The Journal of
Physical Chemistry
0 Copyright, 1984, by the American Chemical Society
VOLUME 88, NUMBER 1
JANUARY 5,1984
LETTERS Rotational Energy Transfer in the He-N, Collision System Aristophanes Metropoulos' Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation,$Athens 50111, Greece, and Department of Marine Sciences,l Texas A&M University at Galveston, Galveston, Texas 77553 (Received: July 22, 1983; In Final Form: September 30, 1983)
Various cross sections of the He-N, system are obtained, many for the first time, by the classical trajectory method. The total differential cross sections are compared with available experimental and quantum mechanical results. The existence of a lower scattering angle threshold for each final rotational state of Nz is noted.
Introduction In recent years there has been strong interest in extending our understanding of van der Waals systems of the type (rare atom)-H,] to heavier but chemically more typical systems such Habitz et aL6 have extended the disas the He-N2 persion type potential model of Tang and Toennies7 from its (rare atom)-(rare atom) form to a (rare atom)-(homonuclear diatom, rigid rotor) form with parameters especially selected for the H e N z system. Keil et aL3 have performed crossed beam experiments to study the rotational energy transfer in He-N2 collisions at a relative collision energy that does not excite the vibrational modes of N, (64 meV). Habitz et a1.6 using their He-N, potential and the close coupling approximation reproduced to a very good degree the undulatory form of the experimental differential cross sections of Keil et aL3 Here, we study mainly some of the unexplored aspects of the reaction He
+ N2(j)
-
He
+ N2(j1)
(1)
at 64-meV relative collision energy, using the classical trajectory method with the potential of Habitz et a1.6 We obtain the integral 'Address correspondence to the Texas A&M University until March 1984. *Vas. Constantinou 48. PO Box 1675.
0022-3654/84/2088-0001.$01.50/0
state-to-state cross sections ujdY for rotational energy transfer, the integral inelastic differential cross sections dcy,,/dw, the integral state-to-state differential cross sections dupy/dw for each individual j', and the integral total (elastic plus inelastic) differential cross sections da/do. The last cross sections are compared to the corresponding experimental3 and close coupling6cross sections and serve as a qualitative test of the classical trajectory method but mainly as an accuracy test for the state-to-state cross sections for which no other data are available to our knowledge. (1) L. Zandee and J. Reuss, Chem. Phys., 26, 327, 345 (1977); W. R. Gentry and C. F. Giese, J . Chem. Phys., 67, 5389 (1977); U. Buck, F. Huisken, and J. Schleusener, Ibid., 68, 5654 (1978); K. T. Tang and J. P. Toennies, Ibid., 68, 5501 (1978); 74, 1148 (1981); 76, 2524 (1982); J. Andres, U. Buck, F. Huisken, J. Schleusener, and F. Torello, Ibid., 73, 5620 (1980); W. Meyer, P. C. Hahiharn, and W. Kutzelnigg, ibid., 73, 1880 (1980); D. E. Fitz, V. Khare, and D. J. Kouri, Chem. Phys., 56, 267 (1981). (2) W. Erlewein, M. von Seggern, and J. P. Toennies, Z. Phys., 211, 35 (1968). (3) M. Keil, J. T. Slankas, and A. Kuppermann, J . Chem. Phys., 70, 541 (1979). (4) M. Faubel, K. H. Kohl, and J. P. Toennies, J . Chem. Phys., 73,2506 (1980); Prog. Astronaut. Aeronaut., 74, 862 (1981). (5) M. Faubel, K. H. Kohl, J. P. Toennies, K. T. Tang, and Y. Y. Yung, Faraday Discuss. Chem. SOC.,73 (1982). (6) P. Habitz, K. T. Tang, and J. P. Toennies, Chem. Phys. Lett., 85, 461 (1982). (7) K. T. Tang and J. P. Toennies, J . Chem. Phys., 66, 1496 (1977); for errata see Ibid., 67, 375 (1977); 68, 786 (1978).
0 1984 American Chemical Society
2
The Journal of Physical Chemistry, Vol. 88, No. 1, 1984
Computational Method We employ the usual classical trajectory method,* using the coordinate system of Chapman et alS9with an initial orientation given by LaBudde et al.IO Briefly, this amounts to fixing the origin of the coordinate system on the center of mass (CM) of N2,using Cartesian coordinates for the motion of He and spherical coordinates for the rotation of N2. Initially, He is assumed to move on the yz plane parallel to the z axis. The canonical coordinates are initialized and the equations of motion are integrated by the Runge-Kutta-Gill method with a variable step. The computation of uJdJt is done by approximating the expression uJ-Jt = 2 ~ l ; b P ~ , ~(b) , db by the sum uJdJI= 2aC~,b,PJ,, (b,) Ab, = ( 2 ~ b ~ , , / N ) ~ ~ ~ b(b,), , P , where - ~ ~ b is the impact parameter, P,-], is the probability of the transition j j’, b,,, is that b for which Pl,,(bLbmax) E 0, N is the total number of trajectories run, and we have chosen to replace the interval Ab, by b,,,/N so that each such interval contains only one value of b. By inverting the expression J: = j,G, + l)h2,where J, is the computed final rotational angular momentum of N2,we obtain a “classical” j, laying between two integers j’and j’+ 2 (or J’ and J’+ 1 for heteronuclear diatoms). We can now express Ppx (b,)in two ways which is equivalent to devising two different binning methods. First, if j , Ij’ + 1 we set PJdJ,(bi) = 1 and all other P’s equal to zero; if]’+ 1 C jCI j’+ 2 we set PJ-J,+2(b,) = 1 and all other P‘s equal to zero. This is equivalent to the usual procedure of quantizing j , and it is called here the direct binning method. Second, we can assume that each j , may be “distributed” between j’and j’+ 2, in a way depending on its value, rather than being assigned exclusively to either j’or j’ 2. This is done by setting PJ+J,(b,)= (j’ 2 - j c ) / 2 and PJyJ,+2(b,) = (j, - j 9 / 2 . This is called here the proportional binning method. Thus, the direct binning method gives
Letters 30
1 ---- proportional binning method -direct binning method
a -
9
‘7
6-
-
+
+
N uj-j(
= (2Tbmax/N)CbiAjf
