Skip to main content
SpringerLink
Log in

Characterizing vibrational motion beyond internal coordinates

  • Regular Article
  • Published:
Theoretical Chemistry Accounts Aims and scope Submit manuscript

Abstract

We present a procedure for the decomposition of the normal modes of a composite system, including its rotations and translations, into those of fragments. The method permits—by the cross-contraction of dyads of mass-weighted displacement vectors, without recourse to valence coordinates—the direct comparison of nuclear motions of structurally similar but otherwise arbitrary fragments of molecules, and it leads to a quantitative definition of the similarity and the overlap of nuclear motions. We illustrate its usefulness by the quantification of the mixing of the normal modes of formic acid monomers upon the formation of a dimer, by the comparison of the overlap of the intermolecular normal vibrations of the water dimer computed with different ab initio schemes, and by the comparison of similarity and overlap of vibrations of (4S,7R)-galaxolide and (4S)-4-methylisochromane. The approach is expected to become a standard tool in vibrational analysis.

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. Sverdlov LM, Kovner MA, Krainov EP (1974). Vibrational spectra of polyatomic molecules. Halsted, New York

    Google Scholar 

  2. Holzwarth G, Hsu EC, Mosher HS, Faulkaner TR, Moscowitz A (1974). J Am Chem Soc 96:251

    Article  CAS  Google Scholar 

  3. Nafie LA, Cheng JC, Stephens PJ (1975). J Am Chem Soc 97:3842

    Article  CAS  Google Scholar 

  4. Nafie LA, Keiderling TA, Stephens PJ (1976). J Am Chem Soc 98:2715

    Article  CAS  Google Scholar 

  5. Barron LD, Bogaard MP, Buckingham AD (1973). J Am Chem Soc 95:603

    Article  CAS  Google Scholar 

  6. Barron LD, Bogaard MP, Buckingham AD (1973). Nature 241:113

    Article  CAS  Google Scholar 

  7. Hug W, Kint S, Bailey GF, Scherer JR (1975). J Am Chem Soc 97:5589

    Article  CAS  Google Scholar 

  8. Herzberg G (1945) Molecular structure and molecular spectra. II. Infrared and Raman spectra of polyatomic molecules. van Nostrand, New York

  9. Wilson EB, Decius JC, Cross PC (1955) Molecular vibrations. Dover, New York

    Google Scholar 

  10. Fogarasi G, Pulay P (1985). Vib Spectra Struct 14:125–219

    CAS  Google Scholar 

  11. Dollish FR, Fateley WG, Bentley FF (1974) Characteristic Raman frequencies of organic compounds. Wiley, New York

    Google Scholar 

  12. Colthup NB, Daly LH, Wiberly SE (1975) Infrared and Raman spectroscopy. Academic, New York

    Google Scholar 

  13. Ashvar CS, Devlin FJ, Stephens PJ, Bak KL, Eggimann T, Wieser H (1998). J Phys Chem A 102:6842–6857

    Article  CAS  Google Scholar 

  14. Hug W, Zuber G, de Meijere A, Khlebnikov AF, Hansen H-J (2001). Helv Chim Acta 84:1

    Article  CAS  Google Scholar 

  15. Ruud K, Helgaker T, Bouř P (2002). J Phys Chem A 106:7448

    Article  CAS  Google Scholar 

  16. Zuber G, Hug W (2004). Helv Chim Acta 87:2208

    Article  CAS  Google Scholar 

  17. Jalkanen KJ, Nieminen RM, Frimand K, Bohr J, Bohr H, Wade RC, Tajkhorshid E, Suhai S (2001). Chem Phys 65:125

    Article  Google Scholar 

  18. Jalkanen KJ, Nieminen RM, Knapp-Mohammady M, Suhai S (2003). Int J Quant Chem 92:239

    Article  CAS  Google Scholar 

  19. Stephens PJ, Devlin FJ, Chabalowsky CF, Frisch MJ (1994). J Phys Chem 98:11623

    Article  CAS  Google Scholar 

  20. Stephens PJ, Devlin FJ, Ashvar CS, Chabalowsky CF, Frisch MJ (1994). Farad Discuss 99:103–119

    Article  CAS  Google Scholar 

  21. Hug W (2001). Chem Phys 264:53

    Article  CAS  Google Scholar 

  22. Califano S (1976) Vibrational States. Wiley, New York

    Google Scholar 

  23. Melnik DG, Gopalakrishnan S, Miller TA (2003). J Chem Phys 118:3589

    Article  CAS  Google Scholar 

  24. Cuony B, Hug W (1981). Chem Phys Lett 84:131

    Article  CAS  Google Scholar 

  25. Goldstein H (1980) Classical mechanics. Addison-Wesley, Reading

    Google Scholar 

  26. Rosenfeld L (1965) Theory of electrons. Dover, New York

    Google Scholar 

  27. Kabsch W (1976). Acta Cryst A32:922–923

    Article  Google Scholar 

  28. Kabsch W (1978). Acta Cryst A34:827–828

    Article  Google Scholar 

  29. Heisterberg DJ (1990). A program to superimpose atoms of two molecules by the quaternion method. http://www.ccl.net/cca/software/SOURCES/C/quaternion-mol-fit/quatfit.c

  30. Kneller GR (1991). Mol Simul 7:113–119

    Article  CAS  Google Scholar 

  31. Fedorovsky M (2006). PyVib2, a program for analyzing vibrational motion and vibrational spectra, 2006. To be published under the general public licence.

  32. Becke AD (1997). J Chem Phys 107:8554

    Article  CAS  Google Scholar 

  33. Hamprecht FA, Cohen AJ, Tozer DJ, Handy NC (1998). J Chem Phys 109:6264

    Article  CAS  Google Scholar 

  34. Jensen F (2001). J Chem Phys 115:9113–9125

    Article  CAS  Google Scholar 

  35. Jensen F (2002a). J Chem Phys 116:7372–7379

    Article  CAS  Google Scholar 

  36. Jensen F (2002b). J Chem Phys 117:9234–9240

    Article  CAS  Google Scholar 

  37. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Montgomery JA Jr, Vreven T, Kudin KN, Burant JC, Millam JM, Iyengar SS, Tomasi J, Barone V, Mennucci B, Cossi M, Scalmani G, Rega N, Petersson GA, Nakatsuji H, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Klene M, Li X, Knox JE, Hratchian HP, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Ayala PY, Morokuma K, Voth GA, Salvador P, Dannenberg JJ, Zakrzewski VG, Dapprich S, Daniels AD, Strain MC, Farkas O, Malick DK, Rabuck AD, Raghavachari K, Foresman JB, Ortiz JV, Cui Q, Baboul AG, Clifford S, Cioslowski J, Stefanov BB, Liu G, Liashenko A, Piskorz P, Komaromi I, Martin RL, Fox DJ, xKeith DJ, Al-Laham MA, Peng CY, Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Gonzalez C, Pople JA (2004) Gaussian 03, Revision C.01. Gaussian Inc., Wallingford

  38. Hug W, Fedorovsky M (2006). To be published

  39. Hug W, Haesler J (2005). Int J Quant Chem 104:695–715

    Article  CAS  Google Scholar 

  40. Handy NC, Cohen AJ (2001). Mol Phys 99:403

    Article  CAS  Google Scholar 

  41. Hoe W-M, Cohen AJ, Handy NC Chem Phys Lett 341:319

  42. Kendall RA, Dunning TH Jr (1992). J Chem Phys 96:6796–6806

    Article  CAS  Google Scholar 

  43. Stanton JF, Gauss J, Watts JD, Nooijen M, Oliphant N, Perera SA, Szalay PG, Lauderdale WJ, Kucharski SA, Gwaltney SR, Beck S, Balkova A, Bernholdt DE, Baeck KK, Rozyczko P, Sekino H, Hober C, Bartlett RJ (2005). ACESII, Advanced Concepts in Electronic Structure, v.2.4.0-stable

  44. Cheeseman PJ, Frisch MJ, Devlin FJ, Stephens PJ (1996). J Chem Phys Lett 252:211

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemistry, University of Fribourg, ch. du Musée 9, Fribourg, 1700, Switzerland

    Werner Hug & Maxim Fedorovsky

Authors
  1. Werner Hug
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Maxim Fedorovsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Werner Hug.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hug, W., Fedorovsky, M. Characterizing vibrational motion beyond internal coordinates. Theor Chem Account 119, 113–131 (2008). https://doi.org/10.1007/s00214-006-0185-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00214-006-0185-2

Keywords

Search

Navigation