Variational nature, integration, and properties of Newton reaction path

Journal of Chemical Physics

Volumn 134, Issue 7, 2011, Pages

  Bofill, Josep Maria ^a   Quapp, Wolfgang ^b  

^a UNIVERSITY OF BARCELONA   (Spain)

^b UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CALCULUS OF VARIATIONS; MINIMUM ENERGY PATHS; NEWTON TRAJECTORY; REACTION PATHS; RUNGE-KUTTA;

RUNGE KUTTA METHODS;

ELECTRON ENERGY LEVELS;

EID: 79951931346     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3554214     Document Type: Article

References (47)

1. P. G. Mezey, Potential Energy Hypersurfaces (Elsevier, Amsterdam, 1987).
2. D. Heidrich, The Reaction Path in Chemistry: Current Approaches and Perspectives (Kluwer, Dordrecht, 1995).
3. W. Quapp, Chem. Phys. Lett. 253, 286 (1996). 10.1016/0009-2614(96)00255-2
4. K. Fukui, J. Phys. Chem. 74, 4161 (1970). 10.1021/j100717a029
5. M. J. Rothman and L. L. Lohr Jr., Chem. Phys. Lett. 70, 405 (1980). 10.1016/0009-2614(80)85361-9
6. P. Scharfenberg, Chem. Phys. Lett. 79, 115 (1981). 10.1016/0009-2614(81) 85300-6
7. I. H. Williams and G. M. Maggiora, J. Mol. Struct.: THEOCHEM 89, 365 (1982). 10.1016/0166-1280(82)80095-X
8. W. Quapp, M. Hirsch, O. Imig, and D. Heidrich, J. Comput. Chem. 19, 1087 (1998). 10.1002/(SICI)1096-987X(19980715)19:91087::AID-JCC93.0.CO;2-M
9. J. M. Anglada, E. Besal, J. M. Bofill, and R. Crehuet, J. Comput. Chem. 22, 387 (2001). 10.1002/1096-987X(200103)22:4387::AID-JCC10103.0.CO;2-R
10. W. Quapp, M. Hirsch, and D. Heidrich, Theor. Chem. Acc. 100, 285 (1998). 10.1007/s002140050389
11. D. K. Hoffman, R. S. Nord, and K. Ruedenberg, Theor. Chim. Acta 69, 265 (1986). 10.1007/BF00527704
12. W. Quapp, Theor. Chim. Acta 75, 447 (1989). 10.1007/BF00527676
13. M. V. Basilevsky, Chem. Phys. 67, 337 (1982). 10.1016/0301-0104(82)85194- X
14. J.-Q. Sun and K. Ruedenberg, J. Chem. Phys. 98, 9707 (1993). 10.1063/1.464349
15. W. H. Miller, N. C. Handy, and J. E. Adams, J. Chem. Phys. 72, 99 (1980). 10.1063/1.438959
16. J. Gonzlez, X. Giménez, and J. M. Bofill, J. Phys. Chem. A 105, 5022 (2001). 10.1021/jp003793k (Pubitemid 35361973)
17. J. Gonzlez, X. Giménez, and J. M. Bofill, J. Comput. Chem. 28, 2111 (2007). 10.1002/jcc.20729 (Pubitemid 47265249)
18. J. Gonzlez, X. Giménez, and J. M. Bofill, J. Chem. Phys. 131, 054108 (2009). 10.1063/1.3194135
19. D. G. Truhlar and B. C. Garret, Annu. Rev. Phys. Chem. 35, 159 (1984). 10.1146/annurev.pc.35.100184.001111
20. J. Gonzlez, X. Giménez, and J. M. Bofill, Phys. Chem. Chem. Phys. 4, 2921 (2002).
21. A. S. Sanz, X. Giménez, J. M. Bofill, and S. Miret-Artés, Chem. Phys. Lett. 478, 89 (2009); 10.1016/j.cplett.2009.07.046
22. A. S. Sanz, X. Giménez, J. M. Bofill, and S. Miret-Artés, Chem. Phys. Lett. 488, 235(E) (2010). 10.1016/j.cplett.2010.02.045
23. K. Fukui, Int. J. Quantum Chem. Symp. 15, 633 (1981).
24. R. Olender and R. Elber, J. Mol. Struct.: THEOCHEM 398, 63 (1997). 10.1016/S0166-1280(97)00038-9
25. R. Crehuet and J. M. Bofill, J. Chem. Phys. 122, 234105 (2005). 10.1063/1.1927521 (Pubitemid 41107361)
26. R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley, New York, 1953), vol. 1.
27. J. M. Bofill (unpublished).
28. W. Quapp, Theor. Chem. Acc. 121, 227 (2008). 10.1007/s00214-008-0468-x
29. J. M. Bofill, J. Chem. Phys. 130, 176102 (2009). 10.1063/1.3126266
30. M. Hirsch and W. Quapp, J. Math. Chem. 36, 307 (2004). 10.1023/B:JOMC.0000044520.03226.5f (Pubitemid 39388046)
31. I. M. Gelfand and S. V. Fomin, Calculus of Variations (Dover Publications, New York, 2000).
32. I. G. Petrovsky, Lectures on Partial Differential Equations (Dover Publications, New York, 1991).
33. F. John, Partial Differential Equations (Springer, Heidelberg, 1974).
34. G. A. Bliss, Lectures on the Calculus of Variations (The University Chicago Press, Chicago, 1946).
35. R. Crehuet, J. M. Bofill, and J. M. Anglada, Theor. Chem. Acc. 107, 130 (2002). doi:10.1007/s00214-001-0306-x (Pubitemid 40835019)
36. D. F. Davidenko, Dokl. Akad. Nauk SSSR 88, 601 (1953).
37. F. H. Branin, IBM J. Res. Dev. 504 (1972). 10.1147/rd.165.0504
38. K. Mller and L. D. Brown, Theor. Chim. Acta 53, 75 (1979). 10.1007/BF00547608
39. G. Engeln-Mllges and F. Uhlig, Numerical Algorithms with Fortran (Springer-Verlag, Berlin, 1996).
40. E. Ren, W. E, and E. Vanden-Eijnden, J. Chem. Phys. 126, 164103 (2007). 10.1063/1.2743003 (Pubitemid 46883990)
41. V. S. Melissas, D. G. Truhlar, and B. C. Garret, J. Chem. Phys. 96, 5758 (1992). 10.1063/1.462674
42. A. Aguilar-Mogas, X. Giménez, and J. M. Bofill, Chem. Phys. Lett. 432, 375 (2006). 10.1016/j.cplett.2006.10.061 (Pubitemid 44737458)
43. A. Aguilar-Mogas, X. Giménez, and J. M. Bofill, J. Comput. Chem. 31, 2510 (2010). 10.1002/jcc.21539
44. S. Wolfe, H. B. Schlegel, I. G. Csizmadia, and F. Bernardi, J. Am. Chem. Soc. 97, 2020 (1975). 10.1021/ja00841a005
45. W. Quapp, J. Chem. Phys. 122, 174106 (2005). 10.1063/1.1885467 (Pubitemid 40665963)
46. W. Quapp, M. Hirsch, and D. Heidrich, Theor. Chem. Acc. 112, 40 (2004). 10.1007/s00214-003-0558-8 (Pubitemid 38650832)
47. W. Quapp, J. Mol. Struct.: THEOCHEM 695-696, 95 (2004). 10.1016/j.molstruc.2003.10.034 (Pubitemid 38684157)