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Link to original content: https://doi.org/10.1007/bf00547608
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Location of saddle points and minimum energy paths by a constrained simplex optimization procedure

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Abstract

Two methods are proposed, one for the location of saddle points and one for the calculation of steepest-descent paths on multidimensional surfaces. Both methods are based on a constrained simplex optimization technique that avoids the evaluation of gradients or second derivative matrices. Three chemical reactions of increasing structural complexity are studied within the PRDDO SCF approximation. Predicted properties of reaction hypersurfaces are in good overall agreement with those determined by gradient minimization and gradient following algorithms in connection with various ab initio SCF methods. Computational efforts required by the new procedures are discussed.

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References

  1. Empedocles, P.: Intern. J. Quantum Chem. 3S, 47 (1969)

    Google Scholar 

  2. Dewar, M. J. S., Kirschner, S.: J. Am. Chem. Soc. 93, 4290, 4291, 4292 (1971)

    Google Scholar 

  3. Ermer, O.: Struct. Bonding (Berlin) 27, 161, 202 (1976)

    Google Scholar 

  4. McIver, Jr., J. W., Komornicki, A.: J. Am. Chem. Soc. 94, 2625 (1972)

    Google Scholar 

  5. Komornicki, A., McIver, Jr., J. W.: J. Am. Chem. Soc. 96, 5798 (1974)

    Google Scholar 

  6. Fukui, K.: J. Phys. Chem. 74, 4161 (1970)

    Google Scholar 

  7. Fukui, K., Kato, S., Fujimoto, H.: J. Am. Chem. Soc. 97, 1 (1975)

    Google Scholar 

  8. Pearson, P. K., Schaefer III, H. F., Wahlgren, U.: J. Chem. Phys. 62, 350 (1975)

    Google Scholar 

  9. Ishida, K., Morokuma, K., Komornicki, A.: J. Chem. Phys. 66, 2153 (1977)

    Google Scholar 

  10. Basilevsky, M. V.: Chem. Phys. 24, 81 (1977)

    Google Scholar 

  11. Tachibana, A., Fukui, K.: Theoret. Chim. Acta (Berl.) 49, 321 (1978)

    Google Scholar 

  12. Murrell, J. N.: Struct. Bonding (Berl.) 32, 93, 100 (1977)

    Google Scholar 

  13. Dixon, L. C. W.: Nonlinear optimization, London: The English Universities Press Limited, 1972

    Google Scholar 

  14. Komornicki, A., Ishida, K., Morokuma, K., Ditchfield, R., Conrad, M.: Chem. Phys. Letters 45, 595 (1977)

    Google Scholar 

  15. Poppinger, D.: Chem. Phys. Letters 35, 550 (1975)

    Google Scholar 

  16. Mezey, P. G., Peterson, M. R., Csizmadia, I. G.: Can. J. Chem. 55, 2941 (1977); Peterson, M. R., Csizmadia, I. G., in: Applications of MO theory in organic chemistry, I. G. Csizmadia, Ed., Vol. 2, p. 117. Amsterdam: Elsevier Scientific Publishing Company, 1977

    Google Scholar 

  17. Halgren, T. A., Lipscomb, W. N.: Chem. Phys. Letters 49, 225 (1977)

    Google Scholar 

  18. Fletcher, R.: Mol. Phys. 19, 55 (1970); Dupuis, M., King, H. F.: J. Chem. Phys. 68, 3998 (1978)

    Google Scholar 

  19. Nalewajski, R. F., Carlton, T. S.: Acta Phys. Pol. A53, 321 (1978)

    Google Scholar 

  20. Panćiř, J.: Collect. Czech. Chem. Commun. 40, 1112 (1975)

    Google Scholar 

  21. Largo-Cabrerizo, J.: An. Quim. 73, 1092 (1977)

    Google Scholar 

  22. Müller, K.: unpublished results

  23. Halgren, T. A., Lipscomb, W. N.: J. Chem. Phys. 58, 1569 (1973)

    Google Scholar 

  24. Jug, K.: Theoret. Chim. Acta (Berl.) 42, 303 (1976)

    Google Scholar 

  25. Nelder, J. A., Mead, R.: Comput. J. 7, 308 (1964/5)

    Google Scholar 

  26. Müller, K., Brown, L. D.: to be published

  27. Halgren, T. A., Kleier, D. A., Hall, Jr., J. H., Brown, L. D., Lipscomb, W. N.: J. Am. Chem. Soc. 100, 6595 (1978)

    Google Scholar 

  28. Landolt-Börnstein: Numerical data and functional relationships in science and technology, New Series, Vol. II/7. Berlin: Springer-Verlag, 1976

    Google Scholar 

  29. Ritchie, C. D., Chappell, G. A.: J. Am. Chem. Soc. 92, 1819 (1970)

    Google Scholar 

  30. Dedieu, A., Veillard, A.: J. Am. Chem. Soc. 94, 6730 (1972)

    Google Scholar 

  31. Baybutt, P.: Mol. Phys. 29, 389 (1975)

    Google Scholar 

  32. Leforestier, C.: J. Chem. Phys. 68, 4406 (1978)

    Google Scholar 

  33. Van der Lugt, W. Th. A. M., Ros, P.: Chem. Phys. Letters 4, 389 (1969)

    Google Scholar 

  34. Mulder, J. J. C., Wright, J. S.: Chem. Phys. Letters 5, 445 (1970)

    Google Scholar 

  35. Dyczmons, V., Kutzelnigg, W.: Theoret. Chim. Acta (Berl.) 33, 239 (1974)

    Google Scholar 

  36. Keil, F., Ahlrichs, R.: J. Am. Chem. Soc. 98, 4787 (1976)

    Google Scholar 

  37. Dykstra, C. E., Schaefer III, H. F.: J. Am. Chem. Soc. 100, 1378 (1978)

    Google Scholar 

  38. Davis, J. H., Goddard III, W. A., Harding, L. B.: J. Am. Chem. Soc. 99, 2919 (1977)

    Google Scholar 

  39. Stanton, R. E., McIver, Jr., J. W.: J. Am. Chem. Soc. 97, 3632 (1975)

    Google Scholar 

  40. Powell, M. J. D.: Comput. J. 11, 302 (1968)

    Google Scholar 

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  1. Organisch-chemisches Laboratorium der Eidg. Technischen Hochschule Zürich, Universitätsstr. 16, CH-8092, Zürich, Schweiz

    Klaus Müller & Leo D. Brown

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  1. Klaus Müller
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  2. Leo D. Brown
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Müller, K., Brown, L.D. Location of saddle points and minimum energy paths by a constrained simplex optimization procedure. Theoret. Chim. Acta 53, 75–93 (1979). https://doi.org/10.1007/BF00547608

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  • DOI: https://doi.org/10.1007/BF00547608

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