Abstract
In this chapter approximate quantal methods for predicting reaction probabilities and cross sections will be discussed. Emphasis is placed upon practical methods which employ quantum dynamics for the reactive scattering of neutral, electronically adiabatic A + BC three-dimensional collisions. Some of the terminology and techniques used in this chapter will be considered in somewhat more detail in Chapter 17, where “accurate” methods for atom-diatom reactions are discussed.
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References
P. McGuire and D.J. Kouri, Quantum mechanical close coupling approach to molecular collisions: J z-conserving coupled states approximation, J. Chem. Phys. 60, 2488–2499 (1974).
R.T. Pack, Space-fixed vs. body-fixed axes in atom-diatomic molecule scattering: Sudden approximations, J. Chem. Phys. 60, 633–639 (1974).
T.G. Heil, S. Green, and D.J. Kouri, The coupled states approximation for scattering of two diatoms, J. Chem. Phys. 68, 2562–2583 (1968).
A.B. Elkowitz and R.E. Wyatt, Jz-con serving approximation for the hydrogen exchange reaction, Mol. Phys. 31, 189–201 (1976).
A. Kuppermann, G.C. Schatz, and J.P. Dwyer, Angular momentum decoupling approximations in the quantum dynamics of reactive systems, Chem. Phys. Lett. 45, 71–73 (1977).
R.A. Marcus, Analytical mechanics of chemical reactions III. Natural collision coordinates, J. Chem. Phys. 49, 2610–2616 (1968).
R.E. Wyatt, Theory of three-dimensional reactive collisions using natural collision coordinates, J. Chem. Phys. 56, 390–400 (1972).
A.C. Yates and W.A. Lester, A new H3 potential energy surface and its implication for chemical reaction, Chem. Phys. Lett. 24, 305–309 (1974).
B. Liu, Ab initio potential energy surface for H3, J. Chem. Phys. 58, 1925–1937 (1973).
D. Truhlar and R.E. Wyatt, History of H3 kinetics, Ann. Rev. Phys. Chem. 27, 1–43 (1976).
R.N. Porter and M. Karplus, Potential energy surface for H3, J. Chem. Phys. 40, 1105–1115 (1964).
M.J. Redmon and R.E. Wyatt, Computational methods for reactive scattering, Int. J. Quantum Chem. Symp. 11, 343–351 (1977).
K.T. Tang and M. Karplus, Quantum theory of (H, H2) scattering: Approximate treatments of reactive scattering, Phys. Rev. A 4, 1844–1858 (1971).
P. Roman, Advanced Quantum Theory, Addis on-Wesley, Reading, Mass. (1965), pp. 281–308, 370–377.
B.C. Eu, Energy dependence of reaction cross sections at high energy, Chem. Phys. 5, 95–106 (1974).
L.M. Raff and M. Karplus, Theoretical investigations of reactive scattering in molecular beams, K + CH3I and related systems, J. Chem. Phys. 44, 1212–1229 (1966).
M.E. Gersh and R.B. Bernstein, Measurement of the energy dependence of the cross section for the reaction K + CH3I → KI → + CH3 from 0.1 to 1.0 eV, J. Chem. Phys. 55, 4661–4663 (1971).
A. Kafri, Y. Shimoni, R.D. Levine, and S. Alexander, The Born approximation as a simple diagnostic method for direct molecular collisions with applications to CI + HI and F + H2 reactions, Chem. Phys. 13, 323–337 (1976).
M.J. Berry, F + H2, D2 and HD reactions: Chemical laser determination of the product vibrational state populations, J. Chem. Phys. 59, 6229–6253 (1973).
R.D. Coombe and G.C. Pimentel, Effects of rotation on the vibrational energy distributions in the reaction F + H2, J. Chem. Phys. 59, 1535–1536 (1973).
J.T. Muckerman, Classical dynamics of the reaction of fluorine atoms with hydrogen molecules II. Dependence on the potential energy surface, J. Chem. Phys. 56, 2997–3906 (1972).
M. Kimura, Theoretical consideration of the role of the Franck-Condon factor in chemical reactions, Chem. Phys. Lett. 45, 489–491 (1977).
D.A. Micha, Collision dynamics of three interacting atoms: The Faddeev equations, J. Chem. Phys. 57, 2184–2192 (1972).
S. Datz and R.E. Minturn, Study of the reaction Cs with Br2 in crossed molecular beams, J. Chem. Phys. 41, 1153–1154 (1964).
A. Henglein, Kinematics of ion-molecule reactions, in Molecular Beams and Reaction Kinetics, International School of Physics XLIV, Ch. Schlier, editor, Academic Press, New York (1970), pp. 139–183.
D.A. Micha and J. Yuan, Collision dynamics of three interacting atoms: The multiple collision expansion, J. Chem. Phys. 63, 5462–5469 (1975).
D.A. Micha and P. McGuire, Collision dynamics of three interacting atoms: Foundations of the spectator-stripping model, Chem. Phys. Lett. 17, 207–209 (1972).
J. Yuan and D.A. Micha, Collision dynamics of three interacting atoms: Stripping reactions of Ar+ H2 and K + I2, J. Chem. Phys. 64, 1032–1041 (1976).
J. Yuan and D.A. Micha, Collision dynamics of three interacting atoms: Electron transfer in the reactions of K + Br2, BrI, and I2, J. Chem. Phys. 65, 4876–4884 (1976).
D.H. Herschbach, Reactive scattering in molecular beams, Adv. Chem. Phys. 10, 319–393 (1966).
T.T. Warnock, R.B. Bernstein, and A.E. Grosser, Internal energy of reaction products by velocity analysis III. Product excitation function for K + Br2, J. Chem. Phys. 46, 1685–1693 (1967).
D.A. Micha, The exchange reaction of H and H2, Ark. Fysik 20, 425–436 (1965).
M. Karplus and K.T. Tang, Quantum mechanical study of H + H2 reactive scattering, Discuss. Faraday Soc. 44, 56–67 (1967).
B.H. Choi and K.T. Tang, Theory of distorted-wave Born approximation for reactive scattering of an atom and a diatomic molecule, J. Chem. Phys. 61, 5147–5157 (1974).
M. Karplus, Special results of theory: Distorted waves, in Molecular Beams and Reaction Kinetics, International School of Physics XLIV, Ch. Schlier, editor, Academic Press, New York (1970), pp. 406–426.
K.T. Tang and M. Karplus, Quantum theory of (H, H2) scattering: Two-body potential and elastic scattering, J. Chem. Phys. 49, 1676–1692 (1968).
W.H. Miller, Distorted wave theory for collisions of an atom and a diatomic molecule, J. Chem. Phys. 49, 2373–2381 (1968).
S.H. Suck, Theory of atom-diatom reactive scattering based on the distorted-wave Born approximation, Phys. Rev. A 15, 1893–1899 (1977).
B.H. Choi and K.T. Tang, Three-dimensional quantum mechanical studies of the H + H2 reactive scattering, J. Chem. Phys. 65, 5161–5180 (1976).
A.B. Elkowitz and R.E. Wyatt, Quantum mechanical reaction cross sections for the three-dimensional hydrogen exchange reaction, J. Chem. Phys. 62, 2504–2506 (1975).
G.C. Schatz and A. Kuppermann, Quantum mechanical reactive scattering for three- dimensional atom-diatom systems II. Accurate cross sections for H + H2, J. Chem. Phys. 65, 4668–4682 (1976).
K.T. Tang and B.H. Choi, Three-dimensional quantum mechanical studies of D + H2 → DH + H reactive scattering, J. Chem. Phys. 62, 3642–3658 (1975).
B.H. Choi and K.T. Tang, Three-dimensional quantum mechanical studies of D + H2 DH + H reactive scattering II, J. Chem. Phys. 63, 2854–2860 (1975).
J. Geddes, H.F. Krause, and W.L. Fite, Atom-molecule reaction D + H2 → DH + H studied by molecular beams, J. Chem. Phys. 56, 3298–3307 (1972).
R. Gengenbach, Ch. Hahn, and J.P. Toennies, Molecular beam measurements of the D + H2 potential and recalibration of the reactive cross section, J. Chem. Phys. 62, 3620–3630 (1975).
A. Kuppermann and J.M. White, Energy threshold for the D + H2 → DH + H reaction, J. Chem. Phys. 44, 4352–4353 (1966).
T.F. O’Malley, Simple model for the high energy reaction of O+ ions with N2, J. Chem. Phys. 52, 3269–3277 (1970).
D. Herschbach, Reactive scattering, Discuss. Faraday Soc. 55, 233–251 (1973).
M.J. Berry, Golden rule calculation of reaction product vibronic state distributions, Chem. Phys. Lett. 27, 73–77 (1974).
M. Baer, Isotopic reactive systems H + Cl2 and D + Cl2: A quantum mechanical treatment of the collinear arrangement, J. Chem. Phys. 60, 1058–1063 (1974).
B.C. Eu, Franck-Condon transitions and chemical reaction, Mol. Phys. 31, 1261–1276 (1976).
U. Halavee and M. Shapiro, A collinear analytic model for atom-diatom chemical reactions, J. Chem. Phys. 64, 2826–2839 (1976).
R.B. Walker and R.E. Wyatt, DWBA: Study of the collinear H + H2 reaction, Chem. Phys. Lett. 16, 52–56 (1972).
M. Shapiro and U. Halavee, The London formula and the product vibrational state distributions in A + BC → AB + C chemical reactions, Chem. Phys. Lett. 40, 381–386 (1976).
G.C. Schatz and J. Ross, Franck-Condon factors in studies of dynamics of chemical reactions I. General theory, application to collinear atom-diatom reactions, J. Chem. Phys. 66, 1021–1037 (1977).
S. Fischer and G. Venzl, On the dynamics of exothermic triatomic exchange reaction, J. Chem. Phys. 67, 1335–1343 (1977).
S. Mukamel and J. Ross, On the quasiadabatic description of the dynamics of electronically adiabatic chemical reactions, J. Chem. Phys. 66, 3759–3786 (1977).
G.C. Schatz and J. Ross, Franck-Condon factors in studies of dynamics of chemical reactions II. Vibration-rotation distributions in atom-diatom reactions, J. Chem. Phys. 66, 1037–1053 (1977).
R.E. Wyatt, Information theoretic analysis of quantum mechanical reaction cross sections, Chem. Phys. Lett. 34, 167–169 (1975).
E. Pollak, Rotational surprisal plots for H + H2: A simple theory, Chem. Phys. Lett. 47, 513–516 (1977).
J.C. Polanyi and K.B. Woodall, Energy distribution among reaction products VI. F + H2, D2, J. Chem. Phys. 57, 1574–1586 (1972).
M.J. Berry, F + H2,D2, HD reactions: chemical laser determination of the product vibrational state populations and the F + HD isotope effect, J. Chem. Phys. 59, 6229–6253 (1973).
G.C. Schatz and J. Ross, Franck-Condon factors in studies of the dynamics of chemical reactions III. Analysis of information theory for vibration rotation distributions and isotopic branching ratios, J. Chem. Phys. 66, 2943–2958 (1977).
T.F. George and J. Ross, Analysis of symmetry in chemical reactions, J. Chem. Phys. 55, 3851–3866 (1971).
H. Metiu, J. Ross, and T.F. George, Symmetry rules for nonconcerted reactions, Chem. Phys. 11, 259–272 (1975).
Y.B. Band and K.F. Freed, Energy distribution in selected fragment vibrations in dissociation processes in polyatomic molecules, J. Chem. Phys. 67, 1462–1472 (1977).
K.F. Freed and Y.B. Band, Product energy distributions in the dissociation of polyatomic molecules, in Excited States, Vol. 3, E.C. Lim, editor, Academic Press, New York (1977), pp. 110–203.
D.A. Micha, Optical models in molecular collision theory, in Dynamics of Molecular Collisions, Part A, W.H. Miller, editor, Plenum Press, New York, (1976), p. 81.
J.N.L. Connor, W. Jakubetz, and J. Manz, Information theoretic analysis and collinear to three-dimensional transformation of reaction probabilities for F + H2, H + F2, H + C12 and D + C12, Chem. Phys. 17, 451–469 (1976).
R.B. Bernstein and R.D. Levine, The relation between collinear and 3D dynamical calculations of reactive molecular collisions, Chem. Phys. Lett. 29, 314–318 (1974).
M. Baer, Weak and strong interactions in chemical reactions, J. Chem. Phys. 62, 4545–4550 (1975).
R.B. Walker and R.E. Wyatt, Three-dimensional reaction cross sections from planar scattering data, Mol. Phys. 28, 101–111 (1974).
J.C. Light and A. Altenberger-Siczek, Practical approximation to reaction probabilities from selected initial quantum states, Chem. Phys. Lett. 30, 195–199 (1975).
J.M. Bowman and K.T. Lee, Sudden approximation calculations of reactive scattering: The H + H2 reaction, J. Chem. Phys. 68, 3940–3941 (1978).
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© 1979 Plenum Press, New York
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Wyatt, R.E. (1979). Reactive Scattering Cross Sections II: Approximate Quantal Treatments. In: Bernstein, R.B. (eds) Atom - Molecule Collision Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2913-8_15
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DOI: https://doi.org/10.1007/978-1-4613-2913-8_15
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