J. Phys. Chem. 1981, 85,4041-4046
4041
Infrared Spectra qnd Vibrational Predissociation of (CO,), Clusters Using Laser-Molecular Beam Techniques T. E. Gough, R. E. Mlller,t and G. Scoles” Guelph-Waterloo Centre for Graduate Work in Chemistiy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G 7 (Recelved: July 2, 1981; In Flnal Form: September 14, 1981)
Microcalorimetric detection of molecular beams has been applied, in conjunction with an F-center laser, to observe the infrared spectrum of the carbon dioxide dimer. The observed spectra lie very close to the (vl + v3) and (2v2 + v3) bands of C02. The vibrational predissociation lifetime is estimated to be between 3 x lo4 and 5 X s. By appropriately adjusting the source conditions, a series of spectra has also been obtained showing the evolution of the spectrum from the gas phase up to very large clusters. Even for these rather large clusters, containing a few hundred molecules, the vibrational predissociation channel was open.
Introduction In recent years, the use of spectroscopic techniques in the study of weakly bound van der Waals molecules has lead to a wealth of information concerning the structure and dynamics of these species. This type of study is rapidly becoming our most important source of information about the nonsphericity of the attractive part of molecular interactions and complements the information obtained from state to state inelastic molecular beam scattering measurements which are mainly sensitive to the nonsphericity of the repulsive part of the potential. When one of the partners in the van der Waals molecule has a visible spectrum, laser-induced fluorescence techniques can and have been applied, obtaining energetic and dynamic information for several molecules containing NOz or IZ.l For molecules with no visible spectrum the most detailed information on the structure of their van der Waals complexes has been obtained in the microwave and radio-frequency region of the spectrum by molecular beam electric or magnetic resonance spectroscopy.2+ In the infrared region of the spectrum the studies performed so far can be classified in two main groups. In the first we can put infrared bulk absorption measurements at relatively low temperatures and high pressures (so as to obtain appreciable concentration of dimeric species). This class of experiments has, for obvious reasons, delivered its best results when both partners are, in isolation, infrared inactive and one, at least, of them ceases to be such when bound in the cluster.’ The second class of experiments in the infrared region of the spectrum comprises those which are conducted in a molecular beam environment and make use of laser-induced predissociation for the detection of the spectrum. The first of such experiments was reported by us in 1978 for (NzO), clusters8 and was based on an application of the microcalorimetric technique for the detection of molecular beams. At present, several laboratories also monitoring the predissociation, but with mass spectrometric detection, have obtained photodissociation spectra for clusters of SF,? CzH4,10J1and several hydrogen-bonding molecules.12 The advantage of this technique is that it can provide useful information on the dynamics of the dissociation process. This process, which has important similarities with the process of vibrational relaxation, has been the object of several theoretical *Address correspondence t o this author a t the Physics Department, University of Waterloo. ‘Also with the Physics Department, University of Waterloo. Present address: Research School of Physical Sciences, Australian National University, Canberra, A.C.T. Australia. 0022-3654/81/2085-4041$01.25/0
studies,13J4the results of which remain, unfortunately, rather uncertain mainly due to the lack of accurate potential energy surfaces. It is then important to extend the class of molecules for which photodissociation spectra are available, including molecules for which the interaction potential is known or is likely to become known in the not too distant future. It is with these considerations in mind that we decided to undertake, and report hereafter, a rather detailed study of the infrared spectrum of the COz dimer. In addition we have observed the evolution of the spectrum from that of an isolated molecule to that of rather large molecular clusters (containing up to few hundred molecules), and compare the latter with the IR spectrum of solid COP.
Experimental Section The apparatus used in the present study has been described in some detail previou~ly.~J~ However, as several significant modifications have since been made, a discussion of these seems justified. Figure 1 shows a schematic diagram of the present experimental geometry. As in the previous reports, a 2 K doped silicon bolometer is used to detect the energy deposited in the beam molecules by a tunable infrared laser. Owing to the long excited state lifetimes and to the relative lack of sensitivity to laser amplitude instabilities, this (1) D. H. Levy, A d a Chem. Phys., to be published, and references therein. (2) J. M. Steed, T. A. Dixon, and W. Klemperer, J. Chem. Phys., 70, 4095 (1979); S. E. Novick, K. C. Janda, S. L. Holmgren, M. Waldman, and W. Klemperer, ibid., 65, 1114 (1976); S. E. Novick, S. J. Harris, K. C. Janda, and W. Klemperer, Can. J. Phys., 53, 2007 (1975); S. J. Harris, S. E. Novick, and W. Klemperer, J. Chem. Phys., 60, 3208 (1974). (3) P. D. Soper, A. C. Legon, and W. H. Flygare, J. Chem. Phys., 74, 2138 (1981), and references therein. (4) A. E. Barton, T. J. Henderson, P. R. R. Langridge-Smith, and B. J. Howard, Chem. Phys., 45, 429 (1980). (5) R. L. DeLeon, A. Yokozeki, and J. S. Muenter, J. Chem. Phys., 73, 2044 (1980). (6) J. Verberne and J. Reuss, Chem. Phys., 50, 137 (1980). (7) R. J. Le Roy in “Potential Energy Surfaces”, K. P. Lawley, Ed., Wiley, New York, 1980, and references therein. (8) T. E. Gough, R. E. Miller, and G. Scoles, J. Chem. Phys., 69,1588 (1978). ~ - .--,. (9) J. Geraedts, S. Setiadi, S. Stolte and J. Reuss, Chem. Phys. Lett., 78, 277 (1981). (10) M. A. Hoffbauer, W. R. Gentry, and G. F. Giese in “Laser Induced Processes in Molecules”, K. L. Kompa and S. D. Smith, Ed., SpringerVerlag, Heidelberg, 1979. (11) M. P. Casassa, D. S. Bomse, and K. C. Janda, J. Chem. Phys., 74, 5044 (1981). (12) M. Vernon and Y. T. Lee, private communication. (13) G. Ewing, J. Chem. Phys., 72,2096 (1980), and references therein. (14) J. A. Beswick and J. Jortner, J. Chem. Phys., 71,4737 (1979), and
references therein. (15) T. E. Gough, R. E. Miller, and G. Scoles, Appl. Phys. Lett., 30, 338 (1977); J . Mol. Spectrosc., 72, 124 (1978).
0 1981 American Chemical Society
4042
The Journal of Physical Chem/stty, Vol. 85, No. 26, 1981
m
Gough et al.
rlll I l l
SPLITTER
M1 MIRROR
Figure 2. Schematic diagram demonstrating the Doppler shift tech-
CHOPPER
nique used to obtain the moelcular beam velocity distributions. Ar' LASER
J
technique proves, in this wavelength region, to be much more sensitive than conventional fluorescence and absorption techniques. The bolometer used in this study has a noise equivalent power of W Hz-l12,which, at the laser frequencies used here, corresponds to a minimum detectable number of excited molecules of approximately 107 8-1. The major modification to the vacuum system consists of a third stage of pumping which has been added for the Extranuclear Laboratories quadrupole mass spectrometer (mass range = 0-200 amu). This all-metal sealed chamber is pumped by a 7.6-cm Edwards Diffstak, which has a pumping speed of 600 L/s. The typical operating pressure in this chamber is approximately torr. The molecular beam was formed by expanding 5,10,25, 40, and 100% mixtures of carbon dioxide in helium through a 35-pm diameter room temperature nozzle. The use of these mixtures, as well as a variety of source pressures, gives considerable control over the concentration of the various complexes in the molecular beam. A 300-pm diameter conical skimmer was used to sample the free jet expansion. The laser system consists of a commercially available F-center laser (Burleigh FCL-20) pumped by a krypton ion laser (Spectra Physics 171). The details of F-center laser operation have been well documented in the literaturelB and will not be dealt with here. The intracavity etalon was only required when high-resolution single-mode operation was required. As will be shown in the next section, for the (CO,), cluster spectra, the etalon was not required. With the etalon removed a stepping motor, mounted on the grating control, was used to tune the laser. Two parallel gold-coated mirrors flanked the molecular beam to provide multiple laser-molecular beam crossings. A factor of ten enhancement of the signal-to-noise ratio was obtained in this way.
Results and Discussion Velocity Distributions and State Population Measurements of the Monomer. Although the molecular beam has many advantages in the study of weakly bound complexes, the fact that the resulting sample is not in equilibrium does present some problems. For example, since (16)L.F. Mollenauer and D. H. Olson, J. Appl. Phys., 46,3109 (1975); E. B.Folwer, Ed., 'Physics of Color Centres",Academic Press, New York, 1968.
TABLE I: Velocities and Translational Temperatures for Mixtures of CO, in He cb Au(fwhm)C Ttmnsd pSa 5% CO, in He 1.29 1.56 0.90 7.7 3.47 1.63 0.91 7.9 6.60 1.63 0.74 5.2 11.4 1.65 0.56 3.0 10%C O , in He 3.13 1.17 0.90 7.7 6.60 1.23 0.94 8.4 11.7 1.31 1.09 11.3 14.4 1.32 1.18 13.3
Ps is the source pressure in atm. c is the stream velocity in lo5 cm s - ' . A u is the width of velocity distribution in lo4 cm s - ' . Ttmns is the translational temperatures in K. Those are calculated from the velocity spreads by using normal kinetic theory formulae and the mass of CO,.
the various degrees of freedom are not necessarily in equilibrium with one another, more than one temperature may be required to characterize the beam. In fact, the temperatures may not even be defined if, for example, the rotational populations do not conform to a Boltzmann distribution. Traditionally, the characterization of molecular beams made of molecules with no visible spectrum has been accomplished by using a combination of time-of-flight rneasurementsl7and energy balance techniques.l8 In this study, we make use of the high-resolution capabilities of the laser system to perform these measurements. First, consider the translational degrees of freedom. Figure 2 shows, schematically, the method used to measure the molecular beam velocity distributions. The details of the right angle multiple crossing device have been discussed e1~ewhere.l~It is used here to ensure that the laser crossings are orthogonal to the molecular beam. Mirror MI is then translated so that the laser reflects off M3 and retraces its path. This ensures that M3 is parallel to the molecular beam. M1 is now translated so that the laser, reflects from Mz. Since the angle 0, between M2 and Ma, is accurately machined to 22.5", the second molecular beam crossing is precisely 4 5 O . This second arrangement will obviously give an absorption peak which is Doppler shifted and broadened, with respect to the orthogonal crossing, and diagnostic of the molecular beam velocity and trans(17)E. W.Becker and W. Henkes, 2.Phys., 146,320 (1956). (18)D.R.Miller and R. P. Andres, J. Chem. Phys., 46,3418 (1967). (19)T.E.Gough, D. Gravel, and R. E. Miller, Rev. Sci. Instrum., in press.
The Journal of Physical Chemistty, Vol. 85, No. 26, 1981 4043
I R Study of (COP),, Clusters
TABLE 11: A Summary of the Gas Dimer, and Solid State Absorption Frequencies for the ( v , t v,) and ( 2 v , t v,) Bands (cm-l) of CO, gas phase dimer solid
3716a 3714.8 3711.5b
360ga 3605 3596.5b
a See ref 23. These solid-state measurements were obtained by using the same spectrophotometer used to calibrate the (CO, ),spectrum. The CO, solid sample was prepared on a liquid helium cooled AgBr . . - window ( T , = 15 K).
( C 0 2 ) 2 MODEL FIT TR=14OK
'.
n'
LN (Ps(ATM )) Figure 3. Mass spectrometer pressure profiles of (CO,),' 3, 4).
(n = 1, 2,
lational temperature, respectively. It is worth noting here that no difference was observed in the velocity distributions for the various rotational states observed. Table I summarizes the data for the 5 and 10% mixtures of COPin He. As one would expect, the velocity spread decreases for increasing pressure for the 5% mixture. However, for the 10% mixture the spread in fact increases with source pressure. This behavior is a result of condensation in the jet. In addition to measuring the velocity distributions, the laser was also used to measure the relative rotational populations, giving a direct measure of the rotational temperatures. In fact the distributions observed did not conform to a Boltzmann distribution but showed an apparent overpopulation of the large J states. However, the rotational temperature associated with the lower J states was comparable to the translational temperatures. As we only wish to present here the information pertinent to the cluster spectra, the reader is referred elsewhere20for a more complete discussion of the various temperatures. The Dimer Spectrum. The infrared spectrum of (CO,), has been observed previously by Welsh et a1.,21in the neighborhood of the ul and 2u2 bands, using a long-path gas cell maintained at 192 K. The spectrum of the dimer was obtained by subtracting from the experimental spectrum that of the monomer and the result was interpreted in terms of the vibration and rotation of the (CO,), complex in the T configuration. In our apparatus, at high source pressures and C 0 2 concentrations, it is possible to form beams with appreciable concentrations of C02 clusters (as suggested by the dependence of the velocity spread on the pressure). Pressure profiles for the various (CO,),+ ( n = 1, 2, 3, 4) clusters, obtained by using the mass spectrometer detector and a 10% C02-90% He gas mixture, are shown in Figure 3. As expected, the concentration of clusters increases rapidly with source pressure. The concentration ratios of the different species are not determined absolutely because (20) R. E. Miller, Ph.D. Thesis, University of Waterloo, 1980. (21) L. Mannik, J. C. Stryland, and H. L. Welsh, Can. J. Phys., 49, 3056 (1971).
FREQUENCY(C~ )~
Figure 4. Spectrum of (CO,), recorded by using a 10% mixture of
COPin He at a source pressure of 5.3 atm. On the vertical axis the bolometer signal is reported. The solid line shows the model fit obtained by using a symmetric top model for (CO,),. The zero of the abscissa is at 3714.6 cm-' which is 0.2 cm-' less than the modeled absorption center reported in Table 11.
the fragmentation cross sections are not known. At these high source pressures, a negative signal, corresponding to a decrease in energy reaching the bolometer, was observed as the laser was tuned through the (ul + us) and (2u2+ u3) bands of C02 which are located at 3716 and 3609 cm-l, respectively (see Table 11). As shown in ref 8, this corresponds to a loss of molecules from the beam, resulting from the vibrational predissociation of COz dimers (or higher clusters). The spectrum shown in Figure 4 was obtained with a 10% mixture of C 0 2in He at a source pressure of 5.3 atm (the conditions indicated by the vertical line in Figure 3). Below we will show that this spectrum can be assigned to (CO,),, excited in the neighborhood of the (ul + v3) band of C 0 2 and we will discuss the origin of the left-right assymetry of the experimental points. The center of the spectrum is located at 3714.8 cm-'. Similar spectra were obtained for the (2u2 + v3) band with the dimer centered at 3605 cm-'. In both cases the COz concentration and source pressure were reduced to a minimum in order to reduce the contribution from higher polymers. In order to assign the spectrum shown in Figure 4, we can make use of the pressure profiles shown in Figure 3, as well as similar ones recorded for the infrared spectrum, using the laser-bolometer combination. As in the (NZO), case, reported in ref 8, it is necessary to account for the fact that the bolometer and mass spectrometer have different angular resolutions and hence suffer differently from background gas scattering. Assuming that the background pressure in the bolometer chamber is proportional to source pressure, and that the scattering obeys a Beer's law relationship, we can remove the effects of scattering by plotting the logarithm of the ratio of SL,the laser-induced bolometer signal, to S,, the
Gough et al.
The Journal of Physical Chemistry, Vol. 85, No. 26, 1981
4044
I
I
parallel with a C-C distance of approximately 3.5 8, and one of the OCC angles being 55O. Classically, the C02 dimer can be thought of as a coupled oscillator problem, with the coupling term being associated with the van der Waals bond. This coupling leads to a splitting of the in-phase
0
e 0
+ +
+
+ n=2
.
n.1 0-c-0
\
\ \ \
ZJ-2 and out-of-phase
--.0-c-0
‘\
J
2
0
4
6
S
10
12
14
\
16
O,-:-g
PS(ATM.)
Flgure 5. Plot of In SL/S, vs. source pressure, for n = 1, 2, 3. The linear portlon for n = 2, at low pressure, demonstrates that the iaser-induced signal is due to (COz)z. SL = laser signal, S,,= mass spectrometer signal.
mass spectrometer signals for (CO,), ( n = 1, 2, 3), as a function of source pressure. Figure 5 shows such a plot obtained by using the laser-bolometer pressure profile, recorded with the laser frequency set at the top of the spectrum in Figure 4. The fact that a linear relationship is obtained for the case n = 2, at source pressures less than 7 atm, confirms that the spectrum is due to (CO,),. Again the vertical line represents the conditions under which the spectrum of Figure 4 was obtained. The deviation from linearity at high source pressures results from the formation of higher polymers. The frequencies corresponding to the center of the dimer spectra for the (vl + v3) and (2v2 + vs) bands are summarized in Table 11. Also included in the table are the gasand solid-state absorption frequencies. In both cases the dimer spectrum is located between the gas- and solid-state spectra, as might be expected. The fact that the dimer spectrum is red shifted from the gas phase suggests that the upper vibrational state of the complex is more tightly bound than the ground state. The fact that the spectrum of the dimer is observed as a negative bolometer signal suggests that the experiment is sensitive to the photodissociation dynamics of the complex. Indeed, the lifetime of the vibrationally excited state can be estimated as follows. The lack of fine structure in the (CO,), spectrum, despite the experimental resolution of 5 X cm-l, suggests that either considerable rotational line congestion exists or the predissociation lifetime is sufficiently short so as to contribute to the observed line s is obtained by attribwidth. A lower limit of 5 X uting the full width of the (CO,), spectrum to lifetime broadening. However, the fact that the line shape is not Lorentian suggests that the spectrum is, at least partially, inhomogeneously broadened. Indeed, we shall show later that the line shape can be explained on the basis of rotational line congestion. An upper limit to the lifeime can be obtained by noting that the dissociation occurs before the molecules travel the 50 cm from the point of irradiation to the bolometer. This gives an upper limit of 3 X s, if we note that the beam velocity is 1.7 X lo5cm/s. These estimates are similar to those obtained for (N20),. Recent experimental and theoretical resultsz2indicate that the equilibrium geometry for C02 dimer is slipped ~~
\
vibrations of the complex. However, the presence of the center of symmetry makes the in-phase vibration infrared inactive, which is consistent with the single band observed experimentally. In order to make an estimate of the broadening associated with the rotational structure, we assume the geometry discussed above. The moments of inertia can then be easily calculated, giving IA = 0.85 X kg m2
IB = 5.1 X
kg m2
IC = 5.9
kg m2
X
It is evident from this that the C02 dimer, in the above geometry, is very nearly a prolate symmetric top. Because of the relative simplicity of the symmetric top spectrum, in comparison with that of the asymmetric rotor, and given that the individual lines are not resolved, we approximate the C02dimer by a symmetric top with principal moments of inertia: IA = 0.85 X kg m2
IB = 5.5 X
kg m2
and hence rotational constants: B = 0.051 cm-I A = 0.33 cm-l Since the unique principal axis lies very nearly through the two carbon atoms, and the vibrational coordinate is along the 0-C-0 bond, the resulting rovibrational band will be hybrid.23 The relative intensities of the perpendicular and parallel bands can be written as I l , / I L= cot2 8 where for the nonslipped parallel geometry (0 = goo), only the perpendicular band exists. If we make use of the calculated energy levels and relative intensities of the individual ro-vibrational lines of the symmetric it is therefore possible to calculate the infrared spectrum. One further complication can arise from the fact that the rotational constants need not be the same in the ground and vibrationally excited states. Assuming that A and B change in the same proportion, this can be accounted for by including the parameter
P = Ao/A1 = BdB1 where A,, and B, are the rotational constants in the n’th
~
(22) A. E. Barton, A. Chablo, and B. J. Howard, Chem. Phys. Lett., 60, 414 (1979).
(23) G. Herzberg, “Molecular Spectroscopyand Molecular Structure”, Vol. 11, Van Nostrant, Princeton, NJ, 1945.
The Journal of Physical Chemistty, Vol. 85,No.
I R Study of (C02),, Clusters
vibrational state. The rotational fine structure can now be calculated given any value of TR and 0. In order to compare this model spectrum with the (CO,), spectrum obtained experimentally, two factors must be considered. First, the degeneracies associated with the symmetric top model will be lifted in the (CO,), spectrum. Second the finite resolution of the experiment, resulting from a combination of geometrical factors and the short predissociative lifetime of the dimer, will produce a spectrum which does not show individually resolved lines. In order to account for this, a resolution of 0.2 cm-l was applied to the stick spectrum. (Although this value is rather arbitrary, it was found that the final spectrum was rather insensitive to the value of the resolution chosen.) The resulting fit to the experimental data is shown in Figure 4. Excellent agreement is obtained with TR = 14 K and 0= 0.995. Taking 0 # 1adds the slight asymmetry to the model spectrum which is evident in the experimental points. As discussed earlier, the fact that the (CO,), spectrum is red shifted from the gas-phase spectrum suggests that the well depth for (C02)2is greater in the vibrationally excited state than in the ground state. This interpretation is consistent with 0 being less than unity if we consider the deepening of the well as resulting from an increase in the attractive part of the well only. The result of this would be a smaller R, in the excited state and hence a larger rotational constant, giving < 1. In addition, the rotational temperature of 14 K seems quite consistent with the velocity spreads reported earlier which give translational temperatures around 8 K. As expected, therefore, the rotational temperature of the complex is slightly higher than the translational temperature of the monomer. If we assume that the degeneracies associated with the symmetric top model are lifted, the number of lines in the model spectrum (with intensities > 1% of the most intense lines) is approximately lo5. This suggests an average spacing between adjacent lines of approximately 0.5 MHz and therefore explains the lack of fine structure without the need for introducing further broadening from the fiiite lifetime of the excited state. The quality of the fit suggests that the homogeneous width is considerably less than the width of the spectrum and hence the predissociation lifetime is in all probability much longer than the 3 X 10-l’ s value given earlier. Very recently Beswick and J ~ r t n e r , ~ have performed a new theoretical analysis of vibrational predissociation of polyatomic molecular dimers using atom-atom interactions expressed in terms of Morse potentials. They have analyzed in detail the spectrum of the N20 dimer previously reported by us8 assuming a T-shaped structure for the complex and arriving at a theoretical estimate of the predissociative lifetime of 10-5-10-6 s. It would be quite interesting to apply their theory to the COz dimer, assuming for it the slipped parallel configuration. The Spectrum of the Higher Clusters. Having characterized the dimer spectrum at low source pressures and C 0 2 concentrations, it is interesting to look at the spectra of the higher C02 polymers. Figure 6 shows successive scans of the laser through the (vl + vJ absorption as a function of source pressure and C02concentration, where spectrum A is just that of (CO,),. In spectra A-C, a smooth shift toward the solid (further to the red) is observed. A t a source pressure of 14.8 atm, in the 40% mixture, a second peak begins to appear a t 3709.3 cm-l. At even higher source pressures this low-frequency peak dominates. It is clear that the infrared spectra shown in Figure 6 must (24) J. A. Beswick and J. Jortner,
J. Chem. Phys., 74, 6725 (1981).
‘r*,
4 :, :.
26, 198 1 4045
‘A
P;
10% COP IN HE
Ps 5.3ATM
\! I.!
\ I
ti
. ?.[
‘
t i i
I
40% COP IN HE Ps 9.2 ATM
..’ ’
p
:
‘E40%C021NHE
. ./
Ps 21.4 ATM
.
Ps 29.2 ATM
1
.
.car
..,.
: J
t
3700
3710 cfil
3720
3730
Flgure 8. A series of spectra showlng the evolution of the (CO,), spectra from dimer to very large polymers, as a function of source pressure and C02 concentration. On the vertical axis the bolometer signal is reported.
be ascribed to more highly condensed forms of carbon dioxide. Our mass spectral data clearly show the increasing importance of these higher condensates when source pressure and COz concentration are increased. It we apply the scaling law of Hagena and Obert25we obtain a mean cluster size of several hundred for expansions of pure COz giving spectra similar to E and F of Figure 6. However, the interpretation of these first photodissociation spectra of clusters must remain somewhat speculative. As the size of clusters increases so does the number of vibrational degrees of freedom able to accomodate the excitation energy delivered by the laser. For smaller clusters the concept of photodissociation is appropriate, but for larger clusters it is perhaps better to think in terms of photoevaporation. The absorbed energy relaxes into the lattice modes of the cluster, increasing its temperature, and leading to an increased rate of evaporation from the cluster. The bulk of the cluster proceeds to the bolometer but the evaporated molecule or molecules miss the bolometer generating the “negative”signal. Such a view is supported by the steadily decreasing signal-to-noise ratio apparent in spectra 6C-F which is observed, even though the total amount of condensed carbon dioxide is increasing steadily. The experiment seems sensitive not to the total number of C 0 2 molecules contained in the clusters but to the total number of clusters present in the beam. Actually the S/N ratio for spectra obtained expanding pure COz (see above) was sufficiently poor as for us to decide not to show those spectra here. Two improvements in the techniques are being investigated a t present that may make better measurements possible in a not too distant future, namely, digital signal integration and off-beam detection of the photofragments. We estimate that we dissociate -1 in lo3 of carbon dioxide dimers; therefore, once the cluster size reaches (26)0.F. Hagena and W. Obert, J. C h e n . Phys., 56, 1793 (1972).
4046
J. Phys. Chem. 1981, 85, 4046-4051
-lo3 it seems likely that a cluster will absorb more than one photon. If this is so, one may then understand why we did not observe any “positive” signal associated with large clusters having a rate of photoevaporation low enough to survive passage from the excitation region to the bolometer. We ascribe the smooth red shift in absorption maximum shown by spectra 6A-C to a steady increase in the mean size of the clusters. The widths of the spectra are too large to allow resolution of the spectrum of each successive cluster and so a steady shift in the absorption maximum is observed. Spectra 6D-F are characteristic of the growth of one class of species at the expense of another. They signify a discontinuity in the clustering process which we tentively assign as a structural rearrangement occurring once the clusters reach a critical size. Such a rearrangement occurs because the most stable arrangement of a limited number of molecules is, in general, not the same as the molecular disposition within the unit cell which is the repeating unit of an extended solid. Several studies of metal clusters, using electron diffraction molecular beam techniques,26
have revealed evidence which supports the idea of a critical cluster size. The interpretation of spectra 6D-F contains a serious weakness; the second peak at 3709.3 cm-l is shifted beyond the position of the v1 + v3 of solid carbon dioxide. In fact, the valley between the two peaks coincides, to the accuracy of our measurements, with the absorption of the solid. A similar coincidence for nitrous oxide may be found upon inspection of Figure 2 of ref 8. Although considerable theoretical work2’ has been carried out to establish the growh sequence of rare gas clusters, such as argon, no detailed calculations exist for the case of clusters formed from molecules. Adding to the complexity of the problem is the fact that infrared spectrum depends not only on the ground state properties but also those in the excited vibrational state. A considerable amount of theoretical work will therefore be required before these spectra can be fully interpreted. However, these results do show that much more information is available than simply the gas- and solid-state spectra. Indeed, the investigation of these “intermediate phasesnshould, in the future, be extremely useful in the study of many-body forces as well as the details of condensation phenomena.
(26) A. Yokozeki and G. D. Stein, J. Appl. Phys., 49, 2224 (1978);J. C. Allpress and J. V. Sandors, Surf. Sci., 7 , 1 (1967).
(27) C. L. Briant and J. J. Burton, J. Chem. Phys., 63,2045 (1975); M. R. Hoare and P. Pal, J. Cryst. Growth, 16, 77 (1972).
A Reaction Path for Halogen Elimination from CX2Y2, and Its Dynamical Implications Stephen R. Cain, Roald Hoffmann,“ and Edward R. Grant* Department of Chemlstiy, Cornell Unlverslty, Ithaca, New York 14853 (Received July 7, 1981; In Final Form: September 9, 1981)
-
A qualitative molecular orbital exploration of the reaction path for CX2Yz CY2+ X2 is presented. The least-motton departure is symmetry forbidden and a less symmetrical path is implicated, one likely to result in substantial rotational excitation of the products. The smaller the HOMO-LUMO gap in the expelled dihalogen X2,the smaller should be the reaction barrier and the degree of rotational excitation of the products. The elimination of a diatomic molecule upon thermal or photochemical excitation of a substituted methane, 1,
I is of course the reverse of the addition of a carbene to a single bond. That reverse reaction, carbene insertion, has a long experimental and theoretical history.’“ Surfaces (1) See, for example, (a) “Carbenes”, M. Jones and R. A. Moss, Ed., Vol. I, Wdey, New York, 1973; (b) “Carbenes”,M. Jones and R. A. Moss, Ed., Vol. 11, Wiley, New York, 1975; (c) ‘Carbene Chemistry”, W. Kirmse, Ed., Vol. I, 2nd ed, Academic Press, New York, 1971. (2) (a) H. Kollmar, Tetrahedron, 28, 5893 (1972); (b) J. N. Murrell, J. B. Pedley, and S. Durmaz, J. Chem. Soc., Faraday Trans. 2,69, 1370 (1973); (c) P. Cremaschi and M. Simonetta, ibid., 70,1801 (1974); (d) C. W. Bauschlicher, Jr., H. F. Schaefer, 111, and C. F. Bender, J. Am. Chem. Soc., 98, 1653 (1976); (e) C. W. Bauschlicher, Jr., K. Haber, H. F. Schaefer, 111, and C. F. Bender, ibid., 99,3610 (1977); (0 M. S. Gordon, Chem. Phys. Lett., 52, 161 (1977); (g) H. Kollmar, J. Am. Chem. SOC., 100,2660 (1978); (h) D. Jeziorek and B. Zurawski, Int. J. Quant. Chem., 16,277 (1979); (i) H. Kollmar and V. Staemmler, Theor. Chim. Acta, 51, 207 (1979); 6)M. S. Gordon and J. W. Caldwell, J. Chem. Phys., 70,5503 (1979); (k) H. U. Lee and R. Janoschek, Chem. Phys., 39, 271 (1979). 0022-3654/81/2085-4046$01.25/0
for carbene insertion into hydrogenY2 C-H b ~ n d s , and ~,~~,~ carbon-carbon double bonds4have been studied in detail. The forward reaction, specifically for the case of halogen substituents, is of current experimental intere~t.~ For this reason we have undertaken a qualitative theoretical exploration of the reaction for X = Y = halogen. The Least-Motion Path There is much understanding to be gained from a qualitative orbital-symmetry based analysis of this reac(3) R. C. Dobson, D. M. Hayes, and R. Hoffmann, J. Am. Chem. Soc., 93, 6188 (1971). (4) (a) A. G. Anastassiou, Chem. Commun., 991 (1968); (b) R. Hoffmann, J. Am. Chem. SOC.,90,1475 (1968); (c) N. Bodor, M. J. S. Dewar, and J. Wasson, ibid., 94,9095 (1972); (d) T. Fueno, S. Nagase, K. Tatsumi, and K. Yamaguchi, Theor. Chim. Acta, 26,43 (1972); (e) H. FuJpn., 45,2424 (1972); jimoto, S. Yamabe, and K. Fukui, Bull. Chem. SOC. (f) R. Hoffmann, D. M. Hayes, and P. S. Skell, J. Phys. Chem., 76,664 (1972); (g) H. Fujimoto and R. Hoffmann, ibid., 78,1167 (1974); (h) S. Nagase and T. Fueno, Theor. Chim. Acta, 41, 59 (1976); (i) W. W. Schoeller and E. Yurtsever, J. Am. Chem. SOC.,100,7548 (1978); (j) B. Zurawski and W. Kutzelnigg, ibid., 100,2654 (1978); (k) N. G. Rondan, K. N. Houk, and R. A. Moss, ibid., 102,1770 (1980); (1) S. Y. Chu, A. K. Q.Siu, and E. F. Hayes, ibid., 94, 2969 (1972). (5) See, for example, (a) P. A. Schulz, Aa. S. Sudber, D. J. Krajnovich, H. S. Kwok, Y. R. Shen, and Y. T. Lee, Annu. Rev. Phys. Chem., 30,379 (1979); (b) R. J. S. Morrison and E. R. Grant, J. Chem. Phys., 71,3537 (1979); (c) R. J. S. Morrison, R. F. Loring, R. L. Farley, and E. R. Grant, ibid., in press.
0 1981 American Chemical Society
