Skip to main content
SpringerLink
Log in

Misgivings from the theoretical foundation of the path‐following procedures based on the Elber–Karplus strategy

  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

A mathematical proof against the theoretical foundation of the Elber–Karplus (EK) global reaction path‐following method and the improvements based on the EK strategy have been discussed. According to our arguments the minimization of the average value of the potential energy along a path to two energy minima never defines a reaction path (RP) unless in the chemically irrealistic situation where the points of the curve joining the two minima of reactants and products have constant energy values. Therefore, finding approximate RPs by EK‐strategies for large chemical systems or even in mathematical test examples is impossible or at least strongly doubtful (the larger the system the more doubtful).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V.V. Bulatov, M. Nastar, J. Justo and S. Yip, Nucl. Instrum. Methods Phys. Res. B 121 (1997) 251.

    Article  CAS  Google Scholar 

  2. V.V. Bulatov, S. Yip and A.S. Argon, Philos. Magaz. A 72 (1995) 453.

    CAS  Google Scholar 

  3. S.S.L. Chiu, J.J.W. McDouall and I.H. Hillier, J. Chem. Soc. Farad. Trans. 90 (1994) 1575.

    Article  CAS  Google Scholar 

  4. M.A. Collins, Adv. Chem. Phys. 93 (1996) 389.

    CAS  Google Scholar 

  5. R. Czerminski and R. Elber, Int. J. Quantum Chem. 24 (1990) 167.

    Article  CAS  Google Scholar 

  6. R. Czerminski and R. Elber, J. Chem. Phys. 92 (1990) 5580.

    Article  CAS  Google Scholar 

  7. J.F. Diaz, B. Wroblowski and Y. Engelborghs, Biochem. 34 (1995) 12038.

    Article  CAS  Google Scholar 

  8. R. Elber and M. Karplus, Chem. Phys. Lett. 139 (1987) 375.

    Article  CAS  Google Scholar 

  9. M.A.E.C. Elkettani and J.C. Smith, Compt. Rend. Ser. III 319 (1996) 161.

    CAS  Google Scholar 

  10. C. Guilbert, D. Perahia and L. Mouawad, Comput. Phys. Comm. 91 (1995) 263.

    Article  CAS  Google Scholar 

  11. D. Heidrich, W. Kliesch and W. Quapp, Properties of Chemically Interesting Potential Energy Surfaces (Springer, Berlin, 1991).

    Google Scholar 

  12. S. Huston and J.W. Ponder, TINKER: Software Tools for Molecular Design, Version 3.5, October 1997 (Copyright Jay William Ponder, 1990–97).

  13. E. Jacoby, P. Kruger, J. Schlitter, D. Koper and A. Wollmer, Protein Engrg. 9 (1996) 113.

    CAS  Google Scholar 

  14. F. Jensen, J. Chem. Phys. 102 (1995) 6706.

    Article  CAS  Google Scholar 

  15. R. Khare and M.E. Paulaitis, Chem. Engrg. Sci. 49 (1994) 2867.

    Article  CAS  Google Scholar 

  16. R. Khare and M.E. Paulaitis, Macromol. 28 (1995) 4495.

    Article  CAS  Google Scholar 

  17. G.A. Korn and Th.M. Korn, Mathematical Handbook for Scientists and Enginers (McGraw-Hill, New York, 1961).

    Google Scholar 

  18. T. Lazaridis and M.E. Paulaitis, J. Am. Chem. Soc. 116 (1994) 1546.

    Article  CAS  Google Scholar 

  19. O. Marques and Y.H. Sanejouand, Proteins–Structure, Function and Genetics 23 (1995) 557.

    Article  CAS  Google Scholar 

  20. P.G. Mezey, Potential Energy Hypersurfaces (Elsevier, Amsterdam, 1987).

    Google Scholar 

  21. L. Mouawad and D. Perahia, J. Mol. Biol. 258 (1996) 393.

    Article  CAS  Google Scholar 

  22. M. Nastar, V.V. Bulatov and S. Yip, Phys. Rev. B 53 (1996) 13521.

    Article  CAS  Google Scholar 

  23. I. Ohmine, J. Phys. Chem. 99 (1995) 6767.

    Article  CAS  Google Scholar 

  24. R. Olender and R. Elber, J. Mol. Struct. (Theochem) 398–399 (1997) 63.

    Article  Google Scholar 

  25. R. Poteau, F. Spiegelmann and P. Labastie, Z. Phys. D 30 (1994) 557.

    Article  Google Scholar 

  26. W.H. Press, B.P. Flannery S.A. Teukolsky and W.T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, Cambridge, 1986) p. 294.

    Google Scholar 

  27. H.B. Schlegel, in: Modern Electronic Structure Theory, Part I, Advanced Series in Physical Chemistry, Vol. 2, ed. D.R. Yarkony (World Scientific, Singapore, 1995) p. 482.

    Google Scholar 

  28. J. Schlitter, M. Engels and P. Kruger, J. Mol. Graphics 12 (1994) 84.

    Article  CAS  Google Scholar 

  29. O.S. Smart, Chem. Phys. Lett. 222 (1994) 503.

    Article  CAS  Google Scholar 

  30. L.L. Stachó and M.I. Bán, J. Math. Chem. 11 (1992) 405.

    Article  Google Scholar 

  31. L.L. Stachó and M.I. Bán, Theor. Chim. Acta 83 (1992) 433.

    Article  Google Scholar 

  32. L.L. Stachó and M.I. Bán, Theor. Chim. Acta 84 (1993) 535.

    Article  Google Scholar 

  33. L.L. Stachó, Gy. Dömötör and M.I. Bán, Chem. Phys. Lett. (accepted for publication in 1999).

  34. L.L. Stachó, Gy. Dömötör, M.I. Bán and T. Csendes, J. Mol. Struct. (Theochem) 398–399 (1997) 111.

    Article  Google Scholar 

  35. J.E. Straub and J.K. Choi, J. Phys. Chem. 98 (1994) 10978.

    Article  CAS  Google Scholar 

  36. A. Thomas, M.J. Field and D. Perahia, J. Mol. Biol. 261 (1996) 490.

    Article  CAS  Google Scholar 

  37. A. Ulitsky and R. Elber, J. Chem. Phys. 92 (1990) 1510.

    Article  CAS  Google Scholar 

  38. A. Ulitsky and D. Shalloway, J. Chem. Phys. 106 (1997) 10099.

    Article  CAS  Google Scholar 

  39. J.C. Wang and K.A. Fichthorn, Langmuir 12 (1996) 139.

    Article  Google Scholar 

  40. R.P. Wang and K.A. Fichthorn, Phys. Rev. B 48 (1993) 18288.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bolyai Institute for Mathematics, JATE University of Szeged, Aradi Vértanúk tere 1, H‐6720, Szeged, Hungary

    László L. Stachó

  2. Institute of Physical Chemistry, JATE University of Szeged, P.O. Box 105, H‐6701, Szeged, Hungary

    Gyula Dömötör & Miklós I. Bán

Authors
  1. László L. Stachó
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gyula Dömötör
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Miklós I. Bán
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stachó, L.L., Dömötör, G. & Bán, M.I. Misgivings from the theoretical foundation of the path‐following procedures based on the Elber–Karplus strategy. Journal of Mathematical Chemistry 26, 87–94 (1999). https://doi.org/10.1023/A:1019125626111

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1019125626111

Keywords

Search

Navigation