Skip to main content
SpringerLink
Log in

Performance of different density functionals for the calculation of vibrational frequencies with vibrational coupled cluster method in bosonic representation

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

Abstract

An accurate description of anharmonic vibrational frequencies of polyatomic molecules is a challenging task. It requires an ab initio method to solve the vibrational Schrödinger equation along with extensive electronic structure calculations to generate the quartic potential energy surface (PES) in mass-weighted normal coordinates. The computation of such quartic PES is very expensive. Even for a medium-size molecule, highly accurate ab initio methods like CCSD, CCSD(T) become formidable. The DFT stands as valuable alternative in this case. In this work, we investigate the performances of several commonly used density functionals, namely, B3LYP, BLYP, B3LYPD, M06, M062x, PBE1PBE, B3P86, LC-\(\omega \)PBE, X3LYP, B3PW91, and B97D for the evaluation of anharmonic vibrational frequencies of semi-rigid molecules. The quality of the results is assessed by the comparison with experimental values. To this end, we used a set of 19 molecules of various sizes (4–9 atoms). The vibrational coupled cluster method (VCCM) in bosonic representation is used to solve the vibrational structure problem. The hybrid functionals B3P86, B3LYP, B3PW91, PBE1PBE, and X3LYP found to give more accurate result of the fundamental frequencies than the other functionals. Our results show that the error in the BLYP and B97D calculation is due to the inadequate description of the harmonic force field. For the LC-\(\omega \)PBE, M06, and M062x, the anharmonic force constants leads to the error. It is found that the comparative performances of the DFT functionals with VCCM are consistent with the second-order vibrational perturbation theory.

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

Similar content being viewed by others

References

  1. Lasch P, Kneipp J (2008) Biomedical vibrational spectroscopy. Wiley, Hoboken

    Book  Google Scholar 

  2. Siebert F, Hildebrandt P (2008) Vibrational spectroscopy in life science. Tutorials in biophysics. Wiley, Hoboken

    Google Scholar 

  3. Larkin P (2011) Infrared and raman spectroscopy: principles and spectral interpretation. Elsevier, Amsterdam

    Google Scholar 

  4. Searles D, Nagy-Felsobuki E (2013) Ab initio variational calculations of molecular vibrational-rotational spectra. Lecture notes in chemistry. Springer, Berlin

    Google Scholar 

  5. Atkinson G (2012) Time-resolved vibrational spectroscopy. Elsevier Science, Amsterdam

    Google Scholar 

  6. Wilson E, Decius J, Cross P (1955) Molecular vibrations: the theory of infrared and raman vibrational spectra. Dover books on chemistry series. Dover Publications, Mineola

    Google Scholar 

  7. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery Jr. JA, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam JM, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas o, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2009) Gaussian09 Revision B.01. Gaussian Inc, Wallingford

  8. Werner HJ, Knowles PJ, Knizia G, Manby FR, Schütz M, Celani P, Györffy W, Kats D, Korona T, Lindh R, Mitrushenkov A, Rauhut G, Shamasundar KR, Adler TB, Amos RD, Bernhardsson A, Berning A, Cooper DL, Deegan MJO, Dobbyn AJ, Eckert F, Goll E, Hampel C, Hesselmann A, Hetzer G, Hrenar T, Jansen G, Köppl C, Liu Y, Lloyd AW, Mata RA, May AJ, McNicholas SJ, Meyer W, Mura ME, Nicklass A, O’Neill DP, Palmieri P, Peng D, Pflüger K, Pitzer R, Reiher M, Shiozaki T, Stoll H, Stone AJ, Tarroni R, Thorsteinsson T, Wang M (2015) Molpro, version 2015.1, a package of ab initio programs

  9. Gordon MS, Schmidt MW (2005) Advances in electronic structure theory: GAMESS a decade later. Elsevier, Amsterdam, pp 1167–1189

    Google Scholar 

  10. Nielsen HH (1951) Rev Mod Phys 23:90

    Article  CAS  Google Scholar 

  11. Barone V (2005) J Chem Phys 122:014108

    Article  Google Scholar 

  12. Bloino J, Barone V (2012) J Chem Phys 136:124108

    Article  Google Scholar 

  13. Barone V, Biczysko M, Bloino J (2014) Phys Chem Chem Phys 16:1759

    Article  CAS  Google Scholar 

  14. Culot F, Liévin J (1992) Phys Scr 46:502

    Article  CAS  Google Scholar 

  15. Carter S, Handy NC (1986) Comput Phys Rep 5:117

  16. Boese AD, Martin JML (2004) J Phys Chem A 108:3085

    Article  CAS  Google Scholar 

  17. Bowman JM (1978) J Chem Phys 68:608

    Article  CAS  Google Scholar 

  18. Bowman JM (1986) Acc Chem Res 19:202

    Article  CAS  Google Scholar 

  19. Carney DG, Sprandel LL, Kern CW (1978) Adv Chem Phys 37:305

    CAS  Google Scholar 

  20. Chaban GM, Jung JO, Gerber RB (1999) J Chem Phys 111:1823

    Article  CAS  Google Scholar 

  21. Gerber RB, Chaban GM, Brauer B, Miller Y (2005) In: C.E. Dykstra, G. Frenking, K. Kim, G. Suceria (eds) Theory and applications of computational chemistry: the first fourty years, chap. 9 Elsevier, Tokyo, pp. 165–194

  22. Heislbetz S, Rauhut G (2010) J Chem Phys 132:124102

    Article  Google Scholar 

  23. Hirata S, Hermes MR (2014) J Chem Phys 141:184111

    Article  Google Scholar 

  24. Christiansen O, Kongsted J, Paterson MJ, Luis JM (2006) J Chem Phys 125:214309

    Article  Google Scholar 

  25. Seidler P, Hansen MB, Györffy W, Toffoli D, Christiansen O (2010) J Chem Phys 132:164105

    Article  Google Scholar 

  26. Neff M, Rauhut G (2009) J Chem Phys 131:124129

    Article  Google Scholar 

  27. Seidler P, Kongsted J, Christiansen O (2007) J Phys Chem A 111:11205

    Article  CAS  Google Scholar 

  28. Christiansen O (2004) J Chem Phys 120:2149

    Article  CAS  Google Scholar 

  29. Seidler P, Christiansen O (2007) J Chem Phys 126:204101

    Article  Google Scholar 

  30. Seidler P, Hansen MB, Christiansen O (2008) J Chem Phys 128:154113

    Article  Google Scholar 

  31. Seidler P, Christiansen O (2009) J Chem Phys 131:234109

    Article  Google Scholar 

  32. Nagalakshmi V, Lakshminarayana V, Sumithra G, Durga Prasad M (1994) Chem Phys Lett 217:279

    Article  Google Scholar 

  33. Banik S, Pal S, Durga Prasad M (2008) J Chem Phys 129:134111

    Article  Google Scholar 

  34. Banik S, Pal S, Durga Prasad M (2012) J Chem Phys 137:114108

    Article  Google Scholar 

  35. Banik S, Durga Prasad M (2012) Theory Chem Acc 131:1383

    Article  Google Scholar 

  36. Durga Prasad M (2000) Indian J Chem 39A:196

    Google Scholar 

  37. Faucheaux JA, Hirata S (2015) J Chem Phys 143:134105

    Article  Google Scholar 

  38. Banik S (2016) Theory Chem Acc 135:203

    Article  Google Scholar 

  39. Yagi K, Hirata S, Hirao K (2008) Phys Chem Chem Phys 10:1781

    Article  CAS  Google Scholar 

  40. Yagi K, Otaki H (2014) J Chem Phys 140:084113

    Article  Google Scholar 

  41. Banik S, Ravichandran L, Durga Prasad M (2014) Mol Phys https://doi.org/10.1080/00268976.2017.1321153

  42. Chakraborty S, Banik S, Das PK (2016) J Phys Chem A 120:9707

    Article  CAS  Google Scholar 

  43. Rauhut G, Barone V, Schwerdtfeger P (2006) J Chem Phys 125:54308

    Article  Google Scholar 

  44. Ess DH, Houk K (2005) J Phys Chem A 109:9542

    Article  CAS  Google Scholar 

  45. Andzelm J, Rinderspacher BC, Rawlett A, Dougherty J, Baer R, Govind N (2009) J Chem Theory Comput 5:2835

    Article  CAS  Google Scholar 

  46. Thanthiriwatte KS, Hohenstein EG, Burns LA, Sherrill CD (2010) J Chem Theory Comput 7:88

    Article  Google Scholar 

  47. Maroulis G (2006) Structure and properties of clusters: from a few atoms to nanoparticles. CRC Press, Boca Raton, p 103

    Google Scholar 

  48. Siegbahn PE (2006) J Biological Inorg Chem 11:695

    Article  CAS  Google Scholar 

  49. De Proft F, Martin JML, Geerlings P (1996) Chem Phys Lett 250:393

    Article  Google Scholar 

  50. Zhang G, Musgrave CB (2007) J Phys Chem A 111:1554

    Article  CAS  Google Scholar 

  51. Carbonniere P, Lucca T, Pouchan C, Rega N, Barone V (2005) J Comput Chem 26:384

    Article  CAS  Google Scholar 

  52. Barone V (2004) J Phys Chem A 108:4146

    Article  CAS  Google Scholar 

  53. Biczysko M, Panek P, Scalmani G, Bloino J, Barone V (2010) J Chem Theory Comput 6:2115

    Article  CAS  Google Scholar 

  54. Daniel Boese A, Klopper W, Martin JML (2005) Mol Phys 103:863

    Article  Google Scholar 

  55. Kesharwani MK, Brauer B, Martin JML (2015) J Phys Chem A 119:1701

    Article  CAS  Google Scholar 

  56. Becke AD (1988) Phys Rev A 38:3098

    Article  CAS  Google Scholar 

  57. Perdew JP, Burke K, Ernzerhof M (1996) Phys Rev Lett 77:3865

    Article  CAS  Google Scholar 

  58. Becke AD (1993) J Chem Phys 98:5648

    Article  CAS  Google Scholar 

  59. Lee C, Yang W, Parr RG (1988) Phys Rev B 37:785

    Article  CAS  Google Scholar 

  60. Cohen AJ, Mori-Sanchez P, Yang W (2012) Chem Rev 112:289

    Article  CAS  Google Scholar 

  61. Zhao Y, Truhlar DG (2005) J Chem Theory Comput 1:415

    Article  CAS  Google Scholar 

  62. Lewars E (2010) Computational chemistry: introduction to the theory and applications of molecular and quantum mechanics. Springer, Netherlands

    Google Scholar 

  63. Cheron N, Jacquemin D, Fleurat-Lessard P (2012) Phys Chem Chem Phys 14:7170

    Article  CAS  Google Scholar 

  64. Kang JK, Musgrave CB (2001) J Chem Phys 115:11040

    Article  CAS  Google Scholar 

  65. Song JW, Hirosawa T, Tsuneda T, Hirao K (2007) J Chem Phys 126(15):154105

    Article  Google Scholar 

  66. Grafenstein J, Cremer D (2000) Phys Chem Chem Phys 2:2091

    Article  CAS  Google Scholar 

  67. Pople JA, Head-Gordon M, Fox Douglas J, Raghavachari K, Curtiss LA (1989) J Chem Phys 90:5622

    Article  CAS  Google Scholar 

  68. Vosko SH, Wilk L, Nusair M (1980) Can J Phys 58:1200

    Article  CAS  Google Scholar 

  69. Grimme S (2006) J Comput Chem 27:1787

    Article  CAS  Google Scholar 

  70. Perdew JP (1986) Phys Rev B 33:8822

    Article  CAS  Google Scholar 

  71. Perdew JP (1991) In: Ziesche P, Eschrig H (eds) Electronic structure of solids. Akademie Verlag, Berlin, p 11

  72. Adamo C, Barone V (1999) J Chem Phys 110:6158

    Article  CAS  Google Scholar 

  73. Grimme S (2006) J Comp Chem 27:1787

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  75. Vydrov OA, Scuseria GE (2006) J Chem Phys 125:234109

    Article  Google Scholar 

  76. Xu X, Goddard WA (2004) Proc Natl Acad Sci USA 101:2673

    Article  CAS  Google Scholar 

  77. Zhao Y, Truhlar DG (2008) Theory Chem Acc 120:215

    Article  CAS  Google Scholar 

  78. Christiansen O (2007) Phys Chem Chem Phys 9:2942

    Article  CAS  Google Scholar 

  79. Banik S, Pal S, Durga Prasad M (2010) J Chem Theory Comput 6:3198

    Article  CAS  Google Scholar 

  80. Roy TK, Durga Prasad M (2009) J Chem Sci 121:805

    Article  CAS  Google Scholar 

  81. Mukherjee D (1979) Pramana 12:203

    Article  CAS  Google Scholar 

  82. Madhavi Sastry G, Durga Prasad M (1993) Theory Chim Acta 89:511

    Google Scholar 

  83. Mukherjee D, Mukherjee P (1979) Chem Phys 39:325

    Article  CAS  Google Scholar 

  84. Monkhorst HJ (1977) Int J Quantum Chem 12(S11):421

    Article  Google Scholar 

  85. Dutler R, Rauk A (1989) J Am Chem Soc 111:6957

    Article  CAS  Google Scholar 

  86. Kwiatkowski JS, Leszczynski J, Teca I (1997) J Mol Struct 436–437:451

    Article  Google Scholar 

  87. NIST chemistry webbook, NIST standard reference database number 69, national institute of standards and technology. http://webbook.nist.gov/chemistry/

  88. Kozuch S, Martin JML (2013) J Comput Chem 34:2327

    CAS  Google Scholar 

  89. Bartlett RJ, Musial M (2007) Rev Mod Phys 79:291

    Article  CAS  Google Scholar 

Download references

Acknowledgements

Lalitha Ravichandran acknowledges financial support from UGC, India, under Dr. D. S. Kothari postdoctoral fellowship scheme.

Author information

Authors and Affiliations

  1. School of Chemistry, University of Hyderabad, Hyderabad, 500046, India

    Lalitha Ravichandran

  2. Advanced Centre for Research in High Energy Materials, University of Hyderabad, Hyderabad, 500046, India

    Subrata Banik

  3. Manipal Centre for Natural Sciences, Manipal University, Manipal, 576104, India

    Subrata Banik

Authors
  1. Lalitha Ravichandran
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Subrata Banik
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Subrata Banik.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (pdf 163 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ravichandran, L., Banik, S. Performance of different density functionals for the calculation of vibrational frequencies with vibrational coupled cluster method in bosonic representation. Theor Chem Acc 137, 1 (2018). https://doi.org/10.1007/s00214-017-2177-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00214-017-2177-9

Keywords

Search

Navigation