long-lived complexes in molecular collisions
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LongLived Complexes in Molecular CollisionsDavid O. Ham and James L. Kinsey Citation: The Journal of Chemical Physics 48, 939 (1968); doi: 10.1063/1.1668740 View online: http://dx.doi.org/10.1063/1.1668740 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/48/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in A comparison of exact classical and quantum mechanical calculations of vibrational energy transfer. II.The effect of longlived collision complexes J. Chem. Phys. 67, 5923 (1977); 10.1063/1.434799 Longlived molecular Rydberg states J. Chem. Phys. 62, 741 (1975); 10.1063/1.430444 Classical trajectory studies of longlived collision complexes. I. Reaction of K atoms with NaClmolecules J. Chem. Phys. 58, 1722 (1973); 10.1063/1.1679417 Effects of LongLived Collisions in the Boltzmann Equation J. Chem. Phys. 57, 5562 (1972); 10.1063/1.1678257 LongLived Collision Complexes in Molecular Beam Scattering Experiments J. Chem. Phys. 53, 285 (1970); 10.1063/1.1673777
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THE JOURNAL OF CHEMICAL PHYSICS
Letters to the Editor
T HE Letters to the Editor section is subdivided into four categories entitled Communications, Notes, Comments, and Errata.
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Communications
Long-Lived Complexes in Molecular Collisions*
DAVID O. HAM AND JAMES L. KINSEyt
Department of Chemistry and Research Laboratory of Electronics, Massachusetts Institute of Technology,
Cambridge, Massachusetts
(Received 19 October 1967)
Until recently all chemical reactions studied in crossed molecular beams were found to occur in short times, comparable to a vibrational period.l We have investigated the systems K with S02, CO2, and NO, and Cs with S02, CO2, and N02 for which there was previous evidence from diffusion flame experiments for the existence of long-lived collision complexes.2 Our experiments were crossed molecular beam experiments in which the alkali beam was velocity selected to allow variation of the incident translational energy. We find clear evidence of complexes with lifetimes long compared to a rotation time of the complex. For all systems except Cs+ N02, reaction in a single collision is not possible because all reaction paths are too endothermic. Therefore, observation of a sticky collision in these cases constitutes direct verification of the first step of a multistep reaction mechanism. Miller, Safron, and Herschbach have recently observed similar evidence of long-lived complexes in reactive systems.s '
A complex which sticks together for a very long time (several rotations) should dissociate with equal probability in all ways consistent with the applicable conservation laws. Since the final and initial orbital
VOLUME 48, NUMBER 2 15 JANUARY 1968
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LABORATORY ANGLE e
---<'>- o~ --_~~t::.t::.6.lS. , "-
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80 100 120 140 160 180 CENTER-Of-MASS ANGLE X
FIG. 1. (a) Three laboratory curves at relative energies indicated, displaced vertically for presentation. (b) Circles and triangles: data points for a 1.2 kca1/mole K +S(h run transformed to e&nter-of-mass coordinates with Q=O. Solid line: predicted curve from crude statistical theory. Dotted line: hard-sphere prediction. Dashed line: classical exp-6 prediction for e=O.60 kcal/mole and 0.=12. All curves normalized at 90°.
angular momenta are large compared to the rotational angular momenta of the molecules in these experiments, the trajectories of the scattered particles are confined to within a few degrees of the plane of the initial trajectories. These two conditions combine to give a predicted center-of-mass (c.m.) angular distribution in which u(x)sin~const, except near 00 and 180° ex is the c.m. scattering angle and u(x) is the differential scattering cross section].' When transformed into laboratory coordinates such a distribution gives peaks at laboratory angles near those corresponding to x=O° and x=180°. Our observed angular distributions are the sum of the sticky collision contributions plus forward-peaked contributions from normal, impulsive scattering events not involving complex formation.
Figure 1(a) shows laboratory angular distributions obtained in three of our experimental runs. A large peak is observed near the angle predicted from the above arguments using the c.m.~laboratory transformations for elastic scattering. The smaller amplitude of the peak in the CO2 run shows that the total cross section for complex formation is a smaller fraction of the total scattering cross section for CO2 than for S02. In each case the peak appears at a slightly smaller angle than that predicted for elastic scattering, indicating a negative average value of Q. Q is the difference, ER' -:'!!.R, between the final and initial relative translational energies.
The observed peaks are broadened by: (1) the finite 939
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940 LETTERS TO THE EDITOR J. CHEM. PHYS., VOL. 48, 1968
size of the beams and a distribution of angles of intersections, (2) the velocity distribution in the thermal beam, and (3) a distribution in the values of Q. For an assumed Q distribution the effects of (1) and (2) can be taken into account in a calculation of a predicted curve shape. A Q distribution which is consistent with the experimental results can be determined by comparing such calculated curves with the experimental curves. In this way, we have found that the Q distribution is broad and centered about a negative Q. The change in the 802 curves with energy can be calculated from kinematics only, although ER ranges from below the energy of the lowest vibrational level of 802 to about 2.5 times that amount. Therefore, we conclude that vibrational excitation in a sticky collision is very small in this energy range.
Figure 1 (b) shows the wide-angle part of the data for a 1.2-kcal K +802 run transformed approximately to the c.m. coordinate system assuming Q=O and using only the most probable initial velocities. The fact that the points follow O"(x)sinx=const out to such large angles clearly indicates the existence of a long-lived complex. The open circles correspond to points transformed from laboratory angles (J smaller than (JlJj(), the lab angle corresponding to x= 180°. The triangles are for points with (J>(J180 that map onto the same c.m. angles. The failure of both sets of points to fall on a smooth curve is a further indication that Q is actually slightly negative. The total cross section for complex formation can be estimated as (Acomp/ A tot) 0"1,
where Atot is the total area under the transformed O"(x)sinx curve, Acomp is that part of the area due to the complex, and 0"1 the total scattering cross section (obtained from the tabulation of Rothe and Bernstein6) •
We obtain 350 12 for the K+802 complex. Also shown in the figure are three computed curves.
The solid curve is calculated from a crude statistical theory6 in which there is a single adjustable parameter K roughly equal to the ratio of the average change in rotational angular momentum (I1j)A. to the maximum orbital angular momentum 1* for which a complex can be formed. The curve shown is for K=0.3, the value giving the best fit to the data. This value is only to be taken as qualitatively meaningful, however, because of the approximate nature of both the theory and the transformation. The other two curves shown in Fig. 1 (b) for comparison are those for hard-sphere scattering (dotted line) and scattering from an exp-6 potential with estimated parameters for the K+802
system (dashed line) .7
Calculations are now in progress to predict a Q distribution from the statistical theory of Light and co-workers.8 We are also working on a statistical theory for prediction of angular distribution.
* This work was supported in part by the Joint Services Electronics Program under Contract DA-36-039-AMC-03200(E), and in part by the National Science Foundation.
t Alfred P. Sloan Fellow. 1 D. R. Herschbach, Advan. Chern. Phys. 10, 332 (1966). 2 C. E. H. Bawn and A. G. Evans, Trans. Faraday Soc. 33,
1580 (1937). 8 W. B. Miller, S. A. Safron, and D. R. Herschbach, in a paper
presented at the Discussions of the Faraday Society, Toronto, 6 September 1967, Discussions Faraday Soc. (to be published). A brief description of our work was presented in the general discussion which followed this paper.
4 D. R. Herschbach, Discussions Faraday Soc. 33, 153 (1962). Ii E. W. Rothe and R. B. Bernstein, J. Chern. Phys. 31, 1619
(1959). 6 D. O. Ham and J. L. Kinsey (to be published). 7 E. A. Mason, J. Chern. Phys. 26, 667 (1957). 8 P. Pechukas, J. C. Light, and C. Rankin, J. Chern. Phys. 44,
794 (1966) and references contained therein.
Hydrogen Formation and Superexcited States in the Radiolysis of
Liquid Olefins
YOSHIHIKO HATANO AND SHOJI SHIDA
Tokyo Institute of Technology, Meguro-ku, Tokyo, Japan
AND
MITrO lNOKUTI
Argonne National Laboratory, Argonne, Illinois
(Received 31 October 1967)
In a previous paperl on the radiolyses of liquid 1-butene and trans-2-butene, evidence was presented for a possible role of hot hydrogen atoms in radiation chemistry. Namely, hydrogen formation was interpreted in terms of the hydrogen-atom abstraction reaction by "hot" hydrogen atoms, with kinetic or electronic energies, formed by direct excitation which must at least partially involve superexcitation.2 The purpose of the present Communication is twofold: firstly to report new data on liquid ethylene and propylene, and secondly to attempt quantitative substantiation of the previous viewpoint.!
The yield g., per 100 eV energy absorbed, of a primary decomposition channel s may be estimated by the optical approximation.2 Namely, g. is taken as proportional to an effective dipole matrix element squared for s (in atomic units) :
fOO R df
M2= cp (E) -- dE • J.' E dE '
(1)
where E is the excitation energy, R the Rydberg energy, df/dE the differential oscillator strength, cp.(E) the probability of decomposition s upon excitation at E, and J. the threshold excitation energy for s. Utilizin~ data on ionization, namely the W value (in electron volts) and M.2, the dipole matrix element squared for ionization [defined in a way similar to
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