J. phys. Chem. 1982, 86, 429-430
429
Frame Dlstortlorr as a Possible Mechanism for Colllslon-Induced Infrared Absorption Shmuel We188 Depertment of Chernkm, Bekowkn UnhwdtJf,Beer-Sheva, Israel (Rwiv&: August 6, lS81)
The possibility that frame distortion may be of importance in causing collision-induced infrared absorption is considered and the He-COZcase is chosen as a specific example. It is concluded that frame distortion may be responsible for far-infrared absorption of the same order of magnitude as that caused by overlap momenta. Introduction In collision-induced infrared spectroscopy two mechanisms are usually considered responsible for producing the spectra The main mechanism is the induction of a dipole in one molecule by the electrostatic field due to a multipole moment of another molecule. A leas important-in terms of the intensity produced-mechanism involves the appearance of overlap momenta, caused by electron cloud distortion, during the collision of unlike molecules. It is this last mechanism which is responsible for the collision-induced absorption spectra of rare gas mixtures. It is, however, possible that yet a third mechanism is operative. When, say, an He atom collides with a COz molecule such that it hits the C atom, the COz molecule will be bent and since the C-O bond moment is appreciable, a nonnegligible net dipole moment will appear and may be expected to give rise to absorption. In a sense this mechanism may be viewed as an intensity borrowing coupling between the far-infrared band of the H&02 pair and the allowed, intense, COz bending vibration. A number of years ago an attempt was made by Bar-Ziv and Weiss' to find evidence for this frame distortion mechanism. They studied spectra of mixtures of He with COz, CHI, and CzHBover their high-frequency part. The reason for the use of He was that ita exceptionally low polarizability suppresses absorption induced by the multipole momenta of the polyatomic molecules (the first mechanism mentioned above). The spectra obtained resembled in intensity as well as in position and shape the spectra of mixtures of helium with rare gases. More recently, Afanasev, Bulanin, and Tonkov2studied the farinfrared He-CF4 spectrum with similar results. The integrated intensity they obtained at 213 K is 0.9 X 10" cmm2 amagat-2 as compared to the integrated intensity of the He-Ar spectrum which at the same temperature should bea 1.2 X 10" cm-z amagaF. Since we do not know with which rare gas spectrum an He-C02 or He-CF4 spectrum should be compared or indeed whether rare gas overlap dipoles are closely similar to those of He-polyatomics pairs, we cannot determine by comparison with rare gas spectra to what extent the frame distortion mechanism is operative in producing the Hepolyatomics spectra. To try to answer this question we shall resort to computation. Using the known C-0 bond moment we shall estimate, for a number of simple cases, the magnitude of the "bending dipole" in an He-CO2 collision and calculate the spectrum produced by ita appearance. Computations Ideally the computation should aim at the reproduction of the spectrum of an H&02 mixture from first principles (1)E.Bar-Ziv and S. Weiss, J. Chem. Phys., 67,34 (1972). M. 0. Bulanin, and M. V. Tonkov, Can. J. Phys., (2)A. D.Af-ev, 68, 836 (1980). (3)E.Bar-Ziv and S. Weiss, J. Chem. Phys., 64,2412 (1976). 0022-3654/82/208&0429$01.25/0
using such data as the intermolecular potential, the bond moment, bending force constant and the like. Such a calculation would, however, be very difficult to perform. To characterize a collision one would need no less than six parameters (relative velocity, two numbers to describe the impact parameter, the angle between the initial velocity and the COz axis, and two numbers to describe the state of the bending oscillation). For each collision the trajectory would have to be calculated numerically and the results averaged over the six collision parameters. We therefore content ourselves with calculating trajectories and spectra for only a few simple cases in the hope that they will shed sufficient light on the general case. We thus limit ourselves to cases where the impact parameter relative to the C atom is zero and the motion is at right angles to the COz axis. The calculation is classical which, in view of the low frequency of the COzbending vibration, should not introduce excessive errors. The bending dipoles and the spectra they produce are compared with the overlap moments and the spectra to which they give rise. Our notation is obvious from Figure 1. Setting up the appropriate Lagrange equations we obtain for small oscillations two coupled second-order differential equations 1 a4 M -[mHe(mC 2mo)Y + 2mH,moliu'] = --ar
+
1 -[2(m~,
+ mc)mo12di + 2mHemolP]= -ka
M where M = mHe+ mc + 2mo, r is the C-He distance, 12 is the bending force constant, 1 is the C-0 distance, and 4 is the intermolecular potential. These equations are transformed to contain a single second derivative in each and then solved numerically by the fourth-order R u n g e Kutta m e t h ~ d . ~ k was set so as to reproduce the COz bending frequency (667 cm-l), 1 was taken as 1.16 A, and 4 was taken to be a Lennard-Jones 12-6 potential with = 6.02 X erg and CT = 3.3 A (these values were obtained from potential parameters for COz and for the HeS,using the usual combination rules). Once the trajectory is known, induced dipoles are easily calculated. The bending dipole is obtained from &.,ending = 2 X B.M. X sin a where B.M. is the C-O bond moment which we have taken as 1.33 Das The overlap moment is obtained from Foverhp = PO ~ x P ( - ~ / P ) with po = 153 D and p = 0.34 A, which are parameters (4)See, e.g., H.Margenau and G. M. Murphy, 'The Mathematics of Physics and Chemistry", 2nd ed, D. Van Nostrand Co., Inc., 1956. (5) J. 0.Hirachfelder, C. F. Curtias, and R. B.Bird,'Molecular Theory of Gases and Liquids", Wiley, New York, 1954. (6)D.Steele, Quart. Reu., 18, 21 (1964).
0 1982 American Chemical Society
430
Weiss
The Journal of Physical Chemistry, Vol. 86, No. 3, 1982
.p l a
e
v)
k
Z 3
>.
a: 4
a:
tm. Flgure 1. He-CO, colllslon.
corresponding to He-Ar.' Once the temporal behavior of the dipole is known, it may be Fourier transformed to obtain the corresponding spectrum as outlined by Levine and Birnbaum.8 As a first case we take the C02 to be initially unbent, a = 0, & = 0, and the He atom to approach at thermal velocity '/& = '/&BT &reduced mass, T = 300 K). The At step used was quite small-6 X s; the total energy was found to be constant throughout to better than 0.1%. It turns out that the C02is bent only very slightly during the collision, a reaching a maximum value of 0.27' (a= -0.27Oby our notation) and p= 0.0120D as compared = 0.018 D. Calculations for cases in which the to povarkp C02 was allowed to oscillate before the collision with an amplitude of 2.1° (corresponding to ' / & a 2 = ' / z k ~ T ) c o n f i i that collision at thermal velocity causes only very small additional bending. At lower velocities the bending is of course smaller being a maximum of 0.05' at one-third of the thermal velocity. At twice the thermal velocity, on the other hand, the maximum bending is 0 . 9 2 O with p h b = 0.043D as compared to a maximum overlap moment of only 0.032 D. The spectra reflect the behavior of the dipoles. The spectrum for the thermal relative velocity case is reproduced in Figure 2 and it is seen that at the peak the overlap spectrum is about twice as intense as that of the bending dipole spectrum. At one-third the thermal velocity the overlap spectrum peak is about four times that of the bending spectrum. Finally, we investigated the effect of replacing the He by a heavier atom. To do this we replaced the atomic weight of He by that of Ar,changing the thermal velocity correspondingly but leaving the potential parameters unchanged. The maximum bending was found to be 0.24O, similar to that found for the He-C02 case at thermal velocity (0.27O). The ratio of spectral intensities is also similar.
a:
a
cm"
Flgwe 2. The spectrum produced by He coHkling with CO, at thermal veloctty. The He has zero Impact parameter relative to the C atom and Ita traJectory Is at rlgM angles to the COPaxls: (a) spectrum due to bending dlpole; (b) spectrum due to overlap moment.
possible values for the potential and dipole parameters, we estimate that the ratio of wMhP to the phe* we found could easily be off by f50%. Another point is that in collisions in which the angle between the initial velocity and the C02axis is not 90° only the component of the velocity which is at right angles to the COz axis will be operative in bending the molecule. This will clearly decrease the contributions to the bending spectrum while leaving the overlap spectrum unaffected (to a first approximation). The effect of nonzero impact parameters is harder to assess and lacking further information one may probably assume that both spectra are similarly affected. Finally, we should note that in actuality the bending and overlap momenta add. Now theoretical calculations for the rare gases have shown that the sense of the overlap moplent is always such that the heavier atom is negative? If this carries over to He-C02 it will mean that at collision the overlap and bending momenta have opposite signs since the overlap moment will have the C atom as the negative end whereas the bending dipole, represented by 0'
He-
- IC+ \
0
Discussion Before referring to the resulta, a few complicatingfactors should be considered. The first is that in actuality the H e C 0 2 potential is an anisotropic one rather than the isotropic U potential we used, and the second is that our potential parameters are crude estimates in any case. Also, it is not obvious that the overlap moment parameters for He-C02 should be the same as those for He-Ar even though COz resembles Ar in mass. Having tried other
will have the C as the positive end. Partial cancellation may therefore be expected. Returning now to our results and bearing in mind our previous comments, we reach the following conclusions. (a) Frame distortion gives rise to collision-induced absorption in the far-infrared region. At room temperature, for molecules having a low-frequency bending vibration, this absorption may be of the same order of magnitude as that due to overlap momenta. The relative importance of frame distortion increases with temperature. (b) In analyzing collision-induced far-infrared spectra involving polyatomics one should take into account the possibility of frame distortion contribution.
(7)J. L. Hunt and D. Poll,Can. J. Phys., 66, 960 (1978). (8)H.B. Levine and G. Birnbaum, Phys. Rev., 164,88 (1967).
(9)W.Byers Brown and D. M. Whianant, Mol. Phys., 26,1105 (1973); A. J. Lacey and W. Byers Brown, ibid., 27, 1013 (1974).
