Skip to main content
SpringerLink
Log in

Ab Initio Anharmonic Vibrational Analyses of Non-Rigid Molecules

  • Chapter
Structures and Conformations of Non-Rigid Molecules

Part of the book series: NATO ASI Series ((ASIC,volume 410))

Abstract

A collection of recent state-of-the-art ab initio results is presefted pertaining to anharmonic vibrational analyses of non-rigid molecules. To demonstrate the performance of electronic structure theory in predicting features of potential energy surfaces to quantitative accuracy, investigations of energy barriers for large-amplitude vibrations in ammonia, isocyanic acid, ethane, and cyclopentene are reported. Anharmonic vibrational analyses based on self-consistent-field and configuration interaction quartic force fields are critically evaluated by focusing on representative results for hydrogen sulfide and nitrous oxide. The use of nonstationary reference structures to improve predictions of anharmonic force fields is reviewed and documented. A summary of an investigation using the complete state-of-the-art armamentarium to elucidate vibrational anharmonicity, vibration-rotation interaction, and the precise r e structure of the quasilinear HNCO molecule is given. Finally, difficulties arising in the application of nonstationary reference geometries in vibrational analyses of large-amplitude motions are highlighted to avert potential pitfalls in future ab initio studies.

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

Access this chapter

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P. R. Bunker, P. Jensen, W. P. Kraemer, R. Beardsworth, J. Chem. Phys. 85, 3724 (1986).

    Article  CAS  Google Scholar 

  2. D. C. Comeau, I. Shavitt, P. Jensen, and P. R. Bunker, J. Chem. Phys. 90, 6491 (1989).

    Article  CAS  Google Scholar 

  3. C. L. Janssen, W. D. Allen, H. F. Schaefer III, and J. M. Bowman, Chem. Phys. Lett. 131, 352 (1986).

    Article  CAS  Google Scholar 

  4. P. Botschwina, in Structure/Reactivity and Thermochemistry of Ions, edited by P. Ausloos and S. G. Lias (Reidel, Dordrecht, Holland, 1987 ) pp. 261–270

    Chapter  Google Scholar 

  5. K. Yamashita and K. Morokuma, Institute for Molecular Science Annual Review( Okazaki, Japan, 1987 ) pp. 15–16.

    Google Scholar 

  6. K. Kawaguchi and E. Hirota, J. Chem. Phys. 84, 2953 (1986); 87, 6838 (1987).

    Google Scholar 

  7. V. Špirko, A. Cejchan, and G. H. F. Diercksen, Chem. Phys. 151, 45 (1991).

    Article  Google Scholar 

  8. P. Jensen and P. R. Bunker, J. Mol. Spectrosc. 99, 348 (1983); 118, 18 (1986).

    Google Scholar 

  9. P. Jensen, Comput. Phys. Rep. 1, 1 (1983).

    Article  CAS  Google Scholar 

  10. T. J. Lee, R. B. Remington, Y. Yamaguchi, and H. F. Schaefer III, J. Chem. Phys. 89, 408 (1988).

    Article  CAS  Google Scholar 

  11. To evaluate core correlation effects on the inversion barrier of ammonia, the PZ(3d2f,2pld) basis set described in the appendix was given added flexibility in the core region by uncontracting the nitrogen sp primitives and adding 3 tight d and 2 tight f polarization manifolds in an even-tempered manner. The resulting nitrogen basis is a [13s8p6d4f] set with polarization function exponents αd = {69.3, 23.9, 8.2, 2.837, 0.968, 0.335} and αf = {17.1, 5.9, 2.027, 0.685}. By freezing the nitrogen is core and all virtual orbitals greater than 150 a.u. in energy, the inversion barrier was found to be 4.933 kcal mol-1 at the MP2 level with this flexible [13s8p6d4f/4s3p2dlf] basis, in excellent agreement with the PZ(3d2f,2pld) MP2 result(4.956) of Table 1. An analogous set of MP2 calculations with all orbitals unfrozen subsequently gave a barrier height of 4.742 kcal mo1-1, indicating a -0.191 kcal mol-1 contribution due to core-core and core-valence correlation. Redetermination of this term at the MP3 level produced only a +1.2 cm-1 change in the core-correlation correction.

    Google Scholar 

  12. Relativistic effects on the inversion barrier of ammonia were gauged with the QZ(2d l f,2p1d) basis set and first-order perturbation theory applied to the one-electron mass-velocity and Darwin terms. The resulting shift of the barrier height is +24 cm-1 (K. G. Dyall, personal communication), consistent with recent estimates reported by P. Schwerdtfeger, L. J. Laakkonen, and P. Pyykkö, J. Chem. Phys. 96, 6807 (1992).

    Google Scholar 

  13. An efficient formalism for evaluating the diagonal Born-Oppenheimer correction (DBOC) to potential energy surfaces has been described recently by N. C. Handy, Y. Yamaguchi, and H. F. Schaefer III, J. Chem. Phys. 84, 4481(1986). With the DZP basis used in Table 1, the absolute DBOC terms for planar and pyramidal ammonia are +564.3 and +575.6 cm-1, respectively, giving a DBOC barrier-height shift of -11.3 cm-1 (T. J. Lee, personal communication).

    Google Scholar 

  14. V. Špirko, J. Mol. Spectrosc. 101, 30 (1983).

    Article  Google Scholar 

  15. In an earlier non-rigid bender analysis reported by D. Papoušek and V. Špirko, Top. Curr. Chem. 68, 59 (1976), an effective barrier for NH3 inversion of 5.80 kcal mo1-1 was obtained, of which +219 cm-1 was ascribed to zero-point vibrations. This ZPVE contribution is significantly larger than the +176 cm-1 vibrational term appearing in Ref. [12]. Unfortunately, in neither of the two empirical analyses was it possible to treat properly the changes in the complementary-mode quadratic force constants which occur as the inversion coordinate varies. The magnitude of this effect can be assessed from the DZP CISDTQ results of Lee et al.[8], which include the following harmonic frequencies (in cm-1) for the modes complementary to the inversion coordinate: pyramidal -ωl(al’) = 3527, ω3(e’) = 3676, and ω4(e’) = 1705; planar-ωl(a’) = 3703, ω3(e’) = 3922, and ω4(e’) = 1624. From these data a ZPVE contribution to the barrier of +253 cm-1 is computed in the harmonic approximation, thus bringing the empirical analysis of Ref. [12] into question. No mechanism is envisioned here by which our final ab initio classical barrier (5.30 kcal mol-1) could be in error by more than 0.1 kcal mol-1.

    Google Scholar 

  16. A. L. L. East, C. S. Johnson, and W. D. Allen, J. Chem. Phys., in press (1993).

    Google Scholar 

  17. N. Moazzen-Ahmadi, H. P. Gush, M. Halpren, H. Jagannath, A. Leung, and I. Ozier, J. Chem. Phys. 88, 563 (1988).

    Article  CAS  Google Scholar 

  18. L. E. Bauman, P. M. Killough, J. M. Cooke, J. R. Villarreal, and J. Laane, J. Phys. Chem. 86, 2000 (1982).

    Article  CAS  Google Scholar 

  19. See R. Champion, P. D. Godfrey, and F. L. Bettens, J. Mol. Spectrosc. 147, 488 (1991) and also Ref. [18] for a review of experimentally determined ring-puckering barrier heights of cyclopentene.

    Article  CAS  Google Scholar 

  20. W. D. Allen, A. G. Császár, and D. A. Horner, J. Am. Chem. Soc. 114, 6834 (1992).

    Article  CAS  Google Scholar 

  21. H. F. Schaefer III and Y. Yamaguchi, J. Mol. Struct. (Theochem) 135, 369 (1986).

    Article  Google Scholar 

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

    Article  Google Scholar 

  23. J. F. Gaw and N. C. Handy, Chem. Phys. Lett. 121, 321(1985).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  26. D. A. Clabo, Jr., W. D. Allen, R. B. Remington, Y. Yamaguchi, and H. F. Schaefer III, Chem. Phys. 123, 187 (1988).

    Article  CAS  Google Scholar 

  27. W. D. Allen, Y. Yamaguchi, A. G. Császár, D. A. Clabo, Jr., R. B. Remington, and H. F. Schaefer III, Chem. Phys. 145, 427 (1990).

    Article  CAS  Google Scholar 

  28. T. H. Edwards, N. K. Moncur, and L. E. Snyder, J. Chem. Phys. 46, 2139 (1967).

    Article  CAS  Google Scholar 

  29. I. M. Mills, in Specialist Periodical Reports, Theoretical Chemistry, Vol. 1, edited by R. N. Dixon ( The Chemical Society, London, 1974 ), p. 110.

    Google Scholar 

  30. See also L. Halonen and T. Carrington, Jr., J. Chem. Phys. 88, 4171 (1988).

    Article  CAS  Google Scholar 

  31. P. Helminger, F. C. De Lucia, and W. H. Kirchhoff, J. Phys. Chem. Ref. Data 2, 215 (1973).

    Article  CAS  Google Scholar 

  32. J. -L. Teffo and A. Chédin, J. Mol. Spectrosc. 135, 389 (1989).

    Article  CAS  Google Scholar 

  33. A. G. Maki, J. S. Wells, and M. D. Vanek, J. Mol. Spectrosc. 138, 84 (1989).

    Article  CAS  Google Scholar 

  34. N. C. Handy, R. D. Amos, J. F. Gaw, J. E. Rice, and E. D. Simandiras, Chem. Phys. Lett. 120, 151 (1985).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  36. W. Schneider and W. Thiel, Chem. Phys. Lett. 157, 367 (1989).

    Article  CAS  Google Scholar 

  37. W. H. Green, D. Jayatilaka, A. Willets, R. D. Amos, and N. C. Handy, J. Chem. Phys. 93, 4965 (1990).

    Article  CAS  Google Scholar 

  38. M. Duran, Y. Yamaguchi, R. B. Remington, Y. Osamura, and H. F. Schaefer III, J. Chem. Phys. 90, 334 (1989).

    Article  CAS  Google Scholar 

  39. R. H. Schwendeman, J. Chem. Phys. 44, 556 (1966); 44, 2115 (1966).

    Google Scholar 

  40. P. Pulay, G. Fogarasi, F. Pang, and J. E. Boggs, J. Am. Chem. Soc. 101, 2550 (1979).

    Article  CAS  Google Scholar 

  41. G. Fogarasi and P. Pulay, in Vibrational Spectra and Structure, Vol. 14, edited by J. R. Durig, ( Elsevier, Amsterdam, 1985 ) pp. 125–219.

    Google Scholar 

  42. W. D. Allen and A. G. Császár, J. Chem. Phys., in press (1993).

    Google Scholar 

  43. M. Kobayashi and I. Suzuki, J. Mol. Spectrosc. 125, 24 (1987).

    Article  CAS  Google Scholar 

  44. K. M. T. Yamada, M. Winnewisser, and J. W. C. Johns, J. Mol. Spectrosc. 140, 353 (1990).

    Article  CAS  Google Scholar 

  45. K. Yamada, J. Mol. Spectrosc. 81, 139 (1980).

    Article  CAS  Google Scholar 

  46. D. A. Steiner, K. A. Wishah, S. R. Polo, and T. K. McCubbin, Jr., J. Mol. Spectrosc. 76, 341 (1979).

    Article  CAS  Google Scholar 

  47. L. Fusina, M. Carlotti, and B. Carli, Can. J. Phys. 62, 1452 (1984).

    Article  CAS  Google Scholar 

  48. D. A. Steiner, S. R. Polo, T. K. McCubbin, Jr., and K. A. Wishah, J. Mol. Spectrosc. 98, 453 (1983).

    Article  CAS  Google Scholar 

  49. G. Herzberg and C. Reid, Discuss. Faraday Soc. 9, 92 (1950).

    Article  Google Scholar 

  50. P. Pulay, G. Fogarasi, G. Pongor, J. E. Boggs, and A. Vargha, J. Am. Chem. Soc. 101, 2550 (1979).

    Article  CAS  Google Scholar 

  51. M. E. Jacox, J. Phys. Chem. Ref. Data 19, 1387 (1990).

    Article  Google Scholar 

  52. R. B. Wattson and L. S. Rothman, J. Mol. Spectrosc. 119, 83 (1986).

    Article  CAS  Google Scholar 

  53. R. A. Ashby and R. L. Werner, Spectrochim. Acta 22, 1345 (1966).

    Article  CAS  Google Scholar 

  54. V. E. Bondybey, J. H. English, C. W. Mathews, and R. J. Contolini, J. Mol. Spectrosc. 92, 431 (1982).

    Article  CAS  Google Scholar 

  55. J. H. Teles, G. Maier, B. A. Hess, Jr., L. J. Schaad, M. Winnewisser, and B. P. Winnewisser, Chem. Ber. 122, 753 (1989).

    Article  CAS  Google Scholar 

  56. K. Yamada, J. Mol. Spectrosc. 79, 323 (1980).

    Article  Google Scholar 

  57. W. H. Hocking, M. C. L. Gerry, and G. Winnewisser, Can. J. Phys. 53, 1869 (1975).

    Article  CAS  Google Scholar 

  58. B. Krakow, R. C. Lord, and G. O. Neely, J. Mol. Spectrosc. 27, 148 (1968).

    Article  CAS  Google Scholar 

  59. D. A. Steiner, S. R. Polo, T. K. McCubbin, Jr., and K. A. Wishah, Can. J. Phys. 59, 1313 (1981).

    Article  CAS  Google Scholar 

  60. P. Pulay, in Modern Theoretical Chemistry, Vol. 4, edited by H. F. Schaefer III, ( Plenum Press, New York, 1977 ) pp. 153–185.

    Google Scholar 

  61. P. R. Bunker, M. Kofranek, H. Lischka, and A. Karpfen, J. Chem. Phys. 89, 3002 (1988)

    Article  CAS  Google Scholar 

  62. M. Kofranek, H. Lischka, and A. Karpfen, Chem. Phys. 121, 137 (1988)

    Article  CAS  Google Scholar 

  63. P. R. Bunker, T. Carrington, Jr., P. C. Gomez, M. D. Marshall, M. Kofranek, H. Lischka, and A. Karpfen, J. Chem. Phys. 91, 5154 (1989)

    Article  CAS  Google Scholar 

  64. P. R. Bunker, P. Jensen, A. Karpfen, M. Kofranek, and H. Lischka, J. Chem. Phys. 92, 7432 (1990)

    Article  CAS  Google Scholar 

  65. P. Jensen, P. R. Bunker, A. Karpfen, M. Kofranek, and H. Lischka, J. Chem Phys. 93, 6266 (1990)

    Article  CAS  Google Scholar 

  66. P. Jensen, P. R. Bunker, and A. Karpfen, J. Mol. Spectrosc. 148, 385 (1991)

    Article  CAS  Google Scholar 

  67. P. R. Bunker, P. Jensen, and A. Karpfen, J. Mol. Spectrosc. 149, 512 (1991).

    Article  CAS  Google Scholar 

  68. M. Quack and M. Suhm, Mol. Phys. 69, 791 (1990).

    Article  CAS  Google Scholar 

  69. T. H. Dunning Jr., J. Chem. Phys. 90, 1007 (1989).

    Article  CAS  Google Scholar 

  70. I. Shavitt, in Modern Theoretical Chemistry, Vol. 3, edited by H. F. Schaefer III, ( Plenum Press, New York, 1977 ), pp. 189–275.

    Google Scholar 

  71. R. Krishnan, M. J. Frisch, and J. A. Pople, J. Chem. Phys. 72, 4244 (1980)

    Article  CAS  Google Scholar 

  72. K. Raghavachari, J. A. Pople, E. S. Replogle, and M. Head-Gordon, J. Phys. Chem. 94, 5579 (1990).

    Article  CAS  Google Scholar 

  73. R. J. Bartlett, C. E. Dykstra, and J. Paldus, in Advanced Theories and Computational Approaches to the Electronic Structure of Molecules, edited by C. E. Dykstra, ( Reidel, Dorcrecht, 1984 ) p. 127.

    Chapter  Google Scholar 

  74. K. Raghavachari, G. W. Trucks, J. A. Pople, and M. Head-Gordon, Chem. Phys. Lett. 157, 479 (1989).

    Article  CAS  Google Scholar 

  75. J. A. Pople, M. J. Frisch, B. T. Luke, and J. S. Binkley, Int. J. Quant. Chem. Symp. 17, 307 (1983).

    CAS  Google Scholar 

  76. W. D. Laidig, G. Fitzgerald, and R. J. Bartlett, Chem. Phys. Lett. 113, 151 (1985).

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemistry, Stanford University, Stanford, CA, 94305, USA

    Wesley D. Allen, Allan L. L. East & Attila G. Császár

Authors
  1. Wesley D. Allen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Allan L. L. East
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Attila G. Császár
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Texas A&M University, College Station, Texas, USA

    Jaan Laane

  2. Universität Ulm, Ulm, Germany

    Marwan Dakkouri

  3. Universitair Centrum Antwerpen, Antwerpen, Belgium

    Ben van der Veken

  4. Universität Tübingen, Tübingen, Germany

    Heinz Oberhammer

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer Science+Business Media New York

About this chapter

Cite this chapter

Allen, W.D., East, A.L.L., Császár, A.G. (1993). Ab Initio Anharmonic Vibrational Analyses of Non-Rigid Molecules. In: Laane, J., Dakkouri, M., van der Veken, B., Oberhammer, H. (eds) Structures and Conformations of Non-Rigid Molecules. NATO ASI Series, vol 410. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2074-6_17

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-2074-6_17

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4920-7

  • Online ISBN: 978-94-011-2074-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation