Skip to main content
SpringerLink
Log in

Estimating the carbonyl anharmonic vibrational frequency from affordable harmonic frequency calculations

  • Original Paper
  • Published:
Journal of Molecular Modeling Aims and scope Submit manuscript

Abstract

A linear correlation between harmonic and anharmonic frequencies of water calculated at B3LYP level of theory was observed with a number of basis sets. Similar relationships were found in both the gas phase and solution for several small molecules. The best correlation was found for C = O stretch mode in formaldehyde, formamide and N-methylacetamide. The average difference between B3LYP harmonic and anharmonic ν(C = O) frequencies calculated with several basis sets in these molecules was 30 cm−1. The ad hoc correction of −30 cm−1, added to harmonic frequencies of two different carbonyl groups present in a structure of a larger molecule was tested as a fast way of predicting anharmonic frequencies without elaborated calculations. The proposed approach was tested successfully on a larger molecule of E and Z isomers of N-acetyl-α,β-dehydrophenylalanine N′,N′-dimethylamide [Ac-(E/Z)-ΔPhe-NMe2] and the estimated anharmonic ν(C = O) frequencies were close to directly calculated results.

Correlation between calculated harmonic and anharmonic ν(C = O) frequencies of formamide in the gas phase and several solvents calculated with the B3LYP hybrid exchange-correlation functional using 21 basis sets in vacuum and 11 in solution

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Barth A (2007) Infrared spectroscopy of proteins. Biochim Biophys Acta 1767:1073–1101

    Article  CAS  Google Scholar 

  2. Vass E, Hollosi M, Besson F, Buchet R (2003) Vibrational spectroscopic detection of beta- and gamma- turns in synthetic and natural peptides and proteins. Chem Rev 103:1917–1954

    Article  CAS  Google Scholar 

  3. Hehre WJ, Radom L, PvR S, Pople JA (1986) Molecular orbital theory. Wiley, New York

    Google Scholar 

  4. Scott AP, Radom L (1996) Harmonic vibrational frequencies: an evaluation of Hartree-Fock, Møller-Plesset, quadratic configuration interaction, density functional theory, and semiempirical scale factors. J Phys Chem 100:16502–16513

    Article  CAS  Google Scholar 

  5. Merrick JP, Moran D, Radom L (2007) An evaluation of harmonic vibrational frequency scale factors. J Phys Chem A 111:11683–11700

    Article  CAS  Google Scholar 

  6. Sinha P, Boesch SE, Gu C, Wheeler RA, Wilson AK (2004) Harmonic vibrational frequencies: scaling factors for HF, B3LYP, and MP2 methods in combination with correlation consistent basis sets. J Phys Chem A 108:9213–9217

    Article  CAS  Google Scholar 

  7. Boese AD, Klopper W, Martin JML (2005) Assessment of various density functionals and basis sets for the calculation of molecular anharmonic force fields. Int J Quant Chem 104:830–845

    Article  CAS  Google Scholar 

  8. Boese AD, Klopper W, Martin JML (2005) Anharmonic force fields and thermodynamic functions using density functional theory. Mol Phys 103:863–876

    Article  CAS  Google Scholar 

  9. Barone V (2004) Vibrational zero-point energies and thermodynamic functions beyond the harmonic approximation. J Chem Phys 120:3059–3065

    Article  CAS  Google Scholar 

  10. Carbonniere P, Barone V (2004) Performances of different density functionals in the computation of vibrational spectra beyond the harmonic approximation. Chem Phys Lett 399:226–229

    Article  CAS  Google Scholar 

  11. Carbonniere P, Bégué D, Pouchan C (2004) DFT quartic force field of acetonitrile by using a generalized least-squares procedure. Chem Phys Lett 393:92–97

    Article  CAS  Google Scholar 

  12. Carbonniere P, Barone V (2004) Coriolis couplings in variational computations of vibrational spectra beyond the harmonic approximation: Implementation and validation. Chem Phys Lett 392:365–371

    Article  CAS  Google Scholar 

  13. Carbonniere P, Begue D, Dargelos A, Pouchan C (2004) Construction of an accurate quartic force field by using generalised least-squares fitting and experimental design. Chem Phys 300:41–51

    Article  CAS  Google Scholar 

  14. Barone V (2005) Anharmonic vibrational properties by a fully automated second-order perturbative approach. J Chem Phys 122:014108

    Article  Google Scholar 

  15. Carbonniere P, Lucca T, Pouchan C, Rega N, Barone V (2005) Vibrational computations beyond the harmonic approximation: Performances of the B3LYP density functional for semirigid molecules. J Comput Chem 26:384–388

    Article  CAS  Google Scholar 

  16. Bour P, Bednarova L (1995) Anharmonic force field of formamide. A computational study. J Phys Chem 99:5961–5966

    Article  CAS  Google Scholar 

  17. Bounouar M, Scheurer C (2008) The impact of approximate VSCF schemes and curvilinear coordinates on the anharmonic vibrational frequencies of formamide and thioformamide. Chem Phys 347:194–207

    Article  CAS  Google Scholar 

  18. 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, Keith T, 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 E01. Gaussian, Wallingford

    Google Scholar 

  19. 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 (2009) Gaussian 09, Revision A.02. Gaussian, Wallingford, CT

    Google Scholar 

  20. Bowman JM (1978) Self-consistent field energies and wavefunctions for coupled oscillators. J Chem Phys 68:608–610

    Article  CAS  Google Scholar 

  21. Bowman JM (1986) The self-consistent-field approach to polyatomic vibrations. Acc Chem Res 19:202–208

    Article  CAS  Google Scholar 

  22. Gerber RB, Ratner MA (1988) Self-consistent field methods for vibrational excitation in polyatomic systems. Adv Chem Phys 70:97–132

    Article  CAS  Google Scholar 

  23. Bounouar M, Scheurer C (2006) Reducing the vibrational coupling network in N-methylacetamide as a model for ab initio infrared spectra computations of peptides. Chem Phys 323:87–101

    Article  CAS  Google Scholar 

  24. Norris LS, Ratner MA, Roitberg AE, Gerber RB (1996) Moller-Plesset perturbation theory applied to vibrational problems. J Chem Phys 105:11261–11267

    Article  CAS  Google Scholar 

  25. Christiansen O (2007) Vibrational structure theory: New vibrational wave function methods for calculation of anharmonic vibrational energies and vibrational contributions to molecular properties. Phys Chem Chem Phys 9:2942–2953

    Article  CAS  Google Scholar 

  26. Bowman JM, Christoffel K, Tobin F (1979) Application of SCF-CI theory to vibrational motion in polyatomic molecules. J Phys Chem 83:905–920

    Article  CAS  Google Scholar 

  27. Christoffel KM, Bowman JM (1982) Investigations of self-consistent field, SCF CI and virtual state configuration interaction vibrational energies for a model three-mode system. Chem Phys Lett 85:220–224

    Article  CAS  Google Scholar 

  28. Carter S, Bowman JM, Handy NC (1998) Extensions and tests of "multimode": a code to obtain accurate vibration/rotation energies of many-mode molecules. Theor Chem Acc 100:191–198

    Article  CAS  Google Scholar 

  29. Christiansen O (2004) Vibrational coupled cluster theory. J Chem Phys 120:2149–2159

    Article  CAS  Google Scholar 

  30. Buczek A, Kupka T, Broda MA (2011) Extrapolation of water and formaldehyde harmonic and anharmonic frequencies to the B3LYP/CBS limit using polarization consistent basis sets. J Mol Model 17:2029–2040

    Article  CAS  Google Scholar 

  31. Buczek A, Kupka T, Broda MA (2011) Estimation of formamide harmonic and anharmonic modes in the Kohn-Sham limit using the polarization consistent basis sets. J Mol Model 17:2265–2274

    Article  CAS  Google Scholar 

  32. Tomasi J, Mennucci B, Cammi R (2005) Quantum mechanical continuum solvation models. Chem Rev 105:2999–3093

    Article  CAS  Google Scholar 

  33. Buczek A, Siodłak D, Bujak M, Broda MA (2011) The effects of side-chain orientation on the backbone conformation of dehydrophenylalanine residue. Theoretical and X-ray study. J Phys Chem B 115:4295–4306

    Article  CAS  Google Scholar 

  34. Buczek AM, Ptak T, Kupka T, Broda MA (2011) Experimental and theoretical NMR and IR studies of the side-chain orientation effects on the backbone conformation of dehydrophenylalanine residue. Magn Reson Chem 49:343–349

    Article  CAS  Google Scholar 

  35. Lee C, Yang W, Parr RG (1988) Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys Rev B 37:785–789

    Article  CAS  Google Scholar 

  36. Vosko SH, Wilk L, Nusair M (1980) Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Can J Phys 58:1200–1211

    Article  CAS  Google Scholar 

  37. Becke AD (1993) Density-functional thermochemistry. III. The role of exact exchange. J Chem Phys 98:5648–5652

    Article  CAS  Google Scholar 

  38. Stephens PJ, Devlin FJ, Chabalowski CF, Frisch MJ (1994) Ab initio calculations of vibrational absorbtion and circular dichroism spectra using density functional force fields. J Chem Phys 98:11623–11627

    Article  CAS  Google Scholar 

  39. Dunning TH Jr (1989) Gaussian basis sets for use in correlated molecular calculations, I. The atoms boron through neon and hydrogen. J Chem Phys 90:1007–1023

    Article  CAS  Google Scholar 

  40. Dunning TH Jr (2000) A road map for the calculation of molecular binding energies. J Phys Chem A 104:9062–9080

    Article  CAS  Google Scholar 

  41. Wilson A, van Mourik T, Dunning TH Jr (1996) Gaussian basis sets for use in correlated molecular calculations. VI. Sextuple zeta correlation consistent basis sets for boron through neon. J Mol Struct (THEOCHEM) 388:339–349

    CAS  Google Scholar 

  42. Kendall RA, Dunning TH Jr, Harrison RJ (1992) Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions. J Chem Phys 96:6796–6806

    Article  CAS  Google Scholar 

  43. Jensen F (1999) The basis set convergence of the Hartree-Fock energy for H2. J Chem Phys 110:6601–6605

    Article  CAS  Google Scholar 

  44. Jensen F (2001) Polarization consistent basis sets: Principles. J Chem Phys 115:9113–9125

    Article  CAS  Google Scholar 

  45. Jensen F (2002) Polarization consistent basis sets. II. Estimating the Kohn-Sham basis set limit. J Chem Phys 116:7372–7379

    Article  CAS  Google Scholar 

  46. Jensen F (2003) Polarization consistent basis sets. IV. The basis set convergence of equilibrium geometries, harmonic vibrational frequencies, and intensities. J Chem Phys 118:2459–2463

    Article  CAS  Google Scholar 

  47. Jensen F, Helgaker T (2004) Polarization consistent basis sets. V. The elements Si-Cl. J Chem Phys 121:3463–3470

    Article  CAS  Google Scholar 

  48. Jensen F (2005) The effect of different density functional methods on basis set parameters. Chem Phys Lett 402:510–513

    Article  CAS  Google Scholar 

  49. Clabo DA Jr, Allen WD, Remington RB, Yamaguchi Y, Schaefer HF III (1988) A systematic study of molecular vibrational anharmonicity and vibration-rotation interaction by self-consistent-field higher-derivative methods. Asymmetric top molecules. Chem Phys 123:187–239

    Article  CAS  Google Scholar 

  50. Bruna PJ, Hachey MR, Grein F (1997) Benchmark ab initio calculations of formaldehyde, H2CO. J Mol Struct (THEOCHEM) 400:177–221

    CAS  Google Scholar 

  51. McNaughton D, Evans CJ, Lane S, Nielsen CJ (1999) The high resolution FTIR far-infrared spectrum of formamide. J Mol Spectrosc 193:104–117

    Article  CAS  Google Scholar 

  52. Ataka S, Takeuchi H, Tasumi M (1984) Infrared studies of the less stable cis form of N-methylformamide and N-methylacetamide in low temperature nitrogen matrices and vibrational analyses of the trans and cis forms of these molecules. J Mol Struct 113:147–160

    Article  CAS  Google Scholar 

  53. Wang J, Hochstrasser RM (2006) Anharmonicity of amide modes. J Phys Chem B 110:3798–3807

    Article  CAS  Google Scholar 

  54. GRAMS/AI Version 9.00 R2 (2009) Thermo Fisher Scientific; http://www.thermofisher.com

Download references

Acknowledgments

A.B. is the recipient of a PhD fellowship from a project funded by the European Social Fund. Calculations were carried out in Wroclaw Centre for Networking and Supercomputing (http://www.wcss.wroc.pl), and in the Academic Computer Centre CYFRONET, AGH, Kraków, grant MEiN/SGI3700/UOpolski/063/2006. T.K. was supported by the University of Opole grant (10/WCh/2011-S). S.P.A.S thanks the Danish Center for Scientific Computing and the Danish Councils for Independent Research.

Author information

Authors and Affiliations

  1. Faculty of Chemistry, University of Opole, 48 Oleska Street, 45-052, Opole, Poland

    Aneta Buczek, Teobald Kupka & Małgorzata A. Broda

  2. Department of Chemistry, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark

    Stephan P. A. Sauer

Authors
  1. Aneta Buczek
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Teobald Kupka
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stephan P. A. Sauer
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Małgorzata A. Broda
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Teobald Kupka.

Electronic supplementary material

Below is the link to the electronic supplementary material.

ESM 1

(DOC 500 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Buczek, A., Kupka, T., Sauer, S.P.A. et al. Estimating the carbonyl anharmonic vibrational frequency from affordable harmonic frequency calculations. J Mol Model 18, 2471–2478 (2012). https://doi.org/10.1007/s00894-011-1262-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00894-011-1262-6

Keywords

Search

Navigation