Skip to main content
SpringerLink
Log in
Book cover

New Theoretical Concepts for Understanding Organic Reactions pp 33–53Cite as

Some Practical Suggestions for Optimizing Geometries and Locating Transition States

  • Chapter

Part of the book series: NATO ASI Series ((ASIC,volume 267))

Abstract

The optimization of equilibrium geometries and transition states by molecular orbital methods is discussed from a practical point of view. Most of the efficient geometry optimization methods rely on analytical energy gradients and quasi-Newton algorithms. For any optimization method, there are three areas of input that directly affect the behavior of the optimization: (a) the choice of internal coordinates, (b) the starting geometry and (c) the initial estimate of the Hessian. A number of topics related to these three areas are discussed with the aim of improving the performance of optimizations; these include symmetry, dummy atoms, avoiding coordinate redundancy, overcoming strong coupling among coordinates, conversion between coordinate systems, testing stationary points and what to do when optimizations fail.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Hehre, W. J., Radom, L., Schleyer, P. vR., and Pople, J. A., Ab Initio Molecular Orbital Theory, Wiley-Interscience, New York, 1986.

    Google Scholar 

  2. Ohno, K., and Morokuma, K., Quantum Chemistry Literature Data Base, Elsevier, Amsterdam, 1982; yearly supplements published in special issues of the journal J. Mol. Struct./Theochem.; on-line version available through Japan Assoc. for International Chemical Information.

    Google Scholar 

  3. Whiteside, R. A., Frisch, M. J., and Pople, J. A., The Carnegie-Mellon Quantum Chemistry Archive, 3rd Ed., Carnegie-Mellon University, Pittsburgh, 1983; current version available on-line from Gaussian, Inc.

    Google Scholar 

  4. Frisch, M. J., Binkley, J. S., DeFrees, D. J., Raghavachari, K., Schlegel, H. B., Whiteside, R. A., Fox, D. J., Martin, R. L., Fluder, E. M., Melius, C. F., Kahn, L. R., Stewart, J. J. P., Bobrowicz, F. W., and Pople, J. A., GAUSSIAN 86, Carnegie-Mellon Publishing Unit, Pittsburgh, 1984, and subsequent releases.

    Google Scholar 

  5. Pulay, P., Adv. Chem. Phys., 69, 241 (1987).

    Article  CAS  Google Scholar 

  6. Jørgensen, P., and Simons, J. (Eds.), Geometrical Derivatives of Energy Surfaces and Molecular Properties, Reidel, Dordrecht, 1986.

    Google Scholar 

  7. Gaw, J. F., and Handy, N. C., Annu. Rep. Prog. Chem. Sec. C, 81, 291 (1985).

    Article  CAS  Google Scholar 

  8. Fogarasi, G., and Pulay, P., Annu. Rev. Phys. Chem., 35, 191 (1984).

    Article  CAS  Google Scholar 

  9. Fitzgerald, G., Harrison, R., Laidig, W. D., and Bartlett, R. J., J. Chem. Phys., 82, 4379 (1985).

    Article  CAS  Google Scholar 

  10. Gauss, J., and Cremer, D., Chem. Phys. Lett., 138, 131 (1987).

    Article  CAS  Google Scholar 

  11. Krishnan, R., Schlegel, H. B., and Pople, J. A., J. Chem. Phys., 72, 4654 (1980)

    Article  CAS  Google Scholar 

  12. Brooks, B. R., Laidig, W. D., Saxe, P., Goddard, J. D., Yamaguchi, Y., and Schaefer, H. F., J. Chem. Phys., 72, 4652 (1980)

    Article  CAS  Google Scholar 

  13. Osamura, Y.; Yamaguchi, Y., and Schaefer, H. F., J. Chem. Phys., 77, 383 (1982)

    Article  CAS  Google Scholar 

  14. Rice, J. E., Amos, R. D., Handy, N. C., Lee, T. J., and Schaefer, H. F., J. Chem. Phys., 85, 963 (1986)

    Article  CAS  Google Scholar 

  15. Shepard, R., Int. J. Quantum Chem., 31, 33 (1987).

    Article  CAS  Google Scholar 

  16. Scheiner, A. C, Scuseria, G. E., Rice, J. E., Lee, T. J., and Schaefer, H. F., J. Chem. Phys., 87, 5361 (1987)

    Article  CAS  Google Scholar 

  17. Fitzgerald, G., Harrison, R., Laidig, W. D., and Bartlett, R. J., Chem. Phys. Lett., 117, 433 (1985)

    Article  CAS  Google Scholar 

  18. Adamowicz, L., Laidig, W. D., and Bartlett, R. J., Int. J. Quantum Chem. Symp, 18, 245 (1984).

    Article  CAS  Google Scholar 

  19. Kato, S., and Morokuma, K., Chem. Phys. Lett., 65, 19 (1979)

    Article  CAS  Google Scholar 

  20. Goddard, J. D., Handy, N. C, and Schaefer, H. F., J. Chem. Phys., 11, 1525 (1979)

    Article  Google Scholar 

  21. Schlegel, H. B., and Robb, M. A., Chem. Phys. Lett., 92, 43 (1982)

    Article  Google Scholar 

  22. Knowles, P. J., Sexton, G. J., and Handy, N. C., Chem. Phys., 72, 337 (1982)

    Article  CAS  Google Scholar 

  23. Taylor, P. R., J. Comput. Chem., 5, 589 (1984).

    Article  CAS  Google Scholar 

  24. Pople, J. A., Krishnan, R., Schlegel, H. B., and Binkley, J. S., Int. J. Quantum Chem. Symp, 13, 225 (1979).

    CAS  Google Scholar 

  25. Handy, N. C, Arnos, R. D., Gaw, J. F., Rice, J. E., Simandiras, T. J., Lee, T. J., Harrison, R. J., Laidig, W. D., Fitzgerald, G., and Bartlett, R. J., in réf. [6]; Handy, N. C., Arnos, R. D., Gaw, J. F., Rice, J. E., and Simandiras, T. J., Chem. Phys. Lett., 120, 151 (1985).

    Article  CAS  Google Scholar 

  26. Lee, T. J., Handy, N. C, Rice, J. E., Scheiner, A. C., and Schaefer, H. F., J. Chem. Phys., 85, 3930 (1986).

    Article  CAS  Google Scholar 

  27. Camp, R. N., King, H. F., Mclver, J. W., and Mullally, D., J. Chem. Phys., 79, 1088 (1983)

    Article  CAS  Google Scholar 

  28. Hoffman, M. R., Fox, D. F., Gaw, J. F., Osamura, Y., Yamaguchi, Y., Grev, R. S., Fitzgerald, G., Schaefer, H. F., Knowles, P. L, and Handy, N. C., J. Chem. Phys., 80, 2660 (1984)

    Article  Google Scholar 

  29. Page, M., Saxe, P., Adams, G. F., and Lengsfield, J. Chem. Phys., 81, 434 (1984)

    Article  CAS  Google Scholar 

  30. Gaw, J. F., Yamaguchi, Y., and Schaefer, H. F., J. Chem. Phys., 81, 6395 (1984)

    Article  Google Scholar 

  31. Gaw, J. F., Yamaguchi, Y., Schaefer, H. F., and Handy, N. C, J. Chem. Phys., 85, 5132 (1986)

    Article  CAS  Google Scholar 

  32. Gaw, J. F., Yamaguchi, Y., Remington, R. B., Osamura, Y., and Schaefer, H. F., Chem. Phys., 109, 237 (1986)

    Article  CAS  Google Scholar 

  33. Schaefer, H. F., and Yamaguchi, Y., J. Mol. Struct., 135, 369 (1986); Gaw, J. F., and Handy, N. C, in [6].

    Google Scholar 

  34. Duran, M., Yamaguchi, Y., Osamura, Y., and Schaefer, H. F., J. Mol. Struct.,163, 389 (1988).

    Google Scholar 

  35. Pulay, P., J. Chem. Phys., 78, 5043 (1983)

    Article  CAS  Google Scholar 

  36. Almlöf, J., and Taylor, P. R., Int J. Quantum Chem., 27, 743 (1985).

    Article  Google Scholar 

  37. Jørgensen, P., and Simons, J. J. Chem. Phys., 79, 334 (1983).

    Article  Google Scholar 

  38. Schlegel, H. B., in Computational Theoretical Organic Chemistry (Eds. Csizmadia, L G., and Daudel, R.), Reidel, Dordrecht, 1981.

    Google Scholar 

  39. Schlegel, H. B., Adv. Chem. Phys., 67, 249 (1987).

    Article  CAS  Google Scholar 

  40. Bell, S., and Crighton, J. S., J. Chem. Phys., 80, 2464 (1984).

    Article  CAS  Google Scholar 

  41. Head, J. D., Weiner, B., and Zerner, M. C, Int. J. Quantum Chem., 33, 177 (1988).

    Article  CAS  Google Scholar 

  42. Scales, L. E., Introduction to Non-linear Optimization, MacMillan, Basingstoke, 1985.

    Google Scholar 

  43. Fletcher, R., Practical Methods of Optimization, Wiley, Chichester, 1981.

    Google Scholar 

  44. Gill, P. E., Murray, W., and Wright, M. H., Practical Optimization,.Academic Press, New York, 1982

    Google Scholar 

  45. Powell, R., Non-linear Optimization, Academic Press, New York, 1982.

    Google Scholar 

  46. Clark, T., A Handbook of Computational Chemistry, Wiley-Interscience, New York, 1985.

    Google Scholar 

  47. Stanton, R. E., and Mclver, Jr, J. W., J. Am. Chem. Soc, 97, 3632 (1975).

    Article  CAS  Google Scholar 

  48. Thiel, W., J. Mol. Struct, 163, 415 (1988).

    Google Scholar 

  49. (a) The author wishes to thank Dr. M. J. Frisch for the guidelines for using symmetry to place dummy atoms. These algorithms have been incorporated in the program NewZmat [33b]; (b) Frisch, M. J., NewZmat, 1986.

    Google Scholar 

  50. Pople, J. A., J. Am. Chem. Soc., 102, 4615 (1980)

    Article  CAS  Google Scholar 

  51. Pople, J. A., Sataty, Y. A., and Halevi, E. A., Israel J. Chem., 19, 290 (1980).

    CAS  Google Scholar 

  52. Pople, J. A., and Gordon, M. S., J. Am. Chem. Soc., 89, 4253 (1967)

    Article  CAS  Google Scholar 

  53. Radom, L., Hehre, W. J., and Pople, J. A, J. Am. Chem. Soc., 93, 289 (1971).

    Article  Google Scholar 

  54. Peterson, M. R., and Csizmadia, I. G., J. Mol. Struct, 125, 399 (1985).

    Google Scholar 

  55. Burkert, U., and Allinger, N. L., Molecular Mechanics, American Chemical Society, 1981.

    Google Scholar 

  56. Sadlej, J., (Cooper, I. L., trans). ed.) Semi-empirical Methods of Quantum Chemistry, Ellis Horwood, Chichester, 1985.

    Google Scholar 

  57. Segal, G. A., Semi-empirical Methods of Electronic Structure Calculation, (Modern Theoretical Chemistry Vol. 7 and 8) Plenum, New York, 1977.

    Google Scholar 

  58. Halgren, T. A., and Lipscomb, W. N., Chem. Phys. Lett., 49, 225 (1977).

    Article  CAS  Google Scholar 

  59. Cerjan, C. J., and Miller, W. H., J. Chem. Phys., 75, 2800 (1981)

    Article  CAS  Google Scholar 

  60. Simons, J. Jørgensen, P., Taylor, H., and Ozment, J., J. Chem. Phys., 87, 2745 (1983)

    Article  CAS  Google Scholar 

  61. Nguyen, D. T., and Case, D. A., J. Phys. Chem., 89 4020 (1985)

    Article  CAS  Google Scholar 

  62. Banerjee, A., Adams, N., Simons, J., and Shepard, J. Phys. Chem., 89 52 (1985).

    Article  CAS  Google Scholar 

  63. Hoffman, D. K., Nord, R. S., Ruedenberg, K., Theor. Chim. Acta., 69, 265 (1986)

    Article  CAS  Google Scholar 

  64. Jørgensen, P., Jensen, H. J. A., and Helgaker, T., Theor. Chim. Acta., 73, 55 (1988)

    Article  Google Scholar 

  65. Baker, J., J. Comput Chem., 7, 385 (1986).

    Article  CAS  Google Scholar 

  66. Schlegel, H. B., J. Comput. Chem., 3, 214 (1982).

    Article  CAS  Google Scholar 

  67. Scharfenberger, P., J. Comput Chem., 3, 277 (1982).

    Article  Google Scholar 

  68. Tapia, O., and Andres, J., Chem. Phys. Lett., 109, 471 (1984).

    Article  CAS  Google Scholar 

  69. Bell, S., Crighton, J. S., and Fletcher, R., Chem. Phys. Lett., 82, 122 (1981).

    Article  CAS  Google Scholar 

  70. Head, J. D., Weiner, B., and Zerner, M. C., Int J. Quantum Chem., 33, 177 (1988),

    Article  CAS  Google Scholar 

  71. Bálint, I., and Ban, M. I., Theor. Chim. Acta., 63, 255 (1983).

    Article  Google Scholar 

  72. Schlegel, H. B., Theor. Chim. Acta., 66, 333 (1984).

    Article  CAS  Google Scholar 

  73. Under some circumstances an imaginary frequency may also signal an instability in the wavefunction.

    Google Scholar 

  74. Ishida, K., Morokuma, K., and Komornicki, A., J. Chem. Phys., 66, 2153 (1977)

    Article  CAS  Google Scholar 

  75. Schmidt, M. W., Gordon, M. S., and Dupuis, M., J. Am. Chem. Soc, 107, 2585 (1985).

    Article  CAS  Google Scholar 

  76. Müller, K., and Brown, L. D., Theor. Chim. Acta., 53, 75 (1979).

    Article  Google Scholar 

  77. Garrett, B. C., Redmon, M. J., Steckler, R., Truhlar, D. G., Baldridge, K. K., Bartol, D., Schmidt, M.W., and Gordon, M.S., J. Phys. Chem., 92 1476 (1988).

    Article  CAS  Google Scholar 

  78. Page, M., and McIver, Jr, J. W., J. Chem. Phys., 88, 922 (1988).

    Article  CAS  Google Scholar 

  79. Gonzalez, C., Schlegel, H. B., submitted; also described in ref [23].

    Google Scholar 

  80. Fletcher, R., and Powell, M. J. D., Comput J., 6, 163 (1963)

    Google Scholar 

  81. Davidon, W., Argonne Nat Lab. Report, ANL-5990; Binkley, J. S., J. Chem. Phys., 64, 5142 (1976).

    Article  Google Scholar 

  82. Murtagh, B. A., and Sargent, R. W. H., Comput. J., 13, 185 (1972).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemistry, Wayne State University, Detroit, Michigan, 48202, USA

    H. Bernhard Schlege

Authors
  1. H. Bernhard Schlege
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Chemistry, Universitat Autònoma de Barcelona, Spain

    J. Beltrán

  2. Department of Chemistry, University of Toronto, Canada

    I. G. Csizmadia

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Kluwer Academic Publishers

About this chapter

Cite this chapter

Schlege, H.B. (1989). Some Practical Suggestions for Optimizing Geometries and Locating Transition States. In: Beltrán, J., Csizmadia, I.G. (eds) New Theoretical Concepts for Understanding Organic Reactions. NATO ASI Series, vol 267. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2313-3_2

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-2313-3_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7539-8

  • Online ISBN: 978-94-009-2313-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation