Dispersion corrections applied to the TCA family of exchange-correlation functionals


Dispersion corrections, namely the D3 and VV10 methodologies, have been added to the TCA GGA-like family of functionals. Without corrections, these functionals give very good results for iono-covalent systems, but they are inferior to other GGAs (e.g., PBE) for weakly interacting complexes. Applying dispersion corrections, this failure is completely overcome. In particular, RevTCA, which is the best functional for iono-covalent systems, becomes the best for weakly interacting complexes too, with mean absolute errors very often smaller than one tenth of \({\AA }\) for the geometries and 1 kcal/mol for the dissociation energies.

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  1. 1.

    The RC functional was tested on molecules. RC solid-state calculations are reported in Refs. [58, 59]. It performs considerably better than the standard LDA.


  1. 1.

    Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev 136:B864–B871. doi:10.1103/PhysRev.136.B864

    Article  Google Scholar 

  2. 2.

    Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140:A1133–A1138. doi:10.1103/PhysRev.140.A1133

    Article  Google Scholar 

  3. 3.

    Scuseria GE, Staroverov VN (2005) Progress in the development of exchange-correlation functionals. In: Dykstra CE, Frenking G, Kim KS, Scuseria GE (eds) Theory and applications of computational chemistry: the first 40 years (a volume of technical and historical perspectives). Elsevier, Amsterdam, pp 669–724

  4. 4.

    Della Sala F, Fabiano E, Constantin LA (2016) Kinetic-energy-density dependent semilocal exchange-correlation functionals. Int J Quantum Chem 116(22):1641–1694. doi:10.1002/qua.25224

    CAS  Article  Google Scholar 

  5. 5.

    Peverati R, Truhlar DG (2014) Quest for a universal density functional: the accuracy of density functionals across a broad spectrum of databases in chemistry and physics. Philos Trans R Soc Lond A Math Phys Eng Sci 372(2011):20120476. doi:10.1098/rsta.2012.0476.http://rsta.royalsocietypublishing.org/content/372/2011/20120476, http://rsta.royalsocietypublishing.org/content/372/2011/20120476.full.pdf

  6. 6.

    Yu HS, He X, Truhlar DG (2016) MN15-L: a new local exchange-correlation functional for Kohn–Sham density functional theory with broad accuracy for atoms, molecules, and solids. J Chem Theory Comput 12(3):1280–1293. doi:10.1021/acs.jctc.5b01082

    CAS  Article  Google Scholar 

  7. 7.

    Guido CA, Brémond E, Adamo C, Cortona P (2013) Communication: one third: a new recipe for the PBE0 paradigm. J Chem Phys 138(2):021104. doi:10.1063/1.4775591

    Article  Google Scholar 

  8. 8.

    Fabiano E, Constantin LA, Cortona P, Della Sala F (2015) Global hybrids from the semiclassical atom theory satisfying the local density linear response. J Chem Theory Comput 11(1):122–131. doi:10.1021/ct500902p

    CAS  Article  Google Scholar 

  9. 9.

    Constantin LA, Fabiano E, Della Sala F (2013) Meta-GGA exchange-correlation functional with a balanced treatment of nonlocality. J Chem Theory Comput 9(5):2256–2263. doi:10.1021/ct400148r

    CAS  Article  Google Scholar 

  10. 10.

    Goerigk L, Grimme S (2011) Efficient and accurate double-hybrid-meta-GGA density functionals evaluation with the extended GMTKN30 database for general main group thermochemistry, kinetics, and noncovalent interactions. J Chem Theory Comput 7(2):291–309. doi:10.1021/ct100466k

    CAS  Article  Google Scholar 

  11. 11.

    Zhao Y, Truhlar DG (2005a) Design of density functionals that are broadly accurate for thermochemistry, thermochemical kinetics, and nonbonded interactions. J Phys Chem A 109(25):5656–5667. doi:10.1021/jp050536c

    CAS  Article  Google Scholar 

  12. 12.

    Zhao Y, Truhlar DG (2005b) Benchmark databases for nonbonded interactions and their use to test density functional theory. J Chem Theory Comput 1(3):415–432. doi:10.1021/ct049851d

    CAS  Article  Google Scholar 

  13. 13.

    Burns LA, Vázquez-Mayagoitia A, Sumpter BG, Sherrill CD (2011) Density-functional approaches to noncovalent interactions: a comparison of dispersion corrections (DFT-D), exchange-hole dipole moment (XDM) theory, and specialized functionals. J Chem Phys 134(8):084107. doi:10.1063/1.3545971

    Article  Google Scholar 

  14. 14.

    Marom N, Tkatchenko A, Rossi M, Gobre VV, Hod O, Scheffler M, Kronik L (2011) Dispersion interactions with density-functional theory: benchmarking semiempirical and interatomic pairwise corrected density functionals. J Chem Theory Comput 7(12):3944–3951. doi:10.1021/ct2005616

    CAS  Article  Google Scholar 

  15. 15.

    DiLabio GA, Otero-de-la Roza A (2016) Noncovalent interactions in density functional theory. Wiley, New York. doi:10.1002/9781119148739.ch1

    Book  Google Scholar 

  16. 16.

    Riley KE, Pitoňák M, Jurečka P, Hobza P (2010) Stabilization and structure calculations for noncovalent interactions in extended molecular systems based on wave function and density functional theories. Chem Rev 110(9):5023–5063. doi:10.1021/cr1000173

    CAS  Article  Google Scholar 

  17. 17.

    Grimme S (2011) Density functional theory with London dispersion corrections. Wiley Interdiscip Rev Comput Mol Sci 1(2):211–228. doi:10.1002/wcms.30

    CAS  Article  Google Scholar 

  18. 18.

    Hermann J, DiStasio RA, Tkatchenko A (2017) First-principles models for van der Waals interactions in molecules and materials: concepts, theory, and applications. Chem Rev 117(6):4714–4758. doi:10.1021/acs.chemrev.6b00446

    CAS  Article  Google Scholar 

  19. 19.

    Tkatchenko A (2015) Current understanding of van der waals effects in realistic materials. Adv Funct Mater 25(13):2054–2061. doi:10.1002/adfm.201403029

    CAS  Article  Google Scholar 

  20. 20.

    Corminboeuf C (2014) Minimizing density functional failures for non-covalent interactions beyond van der waals complexes. Acc Chem Res 47(11):3217–3224. doi:10.1021/ar400303a

    CAS  Article  Google Scholar 

  21. 21.

    Wu J, 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(16):1021–1031. doi:10.1002/qua.24919

    CAS  Article  Google Scholar 

  22. 22.

    Gao T, Li H, Li W, Li L, Fang C, Li H, Hu L, Lu Y, Su ZM (2016) A machine learning correction for DFT non-covalent interactions based on the S22, S66 and X40 benchmark databases. J Cheminform 8(1):24. doi:10.1186/s13321-016-0133-7

    Article  Google Scholar 

  23. 23.

    Grimme S, Hansen A, Brandenburg JG, Bannwarth C (2016) Dispersion-corrected mean-field electronic structure methods. Chem Rev 116(9):51055154. doi:10.1021/acs.chemrev.5b00533

    Article  Google Scholar 

  24. 24.

    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):215–241. doi:10.1007/s00214-007-0310-x

    CAS  Article  Google Scholar 

  25. 25.

    Goerigk L, Grimme S (2014) Double-hybrid density functionals. Wiley Interdiscip Rev Comput Mol Sci 4(6):576–600. doi:10.1002/wcms.1193

    CAS  Article  Google Scholar 

  26. 26.

    Reilly AM, Tkatchenko A (2015) Van der waals dispersion interactions in molecular materials: beyond pairwise additivity. Chem Sci 6:3289–3301. doi:10.1039/C5SC00410A

    CAS  Article  Google Scholar 

  27. 27.

    Wu Q, Yang W (2002) Empirical correction to density functional theory for van der waals interactions. J Chem Phys 116(2):515–524. doi:10.1063/1.1424928

    CAS  Article  Google Scholar 

  28. 28.

    Johnson ER, Becke AD (2005) A post-Hartree–Fock model of intermolecular interactions. J Chem Phys 123(2):024101. doi:10.1063/1.1949201

    Article  Google Scholar 

  29. 29.

    Grimme S (2004) Accurate description of van der waals complexes by density functional theory including empirical corrections. J Comput Chem 25(12):1463–1473. doi:10.1002/jcc.20078

    CAS  Article  Google Scholar 

  30. 30.

    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

    CAS  Article  Google Scholar 

  31. 31.

    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(15):154104. doi:10.1063/1.3382344

    Article  Google Scholar 

  32. 32.

    Tkatchenko A, Scheffler M (2009) Accurate molecular van der waals interactions from ground-state electron density and free-atom reference data. Phys Rev Lett 102:073005. doi:10.1103/PhysRevLett.102.073005

    Article  Google Scholar 

  33. 33.

    Langreth DC, Dion M, Rydberg H, Schrder E, Hyldgaard P, Lundqvist BI (2005) Van der waals density functional theory with applications. Int J Quantum Chem 101(5):599–610. doi:10.1002/qua.20315

    CAS  Article  Google Scholar 

  34. 34.

    Vydrov OA, Van Voorhis T (2009) Nonlocal van der waals density functional made simple. Phys Rev Lett 103:063004. doi:10.1103/PhysRevLett.103.063004

    Article  Google Scholar 

  35. 35.

    Vydrov OA, Van Voorhis T (2010) Nonlocal van der waals density functional: the simpler the better. J Chem Phys 133(24):244103. doi:10.1063/1.3521275

    Article  Google Scholar 

  36. 36.

    Hujo W, Grimme S (2011) Performance of the van der waals density functional VV10 and (hybrid)GGA variants for thermochemistry and noncovalent interactions. J Chem Theory Comput 7(12):3866–3871. doi:10.1021/ct200644w

    CAS  Article  Google Scholar 

  37. 37.

    Jurečka P, Černỳ J, Hobza P, Salahub DR (2007) Density functional theory augmented with an empirical dispersion term. interaction energies and geometries of 80 noncovalent complexes compared with ab initio quantum mechanics calculations. J Comput Chem 28(2):555–569. doi:10.1002/jcc.20570

    Article  Google Scholar 

  38. 38.

    Thanthiriwatte KS, Hohenstein EG, Burns LA, Sherrill CD (2011) Assessment of the performance of DFT and DFT-D methods for describing distance dependence of hydrogen-bonded interactions. J Chem Theory Comput 7(1):88–96. doi:10.1021/ct100469b

    CAS  Article  Google Scholar 

  39. 39.

    Hujo W, Grimme S (2011) Comparison of the performance of dispersion-corrected density functional theory for weak hydrogen bonds. Phys Chem Chem Phys 13:13942–13950. doi:10.1039/C1CP20591A

    CAS  Article  Google Scholar 

  40. 40.

    Fabiano E, Constantin LA, Della Sala F (2014) Wave function and density functional theory studies of dihydrogen complexes. J Chem Theory Comput 10(8):3151–3162. doi:10.1021/ct500350n, pMID: 26588286

  41. 41.

    Roy D, Marianski M, Maitra NT, Dannenberg JJ (2012) Comparison of some dispersion-corrected and traditional functionals with CCSD(T) and MP2 ab initio methods: Dispersion, induction, and basis set superposition error. J Chem Phys 137(13):134109. doi:10.1063/1.4755990

    Article  Google Scholar 

  42. 42.

    Schneebeli ST, Bochevarov AD, Friesner RA (2011) Parameterization of a B3LYP specific correction for noncovalent interactions and basis set superposition error on a gigantic data set of CCSD(T) quality noncovalent interaction energies. J Chem Theory Comput 7(3):658–668. doi:10.1021/ct100651f

    CAS  Article  Google Scholar 

  43. 43.

    Sedlak R, Janowski T, Pitoňák M, Řezáč J, Pulay P, Hobza P (2013) Accuracy of quantum chemical methods for large noncovalent complexes. J Chem Theory Comput 9(8):3364–3374. doi:10.1021/ct400036b

    CAS  Article  Google Scholar 

  44. 44.

    Becke AD (1988) Density-functional exchange-energy approximation with correct asymptotic behavior. Phys Rev A 38:3098–3100. doi:10.1103/PhysRevA.38.3098

    CAS  Article  Google Scholar 

  45. 45.

    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. doi:10.1103/PhysRevB.37.785

    CAS  Article  Google Scholar 

  46. 46.

    Pernal K, Podeszwa R, Patkowski K, Szalewicz K (2009) Dispersionless density functional theory. Phys Rev Lett 103:263201. doi:10.1103/PhysRevLett.103.263201

    Article  Google Scholar 

  47. 47.

    Tognetti V, Cortona P, Adamo C (2008a) A new parameter-free correlation functional based on an average atomic reduced density gradient analysis. J Chem Phys 128(3):034101. doi:10.1063/1.2816137

    Article  Google Scholar 

  48. 48.

    Tognetti V, Cortona P, Adamo C (2008) Increasing physical constraints and improving performances in a parameter-free GGA functional. Chem Phys Lett 460(46):536–539. doi:10.1016/j.cplett.2008.06.032. http://www.sciencedirect.com/science/article/pii/S0009261408008464

  49. 49.

    Brémond É, Pilard D, Ciofini I, Chermette H, Adamo C, Cortona P (2012) Generalized gradient exchange functionals based on the gradient-regulated connection: a new member of the TCA family. Theor Chem Acc 131(3):1184. doi:10.1007/s00214-012-1184-0

    Article  Google Scholar 

  50. 50.

    Ragot S, Cortona P (2004) Correlation energy of many-electron systems: a modified Colle–Salvetti approach. J Chem Phys 121(16):7671–7680. doi:10.1063/1.1792153

    CAS  Article  Google Scholar 

  51. 51.

    Tognetti V, Cortona P, Adamo C (2007) Chem Phys Lett 439:381

    CAS  Article  Google Scholar 

  52. 52.

    Tognetti V, Adamo C, Cortona P (2007) Chem Phys 337:161

    CAS  Article  Google Scholar 

  53. 53.

    Tognetti V, Cortona P, Adamo C (2009a) Activation enthalpies of pericyclic reactions: the performances of some recently proposed functionals. Theor Chem Acc 122(5):257–264. doi:10.1007/s00214-008-0503-y

    CAS  Article  Google Scholar 

  54. 54.

    Tognetti V, Joubert L, Cortona P, Adamo C (2009b) Toward a combined DFT/QTAIM description of agostic bonds: the critical case of a Nb(III) complex. J Phys Chem A 113(44):12322–12327. doi:10.1021/jp9045534

    CAS  Article  Google Scholar 

  55. 55.

    Tognetti V, Cortona P, Adamo C (2010a) Assessing the performances of some recently proposed density functionals for the description of bond dissociations involving organic radicals. Int J Quantum Chem 110(12):2320–2329. doi:10.1002/qua.22571

    CAS  Article  Google Scholar 

  56. 56.

    Tognetti V, Adamo C, Cortona P (2010b) Density-functional calculations for large systems: Can GGA functionals be competitive with hybrid functionals? Interdiscip Sci Comput Life Sci 2(2):163–168. doi:10.1007/s12539-010-0073-2

    Article  Google Scholar 

  57. 57.

    Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865–3868. doi:10.1103/PhysRevLett.77.3865

    CAS  Article  Google Scholar 

  58. 58.

    Fabiano E, Constantin LA, Terentjevs A, Della Sala F, Cortona P (2015) Assessment of the TCA functional in computational chemistry and solid-state physics. Theor Chem Acc 134(11):139. doi:10.1007/s00214-015-1740-5

    Article  Google Scholar 

  59. 59.

    Labat F, Brémond E, Cortona P, Adamo C (2013) Assessing modern GGA functionals for solids. J Mol Model 19(7):2791–2796. doi:10.1007/s00894-012-1646-2

    CAS  Article  Google Scholar 

  60. 60.

    Cedillo A, Torrent M, Cortona P (2016) Stability of the different AlOOH phases under pressure. J Phys Condens Matter 28(18):185401. http://stacks.iop.org/0953-8984/28/i=18/a=185401

  61. 61.

    Perdew JP, Ruzsinszky A, Csonka GI, Vydrov OA, Scuseria GE, Constantin LA, Zhou X, Burke K (2008) Restoring the density-gradient expansion for exchange in solids and surfaces. Phys Rev Lett 100:136406. doi:10.1103/PhysRevLett.100.136406

    Article  Google Scholar 

  62. 62.

    Fabiano E, Constantin LA, Della Sala F (2010) Generalized gradient approximation bridging the rapidly and slowly varying density regimes: a PBE-like functional for hybrid interfaces. Phys Rev B 82:113104. doi:10.1103/PhysRevB.82.113104

    Article  Google Scholar 

  63. 63.

    Grüning M, Gritsenko OV, van Gisbergen SJA, Baerends EJ (2001) Shape corrections to exchange-correlation potentials by gradient-regulated seamless connection of model potentials for inner and outer region. J Chem Phys 114(2):652–660. doi:10.1063/1.1327260

    Article  Google Scholar 

  64. 64.

    Zhang Y, Pan W, Yang W (1997) Describing van der waals interaction in diatomic molecules with generalized gradient approximations: The role of the exchange functional. J Chem Phys 107(19):7921–7925. doi:10.1063/1.475105

    CAS  Article  Google Scholar 

  65. 65.

    Brémond É, Kalhor MP, Bousquet D, Mignon P, Ciofini I, Adamo C, Cortona P, Chermette H (2013) Assessing the performances of some recently proposed density functionals for the description of organometallic structures. Theor Chem Acc 132(12):1401. doi:10.1007/s00214-013-1401-5

    Article  Google Scholar 

  66. 66.

    Cooper V (2010) Van der waals density functional: an appropriate exchange functional. Phys Rev B 81:161104(R). doi:10.1103/PhysRevB.81.161104

    Article  Google Scholar 

  67. 67.

    Jurečka P, Şponer J, Černý J, Hobza P (2006) Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, dna base pairs, and amino acid pairs. Phys Chem Chem Phys 8:1985–1993. doi:10.1039/B600027D

    Article  Google Scholar 

  68. 68.

    Marshall MS, Burns LA, Sherrill CD (2011) Basis set convergence of the coupled-cluster correction, MP2CCSD(T): best practices for benchmarking non-covalent interactions and the attendant revision of the S22, NBC10, HBC6, and HSG databases. J Chem Phys 135(19):194102. doi:10.1063/1.3659142

    Article  Google Scholar 

  69. 69.

    Schäfer A, Huber C, Ahlrichs R (1994) Fully optimized contracted gaussian basis sets of triple zeta valence quality for atoms Li to Kr. J Chem Phys 100(8):5829–5835. doi:10.1063/1.467146

    Article  Google Scholar 

  70. 70.

    Weigend F, Ahlrichs R (2005) Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: design and assessment of accuracy. Phys Chem Chem Phys 7:3297–3305. doi:10.1039/B508541A

    CAS  Article  Google Scholar 

  71. 71.

    Aragó J, Ortí E, Sancho-García JC (2013) Nonlocal van der waals approach merged with double-hybrid density functionals: toward the accurate treatment of noncovalent interactions. J Chem Theory Comput 9(8):3437–3443. doi:10.1021/ct4003527

    Article  Google Scholar 

  72. 72.

    TURBOMOLE (2017) TURBOMOLE, V7.0; TURBOMOLE GmbH: Karlsruhe, Germany, 2011. http://www.turbomole.com. Accessed Mar 2017

  73. 73.

    Furche F, Ahlrichs R, Hättig C, Klopper W, Sierka M, Weigend F (2014) Turbomole. Wiley Interdiscip Rev Comput Mol Sci 4(2):91–100. doi:10.1002/wcms.1162

    CAS  Article  Google Scholar 

  74. 74.

    Rappoport D, Furche F (2010) Property-optimized gaussian basis sets for molecular response calculations. J Chem Phys 133(13):134105. doi:10.1063/1.3484283

    Article  Google Scholar 

  75. 75.

    Řezáč J, Riley KE, Hobza P (2011) S66: a well-balanced database of benchmark interaction energies relevant to biomolecular structures. J Chem Theory Comput 7(8):2427–2438. doi:10.1021/ct2002946

    Article  Google Scholar 

  76. 76.

    Lynch BJ, Truhlar DG (2003) Small representative benchmarks for thermochemical calculations. J Phys Chem A 107(42):8996–8999. doi:10.1021/jp035287b

    CAS  Article  Google Scholar 

  77. 77.

    Haunschild R, Klopper W (2012) Theoretical reference values for the AE6 and BH6 test sets from explicitly correlated coupled-cluster theory. Theor Chem Acc 131(2):1112. doi:10.1007/s00214-012-1112-3

    Article  Google Scholar 

  78. 78.

    Lynch BJ, Truhlar DG (2003) Robust and affordable multicoefficient methods for thermochemistry and thermochemical kinetics: the MCCM/3 suite and SAC/3. J Phys Chem A 107(19):3898–3906. doi:10.1021/jp0221993

    CAS  Article  Google Scholar 

  79. 79.

    Zhao Y, Truhlar DG (2006) A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions. J Chem Phys 125(19):194101. doi:10.1063/1.2370993

    Article  Google Scholar 

  80. 80.

    Gráfová L, Pitoňák M, Řezáč J, Hobza P (2010) Comparative study of selected wave function and density functional methods for noncovalent interaction energy calculations using the extended s22 data set. J Chem Theory Comput 6(8):2365–2376. doi:10.1021/ct1002253. pMID: 26613492

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We thank TURBOMOLE GmbH for providing the TURBOMOLE program package. E. Fabiano acknowledges the partial funding of this work from a CentraleSupélec visiting professorship.

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Fabiano, E., Cortona, P. Dispersion corrections applied to the TCA family of exchange-correlation functionals. Theor Chem Acc 136, 88 (2017). https://doi.org/10.1007/s00214-017-2120-0

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  • Density functional theory
  • TCA correlation
  • Dispersion correction
  • Non-covalent interactions