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A new tunneling path for reactions such as H+H2→H2+H
1.E.g., D. G. Truhlar and A. Kuppermann, J. Am. Chem. Soc. 93, 184 (1970);
1.D. G. Truhlar and A. Kuppermann, Chem. Phys. Lett. 9, 269 (1971);
1.G. C. Schatz and A. Kuppermann, J. Chem. Phys. 65, 4668 (1976) and references cited therein;
1.E. Mortensen, J. Chem. Phys. 48, 4029 (1968)., J. Chem. Phys.
2.(a) T. F. George and W. H. Miller, J. Chem. Phys. 56, 5722 (1972);
2.(b) T. F. George and W. H. Miller, J. Chem. Phys. 57, 2458 (1972)., J. Chem. Phys.
3.J. R. Stine, Ph.D. Thesis, University of Illinois, 1974.
4.(a) W. H. Miller, J. Chem. Phys. 62, 1899 (1975);
4.(b) S. Chapman, B. C. Garrett, and W. H. Miller, J. Chem. Phys. 63, 2710 (1975).
5.S. Glasstone, K. J. Laidler, and H. Eyring, The Theory of Rate Processes (McGraw‐Hill, New York, 1941), p. 100.
6.For a reaction of three atoms of masses and in a line, with denoting the distance between and and denoting the distance between and the coordinates x and y in Figs. 1–3 are defined by with and Here, denotes the acute angle in Fig. 1. The coordinates x, y have the property that they di‐agonalize the kinetic energy, and both have a single mass μ, in the center of mass system of coordinates, i.e., the kinetic energy in this system is with
7.Compare with J. N. L. Connor, Molec. Phys. 15, 37 (1968), Eqs. (14), (15), (18), and (19). The transmission coefficient is the ratio of the transmitted to incident flux, and is calculated from the wave functions in Eqs. (14) and (15), and found to give the present Eq. (2.6). The mapping equations are Eqs. (18) and (19).
8.R. N. Porter and M. Karplus, J. Chem. Phys. 40, 1105 (1964).
9.G. C. Schatz and A. Kuppermann (private communication from G. C. Schatz);
9.cf. Fig. 6 of Ref. 4(b);
9.J. W. Duff and D. G. Truhlar, Chem. Phys. Lett. 23, 327 (1973).
10.(a) D. G. Truhlar and A. Kuppermann, J. Chem. Phys. 52, 3841 (1970);
10.(b) D. G. Truhlar and A. Kuppermann, J. Chem. Phys. 56, 2232 (1972)., J. Chem. Phys.
11.Reference 10 gives a fit to the results of a calculation of the surface in I. Shavitt, R. M. Stevens, F. L. Minn, and M. Karplus, J. Chem. Phys. 48, 2700 (1968)
11.to the functional form given in F. T. Wall and R. N. Porter, J. Chem. Phys. 36, 3256 (1962).
11.The fit is actually to a scaled version of SSMK, scaled as per the suggestion of I. Shavitt, J. Chem. Phys. 49, 4048 (1968).
12.R. A. Marcus, J. Chem. Phys. 45, 2138 (1966). cf. Eqs. (3) and (4).
13.For example, (a) M. Born, Mechanics of the Atom (Ungar, New York, 1960);
13.(b) J. B. Keller, Ann. Phys. (N.Y.) 4, 180 (1958);
13.(c) R. A. Marcus, Chem. Phys. Lett. 7, 525 (1970);
13.(d) R. A. Marcus, J. Chem. Phys. 59, 5125 (1973);
13.(e) W. H. Miller, Adv. Chem. Phys. 25, 69 (1974) and references cited therein;
13.(f) W. H. Miller, J. Chem. Phys. 54, 5386 (1971);
13.(g) cf. integral expression in W. H. Miller, J. Chem. Phys. 53, 3578 (1970).
14.(a) J. O. Hirschfelder and E. Wigner, J. Chem. Phys. 7, 616 (1939), who considered a quantum system rather than a trajectory;
14.(b) Nonadiabatic effects in the classical mechanics of reactions are discussed in R. A. Marcus, J. Chem. Phys. 45, 4500 (1966).
14.Vibrational adiabaticity has been used by (c) M. A. Eliason and J. O. Hirschfelder, J. Chem. Phys. 30, 1426 (1959); , J. Chem. Phys.
14.(d) L. Hofacker, Z. Naturforsch. Teil A 18, 607 (1963);
14.(e) R. A. Marcus, J. Chem. Phys. 43, 1598 (1966), which coined the term “vibrational adiabaticity,”
14.and (f) R. A. Marcus, J. Chem. Phys. 46, 959 (1967).
15.Compare with H. C. Corben and P. Stehle, Classical Mechanics (Wiley, New York, 1964), 2nd ed., p. 170 Eq. (57.12).
16.For example, in Fig. 8 of S. F. Wu and R. A. Marcus, J. Chem. Phys. 53, 4026 (1970), the trajectories for some initial phases are unreactive while others are reactive.
16.The second group thereby has no real‐valued Unpublished trajectory studies of J. R. Stine in this laboratory showed analogous effects.
16.Compare with R. A. Marcus, Ber. Bunsenges. Phys. Chem. 81, 190 (1977) for a qualitative discussion of nonadiabatic effects.
17.R. A. Marcus, Ref. 13(f) cf, Ref. 13(b).
18.Judging from the results near these effects appear to be larger for the Porter‐Karplus surface than for the Wall‐Porter one.
19.H. S. Johnston and D. Rapp, J. Am. Chem. Soc. 83, 1 (1961).
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