Reaction pathways and convexity of the potential energy surface: Application of Newton trajectories

Journal of Mathematical Chemistry

Volumn 36, Issue 4, 2004, Pages 307-340

  Hirsch, Michael ^a   Quapp, Wolfgang ^a  

^a UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

IRC; Newton trajectory; potential energy surface; projected gradient; pseudo convexity; reaction path

Indexed keywords

ANALYTIC METHOD; ARTICLE; ENERGY; MATHEMATICAL MODEL; REACTION ANALYSIS;

EID: 6344256224     PISSN: 02599791     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JOMC.0000044520.03226.5f     Document Type: Article

References (42)

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. K. Fukui, J. Phys. Chem. 74 (1970) 4161.
4. I.H. Williams and G.M. Maggiora, J. Mol. Struct. (Theochem) 89 (1982) 365.
5. R. Czerminski and R. Elber, J. Chem. Phys. 92 (1990) 5580.
6. W. Quapp, M. Hirsch, O. Imig and D. Heidrich, J. Comput. Chem. 19 (1998) 1087.
7. W. Quapp, M. Hirsch and D. Heidrich, Theor. Chem. Acc. 100 (1998) 285.
8. W. Quapp, M. Hirsch and D. Heidrich, Theor. Chem. Acc. 112 (2004) 40.
9. W. Quapp, J. Comput. Chem. 22 (2001) 537.
10. K. Müller and L.D. Brown, Theor. Chim. Acta 53 (1979) 75.
11. M. Hirsch, Zum Reaktionswegcharakter von Newtontrajektorien, Dissertation, (Fakultät für Chemie and Mineralogie, Universität Leipzig, (Dezember 2003). www.mathematic.uni-leipzig.de/MI/quapp/refs_mh
12. W. Quapp, J. Theor. Comp. Chem. 2 (2003) 385.
13. W. Kutzelnigg, Einführung in die Theoretische Chemie (VCH Verlagsgesellschaft, Weinheim, 1992).
14. W.J. Hehre, L. Radom, P.v.R. Schleyer and J.A. Pople, Ab initia Molekular Orbital Theory (Wiley, New York, Chichester, Brisbane, Toronto, Singapore, 1986).
15. H.T. Jongen, P. Jonker and F. Twilt, Nonlinear Optimization in Finite Dimensions - Morse Theory, Chebychev Approximation, Transversality, Flows, Parametric Aspects (Kluwer, Dordrecht, 2000).
16. J. Milnor, Morse Theory (Princeton University Press, 5th Printing, 1973).
17. J. Baker and P.M.W. Gill, J. Comput. Chem. 9 (1988) 465.
18. W. Quapp, J. Chem. Soc. Faraday Trans. 90 (1994) 1607.
19. J.H. Hubbard and B.H. West, Differential Equations, A Dynamical System Approach, Part I (Springer, New York, 1991).
20. W. Quapp, Chem. Phys. Lett. 253 (1996) 286.
21. J.M. Anglada, E. Besalú, J.M. Bofill and R. Crehuet, J. Comput. Chem. 22 (2001) 387, J.M. Bofill and J.M. Anglada, Theor. Chem. Acc. 105 (2001) 463, R. Crehuet, J.M. Bofill and J.M. Anglada, Theor. Chem. Acc. 107 (2002) 130.
22. J.M. Anglada, E. Besalú, J.M. Bofill and R. Crehuet, J. Comput. Chem. 22 (2001) 387, J.M. Bofill and J.M. Anglada, Theor. Chem. Acc. 105 (2001) 463, R. Crehuet, J.M. Bofill and J.M. Anglada, Theor. Chem. Acc. 107 (2002) 130.
23. J.M. Anglada, E. Besalú, J.M. Bofill and R. Crehuet, J. Comput. Chem. 22 (2001) 387, J.M. Bofill and J.M. Anglada, Theor. Chem. Acc. 105 (2001) 463, R. Crehuet, J.M. Bofill and J.M. Anglada, Theor. Chem. Acc. 107 (2002) 130.
24. E.L. Allgower and K. Georg, Numerical Continuation Methods - An Introduction (Springer, Berlin, 1990).
25. I. Diener, Globale Aspekte des kontinuierlichen Newtonverfahrens (Habilitation, Göttingen, 1991).
26. F.H. Branin, IBM J. Res. Dev. 16 (1972) 504.
27. K. Müller, Angew. Chem. 92 (1980) 1.
28. A. Kiełbasiński and H. Schwetlick, Numerische Lineare Algebra (Deutscher Verl. Wiss., Berlin, 1988).
29. P.G. Mezey, M.R. Peterson and I.G. Csizmadia, Can. J. Chem. 5 (1977) 2941.
30. S. Pancíř, Collect. Czech. Chem. Comm. 40 (1975) 1112.
31. M.V. Basilevsky and A.G. Shamov. Chem. Phys. 60 (1981) 347.
32. W. Quapp, Optimization 52 (2003) 317.
33. A. Cambini, E. Castagnoli, L. Martein, P. Mazzoleni and S. Schaible, Generalized Convexity and Fractional Programming in Economic Applications, (Springer, Berlin, 1990).
34. P.G. Mezey, Chem. Phys. Lett. 87 (1982) 277.
35. J. Kurchan and L. Laloux, J. Phys. A 29 (1996) 1929.
36. M. Hirsch and W. Quapp, Chem. Phys. Lett. 395 (2004) 150.
37. W. Quapp, J. Mol. Struct. 695-696 (2004) 95.
38. V.I. Arnold, Arnold's Problems (Springer, Berlin, 2004).
39. Y.G. Smeyer, M. Villa and M.L. Senent, J. Mol. Spectrosc. 177 (1996) 66.
40. E. Neria, S. Fischer and M. Karplus, J. Chem. Phys. 105 (1996) 1902.
41. J. González, X. Giménez and J.M. Bofill, Phys. Chem. Chem. Phys. 4 (2002) 2921.
42. J. González, X. Giménez and J.M. Bofill, Theor. Chem. Acc. 112 (2004) 75.