Abstract
Substantial effort has been directed toward developing methods for describing molecular collision processes that are electronically adiabatic, i.e., for which it can be assumed that nuclear motion evolves on a single potential energy hypersurface. A number of recent reviews are devoted to this subject.(1–8) Considerably less attention has been paid to processes that are nonadiabatic,i.e., that involve electronic transitions between potential energy surfaces. This is in spite of the fact that nonadiabatic behavior is both common and important, even in thermal energy collisions.
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References
D. Rapp and T. Kassal. The theory of vibrational energy transfer between simple molecules in nonreactive collisions, Chem. Rev. 69, 61–102 (1969).
R. J. Cross, Jr., in: Molecular Beams and Reaction Kinetics (Ch. Shlier, ed.), pp. 50–61, Academic Press, Inc., New York (1970).
D. L. Bunker, Classical trajectory methods, Methods Comput. Phys. 10, 287–325 (1971).
R. D. Levine, in: MTP International Review of Science, Physical Chemistry (W. Byers-Brown, ed.), Vol. I, pp. 229–266, University Park Press, Baltimore (1972).
D. Secrest, Theory of rotational and vibrational energy transfer in molecules, Annu. Rev. Phys. Chem. 24, 379–406 (1973).
T. F. George and J. Ross, Quantum dynamical theory of molecular collisions, Annu. Rev. Phys. Chem. 24, 263–300 (1973).
J. C. Polanyi and J. L. Schreiber, in: Kinetics of Gas Reactions (H. Eyring, W. Jost, and D. Henderson, eds.), Chap. 9, Academic Press, Inc., New York (1974).
D. A. Micha, Quantum theory of reactive molecular collisions, Adv. Chem. Phys. 30, 221–260 (1975).
E. E. Nikitin, in: Chemische Elementarprozesse ( H. Hartmann, ed.), pp. 43–77, Springer-Verlag, Berlin (1968).
T. Watanabe, in: Advances in Chemistry. Radiation Chemistry II ( E. J. Hart, ed.), pp. 176–193, American Chemical Society, Wahington, D.C. (1968).
F. T. Smith, Elastic and inelastic atom-atom scattering, Lect. Theor. Phys. XIC, 95–117 (1969).
J. Callaway, Inelastic atom-atom collisions, Lect. Theor. Phys. XIC, 119–137 (1969).
E. Bauer, in: Kinetic Processes in Gases and Plasmas ( R. A. Hochstim, ed.), pp. 381–429, Academic Press, Inc., New York (1969).
R. S. Berry, in: Molecular Beams and Reaction Kinetics ( Ch. Schlier, ed.), pp. 193–228, Academic Press, Inc., New York, (1970).
R. S. Berry, in: Molecular Beams and Reaction Kinetics ( Ch. Schlier, ed.), pp. 229–248, Academic Press, Inc., New York, (1970).
N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions, Oxford University Press, London (1965).
H. S. W. Massey, Electronic and Ionic Impact Phenomena,Vol. III, Oxford University Press, London (1971), Chap. 18.
R. A. Mapelton, The Theory of Charge Exchange, John Wiley and Sons, Inc. ( Interscience Division ), New York (1972).
E. W. Thomas, Excitation in Heavy Particle Collisions, John Wiley and Sons, Inc. ( Interscience Division ), New York (1972).
E. E. Muschlitz, Collisions of electronically excited atoms and molecules, Adv. Chem. Phys. 10, 171–194 (1966).
B. A. Thrush, Gas reactions yielding electronically excited species, Annu. Rev. Phys. Chem. 19, 371–388 (1968).
F. R. Gilmore, E. Bauer, and J. W. McGowan, A review of atomic and molecular excitation mechanics in non-equilibrium gases up to 20,000°K, J. Quant. Spectrosc. Radiat. Transfer 9, 157–183 (1969).
R. B. Cundall, in: Transfer and Storage of Energy by Molecules (G. M. Burnett and A. M. North, eds.), Vol. I, pp. 1–63, John Wiley and Sons, Inc. (Interscience Division), New York (1969).
A. B. Callear and J. D. Lambert, in: Comprehensive Chemical Kinetics (C. H. Bamford and C. F. H. Tipper, eds.), Vol. 3, pp. 182–273, Elsevier Publishing Company, Amsterdam (1969).
I. W. M. Smith, in: The Role of the Excited State in Chemical Physics (J. W. McGowan, ed.), John Wiley and Sons, Inc. ( Interscience Division ), New York (1973).
R. J. Donovan and D. Husain, Recent advances in the chemistry of electronically excited atoms, Chem. Rev. 70, 489–516 (1970).
J. I. Steinfeld, Quenching of fluorescence in small molecules, Acc. Chem. Res. 3, 313–320 (1970).
R. F. Vasil’ev, Chemiluminescence excitation mechanisms, Russ. Chem. Rev. 39, 529–544 (1970).
T. Carrington and J. C. Polanyi, in: MTPlnternational Review of Science, Physical Chemistry (J. C. Polanyi, ed.), Vol. 9, pp. 135–171, University Park Press, Baltimore (1972).
D. H. Stedman and D. W. Setzer, Chemical applications of metastable rare gas atoms, Prog. React. Kinet. 6, 193–238 (1972).
M. Born and J. R. Oppenheimer, Zur Quantentheorie der Molekeln, Ann. der Phys. 84, 457–484 (1927).
A. Messiah, Quantum Mechanics, Vol. II, Chap. 18, John Wiley and Sons, Inc., New York (1962).
W. H. Miller, The semiclassical nature of atomic and molecular collisions, Acc. Chem. Res. 4, 161–167 (1971).
E. Bauer, E. R. Fisher, and F. R. Gilmore, De-excitation of electronically excited sodium by nitrogen, J. Chem. Phys. 51, 4173–4181 (1969).
J. C. Tully and R. K. Preston, Trajectory surface hopping approach to nonadiabatic molecular collisions, J. Chem. Phys. 55, 562–572 (1971).
W. H. Miller and T. F. George, Semiclassical theory of electronic transitions in low energy atomic and molecular collisions involving several nuclear degrees of freedom, J. Chem. Phys. 56, 5637–5652 (1972).
W. H. Miller, Classical limit quantum mechanics and the theory of molecular collisions, Adv. Chem. Phys. 25, 69–177 (1974).
R. G. Newton, Scattering Theory of Waves and Particles, McGraw-Hill Book Company, New York (1966).
M. L. Goldberger and K. M. Watson, Collision Theory, John Wiley and Sons, Inc., New York (1964).
J. R. Taylor, Scattering Theory. The Quantum Theory of Nonrelativistic Collisions, John Wiley and Sons, Inc., New York, (1972).
L. S. Rodberg and R. M. Thaler, Introduction to the Quantum Theory of Scattering, Academic Press, Inc., New York (1967).
H. Laue, Coupling between nuclear and electronic motion in diatomic molecules, J. Chem. Phys. 46, 3034–3040 (1967).
W. Kolos, Adiabatic approximation and its accuracy, Adv. Quantum. Chem. 5, 99–133 (1970).
J. C. Tully, Diatomics-in-Molecules potential energy surfaces. II. Nonadiabatic and spin-orbit interactions, J. Chem. Phys. 59, 5122–5134 (1973).
N. F. Mott, On the theory of excitation by collisions with heavy particles, Proc. Cambridge Philos. Soc. 27, 553–560 (1931).
J. von Neumann and E. P. Wigner, Über das Verhalten von Eigenwerten bei adiabatischen Prozessen, Phys. Z. 30, 467–470 (1929).
G. Herzberg and H. C. Longuet-Higgins, Intersection of potential energy surfaces in polyatomic molecules, Discuss. Faraday Soc. 35, 77–82 (1963).
E. Teller, The crossing of potential surfaces, J. Phys. Chem. 41, 109–115 (1937).
T. F. George, K. Morokuma, and Y.-W. Lin, Real and complex intersections between potential energy surfaces of the same symmetry in polyatomic systems, Chem. Phys. Lett. 30, 54–57 (1975).
W. Lichten, Resonant charge exchange in atomic collisions, Phys. Rev., 131, 229–238 (1963).
T. F. O’Malley, Diabetic state of molecules-Quasistationary electronic states, Adv. At. Mol. Phys. 7, 223–249 (1971).
R. W. Numrich and D. G. Truhlar, Mixing of ionic and covalent configurations for NaH, KH and MgH+, J. Phys. Chem. 79, 2745–2766 (1975).
F. T. Smith, Diabatic and adiabatic representations for atomic collision problems, Phys. Rev. 179, 111–123 (1969).
M. Baer, Adiabatic and diabatic representations for atom-molecule collisions, Chem. Phys. Lett. 35, 112–118 (1975).
T. Carrington, The geometry of intersecting potential surfaces, Acc. Chem. Res. 7, 20–25 (1974).
R. K. Preston and J. C. Tully, Effects of surface crossing in chemical reactions: The H3 system, J. Chem. Phys. 54, 4297–4304 (1971).
S. Chapman and R. K. Preston, Nonadiabatic molecular collisions: Charge exchange and chemical reaction in the Ar.-H2 system, J. Chem. Phys. 60, 650–659 (1974).
H. S. W. Massey, Collisions between atoms and molecules at ordinary temperatures, Rep. Prog. Phys. 12, 248–269 (1949).
H. F. Schaefer III, The Electronic Structure of Atoms and Molecules, Addison-Wesley Publishing Company, Inc., Reading, Mass. (1972).
J. N. Bardsley, Pseudopotentials in atomic and molecular physics, Case Stud. At. Phys. 4, 299–368 (1974).
A. C. Roach and M. S. Child, Electronic potential energy surfaces for the reaction K + NaCI-*KC1 + Na, Mol. Phys. 14, 1–15 (1968).
C. F. Melius, W. A. Goddard III, and L. R. Kahn, Use of ab initio G1 effective potentials for calculations of molecular excited states, J. Chem. Phys. 56, 3342–3348 (1972).
W. Moffitt, Atoms in molecules and crystals, Proc. R. Soc. London Ser. A 210, 245–268 (1951).
G. G. Balint-Kurti and M. Karplus, Potential energy surfaces for simple chemical reactions: Li + F2- LiF + F, Chem. Phys. Lett. 11, 203–207 (1971).
F. O. Ellison, A method of diatomics in molecules. I. General theory and application to H2O, J. Am. Chem. Soc. 85, 3540–3544 (1963).
P. J. Kuntz and A. C. Roach, Ion-molecule reactions of rare gases with hydrogen, J. Chem. Soc. Faraday Trans. 2, 68, 259–280 (1972).
J. C. Tully, Diatomics-in-molecules potential energy surfaces. I. First-row triatomic hydrides, J. Chem. Phys. 58, 1396–1410 (1973).
T. E. H. Walker and W. G. Richards, Molecular spin—orbit coupling constants. The role of core polarization, J. Chem. Phys. 52, 1311–1314 (1970).
W. H. Moores and R. McWeeney, The calculation of spin—orbit splitting and g tensors for small molecules and radicals, Proc. R. Soc. London Ser. A 332, 365–384 (1973).
F. H. Mies, Molecular theory of atomic collisions: Fine-structure transitions, Phys. Rev. A 7, 942–957 (1973).
J. S. Cohen and B. Schneider, Ground and excited states of Nee and Net. I. Potential curves with and without spin—orbit coupling, J. Chem. Phys. 61, 3230–3239 (1974).
J. C. Browne, Molecular wave functions: Calculation and use in atomic and molecular processes, Adv. At. Mol. Phy. 7, 47–95 (1971).
W. R. Thorson, Asymptotic coriolis interactions in slow atomic collisions, J. Chem. Phys. 50, 1702–1704 (1969).
V. Sidis, Simple expression for the off-diagonal matrix elements of the d/dR operator between exact electronic states of a diatomic molecule, J. Chem. Phys. 55, 5838–5839 (1971).
W. R. Thorson, Theory of slow atomic collisions. I. Hz, J. Chem. Phys. 42, 3878–3891 (1965).
S. B. Schneiderman and A. Russek, Velocity-dependent orbitals in proton-on-hydrogenatom collisions, Phys. Rev. 181, 311–321 (1969).
D. R. Bates and D. Sprevak, Translation factor in basis functions used in perturbed stationary state approximation and capture in H+—H (IS) collisions, J. Phys. B 4, L47–51 (1971).
C. F. Melius and W. A. Goddard III, The theoretical description of an asymmetric, nonresonant charge transfer process, Chem. Phys. Len. 15, 524–529 (1972).
H. S. W. Massey and R. A. Smith, The passage of positive ions through gases, Proc. R. Soc. London A 142, 142–172 (1933).
R. P. Marchi and F. T. Smith, Theory of elastic differential scattering in low-energy Hem—He collisions, Phys. Rev. 139, A1025–1038 (1965).
E. E. Nikitin, Remarks on different theoretical approaches to the collisionally induced depolarization of atomic states, Comments At. Mol. Phys. 3, 7–14 (1971).
D. G. Truhlar, Multiple potential energy surfaces for reactions of species in degenerate electronic states, J. Chem. Phys. 56, 3189–3190 (1972).
J. T. Muckerman and M. D. Newton, Comment on “multiple potential energy surfaces for reactions of species in degenerate electronic states” by D. G. Truhlar, J. Chem. Phys. 56, 3191–3192 (1972).
J. C. Tully, Collisions of F (2P1,2) with H2, J. Chem. Phys. 60, 3042–3050 (1974).
W. H. Miller, Theory of Penning ionization. I. Atoms, J. Chem. Phys. 52, 3563–3572 (1970).
H. Nakamura, Theoretical considerations on Penning ionization processes, J. Phys. Soc. Jpn 26, 1473–1479 (1969).
S. A. Evans, J. S. Cohen, and N. F. Lane, Quantum-mechanical calculation of cross sections for inelastic atom—atom collisions. I, Phys. Rev. A 4, 2235–2248 (1971).
L. Lenamon, J. C. Browne, and R. E. Olson, Theoretical low-energy inelastic-scattering cross sections for He (23S) + He (1 `S) — He (23P) + He (1 S), Phys. Rev. A 8, 2380–2386 (1973).
R. E. Olson, Low-energy theoretical inelastic-scattering differential cross sections for the process H++ He—*H++ He (23S), Phys. Rev. A 5, 2094–2103 (1972).
F. H. Mies, Molecular theory of atomic collisions: Calculated cross sections for H+ + F (2P), Phys. Rev. A. 7, 957–967 (1973).
R. H. Reid, Transitions among the 3p2 P states of sodium induced by collisions with helium, J. Phys. B 6, 2018–2039 (1973).
J. S. Cohen, S. A. Evans, and N. F. Lane, Quantum-mechanical calculation of cross sections for inelastic atom—atom collisions. II, Phys. Rev. A 4, 2248–2253 (1971).
H. Nakamura, Theoretical studies of inelastic atomic collisions in a two-state model problem. Mol. Phys. 25, 577–602 (1973).
H. G. Guerin, T. P. Tsien, B. C. Eu, and R. E. Olson, Comment on the accuracy of the uniform WKB theory of inelastic collisions, Phys. Rev. A 9, 995–998 (1974).
J. B. Delos, Studies of the potential-curve-crossing problem. III, Phys. Rev. A9, 1626–1634 (1974).
A. C. Allison, The numerical solution of coupled differential equations arising from the Schrödinger equation, J. Comput. Phys. 6, 378–391 (1970).
W. A. Lester, Jr., and R. B. Bernstein, Computational procedure for the close-coupled rotational excitation problem, J. Chem. Phys. 48, 4896–4904 (1968).
R. G. Gordon, Quantum scattering using piecewise analytic solutions, Methods Comput. Phys, 10, 81–110 (1971).
W. N. Sams and D. J. Kouri, Noniterative solutions of integral equations of scattering. II. Coupled channels, J. Chem. Phys. 51, 4815–4819 (1969).
B. R. Johnson and D. Secrest, The solution of the nonrelativistic quantum scattering problem without exchange, J. Math. Phys. (N.Y.) 7, 2187 (1966).
B. R. Johnson, The multichannel log-derivative method for scattering calculations, J. Comput. Phys. 13, 445–449 (1973).
J. C. Light, Quantum theories of chemical kinetics, Adv. Chem. Phys. 19, 1–31 (1971).
W. A. Lester, Jr., Calculation of cross sections for rotational excitation of diatomic molecules by heavy particle impact: Solution of close-coupled equations, Methods Comput. Phys. 10, 211–242 (1971).
W. A. Lester, Jr. and J. Schaefer, Rotational transitions in H2 by Li’ collisions; comparison with experiment, J. Chem. Phys. 60, 1672–1674 (1974).
P. McGuire, Coupled-states approach for elastic and for rotationally and vibrationally inelastic atom-molecule collisions, J. Chem. Phys. 62, 525–534 (1975).
R. A. Marcus, Analytical mechanics of chemical reactions. III. Natural collision coordinates, J. Chem. Phys. 49, 2610–2616 (1968).
G. Wolken, Jr. and M. Karplus, Theoretical studies of H+H2 reactive scattering, J. Chem. Phys. 60, 351–367 (1974).
J. C. Light, Quantum calculations in chemically reactive systems, Methods Comput. Phys. 10, 111–143 (1971).
B. R. Johnson and R. D. Levine, A new approach to non-adiabatic transitions in collision theory, Chem. Phys. Lett. 13, 168–171 (1972).
H. Nakamura, Theory of electronically non-adiabatic chemical reactions: Quantum formulation of collinear reactions, Mol. Phys. 26, 673–685 (1973).
Z. Top and M. Baer, Non-adiabatic transitions in chemical reaction. A quantum mechanical study, Chem. Phys. 10, 95–106 (1975).
I. H. Zimmerman and T. F. George, Quantum resonance effects in electronic-to-vibrational energy transfer in molecular collisions, J. Chem. Phys. 61, 2468–2470 (1974).
I. H. Zimmerman and T. F. George, Quantum mechanical study of electronic transitions in collinear atom-diatom collisions, Chem. Phys. 7, 323–335 (1975).
O. H. Crawford, Calculation of chemical reaction rates by variational methods, J. Chem. Phys. 55, 2571–2574 (1971).
W. H. Miller, Coupled equations and the minimum principle for collision of an atom and a diatomic molecule, including rearrangements, J. Chem. Phys. 50, 407–418(1969).
R. Conn and H. Rabitz, Decomposition of K and T matrices for inelastic scattering using variational principles, J. Chem. Phys. 61, 600–608 (1974).
J. H. Weare and E. Thiele, Variation procedure for multichannel scattering processes, Phys. Rev. 167, 11–13 (1968).
R. G. Gordon and T.-N. Chiu, On a first-order electronic dipole-dipole mechanism for energy transfer in molecular collisions, J. Chem. Phys. 55, 1469–1471 (1971).
R. E. Olson and F. T. Smith, Collision spectroscopy. IV. Semiclassical theory of inelastic scattering with applications to He + Ne, Phys. Rev. A 3, 1607–1617 (1971).
M. Karplus, in: Molecular Beams and Reaction Kinetics ( Ch. Schlier, ed.), pp. 407–426, Academic Press, Inc., New York (1970).
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).
P. Pechukas and J. C. Light, On the exponential form of time-displacement operators in quantum mechanics, J. Chem. Phys. 44, 3897–3912 (1966).
R. D. Levine, Exponential approximations in collision theory, Mol. Phys. 22, 497–523 (1971).
R. A. Marcus, On the analytical mechanics of chemical reactions. Quantum mechanics of linear collisions, J. Chem. Phys. 45, 4493–4499 (1966).
B. C. Eu and J. Ross, Optical potential for a chemically reactive system, Discuss. Faraday Soc. 44, 39–45 (1967).
C. A. Coulson and B. R. Gerber, A lower-bound property of adiabatic phase shifts, Mol. Phys. 14, 117–131 (1968).
R. D. Levine, Variational corrections to decoupling approximations in molecular collision theory, J. Chem. Phys. 50, 1–6 (1969).
D. A. Micha, Optical potentials in molecular collisions, J. Chem. Phys. 50, 722–726 (1969).
R. D. Levine, B. R. Johnson, and R. B. Bernstein, Role of potential curve crossing in subexcitation molecular collisions, J. Chem. Phys. 50, 1694–1701 (1969).
R. E. Roberts, Improved perturbation theory for inelastic encounters, J. Chem. Phys. 55, 100–104 (1971).
R. B. Bernstein and K. H. Kramer, Sudden approximation applied to rotational excitation of molecules in atoms. II, J. Chem. Phys. 44, 4473–4485 (1966).
R. J. Cross, Jr., Semiclassical theory of inelastic scattering: Diagonalization of the phase shift matrix, J. Chem. Phys. 49, 1753 (1968).
M. D. Pattengill, C. F. Curtiss, and R. B. Bernstein, Molecular collisions. XIV. First-order approximation of the generalized phase shift treatment of rotational excitation: Atom-rigid rotor, J. Chem. Phys. 54, 2197–2207 (1971).
M. Wartell and R. J. Cross, Jr., Semiclassical theory of vibrationally inelastic scattering in three dimensions, J. Chem. Phys. 55, 4983–4991 (1971).
R. T. Pack, Relations between some exponential approximations in rotationally inelastic molecular collisions, Chem. Phys. Lett. 14, 393–395 (1972).
D. A. Micha and M. Rotenberg, Collision energy dependence of angular distributions for vibrational excitation of H2 by He, Chem. Phys. Lett. 13, 289–291 (1972).
H. Rabitz, Effective potentials in molecular collisions, J. Chem. Phys. 57, 1718–1725 (1972).
G. Zarur and H. Rabitz, Rotationally inelastic scattering with effective potentials, J. Chem. Phys. 59, 943–951 (1973).
R. A. White, A. Altenberger-Siczek, and J. C. Light, Optical potentials in time-dependent quantum theory, J. Chem. Phys. 59, 200–205 (1973).
G. Zarur and H. Rabitz, Effective potential formulation of molecule-molecule collisions with application to H2–H2, J. Chem. Phys. 60, 2057–2078 (1974).
P. McGuire and D. J. Kouri, Quantum mechanical close-coupling approach to molecular collisions. Jr-conserving coupled-states approximation, J. Chem. Phys. 60, 2488–2499 (1974).
M. Tamir and M. Shapiro, The approximate conservation of P-helicity in rotational excitation: A new decoupling scheme, Chem. Phys. Lett. 31, 166–171 (1975).
D. Secrest, Theory of angular momentum decoupling approximations for rotational transitions in scattering, J. Chem. Phys. 62, 710–719 (1975).
D. A. Micha, Effective Hamiltonian methods for molecular collision, Adv. Quantum Chem. 8, 231–287 (1974).
R. J. Cross, Jr., Semiclassical methods in inelastic scattering, J. Chem. Phys. 51, 5163–5170 (1969).
D. R. Bates and D. S. F. Crothers, Semiclassical treatment of atomic collisions, Proc. R. Soc. London Ser. A 315, 465–478 (1970).
J. B. Delos, W. R. Thorson, and S. Knudson, Semiclassical theory of inelastic collisions. I. Classical picture and semiclassical formulation, Phys. Rev. A 6, 709–720 (1972).
J. B. Delos and W. R. Thorson, Semiclassical theory of inelastic collisions. II. Momentum-space formulation, Phys. Rev. A 6, 720–727 (1972).
A. M. Wooley and S. E. Nielsen, On the limits of applicability of the classical trajectory equations in the two-state approximation, Chem. Phys. Lett. 21, 491–494 (1973).
D. R. Bates and A. R. Holt, Impact parameter and semi-classical treatments of atomic collisions, Proc. R. Soc. London Ser. A 292, 168–179 (1966).
A. M. Arthurs, The mathematical equivalence of the Born approximation and the method of impact parameters, Proc. Cambridge Philos. Soc. 57, 904–905 (1961).
J. C. Y. Chen, C. J. Joachain, and K. M. Watson, Electronic transitions in slow collisions of atoms and molecules. IV, Phys. Rev. A 5, 1268–1285 (1972).
J. Callaway and E. Bauer, Inelastic collisions of slow atoms, Phys. Rev. 140, A1072–1084 (1965).
L. Wilets and S. J. Wallace, Eikonal method in atomic collisions. I, Phys. Rev. 169, 84–91 (1968).
J. C. Y. Chen. T. Ishihara, V. H. Ponce, and K. M. Watson, Electronic transitions in slow collisions of atoms and molecules. V, Phys. Rev. A 8, 1334–1344 (1973).
A. P. Penner and R. Wallace, Semiclassical normalization of a path integral for a multichannel scattering problem, Phys. Rev. A 11, 149–153 (1975).
R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill Book Company, New York (1965).
P. Pechukas, Time dependent semiclassical scattering theory. II. Atomic collisions, Phys. Rev. 181, 174–184 (1969).
P. Pechukas and J. P. Davis, Semiclassical theory of weak vibrational excitation, J. Chem. Phys. 56, 4970–4975 (1972).
L. D. Landau, Zur Theorie der Energieübertragung. II, Phys. Z. Sowjetunion 2, 46–51 (1932).
C. Zener, Non-adiabatic crossing of energy levels, Proc. R. Soc. London Ser. A 137, 696–702 (1932).
E. C. G. Stueckelberg, Theorie der unelastischen Stösse zwischen Atomen, Helv. Phys. Acta 5, 369–422 (1932).
D. R. Bates, Collisions involving the crossing of potential energy curves, Proc. R. Soc. London Ser. A 257, 22–31 (1960).
E. E. Nikitin, The Landau-Zener model and its region of applicability, Comments At. Mol. Phys. 1, 166–172 (1970).
M. S. Child, On the Stueckelberg formula for non-adiabatic transitions, Mol. Phys. 28, 495–501 (1974).
E. E. Nikitin, The theory of nonadiabatic transitions: Recent development with exponential models, Adv. Quantum Chem. 5, 135–184 (1970).
J. B. Delos and W. R. Thorson, Studies of the potential-curve-crossing problem. II, Phys. Rev. A 6, 728–745 (1972).
Yu. N. Demkov, Charge transfer at small resonance defects, Zh. Eksp. Teor. Fiz. 45, 195–201 (1963).
R. E. Olson, Charge transfer at large internuclear distances, Phys. Rev. A 6, 1822–1830 (1972).
L. Vainshtein, L. Presnyakov, and I. Sobel’man, Excitation of atoms by heavy particles, Zh. Eksp. Teor. Fiz. 43, 518–524 (1962).
D. R. Bates, Collision processes not involving chemical reactions, Discuss. Faraday Soc. 33, 7–13 (1962).
E. F. Gurnee and J. L. Magee, Interchange of charge between gaseous molecules in resonant and near-resonant processes, J. Chem. Phys. 26, 1237–1248 (1957).
N. Rosen and C. Zener, Double Stern-Gerlach experiment and related collision phenomena, Phys. Rev. 40, 502–507 (1932).
D. Rapp and W. E. Francis, Charge exchange between gaseous ions and atoms, J. Chem. Phys. 37, 2631–2645 (1962).
H. Nakamura, Collisional excitation transfer between atoms in near-resonant processes, J. Phys. Soc. Jpn 20, 2272–2278 (1965).
K. Birkinshaw and J. B. Hasted, Inelastic collisions between atomic ions and diatomic molecules, J. Phys. B 4, 1711–1725 (1971).
E. I. Dashevskaya, E. E. Nikitin, and A. I. Reznikov, Theory of collisionally induced intramultiplet mixing in excited alkali atoms, J. Chem. Phys. 53, 1175–1180 (1970).
E. E. Nikitin, Nonadiabatic transitions between fine-structure components of alkali metal atoms during atomic collisions, Opt. Spectros. USSR. 19, 19–95 (1965).
C. H. Wang and W. J. Tomlinson, Collision-induced anisotropic relaxation in gases, Phys. Rev. 181, 115–124 (1969).
J. R. Krenos, R. K. Preston, R. Wolfgang, and J. C. Tully, Reaction of H+ with H2: Experiment, ab initio theory and a conceptual model, Chem. Phys. Lett. 10, 17–21 (1971).
J. C. Tully, Trajectories in ion—molecule reactions, Ber. Bunsenges. Phys. Chem. 77, 557–565 (1973).
R. Duren, Differential cross sections for alkali—halogen collisions from trajectory calculations on intersecting surfaces, J. Phys. B 6, 1801–1813 (1973).
J. R. Krenos, R. K. Preston, R. Wolfgang, and J. C. Tully, Molecular beam and trajectory studies of reactions of H` with Hz, J. Chem. Phys. 60, 1634–1659 (1974).
R. K. Preston and R. J. Cross, Jr., Competition between charge exchange and chemical reaction: The D++H2 system, J. Chem. Phys. 59, 3616–3622 (1973).
G. E. Zahr, R. K. Preston, and W. H. Miller, Theoretical treatment of quenching in O (’D) + N2 collisions, J. Chem. Phys. 62, 1127–1135 (1975).
G. Ochs and E. Teloy, Integral cross sections for reactions of H+ with D2, new measurements, J. Chem. Phys. 61, 4930–4931 (1974).
M. Lipeles, Simple model for vibrational transfer in ion—molecule charge-exchange excitation, J. Chem. Phys. 5, 1252–1253 (1969).
E. R. Fisher and E. Bauer, On the quenching of O (`D) by N2 and related reactions, J. Chem. Phys. 57, 1966–1974 (1972).
A. Bjerre and E. E. Nikitin, Energy transfer in collisions of an excited sodium atom with a nitrogen molecule, Chem. Phys. Lett. 1, 179–181 (1967).
E. R. Fisher and G. K. Smith, Vibration—electronic coupling in the quenching of electronically excited alkali atoms by diatomics, App. Opt. 10, 1803–1813 (1971).
A. M. Wooley, Semiclassical scattering theory and total cross sections for systems with many crossing points, Mol. Phys. 22, 607–618 (1971).
G. M. Kendall and R. Grice, Vibrational coordinates in the electron jump model, Mol. Phys. 24, 1373–1382 (1972).
E. A. Gislason, Surface crossing model for ion—molecule reactions, J. Chem. Phys. 57, 3396–3400 (1972).
M. S. Child, Franck—Condon transitions in multi-curve crossing processes, Faraday Discuss. Chem. Soc. 55, 30–33 (1973).
Yu. N. Demkov and V. I. Osherov, Stationary and nonstationary problems in quantum mechanics that can be solved by means of contour integration, Zh. Eksp. Teor. Fiz. 53, 1589–1599 (1967).
J. B. Delos, On the reactions of N2 with O, J. Chem. Phys. 59, 2365–2369 (1973).
J. C. Tully, Collision complex model for spin forbidden reactions: Quenching of O (’D) by N2, J. Chem. Phys. 61, 61–68 (1974).
P. Pechukas, J. C. Light, and C. Rankin, Statistical theory of chemical kinetics, J. Chem. Phys. 44, 794–804 (1966).
J. R. Krenos and J. C. Tully, Statistical partitioning of electronic energy: Reactions of alkali dimers with halogen atoms, J. Chem. Phys. 62, 420–424 (1975).
M. Yen Chu and J. S. Dahler, A theory of the collision-induced singlet to triplet transition of methylene, Mol. Phys. 27, 1045–1069 (1974).
J. C. Tully, Reactions of O (’D) with atmospheric molecules, J. Chem. Phys. 62, 1893–1898 (1975).
R. D. Levine and R. B. Bernstein, Dynamical theory of vibrational state population distribution in electronic-to-vibrational energy transfer, Chem. Phys. Lett. 15, 1–6 (1972).
M. A. Gonzalez, G. Karl, and P. J. S. Watson, Electronic—vibrational energy transfer: Hg* + CO, J. Chem. Phys. 57, 4054–4055 (1972).
Y. Haas, R. D. Levine, and G. Stein, Electronic excitation induced by reactive molecular collisions: A theoretical model, Chem. Phys. Lett. 15, 7–11 (1972).
A. D. Wilson and R. D. Levine, Simple models of vibrational excitation in energy transfer molecular collisions, Mol. Phys. 27, 1197–1216 (1974).
R. E. Olson, Absorbing-sphere model for calculating ion—ion recombination total cross sections, J. Chem. Phys. 56, 2979–2984 (1972).
A. Messiah, Quantum Mechanics, Vol. I, John Wiley and Sons, Inc., New York (1961), Chap. 10.
T. A. Green and M. E. Riley, Strong-coupling semiclassical methods: Phase corrected average approximation for atom—atom collisions, Phys. Rev. A 8, 2938–2945 (1973).
G. A. L. Delvigne and J. Los, Rainbow, Stueckelberg oscillations and rotational coupling on the differential cross sections of Na+I—Na++I, Physica (Utrecht) 67, 166–196 (1973).
B. C. Eu and T. P. Tsien, Uniform WKB theory of inelastic collisions: Application to He+—Ne inelastic collisions, Phys. Rev. A 7, 648–657 (1973).
B. C. Eu, Theory of inelastic collisions: Uniform asymptotic (WKB) solutions and semiclassical S-matrix elements for two-channel problems, J. Chem. Phys. 55, 5600–5609 (1971).
B. C. Eu, Theory of inelastic collisions: Uniform asymptotic (WKB) solutions and semiclassical scattering matrix elements for multichannel problems, J. Chem. Phys. 56, 2507–2516, 5202 (1972).
B. C. Eu, Semiclassical theory of rearrangement and exchange collisions, J. Chem. Phys. 58, 472–478 (1973).
B. C. Eu, Theory of inelastic collisions: Extension to multiple turning point problems of uniform WKB theory, J. Chem. Phys. 59, 4705–4713 (1973).
U.-I. Cho and B. C. Eu, Improved solutions to the equation of motion in the uniform WKB theory for two-channel problems, J. Chem. Phys. 61, 1172–1179 (1974).
L. D. Landau and E. M. Lifshitz, Quantum Mechanics, Addison-Wesley Publishing Company. Inc., Reading, Mass. (1958), p. 178.
R. K. Preston, C. Sloan, and W. H. Miller, Semiclassical theory of collisionally induced fine-structure transitions in fluorine atoms, J. Chem. Phys. 60, 4961–4969 (1974).
Y.-W. Lin, T. F. George,and K. Morokuma, Semiclassical treatment of electronic transitions in molecular collisions: H++D2—*HD++D, J. Chem. Phys: 60, 4311–4322 (1972).
Y.-W. Lin, T. F. George, and K. Morokuma, Semiclassical treatment of electronic transitions in molecular collisions: Three-dimensional H++D2—HD++D2, Chem. Phys. Lett. 30, 49–53 (1975).
T. F. George and Y.-W. Lin, Multiple transition points in a semiclassical treament of electronic transitions in atom (ion)—diatom collisions, J. Chem. Phys. 60, 2340–2349 (1974).
K. Morokuma and T. F. George, Ab initio calculations of potential energy surfaces in the complex plane. I. General theory and one-electron example. J. Chem. Phys. 59, 1959–1973 (1973).
R. L. Jaffe, T. F. George, and K. Morokuma, Calculations of potential energy surfaces in the complex plane. III. Branch-point structure and rational fractions, Mol. Phys. 28, 1489 (1974).
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Tully, J.C. (1976). Nonadiabatic Processes in Molecular Collisions. In: Miller, W.H. (eds) Dynamics of Molecular Collisions. Modern Theoretical Chemistry, vol 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0644-4_5
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