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Reaction Path Hamiltonian for Polyatomic Systems: Further Developments and Applications

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Potential Energy Surfaces and Dynamics Calculations

Abstract

Ab initio quantum chemistry has made important advances recently in developing methods1 for the accurate and efficient calculation of the gradient of the potential energy surface, i.e., the derivative of the Born-Oppenheimer electronic energy with respect to nuclear coordinates, for a general molecular system. This has been used most commonly to facilitate the search for transition states, i.e., saddle points on a potential energy surface, but once a saddle point is found it can be used to follow the steepest descent path down from the transition state to reactants and to products. If mass-weighted cartesian coordinates are used, this is the reaction path,2 and the distance along it the (mass-weighted) reaction coordinate.

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References

  1. See, for example, (a) P. Pulay, Direct use of the gradient for investigation molecular energy surfaces, in: “Applications of Electronic Structure”, H. F. Schaefer III, ed., Plenum, New York (1977), p. 153.

    Chapter  Google Scholar 

  2. J. A. Pople, R. Krishnan, H. B. Schlegel, and J. S. Binkley, Derivative studies in Hartree-Fock and Møller-Plesset theories, Int. J. Quantum Chem. Symp. 13: 225 (1979).

    CAS  Google Scholar 

  3. B. R. Brooks, W. D. Laidig, P. Saxe, J. D. Goddard, Y. Yamaguchi, and H. F. Schaefer III, Analytic gradients from correlated wavefunctions via the two-particle density matrix and the unitary group approach, J. Chem. Phys. 72: 4652 (1980).

    Article  CAS  Google Scholar 

  4. K. Fukui, S. Kato, and H. Fujimoto, Constituent analysis of the potential gradient along a reaction coordinate. Method and an application to CH4 + T reaction, J. Amer. Chem. Soc. 97: 1 (1975).

    Article  CAS  Google Scholar 

  5. H. F. Schaefer III, Potential energy surfaces for methylene reactions, Chem. Britain 11: 227 (1975).

    Google Scholar 

  6. W. H. Miller, N. C. Handy, and J. E. Adams, Reaction path Hamiltonian for polyatomic molecules, J. Chem. Phys. 72: 99 (1980).

    Article  CAS  Google Scholar 

  7. R. A. Marcus, On the analytical mechanics of chemical reactions. Quantum mechanics of linear collisions, J. Chem. Phys. 45: 4493 (1966).

    Article  CAS  Google Scholar 

  8. R. A. Marcus, On the analytical mechanics of chemical reactions. Classical mechanics of linear collisions, J. Chem. Phys. 45: 4500 (1966).

    Article  CAS  Google Scholar 

  9. R. A. Marcus, Analytical mechanics of chemical reactions. III. Natural collision coordinates, J. Chem. Phys. 49: 2610 (1968).

    Article  CAS  Google Scholar 

  10. G. L. Hofacker, Quantentheorie chemischer reaktionen, Z. Naturforsch. A 18: 607 (1963).

    Google Scholar 

  11. S. F. Fischer, G. L. Hofacker, and R. Seiler, Model approach to non-adiabatic reaction processes, J. Chem. Phys. 51: 3951 (1969).

    Article  CAS  Google Scholar 

  12. S. K. Gray, W. H. Miller, Y. Yamaguchi, and H. F. Schaefer III, Reaction path Hamiltonian: Tunneling effects in the unimolecular isomerization HNC → HCN, J. Chem. Phys. 73: 2733 (1980).

    Article  CAS  Google Scholar 

  13. W. H. Miller, Tunneling corrections to unimolecular rate constants, with application to formaldehyde, J. Amer. Chem. Soc. 101: 6810 (1979); S. K. Gray, W. H. Miller, Y. Yamaguchi, and H. F. Schaefer III, Tunneling in the unimolecular decomposition of formaldehyde, a more quantitative study, J. Amer. Chem. Soc., to be published.

    Article  CAS  Google Scholar 

  14. Y. Osamura, H. F. Schaefer III, S. K. Gray, and W. H. Miller, Vinylidene: A shallow minimum on the C2H2 potential energy surface. Static and dynamical considerations, to be published.

    Google Scholar 

  15. W. H. Miller, Unified statistical model for “complex” and “direct” reaction mechanisms, J. Chem. Phys. 65: 2216 (1976).

    Article  CAS  Google Scholar 

  16. See, for example, (a) S. A. Adelman and J. D. Doll, Generalized Langevin equation approach for atom-solid surface scattering: Collinear atom/harmonic chain model, J. Chem. Phys. 61: 4242 (1974).

    Article  CAS  Google Scholar 

  17. S. A. Adelman and J. D. Doll, Generalized Langevin equation approach for atom-solid surface scattering: General formulation for classical scattering of harmonic solids, J. Chem. Phys. 64: 2375 (1976).

    Article  CAS  Google Scholar 

  18. M. Shugard, J. C. Tully, and A. Nitzan, Dynamics of gas-solid interactions: Calculations of energy transfer and sticking, J. Chem. Phys. 66: 2534 (1977).

    Article  CAS  Google Scholar 

  19. H. Goldstein, “Classical Mechanics”, Addison-Wesley, Reading, MA (1950), p. 288.

    Google Scholar 

  20. Ibid., pp. 237-247.

    Google Scholar 

  21. See, for example, M. L. Goldberger and K. M. Watson, “Collision Theory” Wiley, New York (1964), p. 46.

    Google Scholar 

  22. Ibid., p. 48.

    Google Scholar 

  23. See, for example, the presentation by W. H. Miller, Importance of nonseparability in quantum mechanical transition state theory, Acc. Chem. Res. 9: 306 (1976).

    Article  CAS  Google Scholar 

  24. J. C. Light, Statistical theory of bimolecular exchange reactions, Disc. Faraday Soc. 44: 14 (1967).

    Article  Google Scholar 

  25. E. E. Nikitin, “Theory of Elementary Atomic and Molecular Processes in Gases”, Oxford University Press, New York (1974), p. 391.

    Google Scholar 

  26. See, for example, P. J. Robinson and K. A. Holbrook, “Unimolecular Reactions”, Wiley, New York (1972), p. 53.

    Google Scholar 

  27. R. N. Porter and M. Karplus, Potential energy surface for H3, J. Chem. Phys. 40: 1105 (1964).

    Article  CAS  Google Scholar 

  28. S. Chapman, S. M. Hornstein, and W. H. Miller, Accuracy of transition state theory for the threshold of chemical reactions with activation energy. Collinear and three-dimensional H + H2, J. Amer. Chem. Soc. 97: 892 (1975).

    Article  CAS  Google Scholar 

  29. E. Pollak and P. Pechukas, Unified statistical model for “complex” and “direct” reaction mechanics: A test of the collinear H + H2 exchange reaction, J. Chem. Phys. 70: 325 (1979).

    Article  CAS  Google Scholar 

  30. B. C. Garrett and D. G. Truhlar, Generalized transition state theory. Classical mechanical theory and applications to collinear reactions of hydrogen molecules, J. Phys. Chem. 83: 1052 (1979).

    Article  CAS  Google Scholar 

  31. B. C. Garrett and D. G. Truhlar, Generalized transition state theory. Classical mechanical theory and applications to collinear reactions of hydrogen molecules, J. Phys. Chem. 83: 3058(E) (1979).

    Google Scholar 

  32. For examples of applications of the unified statistical model employing this kind of ad hoc quantization, see B. C. Garrett and D. G. Truhlar, Generalized transition state theory. Quantum effects for collinear reactions of hydrogen molecules, J. Chem. Phys. 83: 1079 (1979).

    Article  CAS  Google Scholar 

  33. B. C. Garrett and D. G. Truhlar, Generalized transition state theory. Quantum effects for collinear reactions of hydrogen molecules, J. Chem. Phys. 84: 682(E) (1980).

    Google Scholar 

  34. B. C. Garrett and D. G. Truhlar, Application of variational transition state theory and the unified statistical model to H + Cl2 → HC1 + Cl, J. Phys. Chem. 84: 1749 (1980).

    Article  CAS  Google Scholar 

  35. B. C. Garrett, D. G. Truhlar, R. S. Grev, and R. B. Walker, Comparison of variational transition state theory and the unified statistical theory with vibrationally adiabatic transmission coefficients to accurate collinear rate constants for T + HD → TH + D, J. Chem. Phys. 73: 235 (1980).

    Article  CAS  Google Scholar 

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Miller, W.H. (1981). Reaction Path Hamiltonian for Polyatomic Systems: Further Developments and Applications. In: Truhlar, D.G. (eds) Potential Energy Surfaces and Dynamics Calculations. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-1735-8_11

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  • DOI: https://doi.org/10.1007/978-1-4757-1735-8_11

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-1737-2

  • Online ISBN: 978-1-4757-1735-8

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