Journal of Chemical Physics
Feedback | Help | Exit
The Journal of Chemical Physics
Search:
   
 
 
 
Previous Article
Inhibition and enhancement of positronium formation in aqueous solutions from the Doppler broadening of annihilation peaks
The Doppler broadened positron annihilation line shapes have been determined in aqueous solutions of various inhibiting and enhancing agents of positronium (Ps) formation : H + aq" align="middle"/>, N...
Next Article
Raman investigation of vitreous and molten boric oxide
Raman data have been obtained for vitreous and molten B2O3 from −196 to 1594 °C. A H° of 6.4±0.4 kcal/mole boroxol was obtained from the temperature dependence of ratios of integr...

Reaction path Hamiltonian for polyatomic molecules

J. Chem. Phys. 72, 99 (1980); doi:10.1063/1.438959

Issue Date: 1 January 1980

You are not logged in to this journal. Log in

William H. Miller, Nicholas C. Handy, and John E. Adams
Department of Chemistry and Materials and Molecular Research Division, Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720
The reaction path on the potential energy surface of a polyatomic molecule is the steepest descent path (if mass-weighted Cartesian coordinates are used) connecting saddle points and minima. For an N-atom system in 3d space it is shown how the 3N-6 internal coordinates can be chosen to be the reaction coordinate s, the arc length along the reaction path, plus (3N-7) normal coordinates that describe vibrations orthogonal to the reaction path. The classical (and quantum) Hamiltonian is derived in terms of these coordinates and their conjugate momenta for the general case of an N atom system with a given nonzero value of the total angular momentum. One of the important facts that makes this analysis feasible (and therefore interesting) is that all the quantities necessary to construct this Hamiltonian, and thus permit dynamical studies, are obtainable from a relatively modest number of ab initio quantum chemistry calculations of the potential energy surface. As a simple example, it is shown how the effects of reaction path curvature can be incorporated in the vibrationally adiabatic approximation, and application to the collinear and 3 dH+H2-->H2+H reaction shows that the tunneling probabilities given within this approximation are considerably improved when these curvature effects are included. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.
Permalink: http://link.aip.org/link/?JCPSA6/72/99/1
BUY THIS ARTICLE   (US$24)
Download PDF (1102 kB) View Cart

KEYWORDS and PACS

Keywords
PACS
  • 82.20.Wt
    Physical chemistry Chemical kinetics Computational modeling
  • 87.15.Pk
    Biophysics, medical physics, and biomedical engineering Molecular biophysics Model reactions
  • YEAR: 1980

PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (24)
View in Separate Window/Tab
For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. See, for example, R. N. Porter, and L. M. Raff, in Dynamics of Molecular Collisions, Part B (Vol. 2 of Modern Theoretical Chemistry), edited by W. H. Miller (Plenum, New York, 1976), pp. 1–52;
  2. P. J. Kuntz, ibid., pp. 53–116;
  3. J. C. Tully, ibid., pp. 217–259;
  4. D. L. Thompson, Acc. Chem. Res. 9, 338 (1976).
  5. (a) G. C. Schatz and A. Kuppermann, J. Chem. Phys. 65, 4642, 4668 (1976);
    6. (b) A. B. Elkowitz and R. E. Wyatt, J. Chem. Phys. 63, 702 (1975);
    (c) R. B. Walker, E. B. Stechel, and J. C. Light, J. Chem. Phys. 69, 2922 (1978).
  6. See, for example, W. L. Hase, Ref. 1, pp. 121–164.
  7. (a) B. Liu, J. Chem. Phys. 58, 1924 (1973);
    8. (b) H. F. Schaefer, in Atom-Molecule Collision Theory: A Guide for the Experimentalists, edited by R. B. Bernstein (Plenum, New York, 1979), pp. 45–77.
  8. I. S. Y. Wang and M. Karplus, J. Am. Chem. Soc. 95, 8160 (1973);
    9. A. Warshel and M. Karplus, Chem. Phys. Lett. 32, 11 (1975).
  9. (a) K. Fukui, J. Phys. Chem. 74, 4161 (1970);
    10. K. Fukui, S. Kato, and H. Fuijmoto, J. Am. Chem. Soc. 97, 1 (1975);
    S. Kato, H. Kato, and K. Fukui, J. Am. Chem. Soc. 99, 684 (1977);
    (b) H. F. Schaefer, Chem. Brit. 11, 227 (1975);
    (c) K. Ishida, K. Morokuma, and A. Komornicki, J. Chem. Phys. 66, 2153 (1977).
  10. (a) J. W. McIver and A. Komornicki, Chem. Phys. Lett. 10, 303 (1971);
    11. (b) P. Pulay, in Applications of Electronic Structure Theory (Vol. 4 of Modern Theoretical Chemistry), edited by H. F. Schaefer (Plenum, New York, 1977), pp. 153–185;
    (c) J. D. Goddard, N. C. Handy, and H. F. Schaefer, J. Chem. Phys. (to be published).
  11. J. A. Pople, presented at the Sanibel Symposium, March, 1979.
  12. R. A. Marcus, J. Chem. Phys. 45, 4493, 4500 (1966);
    13. 49, 2610 (1968).
  13. See, for example, (a) S. A. Adelman and J. D. Doll, J. Chem. Phys. 61, 4242 (1974);
    14. (b) M. Shuggard, J. C. Tully, and A. Nitzan, J. Chem. Phys. 66, 2534 (1977);
    (c) G. C. Schatz, Chem. Phys. 31, 295 (1978).
  14. R. A. Marcus, J. Chem. Phys. 46, 959 (1967).
    15. See, also, R. E. Wyatt, J. Chem. Phys. 51, 3489 (1969),
    and D. G. Truhlar, J. Chem. Phys. 53, 2041 (1970).
  15. H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, MA, 1950), p. 237, et seq.
  16. C. W. McCurdy, H. D. Meyer, and W. H. Miller, J. Chem. Phys. 70, 3177 (1979).
  17. D. G. Truhlar and A. Kuppermann, J. Chem. Phys. 56, 2232 (1972).
  18. E. B. Wilson, Jr., J. C. Decius, and P. C. Cross, Molecular Vibrations (McGraw-Hill, New York, 1955).
  19. J. T. Hougen, P. R. Bunker, and J. W. C. Johns, J. Mol. Spectrosc. 34, 136 (1970).
  20. D. C. Moule and Ch. V. S. Ramachandra Rao, J. Mol. Spectrosc. 45, 120 (1973).
  21. The canonical transformation from the Euler angles and their conjugate momenta—(chi,pchi), (theta,ptheta), (phi,pphi)—to the action-angle variables (J,qJ), (M,qM), (K,qK), is independent of any of the other degrees of freedom and thus proceeds just as for a rigid asymmetric rotor.
  22. These equations hold for any angular momentum;
    23. see W. H. Miller, Adv. Chem. Phys. 25, 69 (1974).
  23. J. K. G. Watson, Mol. Phys. 19, 465 (1970).
  24. R. N. Porter and M. Karplus, J. Chem. Phys. 40, 1105 (1964).
  25. J. K. G. Watson, Mol. Phys. 15, 479 (1968).
  26. R. E. Wyatt, J. Chem. Phys. 56, 390 (1972).
  27. W. H. Miller, J. Am. Chem. Soc. (to be published).

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.


Copyright © American Institute of Physics