7452
J . Phys. Chem. 1990, 94, 1452-1451
(or protonated anion radicals) seems thus to be a general occurrence deserving a special comment. We consider that a likely reason is a slow rate of exchange in process 3. Indeed, several studies i n d i ~ a t e ~ ~that v ~ ’the rate constant of process 3 could be as low as 3 X lo6 in nitrobenzene. Nevertheless, a low value of this rate constant could be still sufficient for destroying any nuclear polarization of the nitroaromatic moiety. The difference between (26) Meot-Ner. M.: Neta. P. J . Phvs. Chem. 1986. 90. 4648. (27j Leybff, T:; Miller, T.i Adam, R.N.; Fah, H.; Hokield, A.; Proctor, W. Narure 1965, 205, 382.
the two processes in their dependence on [M’-] is due to the fact that the decay of nuclear polarization is also governed by the very short spin-lattice relaxation time of the radical anion ( s; cf ref I I ) . For this reason nuclear polarization is much more sensitive than selective line broadening to the presence of nitroanion radicals. N
Acknowledgment. We thank Professors E. Lippert and Z. R. Grabowski for helpful discussions on the photochemistry of electron-donor-substituted nitroaromatics. Registry No. 4-Methoxynitrobenzene, 100-17-4; 4-ethoxynitrobenzene, 100-29-8; 4-propoxynitrobenzene, 7244-77- 1.
Ar,CI2 and At3C12: Structure, Bond Energy, and Dissociation Dynamics Craig R. Bieler, Dwight D. Evard; and Kenneth C. Janda* Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania I5260 (Received: March 27, 1990)
The structure, bond energy, and dissociation dynamics of the Ar2C12and Ar3CI2van der Waals molecules are studied by a laser pump-probe technique. Ar2CI2is found to be a distorted tetrahedron with an Ar2-CI2 distance of 3.9 0.5 A and an Ar-Ar bond distance of 4.1 f 0.6 A. For Ar3CI2there is evidence that two isomers exist. In the low-energy isomer, the three argon atoms form a triangle and the C12bonds with its axis parallel to the triangle. In the higher energy, 1 cm-I, isomer the argon atoms each bond perpendicular to the CI, axis. The total van der Waals bond energy is found to be 447.5 f 3.5 cm-’ for Ar2CI2in the ground electronic state and 776 f 3 cm-’ for Ar3Cl2in the ground electronic state. The chlorine fragment rotational-state population distribution produced by the vibrational predissociation of Ar2C12is found to be nearly statistical by surprisal analysis. The chlorine product-rotational-state distribution for the dissociation of the Ar3CI2complex can be described by a Boltzmann distribution.
*
Introduction Weakly bonded clusters serve as prototypical systems to study a variety of interesting chemical phenomena that bridge the detailed understanding of the gas phase and the much more qualitative characterization of liquids. For instance, computer simulation~’-~ have predicted the coexistence of liquid and solidlike phases in rather small clusters. Several experimental observations of phase coexistencec7 have been reported but are not completely unambiguous. Clusters also engage in interesting dynamical phenomena such as the evaporation of atoms upon photoexcitation. This process is expected to play an important role in the dissipation of excess energy and the cage effect. Although a one-atom cage effect was observed experimentally over a decade ago,* it has yet to be characterized in any detail. Theoretical treatmentg of this effect suggests that the rare gas atom induces a nonadiabatic electronic transition from a dissociative state of the halogen into the B state. The overall evaporation of larger clusters, however, has received considerable attention. For instance, photoexcitation of Ar,Br; and (CO2),BrTresults in highly specific fragmentation patterns that can be accurately predicted by statistical energy release modeis.10J’ It is our thesis that cluster phenomena should be studied in as much detail as possible for examples that are simple enough to yield a rather complete interpretation. We have chosen the rare gas-chlorine clusters as such a model system. The geometrical structures and bond energies of HeCI,, NeCI,, and ArClz have each been determined.12 For HeCI, and NeCI, the dissociation dynamics have been studied in enough detail to obtain a rather complete description of the potential energy surface. The prospect of being able to completely characterize the dynamics of such systems for which the potential energy surfaces are known provides a hope of complete theoretical characterization of the important couplings and energy disposal pathways. It seems likely that such ‘Present address: Spectra-Physics AG, Basel, Switzerland.
0022-3654/90/2094-7452!§02.50/0
detail can be provided for significantly larger clusters. Highresolution spectroscopy and pump-probe detection techniques allow for completely unambiguous assignment of cluster size and for determination of the structure and dynamics of the cluster as a function of size. Levy and colleagues13 were the first to discuss the possible structure of larger rare gas-halogen species. In their study of Ne,I, they observed a constant shift of the visible excitation band origin as a function of the number of N e atoms attached to the iodine. This constant shift was interpreted in terms of a structure in which each neon atom occupies an equivalent site on the iodine. The structures proposed were a “belt” structure in which the neon atoms surround the iodine on a plane perpendicular to the I, bond at the center of mass and an “ethanen structure in which three (1) (a) Berry, R. S.; Beck, T. L.; Davis, H. I.; Jellinek, J. In Euolufion of Size Effects in Chemical Dynamics; Prigogine, I., Rice, S. A,, Eds.; Advances in Chemical Physics; Wiley: New York, 1988; Vol. 70, Part 2, p 75. (b) Beck, T. L.; Berry, R. S. J . Chem. Phys. 1988, 88, 3910. (2) Eichenauer, D.; Le Roy, R. J. J . Chem. Phys. 1988,88, 2898. (3) Honeycutt, J. D.; Andersen, H. C. J . Phys. Chem. 1987, 91, 4950. (4) Leutwyler, S.; Jortner, J. J . Phys. Chem. 1987, 91, 5558. (5) BBsiger, J.: Knochenmuss, R.; Leutwyler, S.Phys. Reu. Lett. 1989,62, 3058. (6) (a) Even, U.; Ben-Horin, N.; Jortner, J. Phys. Reu. Lerr. 1989.62, 140. (b) Even, U.; Ben-Horin, N.; Jortner, J. Chem. Phys. Lerr. 1989, 156, 138. (7) (a) Hahn, M. Y.; Whetten, R. L. Phys. Reu. Lerr. 1988,61, 1190. (b)
Easter, D. C.; El-Shall, M. S.; Hahn, M. Y.; Whetten, R. L. Chem. Phys. Lerr. 1989, 157, 217. (8) Valentini, J. J.; Cross, J. B. J. Chem. Phys. 1982, 77, 572. (9) Beswick, J. A,; Monot, R.; Philippoz, J.-M.; van den Bergh, H. J . Chem. Phys. 1981, 86, 3965.
(10) Alexander, M. L.; Levinger, M. A.; Johnson, M. A.; Ray, D.; Lineberger, W. C. J . Chem. Phys. 1988,88, 6200. (11) Perera, L.; Amar, R. G. J . Chem. Phys. 1989, 90, 7354. ( 1 2) Janda, K. C.; Bie!er, C. R. In Afomic and Molecular Clusters; Bernstein, E. R., Ed.: ElseFier: Amsterdam, 1990 p 455. (13) Kenny, J. E.; Johnson, K. E.; Sharfin, W.; Levy, D. H. J . Chem. Phys. 1980, 72, 1109.
0 1990 American Chemical Society
Ar,CI, and Ar,CI,
1rhe Journal of Physical Chemisfry. Vol. 94. No. 19. 1990 7453
1
I
II
Two possible stmctum for the Ar,CI, van der Waals molecule. If the potential far this cluster is assumed to be given by three Ar-Ar potcntials2' plus three A ~ Y C I ~structure ?~ II is predicted to be I cm-' lower in energy than ~tmcture1. and the two isomers are separated by a 61-m.' barrier. Fiyre 1.
neon atoms attach to each iodine atom. They preferred the "belt" model on the basis of the T-shaped structure observed for Hel,." An illustration of the belt structure for a three rare gas atomchlorine cluster is shown in Figure 1 as structure I. Recent experiments have supported the belt structure model for rare gas-hydrogen clusters. Pump-probe studies of Ne2C1215 have shown that this cluster has a distorted tetrahedral configuration. Evidence for the production of Ne,CI, in the belt configuration was also reported. Calculations using simple atomatom potentials have supported a configuration analogous to structure I for Ne,CI,. However, there is a second local minimum on the potential energy surface, slightly higher in energy, in which the rare gas atoms form a triangle in a plane that is parallel to the CI, bond. Such a structure would therefore be favored if the rare gas-rare gas interaction were more significant. This triangular configuration is shown in Figure I as structure 11. In this paper we report a study ofthe structure and dynamics of Ar,CI, and Ar,CI,. With current experimental resolution the structure of Ar,CI, can be determined and that of Ar,CI, estimated. Ar,CI, is found to have a distorted tetrahedral structure similar to that of Ne,CI,. It appears that both isomers of the n = 3 cluster, as discussed above, can be produced. ,Additionally, the bond energy for each of these clusters can be determined. It is also shown that the addition of a second argon atom to ArCI, has a dramatic effect on the dissociation dynamics. ArCI, vibrationally predissociates with a highly specific product-state distribution that has k e n attributed to intramolecular vibrational relaxation, IVR, via specific intermediate resonances.I6 By comparison, Ar2CIz and Ar,CI, dissociate randomly, giving a uniform distribution of CI, product rotational levels.
Experimental Section The pump-probe scheme that was used to study ArZCl2and Ar,CI, has been described in detail elsewhere." The experiment can be summarized in four steps: Ar.CI,(X,u"=O) + h w , Ar.CI,(B,u') pump (1) Ar.Cl,(B,u?
-+ +- +
CIz(B,u'-zJ) CI,(E)
nAr
hw,
CI,(B)
C12(B.u'-~J)
vibr pred
CIz(E,uJ~I)
hwnuar
probe
detection
(2) (3) (4)
Two types of spectra are recorded by using this technique. First, cluster excitation spectra are recorded when hw, is positioned on a particular CI,(E-B) transition and h o l is scanned. Second, product-state distributions for the vibrational predissociation step are recorded by scanning hw,. In this study, all product-state distributions are recorded by setting the pump laser to the maximum of a particular Ar.CI, vibronic band. Spectral congestion due to the small rotational constants of the complex does not permit individual J . K states to be resolved. Two dye lasers, pumped by a single excimer laser, are utilized to provide the tunable pump and probe pulses. Both lasers have (14) Smalley, R. E.: Wharton. L.;Lcvy, D. H. 1. Chem. Phys. 1970.68,
". ..
19525
19535
Pump Energy/cm-'
- -
-
Figure 2. ArCI, and Ar2Cl2excitation spectra (R X. 9 0) observed by probing the CI, E E, 0 6 transition after the clusters disswiate. Thc Ar,CI, transition at 19 540 cm-' is blueshifted 10.5 cm-' from that of ArCI, at 19529 cm-I. f
a 0.2-cm-' bandwidth and 20-11s pulse duration. The beams are combined and travel collinearly through the vacuum apparatus. A delay of IO ns between the pump and probe pulses allows complete dissociation to occur before product states are detected. The molecular beam and vacuum apparatus has also been described in detail previously.I8 To make Ar,CI, and ArICIz, a mixture of 5% Ar/95% He seeded with CI, held at -77 "C was expanded through a 150-pm pulsed valve aperture at 25-30-bar backing pressure. Results Structure. Information about the structure of Ar,CI, and Ar3CI, is obtained from the excitation spectra. In analyzing these spectra, the first task is to assign each band to a specific cluster. Four types of evidence are used for such assignments. First, the band shift rulet9is used to estimate the position of a band for each cluster size with respect to the position of the analogous band of the free molecule. Second, the final vibrational level of the CI, after complete dissociation gives limits for the amount of energy needed to dissociate the molecule. The dissociation energy can then be used to estimate the number of rare gas atoms removed from the cluster. Third, the qualitative dependence of the intensity of each band on the nozzle backing pressure helps to identify the van der Waals species. Finally, as in the case of Ar,CI,, the band shape can be fitted and shown to be consistent with a particular mass distribution in the cluster. An ArCI, band has been previously observedz0 to occur 10.5 cm-' to the blue of the free CI, B-X,9--0 transition. Application of the band shift rule predicts an Ar,CI, band 5 2 1 cm-l to the blue of the free CI, transition, Estimating the Ar,CI, bonding energy to be 2D0(ArClz) Do(Ar-Ar) suggests that three quanta of CI, stretch must be transferred to the van der Waals degrees of freedom to dissociate the Ar,CI, complex. The spectrum observed when CI,(B,u=6) is probed while the excitation laser is scanned in the region ofthe CI,(B-X,9--0) transition is shown in Figure 2. The ArCI, feature is shifted by 10.5 cm-' to the blue of the CI, band, and Ar2CI, is shifted 10.5 cm-' from the ArCI, peak. Although 595% of the ArCI, molecules excited to this vibrational level dissociate via the Au = -2 channel, the integrated intensities of the ArCI, and Ar,CI, Au = -3 peaks are nearly equal. The feature midway between these two transitions has not been assigned but is probably due to ArHeCI,. Although the ArZCl2band is not clearly resolved, fitting the contour can be performed to place limits on the structure of the complex. As a first estimate. it seems appropriate to assume a tetrahedral structure as would result from atom-atom additive forces and which has been shown to be appropriate for Ne,CI,.'5 The spectrum shown in Figure 3 was calculated assuming that
+
67 I
(IS) Hair. S. R.; Cline. J. 1.; Bider, C. R.: Janda. K. C. 1. Chem. Phys. 1989. 90,2935. ( I 6) Evard. D. D.: Rieler. C. R.: Cline. 1. 1.: Sivakumar. N.:Janda, K. C. J. Chcm. Phys. 1989.89.2829. (17) Cline. J. 1.: Sivakumar, N.;Evard, D. D.: Bider. C. R.: Reid, R. P.; Halberrtadt. N.: Hair. S. R.; Janda. K. C. J . Chem. Phys. 1989. 90, 2605.
(18) Rrinia. D E : Wcs1cm.C. M.. Evard. D. D.Thommcn. F:Svartz. R A ; Janda. K. C J. Phyr. ('hem 1984.88, 2004 (191 Shxfin. W.: Johnson. K. E ,W h m o n . 1:Levy D H J Chem. Phyr.
.,I,.
,070
I,
I,O, ~ , - . ~
(20) Evard. D. D.: Cline. 1. I.;
Janda. K. C. J. Chcm. Phys. 1908.88,5433.
7454
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990
Bieler et al.
(a)
19535
19537.5
, I " " I " " l " 19850 19851 19852
19540
Pump Enercjy/cm-'
" l
19853
19854
Pump Energy/&'
Figure 3. Experimental (dots) and calculated (line) spectra for the Ar2CI2(B+-X,94) transition observed while probing Cl2(EcB,0+6). The structure assumed for the calculated spectrum is described in the text.
i
-,
'
l " " l " " l " " I
I
19850 19851
19852
19853
19854
Pump Energy/cm-' 19850
19853
19856
PuMp Energy/cm-'
-
Figure 4. Excitation spectra of Ar3Cl2(B+X,I 1 4 ) observed with the probe laser positioned on the C12 E B, 0 6 transition. Peak a is
Figure 5. Comparison of peak a from Figure 4 to calculated spectra (solid lines) determined by assuming specific geometries for Ar3CI2. Trace a is calculated by using structure 11. Trace b is calculated by using structure I. The experimental spectrum is the dotted line.
+
blue-shifted 9.4 cm-l from the Ar2CI2transition while peak b is shifted 13.0 cm-l.
Ar2C12has a rigid tetrahedral structure which can be described as an Ar-Ar dimer, Ro = 4.1 f 0.6 A, attached perpendicular to the CI2 axis with the Ar-Ar and Clz centers of mass separated by 3.9 f 0.5 A. The calculated spectrum uses a rotational temperature of 1.6 K and a homogeneous line width of 0.05 cm-l in addition to the laser line width of 0.2 cm-l. As was the case for Ne2C1,, no other rigid structure with reasonable bond lengths could reproduce the observed spectrum. Reasoning analogous to that used for Ar2C12predicts that to observe spectra associated with Ar3Cl2,one must detect a Av = -5 dissociation channel. Scanning the excitation laser past the CI,(B+X,I 1-0) transition while probing C12(B,u=6) produces a spectrum, shown in Figure 4, with two features approximately (a) 9.4 and (b) 13.0 cm-' to the blue of the analogous Ar2CI2band. The values of the blue shifts for ArClz and Ar,CIz for this C12 vibrational level are each about 12 cm-l per argon. The pressure dependence of these features is not the same: a decrease in the nozzle backing pressure decreased the integrated intensity of peak a faster than that of peak b. Fitting the Ar3C12spectra is less useful than for Ar2CI, at the present level of resolution. However, calculations can be performed to estimate a likely structure for the species. Model intramolecular potential calculations based on atom-atom (Ar-Ar)Z' and atommolecule (Ar-C12)22potentials were used to maximize the total van der Waals attraction. By use of a grid search method, two minima were observed on this multidimensional potential surface as discussed in the introduction and illustrated in Figure I . Structure 11, with a triangular argon configuration is found to have a slightly lower, -1 cm-', well depth than structure I, the "belt" isomer. There is a substantial barrier, 67 cm-I, between the two configurations. (21) Aziz, R. A.; Chen, H. H. J . Chem. Phys. 1977, 67, 5719. (22) Reid, B. P.; Janda, K. C.; Halberstadt, N . J . Phys. Chem. 1988. 92, 587. The actual Ar-C12 potential used is slightly modified from the one in this reference to agree with more recent experimental data.
38650
38660
38670
38680
Probe Energy/cm-' Figure 6. Fragment C12 spectrum observed after exciting Ar,CI,(B+ X , l l c O ) and probing C12(E+B,0c6). The arrow marks the highest strongly observed rotational line, j = 22. Significant extra signal averaging was employed to record the high-j data shown above the overall
spectrum. The structures estimated from the potential energy calculation were used to calculate band shapes for the excitation spectra. The band calculated for structure I1 is quite similar to the experimentally observed peak a as seen in Figure Sa. The spectrum calculated by using the belt model, structure I, shown in Figure 5b, is quite different from that of the peak a band shape. Neither structure can be adjusted to fit band b. Thus, the results for Ar3CI2 are somewhat ambiguous. The band shift rule suggests that peak b should be assigned to Ar3CI2 while band shape analysis suggests that peak a corresponds to this cluster. We propose that peak a corresponds to structure I1 while peak b corresponds to structure I. Although evidence from the excitation spectra for this hypothesis is not conclusive, further evidence that two isomers have been observed for the cluster comes from product-state distributions described below. Bond Energy. Product-rotational-state distributions in combination with conservation of energy constraints can be used to determine the total van der Waals bond energy of a complex. These energies can be determined by noting the maximum rota-
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 7455
Ar2CI2and Ar3C12
j=10
38540
38550
+
I !
38560
38570
Probe Energy/%’ Figure 7. Fragment CI, spectrum observed after exciting Ar2CI2(B+ X,llCO) and probing C12(EtB,l+8). The arrows mark the highest strongly observed rotational lines for the two possible dissociation channels: j = 10 for complete dissociation and j = 22 for dissociation to an Ar2 product. As in Figure 6, extra signal averaging was used for the high-j portion of the spectrum.
tional level obtained upon dissociation of a complex via loss of a specific number of C12 vibrational quanta. Rotational distributions of the CI2 product produced by vibrational predissociation have been recorded for Ar2C12(B,u’=1 1,Au=-3), ArC12(B,u’= 9,pO=-3), and Ar3CI2(B,u’=1l,h=-5). From these three studies, van der Waals bond energies for the clusters can be estimated as described by Cline et al.I7 For example, Figure 6 shows the product distribution observed when Ar2CI2dissociates by Au = -3 from the u ’ = 9 level. It is apparent from the spectrum that there is not a sufficient amount of kinetic energy remaining after the dissociation to produce CI2rotational levels above j = 22. The dissociation energy and the j = 22 rotational energy must equal the energy lost from the CI2 vibration during the dissociation (Au = -3). Therefore, one can calculate that the sum of the van der Waals energies in Ar2C12(B,u’=9)is 447.5 f 3.5 cm-l. The bond energy of Ar2C12in the ground state, Do(X),is found to be 468.5 f 3.5 cm-l by adding the Ar2C12blue shift of 21 cm-l to the B-state value. A similar spectrum for Ar2C12(B,u’=1 1,Au=-3) is shown in Figure 7. In this case, it is observed that the distribution has an intense initial rotational distribution extending to j = 10 with a less intense tail out to j = 22. We believe that these two distributions correspond to the two possible dissociation channels: Ar2CI2(B,u’=l 1) -.2Ar + C12(B,u=8) (5) Ar2C12(B,u’=l 1) -.Ar2
+ C12(B,u=8)
(6) Although one might expect reaction 5 to be the more likely mechanism, reaction 6 may also occur. Reaction 6 can release more kinetic energy to the product degrees of freedom because no energy needs to be used to break the Ar-Ar bond. If energy limitations produce a cutoff at j = 10 for reaction 5, this implies a total cluster bond energy of 441.5 f 1.5 cm-’ in the B state and 466.5 f 1.5 cm-’ in the X state. This is in reasonable accord with the u ’ = 9 data. For reaction 6, the maximum allowed value of j appears to be j = 22. This is consistent with an Ar2-CI2 bond energy of 385.5 f 3.5 cm-I in the B state and 410.5 f 3.5 cm-l in the ground state. Also, the data then imply an Ar-Ar bond energy of about 56 cm-l, compared to 85 cm-’ of free Ar2.23 The low estimate obtained for the Ar-Ar bond energy may indicate that the Ar2 dissociation product is usually vibrationally excited so that the highest possible C12 product j state for reaction 6 is not actually observed. Expected values for the van der Waals bond energy of these clusters can be calculated by assuming a bond-bond additive model for cluster bonding. The Ar-CI2 bond energy in the X state is 188 cm-Is2OThe Ar-Ar bond energy is 85 In the simplest approximation the total van der Waals bond energy would be calculated as Do = 2Do(Ar-Cl,) + Do(Ar-Ar) = 461 cm-I. Similarly, the dissociation to an Ar2 product would require 376 (23) Colburn, E. A.; Douglas, A.
E.J . Chem. Phys. 1976, 65, 1741.
38645
38665
Probe Energy/&’ Figure 8. Fragment C12 spectrum observed after exciting Ar,CI,(BX , l l d ) peak a and probing CI2(E+B,Oc6). The arrow marks the highest strongly observed rotational line, j = 22. The peaks to the red of the j = 22 transition are believed to be due to double-resonance transitions of clusters.
cm-’ of energy [Do= 2Do(Ar-C12) = 376 cm-I]. These values are quite close to those obtained experimentally. Figure 8 shows the C12(B,u=6) rotational distribution produced by the dissociation of Ar3C12(B,u’=1 l ) , reached by exciting via band a of Figure 4. The highest observed rotational level is again j = 22. This is consistent with a complete van der Waals dissociation energy in the B state of 742 f 3 cm-I and Do(X) = 776 f 3 cm-l. This is strong evidence for our assignment of this transition to Ar3CI2since D o ( X ) = 3Do(Ar-C12) 3Do(Ar-Ar) = 8 19 cm-l. If peak a were due to Ar2HeC12,significantly higher product C12 rotational states should be observed. The product-state distribution observed upon exciting via peak b of Figure 4 is quite similar to that observed upon exciting via peak a except that the signal-to-noise ratio is less and no clear cutoff is observed at j = 22. Since no higher j levels are observed, however, the total bonding energy of the cluster that gives rise to peak b is on the order of 750 cm-I. This is consistent with the assignment as due to an isomer of Ar3CI2. Dynamics. In addition to bond energy measurements, the product-state distributions also provide insight into the dynamical aspects of the cluster dissociation. It was observed that there is a strong propensity for Ar2C12and Ar3C12to dissociate via the first available vibrational channel. Rigid Au propensity rules are also observed for ArC12,16but not for HeC1*4 and NeCI2.l7 The rotational distributions observed for ArCI2 and Ar3CI2are quite smooth, while those of ArC12 were highly structured. A smooth product-state distribution is a first sign that the dynamics of the dissociation may be “statistical”. To test this assumption more quantitatively, a surprisal analysis of the product rotational distribution was performed. Surprisal analysis is a method by which one can compare the experimental distribution to that of a calculated, “statistical” distribution (termed the prior). The prior distribution is calculated assuming that all final quantum states are equally probable and is formed by calculating the density of final rotational and translational statesZ5
+
POW 0: W + I)[Eavaii - EmO’)12 This rotational prior is calculated assuming only conservation of energy constraints. The surprisal is a measure of the deviation of the experimental distribution from the prior I = -In ( P I P ” ) Figure 9 shows both the experimental (P)and prior distributions ( P ” ) (lower plot) and the surprisal (upper plot) as a function of the reduced rotational energy, g, for the Ar2C12(B,u’=9,Au=-3) dissociation. E,,,,, was taken to be 77 cm-I. The plot of the surprisal as a function of g can be characterized by a straight line (24) Cline, J. 1.; Reid, B. P.; Evard, D. D.; Sivakumar, N.; Halberstadt, N.; Janda, K. C. J . Chem. Phys. 1988, 89, 3535. (25) (a) Kafri, A.; Levine, R. D. J . Chem. Phys. 1976,64,5320. (b) Kafri, A. Chem. Phys. 1976, 13, 309.
7456 The Journal of Physical Chemistry, Vol. 94, No. 19, 1990
Bieler et al. 1
1
er = -4.9
-L I
!I
I
a
2
I
I
13549
‘9546 n
Pump Enersy/crr-’
s
a6
Figure 11. Calculated spectrum of Ar2C12assuming the structural parameters mentioned in the text and an instrumental line width of 0.001 cm-’ and a homogeneous line width of 0.01 cm-I.
8 0
0.3
0.6
0.9
9 Figure 9. Rotational surprisal analysis of the dissociation product-state distribution of ArzCl2(B,u’=9,Au=-3). The lower plot shows the prior distribution (solid circtes) and the experimental distribution (open circles) as a function of relative rotational energy, g. The upper plot shows the rotational surprisal as a function of g. The line is a best fit to the
calculated surprisal.
\
u
(n = 1-5),,’ as well as for other rare gases and mixed rare gas combinations. Known structures of a few of these complexes support the belt model for the binding of these higher order clusters. Ar2C12and NeZCl2l5are two such complexes. Although the accuracy with which the structure for the argon complex is determined is not as good as that for NeZCl2,many similarities exist between the two clusters. Both clusters have a distorted tetrahedron structure as would be predicted both by the belt model and from additive atom-atom interactions. The Ar-Ar distance in the complex, 4.1 A, is somewhat larger than the accepted distance associated with the argon dimer,233.8 A. For NezC1 , the Ne-Ne experimental distance is 3.23 8,compared to 3.1 1 8, in the neon dimer. The Ar-Cl, bond distance in ArZCl2is 4.4 A, larger than the value found in ArC1z,203.7 A. However, the Ne-CI, distances in Ne2C12were the same, within experimental error, as that found in NeCl, (3.54 A). These deviations from bond-bond additivity for Ar2C12 are large enough that higher resolution spectra should be obtained to confirm (or correct if necessary) the above analysis. To illustrate the resolution needed for such a study, Figure 11 shows a calculated spectrum for the Ar2CI2B X, 6 0 transition, using the bond lengths reported above and assuming at least O.OO1-cm-l resolution. For this transition the cluster lifetime may be long enough, -0.5 ns, for a resolved spectrum to be recorded and compared with the assumption of atom-atom additivity. Only one deviation from the constant band shift rule has previously been reported for rare gas-halogens. The average shift for Ne,12 (n = 1-6) is 6.7 cm-I whereas the shift for Ne712is only 6.06 cm-l. Kenney et al.” suggest that it takes six neons to fill the first-coordination shell (six equivalent positions) and the seventh atom must add to a nonequivalent site outside of this initial shell. Apparently, a somewhat similar situation occurs for Ar3CI2 in that the band shift is less than expected, indicating that the third argon atom does not affect the CI-Cl bond as strongly as the other two argons. In this case, however, the equatorial positions are not all occupied before the rule breaks down. Instead, the structure deviates from the belt model in order to form a third Ar-Ar bond. This is supported by the calculations discussed above to find the minimum of the van der Waals potential assuming atomatom additivity and the anisotropic Ar-Cl2 potential of ref 22. The Ar3C12potential predicts that displacing an Ar from the “belt” to form a third Ar-Ar bond results in a I-cm-’ stabilization. Of course, zero-point dynamics and possible errors in the assumed anisotropy are both large enough that this prediction can only be used qualitatively. The large barrier predicted between the two isomers strongly suggests that both should be observed. Although the spectrum-fitting procedure does not conclusively prove that the Ar3CI2peak (b) corresponds to structure I, there are several reasons to believe that it does. First, the observed blue shift is similar to what one would expect for equivalent binding sites. Second, the pressure studies indicate that peak b decreases
- -
0
0 2 4
6 8 1 0 12 14 16 18 20 22
Fragment C\ Rotational State, j Figure 10. Fragment CI, rotational distribution for Ar,CI,(B,u’= 1 l,Au=-5). The experimental distribution is plotted as solid circles. The
open circles are a calculated Boltzmann distribution with a characteristic temperature of 45 K (31 cm-I). with slope equal to -4.9. The observed slope of the surprisal indicates there is a greater amount of rotational excitation in the experimental distribution than that predicted by the prior. The CI2rotational-state population distribution obtained by the dissociation of Ar3C12(B,u’= 1 I,Au=-5) can be rather well described by a Boltzmann distribution. In Figure 10 the experimental distribution is compared to a Boltzmann distribution with a temperature of 45 K, which corresponds to a mean rotational energy of 3 1 cm-I. Since the total product kinetic energy is 76.6 cm-I, the fraction that on average goes into Clz rotation is 0.4. This is again higher than would be predicted by equipartition, indicating that the Ar atoms leave the cluster with lower velocities than would be ‘statistical”.
Discussion Structure. The band shift ruleLghas traditionally been used to determine cluster identity and size for many rare gas-halogen systems. It has been accepted that the shifts per rare gas atom for He, Ne, and Ar are approximately 3.5, 5.5, and 11 cm-I, respectively. Additional rare gas atoms added to the cluster shift the observed bands further to the blue by a constant amount for each atom. This has often been interpreted to imply that the atoms bind to equivalent sites in the cluster, and each perturbs the Cl-Cl interaction in the same way. The “constant band shift” rule has been observed for Ne,12 (n = 1-6),13 Ne,Brz (n = 1-4),26 Ne,CI2 ( n = 1-3),15 and Ne,ICI
( 2 6 ) Swartz. B. A.; Brinza, D. E.; Western, C. M.; Janda, K.C . J . Phys. Chem. 1984, 88, 6212. ( 2 7 ) Drobits. J. C.; Lester, M. 1. J . Chem. Phys. 1987, 86, 1662.
Ar2C12and Ar3CI2 in intensity more slowly than that of peak a as the pressure is lowered. Since structure I is calculated to have a slightly higher potential energy than the triangle structure, a higher beam temperature would shift intensity from structure I1 to structure I. Leutwyler and co-workers4 have performed model calculations of potential surfaces for Ar clusters on large organic molecules. For such clusters, several geometrical isomers are found a few wavenumbers above the minimum-energy configuration. By increasing the temperature of the cluster, a fluxional condition between the isomers is produced which broadens the observed s p e c t r ~ m .Perhaps ~ if the signal-to-noise ratio of our experiments can be increased allowing higher beam temperatures to be studied, peaks a and b would be seen to coalesce. If so, the dynamics of isomerization could be directly studied. The possibility that peak b is due to different clusters must be considered. The shift of peak b from peak a (Ar3C12,structure 11) is =3.6 cm-I, about that which one would associate with the addition of a helium atom to the complex (HeAr3Clz). However, the fact that this peak’s intensity decreases more slowly than does peak a as the source pressure is lowered does not support this assignment. To create a larger cluster more collisions must occur, a condition which happens at higher pressures. Another hypothetical assignment would be to an excited van der Waals vibrational mode of Ar2C12or ArC12 which happens to lie in this region. This possibility is excluded because the AD = -5 dissociation channel is not observed for either of these clusters in the ground van der Waals vibrational levels and would, therefore, be unlikely to occur for a higher vibrational level. Finally, the feature could be attributed to a hot band of the Ar3CI, cluster. The pressure dependence is roughly consistent with this hypothesis. It is unlikely, however, that the shape of the feature would change significantly from that of the ground van der Waals state’s feature unless vibrationally averaged atomic positions are quite different in the vibrationally excited state. This would correspond to a “dynamical isomerization”. Bond Energy. More support for the identity of the larger clusters is found when one investigates the bond energies of the Ar,,Cl2 complexes in the X state. The T-shaped ArClz has a bond energy of 188 cm-’.20 Ar2C12is determined to have a distorted tetrahedral configuration and an experimental bond energy of 467 cm-I. Both of these discoveries are consistent with a bond-bond additivity model in which the van der Waals attractions are simply added together. For Ar3CI2,both experiment and calculations support that the atom-atom additivity of potentials is useful in determining the structure of clusters. Using bond-bond additivity does not perfectly describe the experimental value of the bond energy, but this can be explained by the weakened bond between the off-equatorial argon and the C12. Given this structure, one would expect the calculated bond energy to be too large. Determination of the bond energy of a large cluster is complicated by the many reaction channels available to the complex. This is evidenced in Figure 7 for Ar2CI2. Excitation to u’ = 1 1 in the B state is the last open Au = -3 channel, and only a few rotational states are available for dissociation. At this point a second reaction channel (reaction 6) becomes nearly as important as the complete dissociation. This problem is not encountered in Ar2Clz(u’=9) or Ar3Cl2(u’= 11) because of the large range of rotational levels available for dissociation. Reaction 6 leaves the Ar-Ar bond intact, allowing a greater amount of energy to go into C12 rotation. Cutoff for this channel appears to be CI2(B, u = 8 j = 2 2 ) , producing a bond energy measurement of 410 cm-l. This compares to the calculated bond-bond additive value of 376 cm-I. The difference can be rationalized by noting that the bond energy calculated from experiment assumes that the Ar2 product is in the ground vibrational and rotational state. Perhaps this assumption is unrealistic and the “missing” energy is stored in the Ar2 vibrational degree of freedom. Dynamics. The availability of more reaction channels and the increased number of available vibrational modes in the larger clusters suggest that the dissociation of such species could take on statistical properties. In comparing the cases of Ar2CI2and Ar3CI2to that of ArCI2,l6we can already see a distinct difference
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 7451 in the dynamics of the reaction. ArC12 dissociations produce C12 vibrational distributions primarily in the first available open channel. Similarly, it was found that the reported reaction channels in the larger clusters were the only ones with significant population. In the rotational manifold, one finds the ArCI, dissociation to produce very complicated population distributions with a few rotational levels seemingly preferred in the dissociation. This observation has been used to predict that IVR is important in this dissociation. On the other hand, the Ar2C12and Ar3CI2 product rotational distributions vary smoothly with j , indicating that a greater amount of energy mixing is involved in the dissociation. Surprisal analysis of the Ar2Clzdissociation product rotational distributions shows very nearly linear behavior in the surprisal versus rotational energy plots, as had been previously observed for the Ne2CI2 dissociati~n.’~These results suggest that the distributions are statistical in nature within the rotational manifold. The slopes of the surprisal plots are positive for NqCl2 but negative for Ar2C12. A positive slope indicates that less energy has entered the rotational manifold than predicted by the prior. This was attributed to the fact that the prior distribution ignores angular momentum constraints on the dynamics. The negative slope observed for Ar2Clzindicates more rotational excitation is observed than predicted by the prior. That is, the Ar atoms carry away less translational energy than expected. This may be due to the fact that the prior ignores alternate dissociation mechanisms such as reaction 6. Alternatively, if the first Ar atom departs before the Clz vibrational energy is relaxed, it might be expected to carry away only a small amount of translational energy. It would be expected that as the clusters get larger the dynamics will become more “statistical”. Indeed, for dissociation of Ar3C12 the ClZproduct rotational distribution is well-characterized by a Boltzmann distribution with a temperature of 45 K. It may be possible to use this temperature to determine the energy available to the dissociation products so that a van der Waals bond energy can be calculated. Waller et aLZ8have described a microcanonical model for the photofragmentation of Fe(CO)S which may be useful in this situation. It is quite interesting that only increasing the cluster size from one rare gas atom to three spans such a wide range of dissociation dynamics, going from highly state specific for ArCI, to nearly statistical distributions for the Ar3CI2rotational and translational degrees of freedom. Even for Ar3C12,however, the C12vibrational degree of freedom follows a rather rigid propensity rule of dissociating via the highest energy open vibrational channel. Only when the vibrational distribution becomes statistical can the dissociation be said to have reached the statistical limit. The point at which this occurs can only be determined by further experimental studies on larger clusters.
Summary Excitation spectra and fragment CIz distributions have been measured for Ar2CI2and Ar3CI2. Ar2CI2is found to be a distorted tetrahedron with van der Waals bond distances similar to those found in ArC12 and Ar2. The bond energy for Ar2C12is experimentally determined as 468.5 cm-’ in the X state. This value is slightly higher than the value calculated by assuming bond-bond additivity. Two excitation peaks are observed in the spectral region expected for Ar3C12. Arguments were presented that suggest that the first peak is Ar3CI2,which has a structure formed of a triangle of argons positioned above the chlorine molecule. The second peak is believed to be Ar3CI2,which is in the belt configuration. Bond energy measurements for the first Ar3C12peak determine the bond energy to be 776 cm-l in the X state. Surprisal analysis of the rotational distribution of Ar2Cl2(B,u’=9) was found to produce a straight line with slope equal to -4.9. The rotational distribution for Ar3C12(B,u’=11) was fit to a Boltzmann distribution with a temperature of 45 K. The increase in the statistical nature of the rotational distributions suggests that as the size of the cluster increases we are beginning to approach the statistical limit. (28) Waller, I. M.; Hepburn, J. W. J . Chem. Phys. 1988,88, 6658.
