Theoretical Chemistry Accounts

, Volume 130, Issue 4–6, pp 851–857 | Cite as

An examination of density functional theories on isomerization energy calculations of organic molecules

  • Jong-Won Song
  • Takao Tsuneda
  • Takeshi Sato
  • Kimihiko Hirao
Regular Article

Abstract

Long-range corrected (LC) density functional theories (DFTs) were applied to the isomerization energy calculations of organic molecules to make clear why conventional DFTs including B3LYP have given poor isomerization reaction energies. Combining with local response dispersion (LRD) method, we performed LC-DFT calculations for the benchmark set of isomerization reactions. Consequently, we found that LC-DFT + LRD methods give accurate reaction energies equivalent to up-to-date DFTs containing many semi-empirical parameters. This result indicates that long-range exchange and intramolecular dispersion correlation interactions, which have been neglected in conventional DFTs, play prominent roles in isomerization reactions. However, we also found that these interactions are not sufficient to give accurate isomerization energies especially for cyclization reactions. Considering that Gaussian-attenuated LC-DFTs (LCgau-DFTs) give better isomerization reaction energies than LC-DFTs, we suggested that the isomerization energies will be further improved by correcting the short-range part of exchange functionals in DFT with keeping the whole long-range exchange interactions.

Keywords

Density functional theory (DFT) Long-range correction (LC) Isomerization energy 

Supplementary material

214_2011_997_MOESM1_ESM.docx (41 kb)
Supplementary material 1 (DOCX 41 kb)

References

  1. 1.
    Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140(4A):1133Google Scholar
  2. 2.
    Kamiya M, Sekino H, Tsuneda T, Hirao K (2005) Nonlinear optical property calculations by the long-range-corrected coupled-perturbed Kohn–Sham method. J Chem Phys 122(23):234111, doi:10.1063/1.1935514
  3. 3.
    Song J-W, Watson MA, Sekino H, Hirao K (2008) Nonlinear optical property calculations of polyynes with long-range corrected hybrid exchange-correlation functionals. J Chem Phys 129(2):024117, doi:10.1063/1.2936830 Google Scholar
  4. 4.
    Kamiya M, Tsuneda T, Hirao K (2002) A density functional study of van der Waals interactions. J Chem Phys 117(13):6010, doi:10.1063/1.1501132 Google Scholar
  5. 5.
    Sato T, Tsuneda T, Hirao K (2005) Van der Waals interactions studied by density functional theory. Mol Phys 103(6–8):1151–1164. doi:10.1080/00268970412331333474 CrossRefGoogle Scholar
  6. 6.
    Tawada Y, Tsuneda T, Yanagisawa S, Yanai T, Hirao K (2004) A long-range-corrected time-dependent density functional theory. J Chem Phys 120(18):8425, doi:10.1063/1.1688752 Google Scholar
  7. 7.
    Savin A (1996) In: Seminario jm (ed) Recent developments and applications of modern density functional theory. Elsevier, Amsterdam, p 327CrossRefGoogle Scholar
  8. 8.
    Iikura H, Tsuneda T, Yanai T, Hirao K (2001) A long-range correction scheme for generalized-gradient-approximation exchange functionals. J Chem Phys 115(8):3540, doi:10.1063/1.1383587
  9. 9.
    Song J-W, Hirosawa T, Tsuneda T, Hirao K (2007) Long-range corrected density functional calculations of chemical reactions: redetermination of parameter. J Chem Phys 126(15):154105, doi:10.1063/1.2721532
  10. 10.
    Tsuneda T, Song J-W, Suzuki S, Hirao K (2010) On Koopmans’ theorem in density functional theory. J Chem Phys 133(17):174101, doi:10.1063/1.3491272 Google Scholar
  11. 11.
    Yanai T, Tew DP, Handy NC (2004) A new hybrid exchange-correlation functional using the Coulomb-attenuating method (CAM-B3LYP). Chem Phys Lett 393(1–3):51–57. doi:10.1016/j.cplett.2004.06.011 CrossRefGoogle Scholar
  12. 12.
    Vydrov OA, Scuseria GE (2006) Assessment of a long-range corrected hybrid functional. J Chem Phys 125(23):234109, doi:10.1063/1.2409292 Google Scholar
  13. 13.
    Song J-W, Tokura S, Sato T, Watson MA, Hirao K (2007) An improved long-range corrected hybrid exchange-correlation functional including a short-range Gaussian attenuation (LCgau-BOP). J Chem Phys 127(15):154109, doi:10.1063/1.2790017 Google Scholar
  14. 14.
    Song J-W, Tokura S, Sato T, Watson MA, Hirao K (2009) Erratum: “An improved long-range corrected hybrid exchange-correlation functional including a short-range Gaussian attenuation (LCgau-BOP)” [J. Chem. Phys. 127, 154109 (2007)]. J Chem Phys 131(5):059901(E), doi:10.1063/1.3202436 Google Scholar
  15. 15.
    Cohen AJ, Mori-Sánchez P, Yang W (2007) Development of exchange-correlation functionals with minimal many-electron self-interaction error. J Chem Phys 126(19):191109, doi:10.1063/1.2741248
  16. 16.
    Chai J-D, Head-Gordon M (2008) Systematic optimization of long-range corrected hybrid density functionals. J Chem Phys 128(8):084106, doi:10.1063/1.2834918 Google Scholar
  17. 17.
    Livshits E, Baer R (2007) A well-tempered density functional theory of electrons in molecules. Phys Chem Chem Phys 9(23):2932, doi:10.1039/b617919c Google Scholar
  18. 18.
    Song J-W, Watson MA, Nakata A, Hirao K (2008) Core-excitation energy calculations with a long-range corrected hybrid exchange-correlation functional including a short-range Gaussian attenuation (LCgau-BOP). J Chem Phys 129(18):184113, doi:10.1063/1.3010372 Google Scholar
  19. 19.
    Wodrich MD, Corminboeuf C, Schleyer PvR (2006) Systematic errors in computed alkane energies using B3LYP and other popular DFT functionals. Org Lett 8(17):3631–3634. doi:10.1021/ol061016i CrossRefGoogle Scholar
  20. 20.
    Sato T, Nakai H (2009) Density functional method including weak interactions: dispersion coefficients based on the local response approximation. J Chem Phys 131(22):224104, doi:10.1063/1.3269802 Google Scholar
  21. 21.
    Song J-W, Tsuneda T, Sato T, Hirao K (2010) Calculations of alkane energies using long-range corrected DFT combined with Intramolecular van der Waals correlation. Org Lett 12(7):1440–1443. doi:10.1021/ol100082z CrossRefGoogle Scholar
  22. 22.
    Grimme S (2006) Seemingly simple stereoelectronic effects in alkane isomers and the implications for Kohn–Sham density functional theory. Angew Chem Int Ed 45(27):4460–4464. doi:10.1002/anie.200600448 CrossRefGoogle Scholar
  23. 23.
    Wodrich MD, Wannere CS, Mo Y, Jarowski PD, Houk KN, Schleyer PvR (2007) The concept of protobranching and its many paradigm shifting implications for energy evaluations. Chem Eur J 13(27):7731–7744. doi:10.1002/chem.200700602 CrossRefGoogle Scholar
  24. 24.
    Grimme S, Steinmetz M, Korth M (2007) How to compute isomerization energies of organic molecules with quantum chemical methods. J Organ Chem 72(6):2118–2126. doi:10.1021/jo062446p CrossRefGoogle Scholar
  25. 25.
    Becke AD (1988) Density-functional exchange-energy approximation with correct asymptotic behavior. Phys Rev A 38(6):3098–3100CrossRefGoogle Scholar
  26. 26.
    Tsuneda T, Suzumura T, Hirao K (1999) A new one-parameter progressive Colle-Salvetti-type correlation functional. J Chem Phys 110(22):10664–10678CrossRefGoogle Scholar
  27. 27.
    Curtiss LA, Raghavachari K, Redfern PC, Pople JA (1997) Assessment of Gaussian-2 and density functional theories for the computation of enthalpies of formation. J Chem Phys 106(3):1063–1079CrossRefGoogle Scholar
  28. 28.
    Perdew JP, Chevary JA, Vosko SH, Jackson KA, Pederson MR, Singh DJ, Fiolhais C (1992) Atoms, molecules, solids, and surfaces—applications of the generalized gradient approximation for exchange and correlation. Phys Rev B 46(11):6671–6687CrossRefGoogle Scholar
  29. 29.
    Lee CT, Yang WT, Parr RG (1988) Development of the Colle-Salvetti correlation-energy formula into a functional of the electron-density. Phys Rev B 37(2):785–789CrossRefGoogle Scholar
  30. 30.
    Becke AD (1993) Density-functional thermochemistry. 3. The role of exact exchange. J Chem Phys 98(7):5648–5652Google Scholar
  31. 31.
    Becke AD (1993) A new mixing of Hartree-Fock and local density-functional theories. J Chem Phys 98(2):1372–1377CrossRefGoogle Scholar
  32. 32.
    Boese AD, Martin JML (2004) Development of density functionals for thermochemical kinetics. J Chem Phys 121(8):3405–3416. doi:10.1063/1.1774975 CrossRefGoogle Scholar
  33. 33.
    Zhao Y, Schultz NE, Truhlar DG (2006) Design of density functionals by combining the method of constraint satisfaction with parametrization for thermochemistry, thermochemical kinetics, and noncovalent interactions. J Chem Theory Comput 2(2):364–382. doi:10.1021/Ct0502763 CrossRefGoogle Scholar
  34. 34.
    Zhao Y, Truhlar DG (2008) The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor Chem Acc 120(1–3):215–241. doi:10.1007/s00214-007-0310-x CrossRefGoogle Scholar
  35. 35.
    Grimme S (2006) Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J Comput Chem 27(15):1787–1799. doi:10.1002/Jcc.20495 CrossRefGoogle Scholar
  36. 36.
    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 J, Jjogo A, 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 NJ, 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 A.1, Gaussian, WallingfordGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Jong-Won Song
    • 1
    • 2
  • Takao Tsuneda
    • 2
    • 3
  • Takeshi Sato
    • 4
  • Kimihiko Hirao
    • 2
    • 3
  1. 1.Department of Chemical System Engineering, School of EngineeringThe University of TokyoTokyoJapan
  2. 2.CREST, Japan Science and Technology AgencySaitamaJapan
  3. 3.Advanced Science InstituteSaitamaJapan
  4. 4.Photon Science Center of the University of TokyoTokyoJapan

Personalised recommendations