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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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.
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).
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).
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).
H. F. Schaefer III, Potential energy surfaces for methylene reactions, Chem. Britain 11: 227 (1975).
W. H. Miller, N. C. Handy, and J. E. Adams, Reaction path Hamiltonian for polyatomic molecules, J. Chem. Phys. 72: 99 (1980).
R. A. Marcus, On the analytical mechanics of chemical reactions. Quantum mechanics of linear collisions, J. Chem. Phys. 45: 4493 (1966).
R. A. Marcus, On the analytical mechanics of chemical reactions. Classical mechanics of linear collisions, J. Chem. Phys. 45: 4500 (1966).
R. A. Marcus, Analytical mechanics of chemical reactions. III. Natural collision coordinates, J. Chem. Phys. 49: 2610 (1968).
G. L. Hofacker, Quantentheorie chemischer reaktionen, Z. Naturforsch. A 18: 607 (1963).
S. F. Fischer, G. L. Hofacker, and R. Seiler, Model approach to non-adiabatic reaction processes, J. Chem. Phys. 51: 3951 (1969).
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).
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.
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.
W. H. Miller, Unified statistical model for “complex” and “direct” reaction mechanisms, J. Chem. Phys. 65: 2216 (1976).
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).
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).
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).
H. Goldstein, “Classical Mechanics”, Addison-Wesley, Reading, MA (1950), p. 288.
Ibid., pp. 237-247.
See, for example, M. L. Goldberger and K. M. Watson, “Collision Theory” Wiley, New York (1964), p. 46.
Ibid., p. 48.
See, for example, the presentation by W. H. Miller, Importance of nonseparability in quantum mechanical transition state theory, Acc. Chem. Res. 9: 306 (1976).
J. C. Light, Statistical theory of bimolecular exchange reactions, Disc. Faraday Soc. 44: 14 (1967).
E. E. Nikitin, “Theory of Elementary Atomic and Molecular Processes in Gases”, Oxford University Press, New York (1974), p. 391.
See, for example, P. J. Robinson and K. A. Holbrook, “Unimolecular Reactions”, Wiley, New York (1972), p. 53.
R. N. Porter and M. Karplus, Potential energy surface for H3, J. Chem. Phys. 40: 1105 (1964).
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).
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).
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).
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).
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).
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).
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).
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).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1981 Springer Science+Business Media New York
About this chapter
Cite this chapter
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
Download citation
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
eBook Packages: Springer Book Archive