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J. Phys. Chem. 1082, 86, 1153-1163
Time-of-Flight Measurements of High-Overtone Mode-Selective Vibrational Excitation of CH,, CF,, and SF6 in Collisions with H', D', and Li' Ions at Energies between 4 and 10 eV Ton Ellenbroek, Uwe Glerr, Martln Noll, and J. Peter Toennles' Max-Plenck-Instnut fik Sfrhungsforschung, 3400 Gbfflngen, Federal Republlc of Germany (Recelv&: August 18, 198 1; In Flnal Fonn: October 8, 1981)
Time-of-flightspectra have been measured for the scattering of H+,D+, and Li+ ions from the spherical molecules CHI, CF4,and SF6at center-of-massangles between 3 and 30'. At angles up to about 15' all the spectra show multiple peaks, which are especially well resolved in the H+and D+ experiments. The observed maxima have been attributed to the overtone excitation of a single vibrational mode with vibrational quanta up to n = 7 in the case of CF4and SF6,whereas the CH4spectra reveal multimode excitation. In all cases the peak locations can be fitted by assuming no rotational excitation consistent with the near-perfect spherical symmetry of the molecules. In H+(D+)-CF4and H+(D+)-SFethe v3 mode is excited at 10 eV. For Li+-CF4the v2 mode is excited at low energies (-4 eV), whereas the v3 mode is excited at 10 eV. In Li+-SF6 the structure is consistent with the vz or v4 modes and is probably due to the v4 mode. The relative transition probabilities in most cases follow a Poisson distribution, implying that the excitation can be attributed to a long-rangeelectrostaticlinear coupling to a harmonic oscillator.
I. Introduction Very little is presently known about the dynamical details of molecular collision processes involving translational-vibrational (T-V) transfer and inter- and intramolecular V-V transfer.l These processes are of great interest for understanding energy flow to and within polyatomic molecules as occurs in unimolecular decomposition and dissociation, intramolecular vibronic transitions, laser multiphoton excitation, and even collisions with solid surfaces. These problems are beyond the range of present rigorous scattering theories because of the large number of degrees of freedom and can only be treated by statistical theories. Scattering experiments with neutral partners in the range of energies above 1 eV, which are needed to excite vibrations, are only now emerging.2 Inelastic scattering experiments with H+ and Li+ ions are, however, feasible and have been used to study vibrational excitation of small molecules at low energies ( 1 a positive slope. In Figures 6 and 7 some of the data reported in Table V for the CF4systems and in Table VI for the SF, systems are plotted in four frames in order of increasing collision velocity. The collision times, which are crucial for the interpretation, depend also sensitively on the angle, decreasing with increasing angle, as well as on the radial dependence of the coupling potential. In each frame the excited mode, determined from the spectra, is indicated in the bottom left corner. As expected, the frequency of the excited mode increases with the collision velocity. Examination of the distributions for a given energy shows the expected trend of increasing slope with scattering angle. At some energies and angles we find significant curvature. Surprisingly, in most cases the curves tend to straighten out with increasing n. Furthermore we note that (17) H. D. Meyer (Chern. Phys., 61, 365 (1981)) has recently shown that a parametric forced oscillator with F ( t ) and G&) has n probability distribution which is non-Poisson. However, the differences between the exact distribution and the Poisson distribution will generally be small.
Elienbroek et ai.
for H+ and D+ the curves tend to be straighter than for the Li+ experiments. However, in the Li+ experiments there are some notable exceptions such as for Li+-SF6 at E , = 4.4 eV and ,91 = 10.5O and at E , = 6.4 eV and 6 , = 6.5’. In the Li+-CF4systems the same trend is observed at large angles, but the curves are not so straight. The deviations at An = 0 and small An suggest that “blast through” of the primary beam may still be affecting some of the Li+ data. As noted previously, this effect is expected to be largest at the smallest angles and will tend to make the small An transitions appear to be more probable. Another source of error comes from the incomplete resolution, especially in the Li+ experiments and the possible unresolved contributions from other vibrational modes and rotations. We recall that the relative size of (M,) was largest at small angles and therefore also leads to errors. These sources of error have to be understood before we can conclude that there is definite evidence for a deviation from a Poisson distribution, as found for H+-02.11 In that case we could show the observed distribution to be consistent with one expected for an additional quadratic term, e.g., Gklin eq 5b.12 For H+-02 this is consistent with the postulated curve-crossing mechanism. Curve crossing is not expected for the Li+ systems and the good Poisson fits for the H+ and D+systems, where curve crossing could occur, indicate that it is unlikely at these angles.
V. Discussion The present experiments provide extensive evidence that for the spherical molecules CF4 and SF6only one of the normal vibrational modes of the molecules is excited in collisions with H+, D+, and Li+. In many cases the relative tmnsition probabilities follow within experimental error a Poisson distribution. This behavior suggests that a simple forced harmonic oscillator model can describe the results. As noted in the Introduction these results came somewhat of a surprise, when viewed in the light of earlier experiments on Li+-N2, CO,s COz, N20,’ and CH4.* Although we did find for C02 and N20 a predominate excitation of the bending mode, which is qualitatively what one would expect from the energy transfer calculated according to eq 8, the relative probabilities do not show a trend, which is a clear indication of a Poisson distribution. In attempting to explain the results for all systems we previously introduced a simple statistical modelg which accounts for the competition between the various degrees of freedom. The statistical model assumes that energy is transferred to all degrees of freedom with equal probability. Thus the relative energy transfer ( M,,)/E,, depends only on the total number of internal degrees of freedom and the collision strength T = E,,6,,. All the previous results, which were mostly at angles beyond the rainbow, for which resolved spectra are not available, could be nicely correlated within at least a factor 2 in the measured values for (a,,)/Ecmby the statistical model. For this reason it is of interest to study the trend of ( M , ) / E , with T for the systems studied here. Note that these data are available for much larger values of T at which the time-of-flightspectra could not be resolved into individual peaks. In Figure 8 we have plotted all the data for ( AEkt) / E , vs. T for H+ and D+ scattering from CH,, CF4, and SFG.All the experimental results are at angles less than the rainbow angles. With the exception of H+-CH4all the results fall on a common straight line. The nearly linear dependence on T is in accord with previous observations even though we do not have statistical behavior since only one mode is excited. The trends found
The Journal of Physical Chemistty, Voi. 86, No. 7, 1982 1181
Vibrational Excitation of CH,, CF, and SF, in Coliisions /
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1162
Ellenbroek et al.
The Journal of Physical Chemistry, Vol. 86, No. 7, 1982
Ecm= 922eV oH*-CH' Ecm= 958eV *D'-CFh =,E, 969eV OH'-CF, OD*-SF6 =E ,, 967eV vH'-SF, Ecm= 8 5 L eV o H*-SF6 Ecm=9 73 eV n H + - S F 6 Ecm=1390eV
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Figure 6. The measured best-fit relative transition probabilities P ( 0 - n ) for scattering from CF, are compared with Poisson distributions. This is achieved by plotting P(0-n )n I on a log scale vs. n. For a Poisson disMbutbn we expect a straight line with slope In e, where e = A€/hw. Thus a negatlve slope indicates e < 1, a horizontal line e = 1, and a positive slope e > 1. The frames a, b, c, and d are plotted in order of increasing relative velocity. The results reveal that e increases with increasing collision velocity and collision angle corresponding to decreasing collision time.
2 3 4 5 Ecm,d ,, CeV rad 1
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Figure 8. The measured total energy transfer, divided by the collision energy, E , is plotted as a function of E8, cm, where 8 is the scattering angle in the center-of-mass system, for all time of flight spectra, involving H+ or D+. The expected location of the classical rainbow angle of H+-SFB is indicated by RB. I
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Figure 9. The measured total energy transfer, divided by the collision energy, ,E IS plotted as a function of E,,$ cm for scattering of Li+ from CH, and CF,. The expected location of the classical rainbow angle of Li+-CF, is indicated by RB. Note the sharp rise in relative energy transfer at the classical rainbow angle.
no longer holds and different curves for ( AE,,) /Ecmare found for different values of Ecm.This is explained by the fact that beyond the classical rainbow repulsive forces begin to dominate in the interaction. The fact that the break occurs at angles larger than the rainbow is explained by semiclassical effects which tend to smear out the rainbow to larger angles. The same behavior was found for Li+-N2, CO, C02,and N 2 0 in the earlier s t ~ d i e s Slow .~~~ collisions lead to relatively more energy transfer than fast collisions. The smaller values for ( AE,,)/Ecmfor CF4 compared to CH4beyond the rainbow are not unexpected in view of the fact that the experimental evidence suggests that probably only one mode is excited in CF4 whereas
The Journal of phvsicel Chemistry, Vol. 86, No. 7, 1982 1163
Vibrational Excitation of CH,, CF, and SF, in Collisions
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Flgm 10. The measued total energy transfer, dMded by the collision energy E,, is plotted as a function of E,19 for scattering of LI+ from SF,.
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several if not all modes are equally excited in CHbu Figure 10 shows a similar plot for the Li+-SFe experimenta. Again the data at angles less than the rainbow angle correlate nicely with 7. The greater energy transfer compared to CF, is in accord with the weaker optical coupling of the ion electric field with the Raman-active u2 excitation found in CF4as compared to the infrared-active u4 excitation in the low-energy Li+-SF6 collisions. The distance dependence of the potential coupling to the Raman-active modes goes as R4 compared to R-2 for the infrared-active modes. At the higher energies, E, > 6.4 eV, no resolved spectra are available for Li+-SFe and thus the excited mode is not known. As found for CF4, the correlation with 7 breaks down for valuea somewhat greater than that a t which the rainbow occurs. As in CF4 slow collisions lead to relatively more energy transfer than fast collisions. Finally, it is perhaps of interest to note that the results for both Li+-CF4and Li+-sFe beyond the rainbow all fall on a common straight line, when (A&,,) is plotted against 7. The slope is greater for Li+-SFe than for Li+-CFb (18)The classical calculations suggest, in fact, that only two modes and the rotations are predominantly excited.lB (19) G. Schweizer, private communication.
In summary then we find that the newly studied systems show a new behavior in which optical coupling via the electrical field of the ion predominates. We do not feel, however, that these results basically invalidate the statistical model. Rather, in collisions of ions with molecules up to 10 eV there are two different types of collision mechanisms possible. For certain systems such as CH4 with special properties such as weak optical activity and small moments of inertia impulsive collisions involving the repulsive hard core predominate. As a result several modes are excited and a statistical model appears to provide a good approximate description. For other systems such as CF4 and SF6with strong optical activity the coupling is via long-range forces so that a specific mode is excited, at least for small values of 7. Even for these systems it is conceivable that for large values of 7 beyond the range of the present resolved experiments where the repulsive forces become important a more statistical distribution of the energy among the normal modes prevails. To gain further insight into the dynamics of these collisions, we have carried out extensive classical trajectory calculations for all the systems reported here.16 One of the important conclusions of this study is that by invoking anisotropic repulsive forces it has been possible to explain most of the observations reported here. This is perhaps surprising in view of the very large field strength (=lo8 V/cm) which the molecule experiences at a distance of closest approach of 0.3 nm. These fields correspond to a laser power of about 1013W/cm2 and are larger than those achieved in focussed high-power Q-switched lasers. Of course the field is only applied for a short time of about s during which the molecule is apparently not able to completely adjust to these high fields. Finally, it is interesting to compare these results with experiments of the neutral systems Ar-SF6 and Ne-SF, at 1 eV,2bwhich show much less energy transfer at small values of 7. However, at large values of 7 where repulsive forces dominate as in the Li+-SF6 collisions the average relative energy transfer shows a similar behavior as found for Li+-CF4 and Li+-SF6. Acknowledgment. We gratefully acknowledge the assistance of M. Wilde with the time-of-flightmeasurements for the Li+ systems. We learned much from discussions with D. Micha (Gainesville, Florida) whose visits were made possible by a NATO research grant. Also we thank M. Child (Oxford), R. N. Porter (Stoney Brook), and M. Quack (Gottingen) for their comments. Finally, we thank many of our laboratory colleagues for discussions and advice.
