared with the bare molecule, can lower the restrictions on the vibrational couplings which characterize IVR [ 13 1. The anthracene-Ar, potential energy, based on twobody interaction potentials between the rare gas atom and each atom in the aromatic molecule [ 191, along the three coordinates involving the motion of the rare gas atom (one stretching and two bendings) was calculated and plotted in fig. 12. The well depth, D,, and Ar,.

Table 1 Experimental and calculated VP and IVR lifetimes for anthracene-Ar. (n= 1,2,3) complexes Complexes Anthracene-Arr 385 cm-’ (isomer 755 cm-’ 766 cm-’ 1380cm-’

Anthracene-Ar, 385 cm-’ (isomer =760cm-’ 1380cm-’ Anthracene-Arj 385 cm-’ (isomer 766 cm-’

rryR(exp.) (ps)

r&exp.)

1390 1350 1300 <20b’ <20 b’ 340

252 471 210 281 485 527

2100 846 508 253 180

228) 315 485 805

1250 781 424

184) 283

‘) Only harmonic frequencies were considered in the calculation. w This time constant was not resolved, and we therefore expect it to be < 20 ps.

(PS)

7dR-)

273) 416 121 1.6”

(ps)

241

A. Heikal et al. / Vibrational predimxiation in anthracene-Ar,,

40”

200

7 E <

o-

E B 9 -200

--

-100

-

b

-zoo-

a

-i

I

h-300 B

400

-500

--

-

~

Fig. 12. me vibrational potential energy along tbree coordinates: the stretching motion in the zdirection, and bending motions along the X- and y axes, for the most stable configuration of the complex (a). The fits of thii potential to a Morse potential and two 1/cosh*x potentials are also shown (b).

the range parameters, were determined from the fitting of those curves with Morse (stretching) and 1lcosh% (bendings) potentials [ 201. The vdW vibrational frequencies and the anharmonicities were calculated from those parameters [ 18 ] and are listed in table 2 for two different geometrical configurations of the anthracene-Ar, complex. To calculate the energies of the different vdW modes, we have used the following expression:

E vdw=o,(nx+f)+o,(n,+f)+o,(n,+f)

-g,(n,+t)2-_gyy(ny+f)2-g,,(n,+1)2 -g,,(n,+f)(n,+1)-g,,(n,+t)(n,+t) -gyz(ny+f)(n*+f)

9

where the o’s are the vibrational frequencies, the g’s are the anharmonic constants, and the n’s are the vibrational quantum numbers. The cross anharmoni-

A. Heikal et al. / Vibrational predissocintionin anthracene-Ar,

242

Table 2 Calculated vdW frequencies and anharmonicities (in wave numbers) for two different configurations of anthracene-Ar, complex Complex configuration (A) x=0.0 A Y=o.o A zz3.43 A D,=519cm-’ (B)x=4.65 A y=o.o A z= 3.29 A De=293 cm-’

Parameters

w,= 8.68 w,= 11.30 w,= 42.60

g-=0.036 g,,=O.O61 g,,=O.873

g,=o.o94 g,,=o.354 g,=O.463

w,= 10.34 o,= 9.35

g,=o.o91 g,=o.o74 g,,=O.873

g,=O.l64 g,,=O.564 g+O.508

w,=32.01

cities were calculated as gti= 2 (giga) I’*, where the gii is the anharmonic constant for the i-coordinate. This expression was used for direct counting of the number and density of bound states in the vdW well. The total density of states calculated by adding the density of states for both the bare anthracene and the complex as a function of the excess energy is shown in fig. 13, for the two different isomers considered (A and B in table 2 ) . The maxima in the total density of states appear when the vdW modes in combination with each anthracene vibration approach the dissociation energy of the complex. In these calculations, the vdW frequencies (listed in table 2) and 47 normal mode frequencies [ 2 1 ] (up to 1400 cm-’ ) of

loooo c 6000 4

L

7000C,,I11111T-,

r- , .I.-r__,

I-

(a)

(b)

-I 6000

7

3 5000

$ a6000 .

the bare anthracene were used. The anharmonicities were taken into account for the energy range O-800 cm-’ , but above that energy only the harmonic frequencies were considered. It is clear from these calculations that with the addition of the vdW vibrational states many more levels are available for vibrational redistribution at a given energy than in the bare molecule. IVR was observed at 385 cm-’ only for the less stable isomer (p=435 states/cm-‘), and for excitation above this energy: 7036 and 2350 states/cm-’ at 755 and 766 cm-‘, respectively, and pharmoniC = 7 1230 states/cm-’ at 1380 cm-‘. The absence of IVR in the most stable isomer at

k

a

-

P a

\4oao

5 9 n 3000

s

34000h ti a d 2000 -

t

1000

0 0

200

400 600 Excess energy / cm-,

600

Fig. 13. The total density of the vibrational states, as a function of the excess energy up to 800 cm-‘, in (a) the most stable configuration of anthracene-Ar and (b) a less stable isomer (see table 2).

243

A. Heikal et al. / Vibrational predissociation in anthracene-Arm

385 cm-’ and the relatively long redistribution times (x 1 ns) at 755 and 766 cm-’ suggest that the coupling#’ between the different levels is relatively ineffective. The decrease in IVR lifetimes with excess vibrational energy for anthracene-Ar, (see table 1) is consistent with the previous studies on IVR in large molecules [ 6,13 1. 3.2.2.4. Vibrationalpredissociation. Comparison with RRKM theory. The RRKM rate constant k(E) is given by k(E) =N*(E-&)l&(E)

,

where E is the total energy, N” is the number of levels of the transition state at the available energy E-D,, p is the density of states of the reactant complex and h is Plan&s constant. The vdW stretching mode of the complex was assumed to be the reaction coordinate and all the other modes were assumed to be the same in both the transition state and the reactant excited state. The RRKM rates were calculated by directly counting anharmonic vibrational levels up to 800 cm-‘. From 800 to 1400 cm-‘, harmonic vibrational levels were used [ 22 1. One does not expect this simple model to be adequate. First, the redistribution involves the vdW modes and since the stretch is the reaction coordinate, the bending modes and their combinations are the important large-amplitude motions. This implies that the motion of the Ar atom around the phenyls and good potentials, including coupling with rotations, are needed. Second, because of such motion, the reaction coordinate may not be the simple stretch motion, and may involve the bend as well. However, we found that the calculation is, within an order of magnitude, in agreement with the observed rates (see table 1 ), except for 1380 cm- ’ for which the calculation was made without anharmonicities. The reason that the mode-selectivity is not so obvious in this molecular system, in comparison with the stilbene case [ 11, may be because of the absence of out-ofplane vibrational modes in the bare anthracene. There may be non-statistical behavior when the excess vibrational energy is increased up to 1380 cm-‘, but the effect, if present, is not very large. X1The coupling is on the order of ~0.052 GHz (or less), which is much less than the typical values of the bare molecule at, e.g. 1792 em-’ (3.8 GHz).

3.3. Larger clusters 3.3.1. Anthracene-Ar, Four of the excitation bands, the origin, 385, x 760 and 1380 cm- ’ have been studied in these experiments for anthracene-Ar,. These bands are shifted 98 cm-’ to the red of the corresponding transitions in the bare molecule [ 5 1. 3.3.1.1. O$. The fluorescence spectrum of anthracene-Ar2 excited to the vibrationless S, level is also similar, except for a 98 cm-’ red shift, to the fluorescence spectrum of the vibrationless state of the bare anthracene (fig. 14a). The fluorescence decay is well fit by a single exponential with a lifetime of 15.4 ns (fig. 14b).

Aatbracene-Arz

0”.

(a)

33m

36m

3700

3mn

Wavelength

L J 01)

Y

3900

4oc0

IO.6

13.2

(i)

I

21

5.3

79

Time (nr) Fig. 14. (a) Dispersed fluorescence spectrum (R= 1.6 A) of vibrationless S, anthraeene-Ar,. (b) Fluorescence decay at 38 17.3 A from vibrationless S, anthraeene-Ar, fit as a single exponential(r=15.4ns,X:=0.969,R=1.6A).

A. He&al et al. / Vibrationalpredissociation in anthracene-Arm

244

3.3.1.2. 385 cm-’ (126). Fig. 15 shows the dispersed fluorescence spectrum of this level under different conditions of excitation, i.e. on resonance and c 9 cm-’ to the blue. Most of the emission is assigned to the initially excited level of the complex. The small peak at 36 18.1 A is more intense when the excitation wavelength is tuned zs9 cm- ’ to the blue and is assigned as anthracene-Ar, 0:. The remaining emission is similar to the spectrum of the vibrationless level. The time-resolved fluorescence from the anthracene-Ar, 126 band at 3625.1 A fits a biexpo-

Anthracene-At-a

Id

nential with a fast decaying component of 2.30 ns (tig. 16). The emission from the unassigned band at 3623.6 A fit a biexponential with a 2.10 ns rising component and no fast decaying component ( fg 16 ) . The fluorescence for the anthracene-Arr @ band, exciting the blue edge of anthracene-Arz 126, fits a triexponential with lifetimes of 228 ps, 846 ps and 12.5 ns (fig. 17). The dispersed fluorescence 3.3.1.3. z 760 cm-‘. spectrum of this band is shown in fig. 18a and it is assigned as anthracene-Ar, 0:. The time-resolved fluorescence of the anthracene-Ar, 0: band at 36 18.0 A tits a triexponential with partial rise of 508 ps and decay components of 3 15 ps and 11.26 ns (fig. 18b). For the same band but exciting the blue edge of the excitation band, the temporal data fits a triexponential with lifetimes of 557 ps, 264 ps and 10.34 ns.

Anthraccne-Ar 0:

Blue -9 cm-l

3.3.1.4. 1380 cm-’ (a$,. The dispersed fluorescence spectrum of this band is shown in fig. 19 along with a high-resolution spectrum in the region of the anthracene origin. The bands at 36 12.5 A and 36 15.2 A in this spectrum have been temporahy resokd. The fluorescence decays of these two bands are fit to triexponentials with rise lifetime of 805 ps and fast decay component of 180 ps (fig. 20) and 485 ps and 253 ps (fig. 2 1) , respectively. 3.3.2. Anthracene-Ar, Three of the excitation bands; the origin, 385 and 766 cm-‘, have been studied for anthracene-ArJ. These bands are shifted 13 1 cm- ’ to the red of the corresponding transitions in the bare anthracene [ 5 1. 3.3.2.1. O$. Fig. 22a shows the fluorescence spectrum of anthracene-Ar, excited to the vibrationless level. The time-resolved fluorescence of this band fits a single exponential with a lifetime of 8.8 ns (fig. 22b).

Wavelength

(A,

Fig. 15. Dispersed fluorescence spectrum (R= 1.6 A) of anthracene-Ar, 12: exciting on resonance and to the blue z 9 cm-‘. The uppertrace in each spectrum corresponds to the high-resolution spectrum of the main band.

3.3.2.2. 385 cm-’ (126). The dispersed fluores cence spectrum under different conditions of excitation, i.e, on resonance and s 9 cm-’ to the blue, is shown in fig. 23. Most of the emission is assigned to the initially excited state. The small band at 3621.2 A is more intense when the excitation wavelength is

A. Heikd et al. / Vibrational predissociation in anthracene-Ar,,

Anthracene-Arz

245

12 Rise

3.1 r-

,:. .:.. . _-,: ._-, ,. ., _( I:.,s.: :L;:T!g ;’ :.;;’ ;j,
I

5.4

Time

8.1

(ns)

Fig. 16. Rise and decay of the emission from anthracene-Ar, 12;. For the decaying fluorescence at 3623.6 A, 71=2.30 ns, AI/A~= and ~~8.42 ns (~f~0.984, R= 1.3 A). For the fluorescence with a rising component at 3625.1 A, 71=2.10 ns, AI/A,=-0.868 rf=lO.l ns (xf=i.037,R=1.6A).

Anthracene-Arz

1.644 and

12: Bicxponential

Tricxponcntial

I f 0.0

I

I

I

I

1

2.1

5.4

8.1

10.8

13.4

Time (ns) Fig. 17. Triexponential tit (7,=228 ps, A,/A,=0.370, 7,=846 ps, AJAf=1.298, 7<=12.5 ns, x:= 1.010, R=1.6 A) ofthe resolved emission at 36 18.1 A corresponding to the vibrationless anthracene-Ar, produced in the dissociation of anthracene-Ar, 12b,exciting zz9 cm-’ to the blue. The upper residual for the best biexponential tit.

A. Heiknl et al. / Vibrational predissociation in anthracene-Ar,

246

Anthracene-Arz

-760 cm-l

(a)

36m

Wavelength

0.0

I

5.4

8.1

3620

Wavelength

(A)

3400

27

3610

10.8

13.4

Time (IIS) Fig. 18. (a) Dispersed fluorescence spectrum (R = 1.6 A) of anthracene-Ar, excited to approximately 760 cm-‘. The asterisk indicates the excitation wavelength. (b) Temporal data for the decay of anthracene-Ar 0: emission produced in the dissociation of anthracene-Ar2 excited to c 760 cm- ’ (?I= 3 15 PS, A, /A*= 1.558, rZ=508 ps, AZ/AC=-2.522, r,=11.26 ns, x:=0.900, R~3.2 A). The best biexponential tit givesxs =2.29.

tuned z 9 cm-’ to the blue and is assigned as anthracene-Ar, 0:. With resonant excitation, the fluorescence decay of the band at 3626.7 A shows a double exponential tit with a rising component of 1.25 ns. The detected fluorescence for anthracene-Arz 08, exciting =: 9 cm-’ to the blue, fits a triexponential with lifetimes of 184 ps, 78 1 ps and 17.7 ns (fig. 24). 3.3.2.3. 766 cm-’ (12;). Most of the emission in the spectrum of this band shown in fig. 25a is assigned as anthracene-Ar, 0:. The temporal decay of the 0: band is fitted to a triexponential with lifetimes of 283 ps, 424 ps and 12.3 ns, and is shown in fig. 25b.

3xm

3600

Wavelength

3630

3640

3650

3800

3900

(;b)

3700

(b)

Fig. 19. Dispersed fluorescence spectrum (R = I.6 A) of anthracene-Ar, 6;. The high-resolution spectrum in the region of the anthracene origin is also shown (upper part). The asterisk marks the excitation wavelength.

3.3.3. IVR and VP in larger clusters For anthracene-Ar2 and the anthracene-Ar3, triexponential decays have been measured for the product state fluorescence and explained by the sequential mechanism. The data from both complexes excited to the 12; transition can be explained considering a less stable isomer to the blue of the main excitation band [ 51 that dissociates into the corresponding vibrationless anthracene-Ar, (n = 1,2), at this low energy. Following the same schemes as in the anthraceneAr,, we distinguished between IVR and VP for these two complexes as listed in table 1. In comparison with anthracene-Ar,, the vibrational levels in anthracene-Ar, (n= 2, 3) become more accessible for energy redistribution due to the increased vibrational density of states when a second

247

A. Heikal et al. / Vibrational predissociation in anthracene-Ar,,

Anthracene-Ar2

1421-

6:

:.

c z 8

I

2.1

I

I

5.4

8.1

Time

I

10.8

I

13.4

(ns)

Fig. 20. Temporal data from the emission at 3612.5 A (r,= 180 ps,A,/Af=0.388, r,=805 ps, AJAr= - 1.323, g= 14.9 ns, R= 1.6 A) corresponding to the product of the dissociation of anthracene-Ar, 6: (x: =2.09 for the best biexponential fit ).

Anthracene-Arz

5.4 Time

xf=1.029,

6’,

8.1

10.8

13.4

(ns)

Fig. 21. Temporal data from the emission at 3615.2 A (~~~253 ps, A,/Af= 1.357, 7,=485 ps, AJAr= -2.308, p= 14.5 ns, Xf=1.147, R= 1.6 A) corresponding to the product of the dissociation ofanthracene-Ar, 6; (x: = 3.33 for the best biexponential).

A. Heikal et al. / Vibrational predissociation in anthracene-Ar,,

248

Anthraccnc-Ar3

12

(a) Anthraccnc-Arz 0:

I

Wavelength Time

(A)

(OS)

Fig. 22. (a) Dispersed fluorescence spectrum (R= 1.6 A) of the vibrationless S, anthracene-ArS. (b) Fluorescence decay of the band at 3824.2 A from the vibrationless S, antbracene-Ar3, titted as a single exponential (T= 8.82 ns, _$ zO.923, R= 3.2 A).

Ar atom is attached to the aromatic molecule. The IVR lifetimes may therefore decrease with increasing the number of argon atoms and also with increasing excess vibrational energy in the different clusters studied. The IVR time constant becomes shorter by increasing the cluster size, and in the higher clusters, it decreases by exciting modes at higher energies. From a simple physical point of view, it is expected, for this kind of system, that the larger the cluster size the smaller the VP rate constant. This trend was observed in our study for the 12: level (see table 1) with VP lifetimes of 2 10 ps versus 3 15 and 283 ps for n= 1 versus n= 2 and 3 (the lifetime of n = 3 is not longer than that of n = 2). Willberg et al.

Fig. 23. Dispersed fluorescence spectrum (R= 1.6 A) of anthracene-ArJ 12: exciting on resonance and to the blue c9 cm-‘. The trace in absence of argon in the molecularbeam is also shown. The upper trace in each spectrum corresponds to the high-resolution (R=0.8 A) spectrum of the main band.

[ 24 ] have very recently studied the vibrational predissociation in iodine-Ne, using picosecond pump/ probe time-resolved techniques. The vibrational predissociation rates are found to increase with the vibrational quantum number and decrease with the cluster size. For a simple molecular system like IZNe,, the physics involves only one intramolecular (II stretch) mode, and the results can be quantitatively related to the effect of cluster size on VP. Here, however, there is an interplay between VP and IVR, and theoretical modelling will be very interesting as it should show how the modes coupling and IVR are influencing the step-wise bond breaking process.

Anthracene-Ar3

‘iii

s 3

12:

1.9:. : '. '. .i.l. ,__.,, ,'..' ,; '..jt..~,.,;,,,. .'.":..... .: ':.'.;." :.'..., Slower decay -+J-J.?;. .>_* ' .-.* 0.01 ~. =... ‘.<.-:.‘._:;’ ,;...::.*,“>‘.‘. ..+ . : :‘..‘,‘.i.:‘~.~r~: ;>......w.*-...>r’,‘;...:.>,:.,..-,2;. i-,....., :;

_2.9

.,y ::;. ,-.:; . .

.,......:‘,‘.‘..,;, :.:;: ..’ ., :;+::: .: .*

. . ,., I :

.( .,i”

. ..” ..,

2061 c S L z ,R B Y d

0.0

5.4

2.1

8.1

10.8

13.4

Time (ns) Fig. 24. Temporal data of the emission from anthracene-ArS l2h at 3626.7 A (faster decay, T,= 1.25 ns, Al /Af= - 0.955, q= 8.94 ns, xf2= 1.045, R= 1.6 A) and the triexponential fit (slower decay, r,= 184 ps, AI/Af=0.348, ~=781 ps, AJAf= - 1.308, rr= 17.7 ns, xf= 1.137, R= 1.6 A) of the time-resolved emission at 362 1.2 A corresponding to vibrationless anthracene-Ar, produced in the dissociation of anthracene-Ar, 12& exciting = 9 cm-’ to the blue of the excitation band.

4. Conchsions (a)

l

35ml

37M

3m

Wavelength

1 s 3

3903

4Oal

(b)

3.8-

In this paper we have studied the dynamics of anthracene-Ar, (n= 1, 2, 3) in real-time by using picosecond time-resolved fluorescence spectroscopy in supersonic jet expansions. These studies allow for examination of IVR and VP as a function of the cluster size and character of the mode (energy) excited. Anthracene, stilbene and other molecules have been used as prototypes for large-sized systems in an attempt to compare with small-sized and more well-defined systems.

-3.8 3265

zi : z =”

B Y 9

0.0

2.7

5.4

Time (as)

8.1

10.8

13.4

Fig. 25. (a) Dispersedfluorescencespectrum (R=1.6A) ofanthracene-Ar, 122. An asterisk indicates the excitation wave length. (b) Temporal data (r,=283 ps, A,/A1=1.876, ?2=424 ps,A,/Ar=-2.827,rr=12.3ns,~~=l.014,R=3.2A)forthedecay of anthracene-Ar2 0: emission at 362 1.O A produced in the dissociation of anthracene-Ar, 12; (best biexponential fit gives XfC3.01).

250

A. Heikal et al. / Vibrational predimxiation in anthracene-Ar.

Acknowledgement This work was supported by a grant from the National Science Foundation (DMR).

References [ 1] D.H. Semmes, J.S. Baskin and A.H. Zewail, J. Chem. Phys. 92 (1990) 3359; D.H. Semmes, J.S. Baskin and A.H. Zewail, J. Am. Chem. sot. 109 (1987) 4104. [ 2 ] D.J. Evans, Spectrochim. Acta 20 ( 1964) 89 1. [ 31 W.R. Lambert, P.M. Felker, J.A. Syage and A.H. Zewail, J. Chem. Phys. 81 (1984) 2195. [4] B.W. Keelan and A.H. Zewail, J. Chem. Phys. 82 (1985) 3011. [ 51W.E. Henke, Weijun Yu, H.L. Selzle, E.W. Schlag, D. Wutz and S.H. Lin, Chem. Phys. 92 (1985) 187. [ 61 W.R. Lambert, P.M. Felker and A.H. Zewail, J. Chem. Phys. 81 (1984) 2217. [7] J.S. Baskin, P.M. Felker and A.H. Zewail, J. Chem. Phys. 86 (1987) 2483. [ 81 J.N. Demas, Excited State Lifetime Measurements (Academic Press, New York, 1983). [ 91 D.V. O’Connor and D. Phillips, Time-Correlated Single Photon Counting (Academic Press, New York, 1984); P.R. Bevington, Data Reduction and Error Analysis for The Sciences (McGraw-Hill, New York, 1969). [ lo] A. Bree and S. Katagiri, J. Mol. Spectry. 17 ( 1965) 24; J. Sidman, J. Chem. Phys. 25 (1956) 115. [ 111 W.R. Lambert, P.M. Felker and A.H. Zewail, J. Chem. Phys. 81 (1984) 2209. [ 121 K. Shari,, Y.J. Yan and S. Mukamel, J. Chem. Phys. 87 (1987) 2021; S. Mukamel, Advan. Chem. Phys. 70 ( 1988) 165; W. Nadler and R. Marcus, J. Chem. Phys. 86 ( 1987) 6982; Chem. Phys. Letters 144 ( 1988) 509; S. Rashev, Chem. Phys. 147 ( 1990) 22 1; W.J. Bullock, D.K. Adams and W.D. Lawrence, J. Chem. Phys. 93 ( 1990) 3085.

[ 131 P.M. Felker and A.H. Zewail, J. Chem. Phys. 82 (1985) 2961; ibid. 2975; ibid. 2994; ibid. 3003; P.M. Felker and A.H. Bewail, Advan. Chem. Phys. 70 (1988) 265. [ 141 L.R. Khundkar and A.H. Zewail, Ann. Rev. Phys. Chem. 4 1 ( 1990) 15; and references therein. [ 151 B.W. Keelan, unpublished work from this laboratory (D.H. Semmes, Ph.D. Thesis, California Institute of Technology, 1990). [ 161 E. Shalev and J. Jortner, Chem. Phys. Letters 178 ( 1991) 31. [ 171 P.M. Felker and A.H. Zewail, J. Chem. Phys. 86 ( 1987) 2460; P.M. Felker and A.H. Zewail, Advan. Chem. Phys. 70 (1988) 265. [ 181 G.E. Ewing, J. Phys. Chem. 90 ( 1986) 1790, and references therein. [ 19) M.J. Ondrechen, Z. Berkovitch-Yellin and J. Jortner, J. Am. Chem. Sot. 103 (1981) 6586. M.M. Doxtader, I.M. Gulis, S.A. Schwartz and M.R. Topp, Chem. Phys. Letters 112 ( 1984) 483; J. Wanna and E.R. Bernstein, J. Chem. Phys. 84 ( 1986) 927. [20] 1.1.Goldman and V.D. Krivchenkov, Problems in Quantum Mechanics ( Pergamon, London, 196 1). (2 1 ] B.N. Cyvin and S.J. Cyvin, J. Phys. Chem. 73 (1969) 1430. [22] L.R. Khundkar, R.A. Marcus and A.H. Zewail, J. Phys. Chem. 87 (1983) 2473; D.F. Kelley and E.R. Bernstein, J. Chem. Phys. 90 (1986) 5164. L.R. Khundkar, J.L. Knee and A.H. Zewail, J. Chem. Pdys. 87 (1987) 77. [23] D.M. Willberg, M. Gutmann, J.J. Breen and A.H. Zewail, to be submitted to J. Chem. Phys; see also J. Chem. Phys. 93 (1990) 9180.