2545
J . Phys. Chem. 1987, 91, 2545-2550
Product Vibrational State Distributions In the Photodissociatlon of Iodine-Rare Gas Clusters J. M. Philippoz, H. van den Bergh,* and R. Monot Laboratoire de Chimie Technique, and Institut de Physique Experimentale, Ecole Polytechnique FZdZraIe de Lausanne, IO15 Lausanne, Switzerland (Received: June 17, 1986)
The photodissociation of I,M van der Waals clusters is studied at several wavelengths above the B state dissociation limit with M = Ne, Ar, Kr, and Xe. The I, product vibrational state distributions are obtained by measuring the dispersed B X fluorescence and analyzing the resulting spectra. Excitation aboue the B state dissociation limit leads to significantly different reaction dynamics compared to excitation of the bound levels of the B state studied previously. Among others the recoil energies of the I, and M fragments are much larger, and the distributions of rovibrational states in the I2 product are much wider in the present experiments. The relative translational energy in the I,* and M photodissociation products is found to be significantly larger than predicted by recent quasi-classical trajectory calculations.
-
Introduction The photodissociation of free molecular iodine in a dilute gas above the dissociation limit of the B state leads to the production of atoms with a quantum yield of unity.’ Clustering of I2 with a n inert gas (M) may hinder the photodissociation and induce processes like IzM
hu
+ + kinetic energy
12(B3110+u)v.,p M
(1)
Reactions such as ( I ) may play a role in the ”solvent cage effect”, where the photodissociationof iodine is also a choice model system., The formation of an electronically excited product which fluoresces, as is the case in reaction 1, allows in principle for the determination of the rovibrational population distributions of the Iz B state molecules. Early reports of such measurements include unevaluated fluorescence data observed in the 12Ar dissociation at 488 nm3 and preliminary results on the photodissociation of 12He, I,Ne, and 12Ar at 496.5, 488, and 476.5 nm.4 In the present work we report on new and improved measurements of product vibrational state distributions obtained a t several photodissociation wavelengths for 12Ne, 12Ar, 12Kr, and 12Xe. The results are compared with quasiclassical trajectory calculation^.^ The present results are consistent with those of ref 4 and 6 in the case of 12Ar,I&, and 12Xe. New measurements on I2 in H e and I, in N e showed that some of the data reported previously on these systems were probably to a large extent due to clusters containing two iodine molecules. Measurements at higher dispersion yielding rotational state distributions, and measurements of 12M in which M is a polyatomic gas, have also been done, and these are presented el~ewhere.~,’
Experimental Section A schematic diagram of the experimental setup is shown in Figure 1. The supersonic free jet is generated by expanding a mixture of iodine and rare gas through a sonic nozzle. The iodine partial pressure is controlled by flowing the rare gas, prior to expansion, through a variable-temperature oven (302 < T < 343 K) containing solid iodine. The temperature of the nozzle could be controlled independently and was always kept well above the iodine oven temperature to prevent clogging. The vacuum (1) Burde, D. H.; McFarlane, R. A.; Wiesenfeld, J. R. Phys. Reu. A 1974, 10,
1917.
(2) van den Bergh, H. Mol. Phys., to be published. (3) Valentini, J. J.; Cross, J. B. J . Chem. Phys. 1982, 77, 572. (4) Philippz, J.-M.; Calpini, 8.; Monot, R.; van den Bergh, H. Helu. Phys. Acta 1985, 58, 875. ( 5 ) Noorbatcha, I.; Raff, L. M.; Thompson, D. L. J . Chem. Phys. 1984, 81, 5658. ( 6 ) Philippoz, J.-M.; Monot, R.; van den Bergh, H. Hela Phys. Acta 1986, 59, 1089.
(7) Philippoz, J.-M.; Monot, R.; van den Bergh, H. to be submitted for publication.
0022-3654/87/2091-2545$01.50/0
chamber is pumped by a baffled 1000 L s-* oil diffusion pump. The 12M complexes are excited 4-mm (or more) downstream from the nozzle exit by a line-selected unfocussed argon ion laser. The free jet is placed inside the laser cavity because of the much higher power levels available, and the output coupler is replaced by a “100%” reflector. This reflector is placed in a sidearm of the vacuum chamber to avoid the use of a fourth Brewster window in the cavity. The latter was found to reduce intracavity power by more than 30%. The intracavity power is monitored by the very small fraction of light passing through the “100%”reflector with a photodiode. Intracavity powers in excess of 20 W were used at 488 nm for instance in a laser which normally gives 2 W on this line outside the cavity. The laser beam diameter ( l/ez) is 1.5 mm. The fluorescence is collected at right angles to both the laser beam and the free jet and is imaged on the entrance slit of a f = 1 m monochromator by using either a lens system and/or a 1-cm-diameter P M M A bar with optically polished ends which functions as a light guide. In laboratory coordinates the laser beam is horizontal and the monochromator slit and the free jet are both vertical (see Appendix). The effectively observed region is a narrow rectangle of about 4 mm high (Le. along the jet axis) and with a small width of typically 200 pm which depends on the slit width chosen. Using a grating with 2400 grooves mm-l the maximum resolution obtained with 10-hm slits is 70 m k The photomultiplier tube is cooled to 220 K and has a dark current of 2 c/s. All metal surfaces inside the vacuum chamber were blackened to reduce scattered light. The photomultiplier signal was preamplified, discriminated, and fed into a single-photoncounting system. The angle of the grating is continuously advanced by a synchronous motor, and at fixed time intervals the photon-counting signal is read into a new channel on the multichannel analyzer.
Results and Discussion The Spectra. Figure 2 shows typical vibrationally resolved fluorescence spectra of 12(B3rb+Jformed in the photodissociation of 12Xeat the different excitation wavelengths: 496.5,488, and 476.5 nm. These wavelengths correspond to excitation of the order of 70,400, and 900 cm-’ above the B state dissociation threshold. Clearly a blue shift can be seen in the emission spectra as more energetic photons are used to photodissociate the I,Xe complexes, indicating that, on the whole, higher vibrational levels v f in the B state of the I2 product are being populated. One observes a clean band progression on the blue side of these spectra, whereas some congestion is observed toward the red. The latter is due to the higher probability in this region for transitions u’ u” with u f f > 1. Emission to vibrationally excited levels of the electronic ground state as high as v“ = 5 is observed. It is essential to establish that the “raw data” such as shown in Figure 2 are independent of certain experimental parameters.
-
0 1987 American Chemical Societv
2546 The Journal of Physical Chemistry, Vol. 91, No. 10, 1987
Philippoz et al.
,
TO PUMP
Figure 1. A schematic diagram of the apparatus. The free jet is intracavity in the line tunable argon ion laser. Fluorescence is collected at
right angles to the laser beam and the free jet Only three intracavity Brewster angle windows are used. A,,,=496 5nm
1
-
Figure 3. The relative fluorescence intensity observed in the photodissociation of 1,Ar on the v’= 41 up’ = 0 transition as a function of the laser power. The excitation wavelength is 488 nm. The oven temperature is 31 3 K; the nozzle temperature (To)is 321 K. The argon pressure (Po) is 1.3 bar. 500
510
520
530
540
550
560
570
* Alnm
where po is the stagnation density, y = Cp/Cu,and M, is also given by9
Ae,,=488.0nm I
500
510
520
530
540
550
560
570
-
Alnm
Ae,,-476 5 n m
500
510
520
530
540
550
560
570
Alnm
Figure 2. Vibrationally resolved fluorescence spectra of 12(B3110+J formed in the photodissociation of 12Xeat 496.5, 488, and 476.5 nm. Po(12)= 0.63 mbar, Po(Xe) = 0.22 bar, To = 310 K. More energetic photons cause a blue shift in the spectral distribution indicating the population of higher vibrational levels in the I, product.
Hence it was established that the relative intensities of the observed bands are unchanged when we irradiate 8-mm rather than the usual 4-mm downstream from the nozzle (i.e. at lower pressure), or when we increase the background pressure in the apparatus. These experiments rule out possible collisional perturbations of the initial distribution prior to fluorescence, as well as the possibility of fluorescence arising from atom recombination into electronically excited states.s These observations are also supported by the calculated density in the free jet in the excitation region which is obtained from9
-_
(8) Stephan-Rossbach, K.-H.; Comes, F. J. Chem. Phys. 1983, 80, 121.
Here D is the diameter of the nozzle and xo may be taken to be approximately as the point of origin of the streamlines of the jet, and A is a tabulated constant9 which depends on y. It has been shownt0that despite the rapid freezing of relaxation in the jet (Le. transition from the continuous to the molecular flow regime) eq 2 is still applicable with Mach numbers calculated from eq 3. For a typical case of argon at a stagnation pressure of 1 bar, with a 50-pm-diameter nozzle, y = ’I3, xo/D = 0.075, and A = 3.26, we obtain at 4 mm downstream from the nozzle (Le. x / D = 80) p = 5 X lOI4~ m - The ~ . Mach number calculated at this location from eq 3 ( M = 59.4) is much higher than the terminal Mach number obtained by9 MT = 1.17Kn0+.~= 14.8; this confirms that x / D = 80 is, as expected, in the molecular flow regime. The local pressure and temperature are calculated to be 2.1 X 10“ mbar and 4.7 K, giving an Ar-Ar collision frequency of about 4 X lo3 s-’ in the “soft-sphere model” (with Lennard-Jones potential parameters from ref 1 1). Rotationally resolved measurements of free I t excited to a bound level of the B state by using a tunable dye laser indicate ”Tr,,”(12) d 5 K in all cases at the same point in the free jet. The relative intensities of the bands are also established to be independent of apparatus resolution, at least in the spectral domain where there is not too much congestion. Furthermore, the fluorescence intensity is established to be proportional to the laser power (see Figure 3) as expected for a bound-free transition. This shows that there are no saturation effects in the detection system at the applied conditions. Contributions of Higher Clusters (12),,,M,,. In clusters beams one tends to generate distributions of clusters, and a high cluster concentration generally implies a wide distribution in cluster “size”, in this case (12)(,,,)M(,,). One of the main goals in our work has been to find experimental conditions at which the fluorescence spectra obtained were essentially due to one species only: (12)1MI, i.e. conditions where at least contributions of clusters (12)mM,,with m and n larger than unity did not significantly perturb spectra due to photodissociation of (12)1MI.Clearly the investigation of the higher homologues is interesting in itself,’ but this will not be treated here in any detail. (9) Anderson, J. B. Molecular Beams and Low Density Gas Dynamics, Wegener, P. P., Ed.; Marcel Dekker: New York, 1974; pp 19-37. (IO) Campargue, R. Thtse, Paris, 1970, pp 36-37. (1 1) Hirschfelder, J. 0.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids;Wiley: New York, 1964; p 11 IO.
The Journal of Physical Chemistry, Vol. 91, No. 10, 1987 2541
Photodissociation of 12-Rare Gas Clusters
>.
cz
v)
w
c
Z
w
U
Z
w
U
v) W
a
0
3 LL W
L
!-
a
A
a
0.1
0.2
0.5 1 Po / bar
2
Figure 4. Relative fluorestence intensity measurements on a particular
':m
vibrational band as a function of Po(M), measured at the following conditions: Ar: oven temperature, 304 K P0(12),0.74 mbar; To,310 K. Kr: oven temperature, 302 K; Po(12), 0.64mbar; To,310 K. Xe: oven temperature, 302 K; P0(12), 0.64 mbar; To,310 K. The excitation wavelength is 488 nm.
1
B
k j W
2
5 W E
0.00
2 3
Figure 5. The relative fluorescence intensity as a function of the iodine partial pressure with M = Ar. Po(Ar) = 1.3 bar, To= 332 K. This measurement is on the u' = 40 u N = 0 transition. The excitation wavelength is 488 nm.
-
Previously, one of the ways to establish the predominant contribution of (12)mMIin the observed spectra has been to do the measurements at inert gas stagnation pressures (Po)at which the fluorescence intensity depends quadratically on the rare gas pressure. This argument comes about in the following way: If for instance 12MIis formed by the mechanism I2 M F! 12M* (4)
+ I2M* + M G I2M + M
(5)
a quadratic dependence of the 12M concentration on [MI (and hence on Po(M)) is to be. expected as two M s are involved in the formation of one 12M. By analogy, a linear dependence on I, concentration, i.e. on PO(I2),is expected. The dependence of the fluorescence intensity on Po(M) is shown in Figure 4 for all the rare gases studied. Toward low stagnation pressures the expected quadratic dependence is found. As I2 is not a t infinite dilution in its carrier gas M one must furthermore demonstrate that in the observed spectra the (I&M, precursor with m = 1 predominates, i.e. one wants to exclude significant contributions from (12)2M1 and higher "iodine homologues". To illustrate this point the dependence of the fluorescence intensity on the iodine partial stagnation pressure, Po(12),is shown in Figure 5 . It was measured at several vibrational bands for M = Ar. The observed slope is unity for the u' = 40 u" = 0 transition as well as for the u'- u" = 44 0, 42 0, 38 0, and 37 0 transitions (not shown). We may conclude that within experimental error the photodissociation of
-
.05
a 0 a
IODINE PRESSURE/&,,
-- -
wavelength is 488 nm.
2
21
0.5
e/bar Figure 6. The relative fluorescence intensity as a function of Po(Ar) taken at the two extreme values of Po&) shown in Figure 5 : (0) P0(12) = 0.74mbar; (0)Po(12)= 3.2 mbar. In both cases a quadratic dependence on Po(Ar) is found at the lower pressures of Ar. The excitation
-+
18000
19000
20000
ENERGYI cm-' Figure 7. Vibrational population distributions in I,B obtained in the photodissociation of (12)mArn at 488 nm. Increasing PO(I2) from 0.74(0) to 3.2 mbar (A)leads to the large differences in population distribution
observed. complexes (12),JM),, is being observed with m essentially equal to unity. Similar measurements are made for the other rare gases, and linear dependence is in each case observed at low iodine pressures. Finally it must be demonstrated that the linear dependence of the fluorescence intensity on P0(12)and the quadratic dependence on Po(M) both hold simultaneously, to establish the predominance of the photodissociationof (12)1MI.Figure 6 shows the dependence of the fluorescence intensity on the u' = 40 u" = 0 transition as a function of Po(Ar) at two values of P0(12). The latter two values correspond to the two extreme values of Figure 5 , i.e. at P0(12)= 0.74 mbar and P0(12)= 3.2 mbar. At both I2 partial pressures the quadratic dependence on Po(Ar) is found up to Po(Ar) = 1.4 bar. The important question to be asked at this point is whether the above-mentioned reasoning concerning the linear dependence on Po(12)and the concurrent quadratic dependence on Po(M) really is a sufficient argument for the observation of the predominant photodissociation of (Iz),M1. To investigate this we measured the dependence of the fluorescence spectral distribution on the I2 and M partial pressures in the regions of linear respectively quadratic pressure dependence mentioned above. In the region of linear intensity dependence on Po(12), changes in spectral distribution with changing Po(M) and mainly with varying PO(I2) are still observed. Typical large differences in spectral distributions are shown in Figure 7 where the vibrational population distributions were obtained at the lowest and highest I2 partial pressures indicated in Figure 5 . This implies that small but significant
-
2548 The Journal of Physical Chemistry, Vol. 91, No. 10, 1987
contributions of higher homologues (12),,,Mn with m > 1 and n > 1 still exist, and the pressure dependence arguments are not quite satisfactory. Apparently more stringent conditions of P0(12)and Po(M) must be adapted to obtain spectra which are due to essentially only (12)lMl. In this work we chose the following method. In the partial pressure domains where the fluorescence depends linearly on Po(12) and quadratically on Po(M), we decrease Po(12) and Po(M) until a limiting situation is obtained in which the spectral distribution no longer changes with the decreasing partial pressures. As the abundance of (12)lM1relative to the other clusters generally increases with decreasing P0(12)and Po(M), we assume the constant spectral distributions obtained at limiting low partial pressures to indicate a predominant photodissociation of the van der Waals dimers (I2),MI. This limiting case is reached for example with M = argon at the lowest pressures in Figure 5 , where between the measurements at lowest two Po(12)values the relative intensities of the vibrational bands (spectral distributions) no longer change. Hence all data reported below have been taken under such low-pressure limiting conditions where we can be fairly sure of a minimal amount of spectral congestion due to higher homologues. Figure 7 is an interesting example which can be used to demonstrate the above-mentioned arguments. The distribution of v’ found at relatively low Po(12) is given by the solid line passing through the open squares (0).The peak of this distribution is near v’ = 40. Measuring the pressure dependence of the fluorescence intensity for wavelengths corresponding to v’ = 40 gives the expected quadratic dependence on Po(Ar) and the linear dependence on P0(12). At higher P0(12)the relative distribution of v’found is given by the dashed line passing through the full triangles (A). Two peaks are discernible: a small peak, again near v’ = 40 which is due to 12Ar, and a larger peak, with its maximum near v ’ = 28 which is due to (12)2. When measuring the pressure dependence of the fluorescence intensity at wavelengths near v’ = 40 the characteristic dependence is found for the IzAr species. However when we measure the pressure dependence of the fluorescence intensity in the wavelength region corresponding to v’= 28 we find a quadratic dependence on P0(12) and a linear dependence on Po(&), characteristic of (12)2. Clearly, measuring the pressure dependence of the fluorescence intensity over a limited wavelength range is not sufficient proof for identifying the cluster which is predominantly responsible for the observed fluorescence. A second measurement, Le. that of a constant relative spectral intensity distribution toward limiting low P0(12)and Po(M) is necessary. Another case which contrasts with that of I2 in Ar of Figure 7 would be that of I2 in Xe. Whereas the fluorescence due to (12)2 and 12Ar is sufficiently different in wavelength to show a double distribution (at least at conditions where the clusters present lead to comparable amounts of fluorescence), the fluorescence due to (12)2 and 12Xe may overlap significantly. Here care should be taken as the test of a change in spectral distribution due to a change in relative concentration of (12)2 and 12Xe may not be as sensitive as in the case of I2 in Ar discussed above. One should also consider the perturbations of the 12Mspectrum due to 12M, with n > 1. Preliminary studies have been made of the v’distributions obtained for instance in the case of M = Ar, in the region where Po(Ar) is larger and beyond the region of quadratic dependence of the fluorescence on Po(Ar) (Le., with Po(Ar) = 2 bar, see Figure 6). Although higher Ar homologues like 12Ar2certainly play a role here, no large changes in the relative distribution of v’are found. One possible explanation for such behavior would be that the first step 12M2
12M(B,u’) + M
+ KE
(6)
would not be too different for the first step in the case of 12M -k.. 12(B,u’) + M
+ KE
(7)
and this first step (reaction 6) would be followed by the wellstudied vibrational predissociation
Philippoz et al. I,M(B,v’)
I~(B,v”Av’)+ M
+ KE
(8) where Au’is known to be small and follows an energy gap law.I2 Processes such as (8) would not perturb the original u’distribution generated in (6) very much. Extraction of Vibrational State Population Distributions. The intensities of unblended vibrational bands are measured at the band head and not integrated over the peak area, as higher resolution measurements have shown essentially identical rotational structure for the different vibrational bands of the ~ p e c t r u m . ~ These intensities are corrected for the frequency dependence of the detection efficiency and are converted to relative vibrational populations Nd by -+
c
where C is an arbitrary constant, is the measured intensity of the B,v’- X,v” transition, crab is the absorption cross section of 12M at the laser wavelength (taken to be equal to that of free I2 given in ref 12), PI,,,, is the laser power, u u ~isD the ~ ~ transition frequency, lpe(Rdd.)12is the transition strength,13 and FCFddf is the Franck-Condon factor.14 The integral is a correction factor for the residence time in the observation region and is discussed term expresses the density decrease in the Appendix. The along the jet axis, the e-r~’(z-zl)/u’ term is due to the spontaneous decay of I2 where rutis the total decay rate of 12(B,v?1Sand B is the mean jet velocity in laboratory coordinates. Corrections due to the additional fragment recoil velocity created by the photodissociation are estimated to be negligible here. The Relative Populations of Vibrational States. Figures 8-10 show the relative populations of vibrational states in the 12(B3110+J product formed in the photodissociation of 12M van der Waals clusters at three wavelengths above the dissociation limit of the B state. A, 0 , and 0 indicate excitation wavelengths of respectively 496.5, 488, and 476.5 nm for M = Ar, Kr, and Xe. In all cases the most probable vibrational state v’ increases with increasing photon energy. The amount of energy appearing as relative translational energy of the photodissociation products Ehv - Ed - EvdW bond is shown in Figure 11 as a function of the excitation energy. Ehuhere means the total energy content in the dissociating 12M complex relative to its zero point energy in the electronic ground state (Le. it includes a very small amount of thermal energy as well as the photon energy); Ed here is the energy of v’relative to the zero point energy of the I2 ground electronic state. Evdwbond is the dissociation energy of the van der Waals bond, which is known in the cases of 12Ne and 1,Ar (73.5 and 237 cm-’, respectivelyI6), whereas for 12Kr and 12Xe,only estimated values are available, 294 and 348 cm-I.l7 A second observation is that the full-width at half-maximum of these distributions does not appear to change much either with M. Finally, the area under the curves drawn in Figure 8-10 tends to decrease with increasing photon energy, Le. the total fluorescence yield decreases with increasing photon energy. To some extent, as in a cage effect, this may be due to competition between the observed reaction channel
(2,/a2
12M -% 12(B3110+,)+ M
(10)
and other channels where the 1-1 bond is broken, like I2M
-+ hv
I
I*
+M
(1 1)
(12) Johnson, K. E.; Sharfin, N.; Levy, D.H. J . Chem. Phys. 1981, 7 4 , 163. (13) Tellinghuisen, J. J . Chem. Phys. 1982, 76, 4736. (14) Tellinghuisen, J. J . Quant. Spectrosc. Radial. Transfer 1978, 19, 149. (15) Vi@, J.; Broyer, M.; Lehmann, J. C. J . Phys. 1981, 42, 961. (16) Blazy, J. A,; Dekoven, B. M.; Russell, T. D.; Levy, D.H. J . Chem. Phys. 1980, 72, 2439. (17) Wensink, W. A,; Van Voorst, J. D.W. Chem. Phys. 1985, 99, 155.
The Journal of Physical Chemistry, Vol. 91, No. 10, 1987 2549
Photodissociation of 12-Rare Gas Clusters ARGON I
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ENERGY / crn-' Figure 8. Relative populations of vibrational states in free 1, formed in its B state upon photolysis of 12Ar at 496.5 (A), 488 ( O ) , and 476.5 nm (0). All excitations are above the dissociation limit of the 1,Ar B state. The energy of the vibrational levels is relative to X'Z' ( u " = 0, J" = 0). Experimental conditions: Po(Ar) = 0.55bar, P0(12) = 0.6mbar, and To = 310 K. The curves at the three wavelengths have been corrected for the laser power and absorption coefficient so that they may be compared
directly with one another in this figure. KRYPTON
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Figure 9. Relative populations of vibrational states in free I2 formed in its B state upon photolysis of 12Kr at 496.5 (A),488 ( O ) , and 476.5 nm (0). All excitations are above the dissociation limit of the 12Kr B state. The energy of the vibrational levels is relative to X'Z' (u" = 0, J"= 0). Experimental conditions: P2(Kr) = 0.32 bar, Po&) = 0.64 mbar, and To= 310 K. The curves at the three wavelengths have been corrected for the laser power and absorption coefficient so that they may be compared directly with one another in this figure. XENON
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ENERGYI cm-' Figure 10. Relative populations of vibrational states in free I, formed in its B state upon photolysis of 12Kr at 496.5 (A),488 ( O ) , and 476.5 nm (0). All excitations are above the dissociation limit of the 1,Xe B state. The energy of the vibrational levels is relative to XIZt (u" = 0, J" = 0). Experimental conditions: Po(Xe) = 0.22 bar, &(I2) = 0.64 mbar, and To= 310 K. The curves at the three wavelengths have been
corrected for the laser power and absorption coefficient so that they may be compared directly with one another in this figure.
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v'
8
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Figure 12. The most probable recoil energy of photodissociation fragments 12(B) and M after exciting the IzM van der Waals molecule above the dissociationlimit of its B state. 0, 0 ,and A correspond to excitation at respectively 476.5,488, and 496.5 nm. 0 are results from quasiclassical trajectory calculations.
At the higher photon energies, channels like (1 1) may be favored. The wavelength dependence of this total fluorescence yield (or "cage effect") is not equally pronounced for all rare gas complexes. It appears quite clearly for M = Ar and Xe. For M = Kr a large decrease in fluorescefice is only observed at 476.5 nm. The "most probable product recoil energy" data from Figures 8-10 are summarized in Figure 12, together with a preliminary result on 12Neand results obtained from quasi-classical trajectory calculation^.^ The latter (0) are to be compared with the data at 496.5 nm (A). As can be seen from Figure 12, the recoil energy predicted by these trajectory calculations lies well below the experimental values for all 12-rare gas complexes. Also, the calculatedSmost probable recoil energy remains nearly constant with photon energy in the case of Xe, and decreases with increasing photon energy in the case of Kr, contrary to our observations where in both cases an increase in product recoil energy with increasing photon energy is observed. Finally, it should be noted that the trajectory calculations predict that an increase in the initial energy of 0.04 eV (i.e. nearly the energy difference between 496.5- and 488-nm excitation) leads to decreases of I2 production by factors of 143.5, 6.7, and 3.7 for Ar, Kr, and Xe, respectively, which is much higher than observed here. These results for excitation of 12M above the dissociation limit of its B state may appear
2550
Philippoz et al.
The Journal of Physical Chemistry, Vol. 91, No. 10, 1987
state followed by a nonadiabatic transition to the B state is to appear in the near future.’* Great care had to be taken to assure that the observed spectra are essentially uniquely due to the desired species 12M,i.e. excluding significant contributions from larger clusters.
Acknowledgment. This paper is dedicated to the memory of Gil Stein who during his stay in Lausanne taught us so much about molecular beams. We will remember him for his enthusiasm and his friendship. We also acknowledge financial support from the Swiss Fonds National and several helpful discussions with M. Broyer and P. Melinon.
Figure 13. Schematic diagram of the geometry of excitation and detection in our free-jet apparatus. The laser beam is horizontal in our laboratory; the free jet and the monochromator slit are vertical. The laser beam is indicated by the arrow, the observation area is marked by the dashed rectangle. The laser is normally 4-mm downstream from the nozzle (Z, = 4 mm) and the maximum distance from which fluorescence is effectively observed (Z,) is 8 mm. The width of the observed area is about 200 lm. The zero of the Z axis is placed at the position of the apparent point source, i.e. x / D = 0.075. 1
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Appendix: Calculation of Vibrational State Populations For the geometric arrangement used in these experiments (see Figure 13), namely a free jet perpendicular to the laser beam (arrow in Figure 13) but parallel to the monochromator slit, the concentration of 12(B,v9 molecules in the observed region (dashed area in Figure 13) decreases essentially by two different mechanisms. First, the density of any species in the collision-freeregion of the jet is inversely proportional to the square of the distance z to an apparent point source, located, for y = at x / D = 0.075.10Second, an exponential decrease of concentration is due to the spontaneous decay of 12(B,v’)by radiation as well as predissociation at a total rate ru,.15 Thus, the local concentration of 12(B,v’)in the observed region is given by 1
~
’
~
’
~
v’
’I;-.*
where Z, is the laser position, d is the mean free jet velocity, and [I2(B,u’)IZlis the concentration of 12(B,u’)produced by dissociation of 12M in the excitation region. [I2(B,u?lz, is the quantity we want to calculate, which is proportional to the relative population Nu,of eq 9. The number of photons emitted at this position per second on the transition 12(B,v9 12(X,u’9 is
-
dn, = [ I , ( B , U ’ ) ] ~ Ad Z ~,~~J
(13)
with a and b the width and depth of the observation region, determined respectively by the monochromator slit andf number of the collection optics, and Add,the Einstein transition probability: Add,= C’~dd~1~Le(~dd,)12FCFdd,, C’being a constant, and the other terms have been defined above. The total number of photons is then
+ + KE
12M --%12(B3110+u)u,,J,M
for several excitation wavelengths above the B state dissociation limit of 12M and for M = Ne, Ar, Kr, and Xe. Excitation above the dissociation limit leads to significantly different dynamics as compared to the previously studied excitation to bound levels of the 12M B state. The results appear to be in qualitative and quantitative disagreement with quasi-classical trajectory calculations. A new theoretical description of the 12Mphotodissociation above the B state dissociation limit involving excitation to the lIIlu
This equation normalized for laser power and absorption cross section gives relative vibrational populations comparable from one excitation wavelength to another for a given rare gas, but not comparable between the different rare gases. It is worth noticing that the integral in this equation has two limiting behaviors as a function of v’: for high velocity d and short observation length along the jet, it is constant throughout v’, whereas for low velocity and long observation length, it tends toward O/l?& Figure 14 shows two cases approaching these limits as well as the curves corresponding to our experimental conditions. Registry No. 11, 7553-56-2;Ne, 7440-01-9; Ar, 7440-37-1; Kr, 50002-7; Xe, 7440-63-3. (18) Beswick, J. A.; Monot, R.; Chem. Phys., in press.
Philippoz, J.-M.: van den Bergh, H. J .
