Chemical reaction paths and calculus of variations

Theoretical Chemistry Accounts

Volumn 121, Issue 5-6, 2008, Pages 227-237

  Quapp, Wolfgang ^a  

^a UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

Euler equations; Newton trajectory; Potential energy surface; Steepest descent; Variation of reaction pathways

Indexed keywords

EID: 56349085909     PISSN: 1432881X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00214-008-0468-x     Document Type: Article

References (81)

1. Laidler K (1969) Theory of reaction rates. McGraw-Hill, New York
2. W Miller NC Handy JE Adams 1980 J Chem Phys 72 99
3. Mezey PG (1987) Potential energy hypersurfaces. Elsevier, Amsterdam
4. Heidrich D, Kliesch W, Quapp W (1991) Properties of chemically interesting potential energy surfaces. Lecture notes in chemistry, vol 56. Springer, Berlin
5. Heidrich D (1995) The reaction path in chemistry: current approaches and perspectives. Kluwer, Dordrecht
6. DG Truhlar BC Garrett 1980 Acc Chem Res 13 440
7. W Quapp D Heidrich 1984 Theor Chim Acta 66 245
8. W Quapp M Hirsch O Imig D Heidrich 1998 J Comput Chem 19 1087
9. W Quapp M Hirsch D Heidrich 1998 Theor Chem Acc 100 285
10. H Hirsch W Quapp D Heidrich 1999 Phys Chem Chem Phys 1 5291
11. R Crehuet JM Bofill 2005 J Chem Phys 122 234105
12. A Aguilar-Mogas R Crehuet X Giménez JM Bofill 2007 Mol Phys 105 2475
13. A Aguilar-Mogas R Crehuet JM Bofill 2008 J Chem Phys 128 104102
14. E Vanden-Eijnden M Heymann 2008 J Chem Phys 128 061103
15. M Heymann E Vanden-Eijnden 2008 Comm Pure Appl Math 61 1052
16. Gelfand IM, Fomin SV (1991) Calculus of variations. Dover, Mineola
17. R Olender R Elber 1997 J Mol Struc (Theochem) 63 398
18. LL Stacho G Dömötör MI Ban 2000 J Math Chem 28 241
19. IH Williams GM Maggiora 1982 J Mol Struct (Theochem) 89 365
20. R Czerminski R Elber 1990 J Chem Phys 92 5580
21. JM Anglada E Besalu JM Bofill R Crehuet 2001 J Comput Chem 22 387
22. JM Bofill JM Anglada 2001 Theor Chem Acc 105 463
23. R Crehuet JM Bofill JM Anglada 2002 Theor Chem Acc 107 130
24. R Elber M Karplus 1987 Chem Phys Lett 139 375
25. R Czerminski R Elber 1990 Int J Quantum Chem S24 167
26. Elber R (1996) In: Elber R (ed) Recent developments in theoretical studies of proteins. World Scientific, Singapore, p 65
27. LR Pratt 1986 J Chem Phys 85 5045
28. MV Basilevsky AG Shamov 1981 Chem Phys 60 337
29. MV Basilevsky AG Shamov 1981 Chem Phys 60 347
30. DK Hoffman RS Nord K Ruedenberg 1986 Theor Chim Acta 69 265
31. W Quapp 1989 Theor Chim Acta 75 447
32. Quapp W, Imig O, Heidrich D (1995) In: Heidrich D (ed) The reaction path in chemistry: current approaches and perspectives. Kluwer, Dordrecht, p 137
33. J-Q Sun K Ruedenberg 1993 J Chem Phys 98 9707
34. K Fukui 1974 J Phys Chem 74 4161
35. Fukui K (1974) In: Daudel R, Pullman P (eds) The world of quantum chemistry. Dordrecht, Reidel, p 113
36. BC Garrett MJ Redmon R Steckler DG Truhlar KK Baldridge D Bartol MW Schmidt MS Gordon 1988 J Phys Chem 92 1476
37. F Jensen 1995 J Chem Phys 102 6706
38. W Quapp M Hirsch D Heidrich 2000 Theor Chem Acc 105 145
39. W Quapp E Kraka D Cremer 2007 J Phys Chem 111 11287
40. H Joo E Kraka W Quapp D Cremer 2007 Mol Phys 105 2697
41. AG Baboul HB Schlegel 1997 J Chem Phys 107 9413
42. K Fukui 1970 J Phys Chem 74 4161
43. A Tachibana K Fukui 1978 Theor Chim Acta 49 321
44. HB Schlegel 1994 J Chem Soc Faraday Trans 90 1569
45. W Quapp 1994 J Chem Soc Faraday Trans 90 1607
46. R Elber M Karplus 1999 Chem Phys Lett 311 335
47. DG Truhlar AJ Kupperman 1971 J Am Chem Soc 93 1840
48. Carathéodory C (1935) Variationsrechnung und partielle Differentialgleichungen erster Ordnung. Teubner, Leipzig and Berlin
49. W Quapp 2003 J Theor Comput Chem 2 385
50. R Steckler DG Truhlar 1990 J Chem Phys 93 6570
51. A Ulitzky R Elber 1990 J Chem Phys 92 1510
52. Branin FH (1972) IBM J Res Develop 504
53. Jongen HT, Jonker P, Twilt F (1987) In: Guddat J et al (eds) Parametric optimization and related topics. Akademie, Berlin, p 209
54. Jongen HT (1990) In: Allgower EL, Georg K (eds) Computational solutions of nonlinear systems of equations. American Mathematical Society, Providence, p 317
55. I Diener R Schaback 1990 J Optim Theory Appl 67 87
56. Diener I (1991) Globale Aspekte des kontinuierlichen Newton-Verfahrens. Habilitation, Göttingen
57. M Hirsch W Quapp 2004 J Mol Struct (Theochem) 683 1
58. M Hirsch W Quapp 2004 J Math Chem 36 307
59. EM Sevick AT Bell DN Theodorou 1993 J Chem Phys 98 3196
60. Kiełbasiński A, Schwetlick H (1988) Numerische Lineare Algebra. Deutscher Verl. Wiss., Berlin
61. SH Huo JE Straub 1997 J Chem Phys 107 5000
62. M Berkowitz JD Morgan JD McCommon SH Northrup 1983 J Chem Phys 79 5563
63. Y Levin M Nediak A Ben-Israel 2002 J Comput Appl Math 139 197
64. SS-L Chiu JW McDouall IH Hillier 1994 J Chem Soc Faraday Trans 90 1575
65. G Henkelman BP Uberuaga H Jónsson 2000 J Chem Phys 113 9901
66. JJ Moré TS Munson 2004 Math Program Ser B 100 151
67. C Jin 2007 Commun Comput Phys 2 1220
68. S Pancíř 1975 Collect Czech Chem Commun 40 1112
69. DJ Rowe A Ryman 1982 J Math Phys 23 732
70. HB Schlegel 1992 Theor Chim Acta 83 21
71. M Hirsch W Quapp 2004 Chem Phys Lett 395 150
72. W Quapp M Hirsch D Heidrich 2004 Theor Chim Acta 112 40
73. CK Reddy H-D Chiang 2006 J Comput Biol 13 745
74. JC Maxwell 1870 Philos Mag 40 421
75. K Ruedenberg J-Q Sun 1994 J Chem Phys 100 5836
76. D Heidrich W Quapp 1986 Theor Chim Acta 70 89
77. H-W Kim D Zeroka 2008 Int J Quantum Chem 108 974
78. Quapp W (2008) J Theor Comput Chem (in press)
79. T Taketsugu T Hirano 1997 J Chem Phys 107 10506
80. S Park MK Sener D Lu K Schulten 2003 J Chem Phys 119 1313
81. A Jiménez R Crehuet 2007 Theor Chem Acc 108 769