The variational structure of gradient extremals

Journal of Chemical Theory and Computation

Volumn 8, Issue 3, 2012, Pages 927-935

  Bofill, Josep Maria ^a   Quapp, Wolfgang ^b   Caballero, Marc ^a  

^a UNIVERSITY OF BARCELONA   (Spain)

^b UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84858313011     PISSN: 15499618     EISSN: 15499626     Source Type: Journal    
DOI: 10.1021/ct200805d     Document Type: Article

References (63)

1. Doubleday, C. J. Phys. Chem. A 2001, 105, 6333
2. Carpenter, B. K. Angew. Chem., Int. Ed. 1998, 37, 3340
3. Doubleday, C.; Li, G.; Hase, W. L. Phys. Chem. Chem. Phys. 2002, 4, 304
4. Carpenter, B. K. J. Phys. Org. Chem. 2003, 16, 858
5. Doubleday, C.; Suhrada, C. P.; Houk, K. N. J. Am. Chem. Soc. 2006, 128, 90
6. Ammal, S. C.; Yamataka, H.; Aida, M.; Dupuis, M. Science 2003, 299, 1555
7. Valtazanos, P.; Ruedenberg, K. Theor. Chim. Acta 1986, 69, 281
8. Pancir, J. Collect. Czech. Chem. Commun. 1975, 40, 1112
9. Basilevsky, M. V.; Shamov, A. G. Chem. Phys. 1981, 60, 347
10. Rowe, D. J.; Ryman, A. J. Math. Phys. 1982, 23, 732
11. Basilevsky, M. V. Chem. Phys. 1982, 67, 337
12. Hoffman, D. K.; Nord, R. S.; Ruedenberg, K. Theor. Chim. Acta 1986, 69, 265
13. Jørgensen, P.; Jensen, H. J. Aa.; Helgaker, T. Theor. Chim. Acta 1988, 73, 55
14. Quapp, W. Theor. Chim. Acta 1989, 75, 447
15. Schlegel, H. B. Theor. Chim. Acta 1991, 83, 15
16. Heidrich, D.; Kliesch, W.; Quapp, W. Properties of Chemically Interesting Potential Energy Surfaces, Lecture Notes in Chemistry; Springer-Verlag: Berlin, Germany, 1991; Vol. 56, Section 3.
17. Sun, J.-Q.; Ruedenberg, K. J. Chem. Phys. 1993, 98, 9707
18. Bondensgård, K.; Jensen, F. J. Chem. Phys. 1996, 104, 8025
19. Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes in Fortran 77: The Art of Scientific Computing; Cambridge University Press: Cambridge, U.K., 2003.
20. Worth, G. A.; Beck, M. H.; Jäckle, A.; Meyer, H.-D. The MCTDH Package, version 8.2; University of Heidelberg: Heidelberg, Germany, 2000.
21. Meyer, H.-D.; Manthe, U.; Cederbaum, L. S. Chem. Phys. Lett. 1990, 165, 73
22. Beck, M. H.; Jäckle, A.; Worth, G. A.; Meyer, H.-D. Phys. Rep. 2000, 324:1, 1
23. González, J.; Giménez, X.; Bofill, J. M. Phys. Chem. Chem. Phys. 2002, 4, 2921
24. González, J.; Giménez, X.; Bofill, J. M. J. Chem. Phys. 2009, 131, 054108
25. Quapp, W.; Hirsch, M.; Imig, O.; Heidrich, D. J. Comput. Chem. 1998, 19, 1087
26. Quapp, W.; Hirsch, M.; Heidrich, D. Theor. Chem. Acc. 1998, 100, 285
27. Anglada, J. M.; Besalú, E.; Bofill, J. M.; Crehuet, R. J. Comput. Chem. 2001, 22, 387
28. Bofill, J. M.; Anglada, J. M. Theor. Chem. Acc. 2001, 105, 463
29. Crehuet, R.; Bofill, J. M.; Anglada, J. M. Theor. Chem. Acc. 2002, 107, 130
30. Quapp, W.; Bofill, J. M.; Aguilar-Mogas, A. Theor. Chem. Acc. 2011, 129, 83
31. Bofill, J. M.; Quapp, W. J. Chem. Phys. 2011, 134, 074101
32. Tachibana, A.; Fukui, K. Theor. Chim. Acta 1978, 49, 321
33. Tachibana, A.; Fukui, K. Theor. Chim. Acta 1979, 51, 189
34. Tachibana, A.; Fukui, K. Theor. Chim. Acta 1979, 51, 275
35. Tachibana, A.; Fukui, K. Theor. Chim. Acta 1980, 57, 81
36. Fukui, K. Int. J. Quantum Chem., Quantum Chem. Symp. 1981, 15, 633
37. Olender, R.; Elber, R. J. Mol. Struc. (THEOCHEM) 1997, 63, 398
38. Stachó, L. L.; Dömötör, G.; Bán, M. I. J. Math. Chem. 2000, 28, 241
39. Crehuet, R.; Bofill, J. M. J. Chem. Phys. 2005, 122, 234105
40. Aguilar-Mogas, A.; Crehuet, R.; Giménez, X.; Bofill, J. M. Mol. Phys. 2007, 105, 2475
41. Aguilar-Mogas, A.; Giménez, X.; Bofill, J. M. J. Chem. Phys. 2008, 128, 104102
42. Vanden-Eijnden, E.; Heymann, M. J. Chem. Phys. 2008, 128, 061103
43. Heymann, M.; Vanden-Eijnden, E. Comm. Pure Appl. Math. 2008, 61, 1052
44. Quapp, W. Theor. Chem. Acc. 2008, 121, 227
45. Bofill, J. M. J. Chem. Phys. 2009, 130, 176102
46. Aguilar-Mogas, A.; Giménez, X.; Bofill, J. M. J. Comput. Chem. 2010, 31, 2510
47. Courant, R.; Hilbert, D. Methods of Mathematical Physics; Wiley: New York, 1953.
48. Carathéodory, C. Variationsrechnung und Partielle Differentialgleichungen Erster Ordnung; Teubner: Leipzig, Germany, 1935.
49. Bliss, G. A. Lectures on the Calculus of Variations; The University of Chicago Press: Chicago IL, 1946.
50. McWeeny, R. Phys. Rev. 1961, 126, 1028
51. Petrovsky, I. G. Lectures on Partial Differential Equations; Dover Publications: New York, 1991.
52. John, F. Partial Differential Equations; Springer: Heidelberg, Germany, 1974.
53. Hirsch, M.; Quapp, W. Chem. Phys. Lett. 2004, 395, 150
54. Müller, K.; Brown, L. D. Theor. Chim. Acta 1979, 53, 75
55. Gelfand, I. M.; Fomin, S. V. Calculus of Variations; Dover Publications: New York, 2000.
56. Rund, H. The Hamilton-Jacobi Theory in the Calculus of Variations; Van Nostrand: London, U.K., 1966.
57. Wolfram, S. Mathematica; Addison-Wesley: New York, 1988.
58. Quapp, W. J. Mol. Struct. (THEOCHEM) 2004, 695-696, 95
59. Quapp, W.; Hirsch, M.; Heidrich, D. Theor. Chem. Acc. 2004, 112, 40
60. Hirsch, M.; Quapp, W. J. Math. Chem. 2004, 36, 307
61. Koch, D. M.; Toubin, C.; Peslherbe, G. H.; Hynes, J. T. J. Phys. Chem. C 2008, 112, 2972
62. Neria, E.; Fischer, S.; Karplus, M. J. Chem. Phys. 1996, 105, 1902
63. Lucas, J. M.; Andrés, J.; de Sogas, J.; Albertí, M.; Bofill, J. M.; Bassi, D.; Ascenzi, D.; Tosi, P.; Aguilar, A. J. Chem. Phys. 2009, 131, 024306