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Semiclassical Transition Probabilities (S Matrix) of Vibrational—Translational Energy Transfer
1.(a) R. A. Marcus, Chem. Phys. Letters 7, 525 (1970);
1.cf. Proc. Conf. Potential Energy Surfaces Chem., University of California, Santa Cruz, California, 1970, 58 (1971).
1.(b) R. A. Marcus, J. Chem. Phys. 54, 3965 (1971).
2.J. N. L. Connor and R. A. Marcus, J. Chem. Phys. 55, 5636 (1971).
3.(a) W. H. Miller, J. Chem. Phys. 53, 1949 (1970);
3.W. H. Miller, (b) 53, 3578 (1970); , J. Chem. Phys.
3.W. H. Miller, (c) Chem. Phys. Letters 7, 431 (1970);
3.(d) J. Chem. Phys. 54, 5386 (1971).
4.Other examples of recent semiclassical work include (a) R. D. Levine and B. R. Johnson, Chem. Phys. Letters 7, 404 (1970);
4.R. D. Levine and B. R. Johnson, 8, 501 (1971), , Chem. Phys. Lett.
4.which also contain an approximate integral expression for the S‐matrix elements; (b) P. Pechukas, Phys. Rev. 181, 166, 174 (1969);
4.(c) I. L. Beigman, L. A. Varnshtein, and I. I. Sobel’man, Zh. Eksp. Teor. Fiz. 57, 1703 (1969)
4.[I. L. Beigman, L. A. Varnshtein, and I. I. Sobel’man, Sov. Phys. JETP 30, 920 (1970)];
4.(d) I. C. Percival and D. Richards, J. Phys. B 3, 315, 1035 (1970).
5.W. H. Wong and R. A. Marcus (unpublished data).
6.R. A. Marcus gives two alternative approximations, of which the one leading to Eq. (3.10) there is the present method (a). (Note: is denoted there by and the given later in Eq. (9a) is denoted there by ). Method (b), which does not employ either of the above approximations, is given in R. A. Marcus, (unpublished). Also derived there are Eqs. (7.7)–(7.9), which are the same as the present (9a), (9b), and (11).
7.J. Stine, W. H. Wong, and R. A. Marcus (unpublished).
8.D. Secrest and B. R. Johnson, J. Chem. Phys. 45, 4556 (1966).
9.H. Goldstein, Classical Mechanics (Addison‐Wesley, Reading, Mass., 1957), Chap. 8 and 9.
10.R. Schiller, Phys. Rev. 125, 1109 (1962).
11.M. Born, The Mechanics of the Atom (Bell and Sons, London, 1960), Chap. 1.
12.For some conditions, though not those in Tables I and II, it would be necessary to solve Hamilton’s equations in Cartesian coordinates, Q and R, and then transform the results to those in terms of w and R. Such a step is needed whenever n̄ becomes too near zero during a trajectory, for then w becomes inaccurate.
13.M. Attermeyer and R. A. Marcus, J. Chem. Phys. 52, 393 (1970).
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