Advertisement

How well can B3LYP heats of formation be improved by dispersion correction models?

  • Yuwei Zhou
  • Jianming Wu
  • Xin XuEmail author
Regular Article

Abstract

In the present work, we have compiled six datasets for heats of formation (HOFs) of hydrocarbons of different chemistries, involving Set 1 for 21 n-alkanes up to n-C32H66, Set 2 for n-C7H16 and its branched isomers, Set 3 for 36 polycyclic saturated hydrocarbons, Set 4 for 41 C6H8 isomers of rings, alkenes, alkynes and cumulenes, Set 5 for 41 benzene-based compounds and Set 6 for 66 radicals. We have performed intensive high-level G4 calculations, which provide the reference data when the experimental data are not available or not reliable. Attention has been paid on how the dispersion-corrected methods, B3LYP-D2, B3LYP-D3 and B3LYP-D3BJ, can improve over the widely used density functional, B3LYP. It was found that, although the dispersion-corrected methods can eliminate the original B3LYP errors to a significant amount, they are unable to cure all B3LYP deficiencies besides the lack of van der Waals interactions. While D3 still underestimates the molecular stabilities as does B3LYP, D3BJ overestimates their stabilities. The more advanced D3 and D3BJ models do not necessarily outperform the simpler D2 model. Except for the PSH set, B3LYP-D3BJ always gives larger errors than does B3LYP-D2 for the other five datasets, showing room for further improvement.

Keywords

Heats of formation Enthalpy of formation Density functional theory B3LYP Dispersion correction Van der Waals forces 

Notes

Acknowledgments

This work was supported by National Natural Science Foundation of China (21373053, 21133004, 91427301) and the Ministry of Science and Technology (2013CB834606).

Supplementary material

214_2015_1801_MOESM1_ESM.docx (191 kb)
Supplementary material 1 (DOCX 190 kb)

References

  1. 1.
    Ruscic B, Boggs JE, Burcat A, Csaszar AG, Demaison J, Janoschek R, Martin JML, Morton ML, Rossi MJ, Stanton JF, Szalay PG, Westmoreland PR, Zabel F, Berces T (2005) IUPAC critical evaluation of thermochemical properties of selected radicals. Part I. J Phys Chem Ref Data 34:573–656CrossRefGoogle Scholar
  2. 2.
    Afeefy HY, Liebman JF, Stein SE (2015) Neutral thermochemical data, in NIST chemistry WebBook, NIST standard reference database number 69. In: Linstrom PJ, Mallard WG (eds) National Institute of Standards and Technology, Gaithersburg. (http://webbook.nist.gov)
  3. 3.
    NIST Computational Chemistry Comparison And Benchmark Database (2015) NIST standard reference database number 101 release 16a, August 2013, Editor: Johnson III RD. (http://cccbdb.nist.gov/)
  4. 4.
    Pedley JB, Naylor RD, Kirby SP (1986) Thermochemical data of organic compounds. Chapman and Hall, New YorkCrossRefGoogle Scholar
  5. 5.
    Knacke O, Kubaschewski O, Hesselmann K (1991) Thermochemical properties of inorganic substances, 2nd edn. Berlin, SpringerGoogle Scholar
  6. 6.
    Dean JA (1999) Langes’ handbook of chemistry, 15th edn. New York, McGraw-HillGoogle Scholar
  7. 7.
    Lide DR (2001) CRC handbook of chemistry and physics, 82nd edn. CRC, Boca RatonGoogle Scholar
  8. 8.
    Chase MW Jr (1998) NIST-JANAF thermochemical tables, fourth edition. J Phys Chem Ref Data Monogr 9:1–1951Google Scholar
  9. 9.
    Rogers DW, Zavitsas AA, Matsunaga N (2013) Determination of enthalpies (‘heats’) of formation. Wires Comput Mol Sci 3:21–36CrossRefGoogle Scholar
  10. 10.
    Pople JA, Head-Gordon M, Fox DJ, Raghavachari K, Curtiss LA (1989) Gaussian-1 theory: a general procedure for prediction of molecular energies. J Chem Phys 90:5622–5629CrossRefGoogle Scholar
  11. 11.
    Curtiss LA, Raghavachari K, Trucks GW, Pople JA (1991) Gaussian-2 Theory for molecular energies of first- and second-row compounds. J Chem Phys 94:7221–7230CrossRefGoogle Scholar
  12. 12.
    Curtiss LA, Raghavachari K, Redfern PC, Rassolov V, Pople JA (1998) Gaussian-3 (G3) theory for molecules containing first and second-row atoms. J Chem Phys 109:7764–7776CrossRefGoogle Scholar
  13. 13.
    Curtiss LA, Redfern PC, Raghavachari K (2007) Gaussian-4 theory. J Chem Phys 126:084108/1–084108/12CrossRefGoogle Scholar
  14. 14.
    Hariharan PC, Pople JA (1973) Influence of polarization functions on molecular-orbital hydrogenation energies. Theor Chem Acc 28:213–222CrossRefGoogle Scholar
  15. 15.
    Krishnan R, Binkley JS, Seeger R, Pople JA (1980) Self-consistent molecular-orbital methods. 20. Basis set for correlated wave-functions. J Chem Phys 72:650–654CrossRefGoogle Scholar
  16. 16.
    Dirac PAM (1930) Note on exchange phenomena in the Thomas atom. Math Proc Camb Phil Soc 26:376–385CrossRefGoogle Scholar
  17. 17.
    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 58:1200–1211CrossRefGoogle Scholar
  18. 18.
    Becke AD (1988) Density-functional exchange-energy approximation with correct asymptotic behavior. Phys Rev A 38:3098–3100CrossRefGoogle Scholar
  19. 19.
    Lee C, Yang WT, Parr RG (1988) Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys Rev B 37:785–789CrossRefGoogle Scholar
  20. 20.
    Becke AD (1993) Density-functional thermochemistry 3: the role of exact exchange. J Chem Phys 98:5648–5652CrossRefGoogle Scholar
  21. 21.
    Stephens PJ, Devlin FJ, Chabalowski CF, Frisch MJ (1994) Ab-initio calculation of vibrational absorption and circular-dichroism spectra using density-functional force-fields. J Phys Chem 98:11623–11627CrossRefGoogle Scholar
  22. 22.
    Redfern PC, Zapol P, Curtiss LA (2000) Assessment of Gaussian-3 and density functional theories for enthalpies of formation of C1-C16 Alkanes. J Phys Chem A 104:5850–5854CrossRefGoogle Scholar
  23. 23.
    Wu JM, Xu X (2007) The X1 method for accurate and efficient prediction of heats of formation. J Chem Phys 127:214105/1–214105/8Google Scholar
  24. 24.
    Wodrich MD, Corminboeuf C, PvR Schleyer (2006) Systematic errors in computed alkane energies using B3LYP and other popular DFT functionals. Org Lett 8:3631–3634CrossRefGoogle Scholar
  25. 25.
    Schreiner PR, Fokin AA, Pascal RA Jr, Meijere A (2006) Many density functional theory approaches fail to give reliable large hydrocarbon isomer energy differences. Org Lett 8:3635–3638CrossRefGoogle Scholar
  26. 26.
    Wodrich MD, Corminboeuf C (2009) Reaction enthalpies using the neural-network-based X1 approach: the important choice of input descriptors. J Phys Chem A 113:3285–3290CrossRefGoogle Scholar
  27. 27.
    Csonka G, Ruzsinszky A, Perdew P, Grimme S (2008) Improved description of stereoelectronic effects in hydrocarbons using semilocal density functional theory. J Chem Theory Comput 4:888–891CrossRefGoogle Scholar
  28. 28.
    Grimme S (2006) Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J Comput Chem 27:1787–1799CrossRefGoogle Scholar
  29. 29.
    Grimme S, Antony J, Ehrlich S, Krieg H (2010) A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J Chem Phys 132:154104/1–154104/19CrossRefGoogle Scholar
  30. 30.
    Grimme S, Ehrlich S, Goerigk L (2011) Effect of the damping function in dispersion corrected density functional theory. J Comput Chem 32:1456CrossRefGoogle Scholar
  31. 31.
    Wu JM, Xu X (2009) Accurate prediction of heats of formation by a combined method of B3LYP and neural network correction. J Compt Chem 30:1424–1444CrossRefGoogle Scholar
  32. 32.
    Wu JM, Xu X (2008) Improving the B3LYP bond energies by using the X1 method. J Chem Phys 129:164103/1–164103/11Google Scholar
  33. 33.
    Wu JM, Zhang IY, Xu X (2010) The X1s method for accurate bond dissociation energies. ChemPhysChem 11:2561–2567CrossRefGoogle Scholar
  34. 34.
    Wu JM, Zhou Y, Xu X (2015) The X1 family of methods that combines B3LYP with neural network corrections for an accurate yet efficient prediction of thermochemistry. Int J Quantum Chem 115:1021–1031CrossRefGoogle Scholar
  35. 35.
    Wu JM, Yang Y, Zhou Y, Xu X (2016) X1se: a combined method of density functional calculation and neural network correction for accurate prediction of heats of formation. Sci Sin Chim.46:38–50 CrossRefGoogle Scholar
  36. 36.
    Cioslowski J, Liu GH (1998) Piskorz P (1998) Computationally inexpensive theoretical thermochemistry. J Phys Chem A 102:9890–9900CrossRefGoogle Scholar
  37. 37.
    Hu LH, Wang XJ, Wong LH, Chen GH (2003) Combined first-principles calculation and neural-network correction approach for heat of formation. J Chem Phys 119:11501–11507CrossRefGoogle Scholar
  38. 38.
    Winget P, Clark T (2004) Enthalpies of formation from B3LYP calculations. J Comput Chem 25:725–733CrossRefGoogle Scholar
  39. 39.
    Long DA, Anderson JB (2005) Bond-based corrections to semi-empirical and ab initio electronic structure calculations. Chem Phys Lett 402:524–528CrossRefGoogle Scholar
  40. 40.
    Friesner RA, Knoll EH, Cao Y (2006) A Localized orbital analysis of the thermochemical errors in hybrid density functional theory: achieving chemical accuracy via a simple empirical correction scheme. J Chem Phys 125:124107/1–124107/24CrossRefGoogle Scholar
  41. 41.
    Sun J, Wu J, Song T, Hu LH, Shan KL, Chen GH (2014) Alternative approach to chemical accuracy: a neural networks-based first-principles method for heat of formation of molecules made of H, C, N, O, F, S, and Cl. J Phys Chem A 118:9120–9131CrossRefGoogle Scholar
  42. 42.
    Zhang Y, Xu X, Goddard WA III (2009) Doubly hybrid density functional for accurate descriptions of nonbond interactions thermochemistry and thermochemical kinetics. Proc Natl Acad Sci USA 106:4963–4968CrossRefGoogle Scholar
  43. 43.
    Zhang IY, Xu X, Jung Y, Goddard WA III (2011) A fast doubly hybrid density functional method close to chemical accuracy using a local opposite spin ansatz. Proc Natl Acad Sci USA 108:19896–19900CrossRefGoogle Scholar
  44. 44.
    Zhang IY, Wu JM, Xu X (2010) Extending the reliability and applicability of B3LYP. Chem Commun 46:3057–3070CrossRefGoogle Scholar
  45. 45.
    Zhang IY, Xu X (2011) Doubly hybrid density functional for accurate description of thermochemistry thermochemical kinetics and nonbonded interactions. Int Rev Phys Chem 30:115–160CrossRefGoogle Scholar
  46. 46.
    Zhang IY, Xu X (2014) A New-generation density functional towards chemical accuracy for chemistry of main group elements. Springer, HeidelbergCrossRefGoogle Scholar
  47. 47.
    Zhang IY, Su NQ, Brémond EAG, Adamo C, Xu X (2012) Doubly hybrid density functional xDH-PBE0 from a parameter-free global hybrid model PBE0. J Chem Phys 123:174103/1–8Google Scholar
  48. 48.
    Su NQ, Xu X (2014) Construction of a parameter-free doubly hybrid density functional from adiabatic connection. J Chem Phys 140:18A512/1–15CrossRefGoogle Scholar
  49. 49.
    Becke AD, Johnson ER (2005) A density-functional model of the dispersion interaction. J Chem Phys 123:154101/1–9CrossRefGoogle Scholar
  50. 50.
    Curtiss LA, Raghavachari K, Redfern PC, Pople JA (2000) Assessment of Gaussian-3 and density functional theories for a larger experimental test set. J Chem Phys 112:7374–7383CrossRefGoogle Scholar
  51. 51.
    Su NQ, Zhang IY, Xu X (2013) Analytic derivatives for the XYG3 type of doubly hybrid density functionals: theory, implementation, and assessment. J Comput Chem 34:1759–1774CrossRefGoogle Scholar
  52. 52.
    Su NQ, Adamo C, Xu X (2013) A comparison of geometric parameters from PBE-based doubly hybrid density functionals PBE0-DH, PBE0-2, and xDH-PBE0. J Chem Phys 139:174106/1–12CrossRefGoogle Scholar
  53. 53.
    Gaussian 09, Revision D.01 (2013) 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 J A, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Keith T, 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, Gaussian, Inc., WallingfordGoogle Scholar
  54. 54.
    Good WD (1969) Enthalpies of combustion and formation of 11 isomeric nonanes. J Chem Eng Data 14:231–235CrossRefGoogle Scholar
  55. 55.
    Pashchenko LL, Kuznetsova TS (2007) The enthalpies of vaporization of some hydrocarbons with three-membered rings. Russ J Phys Chem 81:1738–1742CrossRefGoogle Scholar
  56. 56.
    Fraser FM, Prosen EJ (1955) Heats of combustion of liquid n-hexadecane, 1-hexadecene, n-decylbenzene, n-decylcyclohexane, n-decylcyclopentane, and the variation of heat of combustion with chain length. J Res NBS 55:329–333Google Scholar
  57. 57.
    Morawetz E (1972) Enthalpies of vaporization of n-alkanes from C12 to C20. J Chem Thermodyn 4:139–144CrossRefGoogle Scholar
  58. 58.
    Keshavarz MH, Zamani M, Atabaki F, Monjezi KH (2013) Reliable Approach for prediction of heats of formation of polycyclic saturated hydrocarbons using recently developed density functionals. Comput Theor Chem 1011:30–36CrossRefGoogle Scholar
  59. 59.
    Wodrich MD, Corminboeuf C, Schreiner PR, Fokin AA, PvR Schleyer (2007) How accurate are DFT treatments of organic energies? Org Lett 9:1851–1854CrossRefGoogle Scholar
  60. 60.
    Su NQ, Xu X (2015) Toward the construction of parameter-free doubly hybrid density functionals. Int J Quantum Chem 115:589–595CrossRefGoogle Scholar
  61. 61.
    Su NQ, Xu X (2015) Error accumulations in adhesive energies of dihydrogen molecular chains: performances of the XYG3 type of doubly hybrid density functionals. J Phys Chem A 119:1590–1599CrossRefGoogle Scholar
  62. 62.
    Su NQ, Yang WT, Mori-Sánchez P, Xu X (2014) Fractional charge behavior and band gap predictions with the XYG3 type of doubly hybrid density functionals. J Phys Chem A 118:9201–9211CrossRefGoogle Scholar
  63. 63.
    Taskinen E (2009) Enthalpies of formation and isomerization of aromatic hydrocarbons and ethers by G3(MP2)//B3LYP calculations. J Phys Org Chem 22:632–642CrossRefGoogle Scholar
  64. 64.
    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 106:1063–1079CrossRefGoogle Scholar
  65. 65.
    Ma X, Schobert HH (2000) Estimating heats of formation of hydrocarbon radicals by a combination of semiempirical calculation and family correlation with experimental values. J Phys Chem A 104:1064–1074CrossRefGoogle Scholar
  66. 66.
    Vysotsky YB, Bryantsev VS (2004) Calculation of thermochemical properties of conjugated radicals. Int J Quantum Chem 96:123–135CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Laboratory for Computational Physical Science, Department of ChemistryFudan UniversityShanghaiChina

Personalised recommendations