Extended Hellmann-Feynman forces, canonical representations, and exponential propagators in the mixed quantum-classical molecular dynamics

Journal of Chemical Physics

Volumn 119, Issue 22, 2003, Pages 11541-11555

  Grochowski, P ^a   Lesyng, B ^a  

^a UNIVERSITY OF WARSAW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; ELECTRON ENERGY LEVELS; HAMILTONIANS; INTEGRATION; MATHEMATICAL OPERATORS; MATHEMATICAL TRANSFORMATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES; PROTONS; QUANTUM THEORY; RUNGE KUTTA METHODS;

HELLMANN-FEYNMAN FORCES; LAGRANGIAN TRANSFORM; PROTON TRANSFER; QUANTUM CLASSICAL MOLECULAR DYNAMICS; TIME-DEPENDENT SCHRODINGER EQUATION;

MOLECULAR DYNAMICS;

EID: 0347682295     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1624062     Document Type: Article

References (43)

1. R. B. Gerber, V. Buch, and M. A. Ratner, J. Chem. Phys. 77, 3022 (1982).
2. J. C. Tully, J. Chem. Phys. 93, 1061 (1990).
3. D. K. Remler and P. A. Madden, Mol. Phys. 70, 921 (1990).
4. E. Deumens, A. Diz, R. Longo, and Y. Ohrn, Rev. Mod. Phys. 66, 917 (1994).
5. H. J. C. Berendsen and J. Mavri, in Quantum Mechanical Simulation Methods for Studying Biological Systems, edited by D. Biscout and M. Field (Springer, Berlin, 1996), p. 157.
6. P. Bala, P. Grochowski, B. Lesyng, and J. A. McCammon, in Quantum Mechanical Simulation Methods for Studying Biological Systems, edited by D. Biscout and M. Field (Springer, Berlin, 1996), p. 119.
7. O. V. Preszhdo and P. J. Rossky, J. Phys. Chem. 107, 825 (1997).
8. T. J. Martinez, M. Ben-Nun, and R. D. Levine, J. Phys. Chem. A 101, 6389 (1997).
9. S. Hammes-Schiffer, J. Phys. Chem. A 102, 10443 (1998).
10. A. V. Soudackov and S. Hammes-Schiffer, Chem. Phys. Lett. 299, 503 (1999).
11. K. Drukker, J. Comput. Phys. 153, 225 (1999).
12. S. Nielsen, R. Kapral, and G. Ciccotti, J. Chem. Phys. 112, 6543 (2000).
13. I. Horenko, C. Salzmann, B. Schmidt, and C. Schutte, J. Chem. Phys. 117, 11075 (2002).
14. S. Y. Kim and S. Hammes-Schiffer, J. Chem. Phys. 119, 4389 (2003).
15. P. Bala, B. Lesyng, and J. McCammon, Chem. Phys. 180, 271 (1994).
16. P. Bala, B. Lesyng, and J. McCammon, Chem. Phys. Lett. 219, 259 (1994).
17. P. Bala, P. Grochowski, K. Nowinski, B. Lesyng, and J. McCammon, Biophys. J. 79, 1253 (2000).
18. R. P. Feynman, Phys. Rev. 56, 340 (1939).
19. I. N. Levine, Quantum Chemistry, 5th ed. (Prentice-Hall, Englewood Cliffs, N.J., 1999).
20. E. H. Kerner, Phys. Rev. Lett. 2, 152 (1959).
21. E. F. Hayes and R. G. Parr, J. Chem. Phys. 43, 1831 (1965).
22. H. Tal-Ezer and R. Kosloff, J. Chem. Phys. 81, 3967 (1984).
23. F. M. Fernandez, Chem. Phys. Lett. 233, 651 (1995).
24. U. Schmitt and J. Brickmann, Chem. Phys. Lett. 208, 45 (1996).
25. P. Nettesheim, F. A. Bornemann, B. Schmidt, and C. Schutte, Chem. Phys. Lett. 256, 581 (1996).
26. G. Strang, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 5, 506 (1968).
27. H. F. Trotter, Proc. Am. Math. Soc. 10, 545 (1983).
28. M. D. Feit and J. A. Fleck, J. Chem. Phys. 78, 301 (1983).
29. P. Nettesheim and S. Reich, in Computational Molecular Dynamics: Challenges, Methods, Ideas, edited by P. Deuflhard et al., Lecture Notes in Computer Science Engineering (Springer, Berlin, 1999), Vol. 4, p. 412.
30. S. Reich, J. Comput. Phys. 151, 49 (1999).
31. M. Hochbruck and Ch. Lubich, in Computational Molecular Dynamics: Challenges, Methods, Ideas, edited by P. Deuflhard et al., Lecture Notes in Computer Science Engineering (Springer, Berlin, 1999), Vol. 4, p. 421.
32. H. Jiang and X. S. Zhao, J. Chem. Phys. 113, 930 (2000).
33. S. B. Singh and C. A. Singh, Am. J. Phys. 87, 894 (1989).
34. S. K. Gray and J. M. Verosky, J. Chem. Phys. 100, 5011 (1994).
35. V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer, New York, 1978).
36. J. M. Sanz-Serna, Acta Numerica 1992, 243 (1992).
37. J. M. Sanz-Serna and A. Portillo, J. Chem. Phys. 104, 2349 (1995).
38. A. K. Kerman and S. E. Koonin, Ann. Phys. (N.Y.) 100, 332 (1976).
39. A. D. Bandrauk and H. Shen, J. Chem. Phys. 99, 1185 (1993).
40. K. Takahashi and K. Ikeda, J. Chem. Phys. 99, 8680 (1993).
41. R. I. McLachan, SIAM J. Sci. Comput. 16, 151 (1995).
42. R. Kosloff, J. Phys. Chem. 92, 2087 (1988).
43. L. Jaroszewski, B. Lesyng, and J. A. McCammon, J. Mol. Phys. 283, 57 (1993).