Molecular dynamics simulations of elementary chemical processes in liquid water using combined density functional and molecular mechanics potentials. II. Charge separation processes

Journal of Chemical Physics

Volumn 106, Issue 9, 1997, Pages 3643-3657

  Strnad, M ^a,c   Martins Costa, M T C ^a   Millot, C ^a   Tunon I ^a,b   Ruiz Lopez M F ^a   Rivail, J L ^a  

^a NANCY UNIVERSITÉ   (France)

^b UNIVERSITY OF VALENCIA   (Spain)

^c INSTITUTE OF CHEMICAL PROCESS FUNDAMENTALS   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4143062484     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.473458     Document Type: Article

References (103)

1. R. M. Whitnell and K. R. Wilson, in Reviews in Computational Chemistry, edited by K. B. Lipkowitz, and D. B. Boyd (VCH, New York, 1993), p. 67-148.
2. M. Berkowitz, O. A. Karim, and P. J. Rossky, Chem. Phys. Lett. 105, 577 (1984); O. A. Karim and J. A. McCammon, J. Am. Chem. Soc. 108, 1762 (1986); Chem. Phys. Lett. 132, 219 (1986); G. Ciccotti, M. Ferrario, J. T. Hynes, and R. Kapral, J. Chem. Phys. 85, 925 (1988); Chem. Phys. 129, 241 (1989); J. Chem. Phys. 93, 7137 (1990).
3. M. Berkowitz, O. A. Karim, and P. J. Rossky, Chem. Phys. Lett. 105, 577 (1984); O. A. Karim and J. A. McCammon, J. Am. Chem. Soc. 108, 1762 (1986); Chem. Phys. Lett. 132, 219 (1986); G. Ciccotti, M. Ferrario, J. T. Hynes, and R. Kapral, J. Chem. Phys. 85, 925 (1988); Chem. Phys. 129, 241 (1989); J. Chem. Phys. 93, 7137 (1990).
4. M. Berkowitz, O. A. Karim, and P. J. Rossky, Chem. Phys. Lett. 105, 577 (1984); O. A. Karim and J. A. McCammon, J. Am. Chem. Soc. 108, 1762 (1986); Chem. Phys. Lett. 132, 219 (1986); G. Ciccotti, M. Ferrario, J. T. Hynes, and R. Kapral, J. Chem. Phys. 85, 925 (1988); Chem. Phys. 129, 241 (1989); J. Chem. Phys. 93, 7137 (1990).
5. M. Berkowitz, O. A. Karim, and P. J. Rossky, Chem. Phys. Lett. 105, 577 (1984); O. A. Karim and J. A. McCammon, J. Am. Chem. Soc. 108, 1762 (1986); Chem. Phys. Lett. 132, 219 (1986); G. Ciccotti, M. Ferrario, J. T. Hynes, and R. Kapral, J. Chem. Phys. 85, 925 (1988); Chem. Phys. 129, 241 (1989); J. Chem. Phys. 93, 7137 (1990).
6. M. Berkowitz, O. A. Karim, and P. J. Rossky, Chem. Phys. Lett. 105, 577 (1984); O. A. Karim and J. A. McCammon, J. Am. Chem. Soc. 108, 1762 (1986); Chem. Phys. Lett. 132, 219 (1986); G. Ciccotti, M. Ferrario, J. T. Hynes, and R. Kapral, J. Chem. Phys. 85, 925 (1988); Chem. Phys. 129, 241 (1989); J. Chem. Phys. 93, 7137 (1990).
7. M. Berkowitz, O. A. Karim, and P. J. Rossky, Chem. Phys. Lett. 105, 577 (1984); O. A. Karim and J. A. McCammon, J. Am. Chem. Soc. 108, 1762 (1986); Chem. Phys. Lett. 132, 219 (1986); G. Ciccotti, M. Ferrario, J. T. Hynes, and R. Kapral, J. Chem. Phys. 85, 925 (1988); Chem. Phys. 129, 241 (1989); J. Chem. Phys. 93, 7137 (1990).
8. W. P. Keirstead, K. R. Wilson, and J. T. Hynes, J. Chem. Phys. 95, 5256 (1991).
9. (a) J. P. Bergsma, B. J. Gertner, K. R. Wilson, and J. T. Hynes, J. Chem. Phys. 86, 1356 (1987);
10. (b) J. K. Hwang, G. King, S. Creighton, and A. Warshel, J. Am. Chem. Soc. 110, 5297 (1988);
11. (c) B. J. Gertner, K. R. Wilson, and J. T. Hynes, J. Chem. Phys. 90, 3537 (1989);
12. (d) B. J. Gertner, R. M. Whitnell, K. R. Wilson, and J. T. Hynes, J. Am. Chem. Soc. 113, 74 (1991).
13. For a review, see, for instance, M. A. Fox, Chem. Rev. 92, 365 (1992).
14. D. Borgis, S. Lee, and J. T. Hynes, Chem. Phys. Lett. 162, 19 (1989); A. Warshel and Z. T. Chu, J. Chem. Phys. 93, 4003 (1990); M. Nagaoka, Y. Okuno, and T. Yamabe, J. Am Chem. Soc. 113, 769 (1991); D. Borgis and J. T. Hynes, J. Chem. Phys. 94, 3619 (1991); J. J. I. Timoneda and J. T. Hynes, J. Phys Chem. 95, 10431 (1991); D. Borgis, G. Tarjus, and H. Azzouz, ibid. 96, 3188 (1992); J. Chem. Phys. 97, 1390 (1992); R. P. Muller and A. Warshel, J. Phys. Chem. 99, 17516 (1995); see also Ref. 10.
15. D. Borgis, S. Lee, and J. T. Hynes, Chem. Phys. Lett. 162, 19 (1989); A. Warshel and Z. T. Chu, J. Chem. Phys. 93, 4003 (1990); M. Nagaoka, Y. Okuno, and T. Yamabe, J. Am Chem. Soc. 113, 769 (1991); D. Borgis and J. T. Hynes, J. Chem. Phys. 94, 3619 (1991); J. J. I. Timoneda and J. T. Hynes, J. Phys Chem. 95, 10431 (1991); D. Borgis, G. Tarjus, and H. Azzouz, ibid. 96, 3188 (1992); J. Chem. Phys. 97, 1390 (1992); R. P. Muller and A. Warshel, J. Phys. Chem. 99, 17516 (1995); see also Ref. 10.
16. D. Borgis, S. Lee, and J. T. Hynes, Chem. Phys. Lett. 162, 19 (1989); A. Warshel and Z. T. Chu, J. Chem. Phys. 93, 4003 (1990); M. Nagaoka, Y. Okuno, and T. Yamabe, J. Am Chem. Soc. 113, 769 (1991); D. Borgis and J. T. Hynes, J. Chem. Phys. 94, 3619 (1991); J. J. I. Timoneda and J. T. Hynes, J. Phys Chem. 95, 10431 (1991); D. Borgis, G. Tarjus, and H. Azzouz, ibid. 96, 3188 (1992); J. Chem. Phys. 97, 1390 (1992); R. P. Muller and A. Warshel, J. Phys. Chem. 99, 17516 (1995); see also Ref. 10.
17. D. Borgis, S. Lee, and J. T. Hynes, Chem. Phys. Lett. 162, 19 (1989); A. Warshel and Z. T. Chu, J. Chem. Phys. 93, 4003 (1990); M. Nagaoka, Y. Okuno, and T. Yamabe, J. Am Chem. Soc. 113, 769 (1991); D. Borgis and J. T. Hynes, J. Chem. Phys. 94, 3619 (1991); J. J. I. Timoneda and J. T. Hynes, J. Phys Chem. 95, 10431 (1991); D. Borgis, G. Tarjus, and H. Azzouz, ibid. 96, 3188 (1992); J. Chem. Phys. 97, 1390 (1992); R. P. Muller and A. Warshel, J. Phys. Chem. 99, 17516 (1995); see also Ref. 10.
18. D. Borgis, S. Lee, and J. T. Hynes, Chem. Phys. Lett. 162, 19 (1989); A. Warshel and Z. T. Chu, J. Chem. Phys. 93, 4003 (1990); M. Nagaoka, Y. Okuno, and T. Yamabe, J. Am Chem. Soc. 113, 769 (1991); D. Borgis and J. T. Hynes, J. Chem. Phys. 94, 3619 (1991); J. J. I. Timoneda and J. T. Hynes, J. Phys Chem. 95, 10431 (1991); D. Borgis, G. Tarjus, and H. Azzouz, ibid. 96, 3188 (1992); J. Chem. Phys. 97, 1390 (1992); R. P. Muller and A. Warshel, J. Phys. Chem. 99, 17516 (1995); see also Ref. 10.
19. D. Borgis, S. Lee, and J. T. Hynes, Chem. Phys. Lett. 162, 19 (1989); A. Warshel and Z. T. Chu, J. Chem. Phys. 93, 4003 (1990); M. Nagaoka, Y. Okuno, and T. Yamabe, J. Am Chem. Soc. 113, 769 (1991); D. Borgis and J. T. Hynes, J. Chem. Phys. 94, 3619 (1991); J. J. I. Timoneda and J. T. Hynes, J. Phys Chem. 95, 10431 (1991); D. Borgis, G. Tarjus, and H. Azzouz, ibid. 96, 3188 (1992); J. Chem. Phys. 97, 1390 (1992); R. P. Muller and A. Warshel, J. Phys. Chem. 99, 17516 (1995); see also Ref. 10.
20. D. Borgis, S. Lee, and J. T. Hynes, Chem. Phys. Lett. 162, 19 (1989); A. Warshel and Z. T. Chu, J. Chem. Phys. 93, 4003 (1990); M. Nagaoka, Y. Okuno, and T. Yamabe, J. Am Chem. Soc. 113, 769 (1991); D. Borgis and J. T. Hynes, J. Chem. Phys. 94, 3619 (1991); J. J. I. Timoneda and J. T. Hynes, J. Phys Chem. 95, 10431 (1991); D. Borgis, G. Tarjus, and H. Azzouz, ibid. 96, 3188 (1992); J. Chem. Phys. 97, 1390 (1992); R. P. Muller and A. Warshel, J. Phys. Chem. 99, 17516 (1995); see also Ref. 10.
21. D. Borgis, S. Lee, and J. T. Hynes, Chem. Phys. Lett. 162, 19 (1989); A. Warshel and Z. T. Chu, J. Chem. Phys. 93, 4003 (1990); M. Nagaoka, Y. Okuno, and T. Yamabe, J. Am Chem. Soc. 113, 769 (1991); D. Borgis and J. T. Hynes, J. Chem. Phys. 94, 3619 (1991); J. J. I. Timoneda and J. T. Hynes, J. Phys Chem. 95, 10431 (1991); D. Borgis, G. Tarjus, and H. Azzouz, ibid. 96, 3188 (1992); J. Chem. Phys. 97, 1390 (1992); R. P. Muller and A. Warshel, J. Phys. Chem. 99, 17516 (1995); see also Ref. 10.
22. For recent reviews, see J. Tomasi and M. Persico, Chem. Rev. 94, 2027 (1994); J. L. Rivail and D. Rinaldi, in Computational Chemistry, Reviews of Current Trends, edited by J. Leszczynski (World Scientific, Singapore, 1996), Vol. 1, pp. 139-174.
23. For recent reviews, see J. Tomasi and M. Persico, Chem. Rev. 94, 2027 (1994); J. L. Rivail and D. Rinaldi, in Computational Chemistry, Reviews of Current Trends, edited by J. Leszczynski (World Scientific, Singapore, 1996), Vol. 1, pp. 139-174.
24. M. A. Aguilar, F. J. Olivares del Valle, and J. Tomasi, J. Chem. Phys. 98, 7375 (1993); M. Cozzi, M. Persico, and J. Tomasi, J. Mol. Liq. 60, 87 (1994); M. F. Ruiz-López, D. Rinaldi and J. Bertrán, J. Chem. Phys. 103, 9249 (1995).
25. M. A. Aguilar, F. J. Olivares del Valle, and J. Tomasi, J. Chem. Phys. 98, 7375 (1993); M. Cozzi, M. Persico, and J. Tomasi, J. Mol. Liq. 60, 87 (1994); M. F. Ruiz-López, D. Rinaldi and J. Bertrán, J. Chem. Phys. 103, 9249 (1995).
26. M. A. Aguilar, F. J. Olivares del Valle, and J. Tomasi, J. Chem. Phys. 98, 7375 (1993); M. Cozzi, M. Persico, and J. Tomasi, J. Mol. Liq. 60, 87 (1994); M. F. Ruiz-López, D. Rinaldi and J. Bertrán, J. Chem. Phys. 103, 9249 (1995).
27. J. Gao, in Reviews in Computational Chemistry, edited by K. B. Lipkowitz and D. B. Boyd (VCH, New York, 1996), Vol. 7, pp. 119-185.
28. I. Tuñón, M. T. C. Martins-Costa, C. Millot, and M. F. Ruiz-López, J. Chem. Phys. 106, 3633 (1997), preceding paper.
29. I. Tuñón, M. T. C. Martins-Costa, C. Millot, and M. F. Ruiz-López, J. Mol. Mod. 1, 196 (1995).
30. I. Tuñón, M. T. C. Martins-Costa, C. Millot, M. F. Ruiz-López, and J. L. Rivail, J. Comput. Chem. 17, 19 (1996).
31. J. C. Keck, Faraday Discuss. Chem. Soc. 33, 173 (1962); J. B. Anderson, J. Chem. Phys. 58, 4684 (1973).
32. J. C. Keck, Faraday Discuss. Chem. Soc. 33, 173 (1962); J. B. Anderson, J. Chem. Phys. 58, 4684 (1973).
33. J. B. Anderson, Adv. Chem. Phys. 91, 381 (1995).
34. See Ref. 4(c) and references cited therein for a description on calculation of κ in molecular dynamics simulations. See also Ref. 14 for a discussion on the differences between conversion and transmission coefficients.
35. H. A. Kramers, Physica 7, 284 (1940).
36. P. D. Bartlett and D. S. Tarbell, J. Am. Chem. Soc. 58, 466 (1936).
37. J. E. Dubois and F. Garnier, Chem. Commun. 241 (1968); Bull. Soc. Chim. Fr. 3797 (1968); M. F. Ruasse and J. E. Dubois. J. Am. Chem. Soc. 97, 1977 (1975); C. Reichardt, Solvent Effect in Organic Chemistry (Verlag Chemie, New York, 1979), Chap. 5; M. F. Ruasse and S. Montallebi, J. Phys. Org. Chem. 4, 527 (1991).
38. J. E. Dubois and F. Garnier, Chem. Commun. 241 (1968); Bull. Soc. Chim. Fr. 3797 (1968); M. F. Ruasse and J. E. Dubois. J. Am. Chem. Soc. 97, 1977 (1975); C. Reichardt, Solvent Effect in Organic Chemistry (Verlag Chemie, New York, 1979), Chap. 5; M. F. Ruasse and S. Montallebi, J. Phys. Org. Chem. 4, 527 (1991).
39. J. E. Dubois and F. Garnier, Chem. Commun. 241 (1968); Bull. Soc. Chim. Fr. 3797 (1968); M. F. Ruasse and J. E. Dubois. J. Am. Chem. Soc. 97, 1977 (1975); C. Reichardt, Solvent Effect in Organic Chemistry (Verlag Chemie, New York, 1979), Chap. 5; M. F. Ruasse and S. Montallebi, J. Phys. Org. Chem. 4, 527 (1991).
40. J. E. Dubois and F. Garnier, Chem. Commun. 241 (1968); Bull. Soc. Chim. Fr. 3797 (1968); M. F. Ruasse and J. E. Dubois. J. Am. Chem. Soc. 97, 1977 (1975); C. Reichardt, Solvent Effect in Organic Chemistry (Verlag Chemie, New York, 1979), Chap. 5; M. F. Ruasse and S. Montallebi, J. Phys. Org. Chem. 4, 527 (1991).
41. J. E. Dubois and F. Garnier, Chem. Commun. 241 (1968); Bull. Soc. Chim. Fr. 3797 (1968); M. F. Ruasse and J. E. Dubois. J. Am. Chem. Soc. 97, 1977 (1975); C. Reichardt, Solvent Effect in Organic Chemistry (Verlag Chemie, New York, 1979), Chap. 5; M. F. Ruasse and S. Montallebi, J. Phys. Org. Chem. 4, 527 (1991).
42. J. E. Dubois, F. Garnier, and H. Viellard, Tetrahedron Lett. 17, 1227 (1965); J. E. Dubois and F. Garnier, ibid. 26, 3047 (1966); G. A. Olah and T. R. Hockswender, Jr., J. Am. Chem. Soc. 96, 3574 (1974).
43. J. E. Dubois, F. Garnier, and H. Viellard, Tetrahedron Lett. 17, 1227 (1965); J. E. Dubois and F. Garnier, ibid. 26, 3047 (1966); G. A. Olah and T. R. Hockswender, Jr., J. Am. Chem. Soc. 96, 3574 (1974).
44. J. E. Dubois, F. Garnier, and H. Viellard, Tetrahedron Lett. 17, 1227 (1965); J. E. Dubois and F. Garnier, ibid. 26, 3047 (1966); G. A. Olah and T. R. Hockswender, Jr., J. Am. Chem. Soc. 96, 3574 (1974).
45. M. F. Ruasse, Adv. Phys. Org. Chem. 28, 207 (1993).
46. A. C. Hopkinson, M. H. Lien, K. Yates, and I. G. Czismadia, Theoret. Chim. Acta 38, 21 (1975); 44, 385 (1977).
47. A. C. Hopkinson, M. H. Lien, K. Yates, and I. G. Czismadia, Theoret. Chim. Acta 38, 21 (1975); 44, 385 (1977).
48. T. P. Hamilton and H. F. Shaefer III, J. Am. Chem. Soc. 112, 8260 (1990).
49. S. Yamabe, T. Minato, and S. Inagaki, J. Chem. Soc., Chem. Commun. 532 (1988).
50. T. Iwaoka, C. Kaneko, A. Shigihara, and H. Ichiwaka, J. Phys. Org. Chem. 6, 195 (1993).
51. M. Jaszunski and E. Kochanski, J. Am. Chem. Soc. 99, 4624 (1977); E. Kochanski, in Quantum Theory of Chemical Reactions, edited by R. Daudel, A. Pullman, L. Salem, and A. Veillard (Reidel, Dordtrecht, 1980), Vol. 2, pp. 177-191.
52. M. Jaszunski and E. Kochanski, J. Am. Chem. Soc. 99, 4624 (1977); E. Kochanski, in Quantum Theory of Chemical Reactions, edited by R. Daudel, A. Pullman, L. Salem, and A. Veillard (Reidel, Dordtrecht, 1980), Vol. 2, pp. 177-191.
53. M. Cossi, M. Persico, and J. Tomasi, J. Am. Chem, Soc. 116, 5373 (1994).
54. X. Assfeld, J. Garapon, D. Rinaldi, M. F. Ruiz-López, and J. L. Rivail, Theochem 371, 107 (1996).
55. W. L. Jorgensen, J. Chandrashekar, J. D. Madura, R. W. Impey, and M. L Klein, J. Chem. Phys. 79, 926 (1983).
56. M. T. C. Martins-Costa, B. Finance, C. Millot, and M. F. Ruiz-López (work in progress).
57. J. L. Rivail, D. Rinaldi, and M. F. Ruiz-López, in Theoretical and Computational Models for Organic Chemistry, NATO ASI Series C, Vol. 339, edited by S. J. Formosinho, I. G. Csizmadia, and L. Arnaut (Kluwer Academic, Dordrecht, 1991), pp. 79-92; D. Rinaldi, J. L. Rivail, and N. Rguini, J. Comput. Chem. 13, 675 (1992); V. Dillet, D. Rinaldi, J. G. Angyán, and J. L. Rivail, Chem. Phys. Lett. 202, 18 (1993); M. F. Ruiz-López, F. Bohr, M. T. C. Martins-Costa, and D. Rinaldi, ibid. 221, 109 (1994).
58. J. L. Rivail, D. Rinaldi, and M. F. Ruiz-López, in Theoretical and Computational Models for Organic Chemistry, NATO ASI Series C, Vol. 339, edited by S. J. Formosinho, I. G. Csizmadia, and L. Arnaut (Kluwer Academic, Dordrecht, 1991), pp. 79-92; D. Rinaldi, J. L. Rivail, and N. Rguini, J. Comput. Chem. 13, 675 (1992); V. Dillet, D. Rinaldi, J. G. Angyán, and J. L. Rivail, Chem. Phys. Lett. 202, 18 (1993); M. F. Ruiz-López, F. Bohr, M. T. C. Martins-Costa, and D. Rinaldi, ibid. 221, 109 (1994).
59. J. L. Rivail, D. Rinaldi, and M. F. Ruiz-López, in Theoretical and Computational Models for Organic Chemistry, NATO ASI Series C, Vol. 339, edited by S. J. Formosinho, I. G. Csizmadia, and L. Arnaut (Kluwer Academic, Dordrecht, 1991), pp. 79-92; D. Rinaldi, J. L. Rivail, and N. Rguini, J. Comput. Chem. 13, 675 (1992); V. Dillet, D. Rinaldi, J. G. Angyán, and J. L. Rivail, Chem. Phys. Lett. 202, 18 (1993); M. F. Ruiz-López, F. Bohr, M. T. C. Martins-Costa, and D. Rinaldi, ibid. 221, 109 (1994).
60. J. L. Rivail, D. Rinaldi, and M. F. Ruiz-López, in Theoretical and Computational Models for Organic Chemistry, NATO ASI Series C, Vol. 339, edited by S. J. Formosinho, I. G. Csizmadia, and L. Arnaut (Kluwer Academic, Dordrecht, 1991), pp. 79-92; D. Rinaldi, J. L. Rivail, and N. Rguini, J. Comput. Chem. 13, 675 (1992); V. Dillet, D. Rinaldi, J. G. Angyán, and J. L. Rivail, Chem. Phys. Lett. 202, 18 (1993); M. F. Ruiz-López, F. Bohr, M. T. C. Martins-Costa, and D. Rinaldi, ibid. 221, 109 (1994).
61. X. Assfeld, J. González, R. López, M. F. Ruiz-López, J. A. Sordo, and T. L. Sordo, J. Comput. Chem. 15, 479 (1994); M. F. Ruiz-López, X. Assfeld, J. I. García, J. A. Mayoral, and L. Salvatella, J. Am. Chem. Soc. 115, 8780 (1993); S. Antonczak, M. F. Ruiz-López, and J. L. Rivail, ibid. 116, 3912 (1994); I. Tunón, D. Rinaldi, M. F. Ruiz-López, and J. L. Rivail, J. Phys. Chem. 99, 3798 (1995).
62. X. Assfeld, J. González, R. López, M. F. Ruiz-López, J. A. Sordo, and T. L. Sordo, J. Comput. Chem. 15, 479 (1994); M. F. Ruiz-López, X. Assfeld, J. I. García, J. A. Mayoral, and L. Salvatella, J. Am. Chem. Soc. 115, 8780 (1993); S. Antonczak, M. F. Ruiz-López, and J. L. Rivail, ibid. 116, 3912 (1994); I. Tunón, D. Rinaldi, M. F. Ruiz-López, and J. L. Rivail, J. Phys. Chem. 99, 3798 (1995).
63. X. Assfeld, J. González, R. López, M. F. Ruiz-López, J. A. Sordo, and T. L. Sordo, J. Comput. Chem. 15, 479 (1994); M. F. Ruiz-López, X. Assfeld, J. I. García, J. A. Mayoral, and L. Salvatella, J. Am. Chem. Soc. 115, 8780 (1993); S. Antonczak, M. F. Ruiz-López, and J. L. Rivail, ibid. 116, 3912 (1994); I. Tunón, D. Rinaldi, M. F. Ruiz-López, and J. L. Rivail, J. Phys. Chem. 99, 3798 (1995).
64. X. Assfeld, J. González, R. López, M. F. Ruiz-López, J. A. Sordo, and T. L. Sordo, J. Comput. Chem. 15, 479 (1994); M. F. Ruiz-López, X. Assfeld, J. I. García, J. A. Mayoral, and L. Salvatella, J. Am. Chem. Soc. 115, 8780 (1993); S. Antonczak, M. F. Ruiz-López, and J. L. Rivail, ibid. 116, 3912 (1994); I. Tunón, D. Rinaldi, M. F. Ruiz-López, and J. L. Rivail, J. Phys. Chem. 99, 3798 (1995).
65. R. López, M. F. Ruiz-López, D. Rinaldi, J. A. Sordo, and T. L. Sordo, J. Phys. Chem. 100, 10600 (1996).
66. S. W. de Leeuw, J. W. Perram, and H. G. Petersen, J. Stat. Phys. 61, 1203 (1990).
67. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Clarendon, Oxford, 1989).
68. S. Nosé, Mol. Phys. 52, 255 (1984); W. G. Hoover, Phys. Rev. A 31, 1695 (1985); S. Nosé, Mol. Phys. 57, 187 (1986).
69. S. Nosé, Mol. Phys. 52, 255 (1984); W. G. Hoover, Phys. Rev. A 31, 1695 (1985); S. Nosé, Mol. Phys. 57, 187 (1986).
70. S. Nosé, Mol. Phys. 52, 255 (1984); W. G. Hoover, Phys. Rev. A 31, 1695 (1985); S. Nosé, Mol. Phys. 57, 187 (1986).
71. H. C. Andersen, J. Chem. Phys. 72, 2384 (1980).
72. M. Strnad, C. Millot, M. T. C. Martins-Costa, and M. F. Ruiz-López (work in progress).
73. L. D. Landau and E. M. Lifshitz, Statistical Physics (Pergamon, London, 1958).
74. I. Benjamin, B. J. Gertner, N. J. Tang, and K. R. Wilson, J. Am. Chem. Soc. 112, 524 (1990).
75. M. E. Tuckerman, B. J. Berne, and G. J. Martyna, J. Chem. Phys. 97, 1990 (1992); A. Rossi, ibid. 94, 1465 (1990); G. J. Martyna and B. J. Berne, ibid. 94, 6811 (1991); M. E. Tuckerman and B. J. Berne, ibid. 95, 8362 (1991); J. Phys. Chem. 98, 6885 (1994).
76. M. E. Tuckerman, B. J. Berne, and G. J. Martyna, J. Chem. Phys. 97, 1990 (1992); A. Rossi, ibid. 94, 1465 (1990); G. J. Martyna and B. J. Berne, ibid. 94, 6811 (1991); M. E. Tuckerman and B. J. Berne, ibid. 95, 8362 (1991); J. Phys. Chem. 98, 6885 (1994).
77. M. E. Tuckerman, B. J. Berne, and G. J. Martyna, J. Chem. Phys. 97, 1990 (1992); A. Rossi, ibid. 94, 1465 (1990); G. J. Martyna and B. J. Berne, ibid. 94, 6811 (1991); M. E. Tuckerman and B. J. Berne, ibid. 95, 8362 (1991); J. Phys. Chem. 98, 6885 (1994).
78. M. E. Tuckerman, B. J. Berne, and G. J. Martyna, J. Chem. Phys. 97, 1990 (1992); A. Rossi, ibid. 94, 1465 (1990); G. J. Martyna and B. J. Berne, ibid. 94, 6811 (1991); M. E. Tuckerman and B. J. Berne, ibid. 95, 8362 (1991); J. Phys. Chem. 98, 6885 (1994).
79. M. E. Tuckerman, B. J. Berne, and G. J. Martyna, J. Chem. Phys. 97, 1990 (1992); A. Rossi, ibid. 94, 1465 (1990); G. J. Martyna and B. J. Berne, ibid. 94, 6811 (1991); M. E. Tuckerman and B. J. Berne, ibid. 95, 8362 (1991); J. Phys. Chem. 98, 6885 (1994).
80. S. H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys. 58, 1200 (1980).
81. A. St-Amant and D. Salahub, Chem. Phys. Lett. 169, 387 (1990); D. Salahub, R. Fournier, P. Mlynarski, I. Papai, A. St-Amant, and J. Ushio, in Theory and Applications of Density Functional Approaches to Chemistry, edited by J. Labanowski and J. Andzelm (Springer, Berlin, 1991).
82. A. St-Amant and D. Salahub, Chem. Phys. Lett. 169, 387 (1990); D. Salahub, R. Fournier, P. Mlynarski, I. Papai, A. St-Amant, and J. Ushio, in Theory and Applications of Density Functional Approaches to Chemistry, edited by J. Labanowski and J. Andzelm (Springer, Berlin, 1991).
83. A. D. Becke, Phys. Rev. A 38, 3098 (1988); J. P. Perdew, Phys. Rev. B 33, 8822 (1986); 34, 7406 (E) (1986).
84. A. D. Becke, Phys. Rev. A 38, 3098 (1988); J. P. Perdew, Phys. Rev. B 33, 8822 (1986); 34, 7406 (E) (1986).
85. A. D. Becke, Phys. Rev. A 38, 3098 (1988); J. P. Perdew, Phys. Rev. B 33, 8822 (1986); 34, 7406 (E) (1986).
86. (a) T. P. Lybrand, I. Ghosh, and J. A. McCammon, J. Am. Chem. Soc. 107, 7793 (1985);
87. (b) W. L. Jorgensen, in Biochemical and Organic Simulation System (BOSS), Version 3.5 (Yale University, New Haven, 1994).
88. D. Fincham, CCP5 Q. 2, 6 (1981); D. Fincham and D. M. Heyes, Adv. Chem. Phys. 68, 493 (1985).
89. D. Fincham, CCP5 Q. 2, 6 (1981); D. Fincham and D. M. Heyes, Adv. Chem. Phys. 68, 493 (1985).
90. L. Verlet, Phys. Rev. 159, 98 (1967); W. C. Swope, H. C. Andersen, P. H. Berens, and K. R. Wilson, J. Chem. Phys. 76, 637 (1982).
91. L. Verlet, Phys. Rev. 159, 98 (1967); W. C. Swope, H. C. Andersen, P. H. Berens, and K. R. Wilson, J. Chem. Phys. 76, 637 (1982).
92. J. P. Ryckaert, G. Ciccotti, and H. J. C. Berendsen, J. Comput. Phys. 23, 327 (1977).
93. Constraining the reaction coordinate during the NVT equilibration of the transition state introduces both a configurational and zero velocity constraint. Average over the constrained ensemble is not rigorous and may be affected by some error. For semirigid systems, this error may be avoided using the approach of Ryckaert et al. [J. P. Ryckaert and G. Ciccotti, Mol. Phys. 58, 1125 (1986)] but this is not the case for flexible molecules. In our case, we use SHAKE to constrain the BrBr distance so that the corresponding relative velocity is unconstrained. In other words, the reaction coordinate is restricted only [E. A. Carter, G. Ciccotti, J. T. Hynes, and R. Kapral, Chem. Phys. Lett. 156, 472 (1989)].
94. Constraining the reaction coordinate during the NVT equilibration of the transition state introduces both a configurational and zero velocity constraint. Average over the constrained ensemble is not rigorous and may be affected by some error. For semirigid systems, this error may be avoided using the approach of Ryckaert et al. [J. P. Ryckaert and G. Ciccotti, Mol. Phys. 58, 1125 (1986)] but this is not the case for flexible molecules. In our case, we use SHAKE to constrain the BrBr distance so that the corresponding relative velocity is unconstrained. In other words, the reaction coordinate is restricted only [E. A. Carter, G. Ciccotti, J. T. Hynes, and R. Kapral, Chem. Phys. Lett. 156, 472 (1989)].
95. E. Ruiz, D. R. Salahub and A. Vela, J. Am. Chem. Soc. 117, 1141 (1995).
96. The location of the transition state has been made using GAUSSIAN 92/DFT (Ref. 51) using different exchange-correlation functionals and basis sets. All these calculations showed close structures for the transition state and in particular the reaction coordinate was predicted to be essentially defined by the BrBr bond length in all cases. Using these results, the transition state structure in Table I has been obtained using deMon (Ref. 42) assuming that the reaction coordinate near the transition state is the BrBr bond length.
97. M. J. Frisch, G. W. Trucks, H. B. Schlegel, P. M. W. Gill, B. G. Johnson, M. W. Wong, J. B. Foresman, M. A. Robb, M. Head-Gordon, E. S. Replogle, R. Gomperts, J. L. Andrés, K. Raghavachari, J. S. Binkley, C. Gonzalez, R. L. Martin, D. J. Fox, D. J. Defrees, J. Baker, J. J. P. Stewart, and J. A. Pople, GAUSSIAN 92/DFT, Revision G.1, Gaussian, Inc., Pittsburgh, 1993.
98. R. Car and M. Parrinello, Phys. Rev. Lett. 55, 2471 (1985).
99. K. Laasonen, M. Sprik, and M. Parrinello, J. Chem. Phys. 99, 9080 (1993).
100. I. Tuñón, M. T. C. Martins-Costa, C. Millot, and M. F. Ruiz-López, Chem. Phys. Lett. 241, 450 (1995).
101. P. Å. Bergström, J. Lindgren, and O. Kristiansson, J. Phys. Chem. 95, 8575 (1991).
102. W. L. Jorgensen, J. K. Buckner, S. E. Huston, and P. J. Rossky, J. Am. Chem. Soc. 109, 1891 (1987).
103. J. P. Bergsma, J. R. Reimers, K. R. Wilson, and J. T. Hynes, J. Chem. Phys. 85, 5625 (1986); see also Refs. 16, 53-54 cited in Ref. 4(a).