Quantum corrections to the classical path equations: Multitrajectory and Hermite corrections

Journal of Chemical Physics

Volumn 107, Issue 11, 1997, Pages 4286-4294

  Billing, Gert D ^a  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ATOMS; DEGREES OF FREEDOM (MECHANICS); MATRIX ALGEBRA; POLYNOMIALS; QUANTUM THEORY;

CLASSICAL PATH THEORY; COLLINEAR COLLISION; HERMITE CORRECTION METHOD; MORSE OSCILLATOR; MULTITRAJECTORY METHOD;

EQUATIONS OF MOTION;

EID: 0031572020     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.474804     Document Type: Article

References (24)

1. P. A. M. Dirac, Proc. Cambridge Philos. Soc. 26, 376 (1930).
2. G. D. Billing, J. Chem. Phys. 99, 5849 (1993); Int. Rev. Phys. Chem. 13, 309 (1994).
3. G. D. Billing, J. Chem. Phys. 99, 5849 (1993); Int. Rev. Phys. Chem. 13, 309 (1994).
4. G. D. Billing, Chem. Phys. 189, 523 (1994).
5. R. B. Gerber, V. Buch, and M. A. Rainer, J. Chem. Phys. 77, 3022 (1982); R. B. Gerber, R. Kosloff, and M. Berman, Comp. Phys. Rep. 5, 59 (1986).
6. R. B. Gerber, V. Buch, and M. A. Rainer, J. Chem. Phys. 77, 3022 (1982); R. B. Gerber, R. Kosloff, and M. Berman, Comp. Phys. Rep. 5, 59 (1986).
7. P. Jungwirth and R. B. Gerber, J. Chem. Phys. 102, 6046, 8855 (1995).
8. T. J. Martinez, M. Ben-Nun, and R. D. Levine, J. Phys. Chem. 100, 7884 (1996).
9. H.-D. Meyer, U. Manthe, and L. S. Cederbaum, Chem. Phys. Lett. 165, 73 (1990).
10. G. D. Billing, Int. J. Thermophys. 18, 977 (1997).
11. F. Y. Hansen, N. E. Henriksen, and G. D. Billing, J. Chem. Phys. 90, 3060 (1989).
12. G. D. Billing and K. V. Mikkelsen, Advanced Molecular Dynamics and Chemical Kinetics (Wiley, New York, 1997).
13. K. G. Kay, Chem. Phys. 137, 165 (1989).
14. N. Makri and W. H. Miller, J. Chem. Phys. 87, 5781 (1987).
15. G. D. Billing and G. Jolicard, Chem. Phys. Lett. 221, 75 (1994).
16. Z. Kotler, A. Nitzan, and R. Kosloff, Chem. Phys. Lett. 153, 483 (1988); Z. Kotler, E. Neria, and A. Nitzan, Comput. Phys. Commun. 63, 243 (1991).
17. Z. Kotler, A. Nitzan, and R. Kosloff, Chem. Phys. Lett. 153, 483 (1988); Z. Kotler, E. Neria, and A. Nitzan, Comput. Phys. Commun. 63, 243 (1991).
18. G. D. Billing, Encyclopedia of Computational Chemistry, edited by H. F. Schaefer III (in press). The Hermite correction was here introduced by an expansion of the "higher order correction" terms of Ref. 3 in Hermite polynomials. Later we discovered that these basis functions had been used also by other groups [see e.g., H.-D. Meyer, Chem. Phys. 61, 365 (1981); R. D. Coalson and M. Karplus, Chem. Phys. Lett. 90, 301 (1982); K. B. Møller and N. E. Henriksen, J. Chem. Phys. 105, 5037 (1996)].
19. G. D. Billing, Encyclopedia of Computational Chemistry, edited by H. F. Schaefer III (in press). The Hermite correction was here introduced by an expansion of the "higher order correction" terms of Ref. 3 in Hermite polynomials. Later we discovered that these basis functions had been used also by other groups [see e.g., H.-D. Meyer, Chem. Phys. 61, 365 (1981); R. D. Coalson and M. Karplus, Chem. Phys. Lett. 90, 301 (1982); K. B. Møller and N. E. Henriksen, J. Chem. Phys. 105, 5037 (1996)].
20. G. D. Billing, Encyclopedia of Computational Chemistry, edited by H. F. Schaefer III (in press). The Hermite correction was here introduced by an expansion of the "higher order correction" terms of Ref. 3 in Hermite polynomials. Later we discovered that these basis functions had been used also by other groups [see e.g., H.-D. Meyer, Chem. Phys. 61, 365 (1981); R. D. Coalson and M. Karplus, Chem. Phys. Lett. 90, 301 (1982); K. B. Møller and N. E. Henriksen, J. Chem. Phys. 105, 5037 (1996)].
21. G. D. Billing, Encyclopedia of Computational Chemistry, edited by H. F. Schaefer III (in press). The Hermite correction was here introduced by an expansion of the "higher order correction" terms of Ref. 3 in Hermite polynomials. Later we discovered that these basis functions had been used also by other groups [see e.g., H.-D. Meyer, Chem. Phys. 61, 365 (1981); R. D. Coalson and M. Karplus, Chem. Phys. Lett. 90, 301 (1982); K. B. Møller and N. E. Henriksen, J. Chem. Phys. 105, 5037 (1996)].
22. J. T. Muckerman, R. D. Gilbert, and G. D. Billing, J. Chem. Phys. 88, 4779 (1988); N. Markovic, G. D. Billing, and J. T. Muckerman, Chem. Phys. Lett. 172, 509 (1990); G. D. Billing and N. Markovic, Chem. Phys. 209, 377 (1996).
23. J. T. Muckerman, R. D. Gilbert, and G. D. Billing, J. Chem. Phys. 88, 4779 (1988); N. Markovic, G. D. Billing, and J. T. Muckerman, Chem. Phys. Lett. 172, 509 (1990); G. D. Billing and N. Markovic, Chem. Phys. 209, 377 (1996).
24. J. T. Muckerman, R. D. Gilbert, and G. D. Billing, J. Chem. Phys. 88, 4779 (1988); N. Markovic, G. D. Billing, and J. T. Muckerman, Chem. Phys. Lett. 172, 509 (1990); G. D. Billing and N. Markovic, Chem. Phys. 209, 377 (1996).