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5.3 Overview of Available Functionals

5.3.3 Exchange Functionals

(December 20, 2021)

Note:  All exchange functionals in this section can be invoked using the $rem variable EXCHANGE. Popular and/or recommended functionals within each class are listed first and indicated in bold. The rest are in alphabetical order.

  • Local Spin-Density Approximation (LSDA)

    • Slater: Slater-Dirac exchange functional (Xα method with α=2/3) 272 Dirac P. A. M.
      P. Camb. Philos. Soc.
      (1930), 26, pp. 376.
      Link

    • SR_LSDA (BNL): Short-range version of the Slater-Dirac exchange functional 362 Gill P. M. W., Adamson R. D., Pople J. A.
      Mol. Phys.
      (1996), 88, pp. 1005.
      Link

  • Generalized Gradient Approximation (GGA)

    • PBE: Perdew, Burke, and Ernzerhof exchange functional 867 Perdew J. P., Burke K., Ernzerhof M.
      Phys. Rev. Lett.
      (1996), 77, pp. 3865.
      Link

    • B88: Becke exchange functional from 1988 77 Becke A. D.
      Phys. Rev. A
      (1988), 38, pp. 3098.
      Link

    • revPBE: Zhang and Yang one-parameter modification of the PBE exchange functional 1276 Zhang Y., Yang W.
      Phys. Rev. Lett.
      (1998), 80, pp. 890.
      Link

    • AK13: Armiento-Kümmel exchange functional from 2013 44 Armiento R., Kümmel S.
      Phys. Rev. Lett.
      (2013), 111, pp. 036402.
      Link

    • B86: Becke exchange functional (Xαβγ) from 1986 74 Becke A. D.
      J. Chem. Phys.
      (1986), 84, pp. 4524.
      Link

    • G96: Gill exchange functional from 1996 370 Gill P. M. W.
      Mol. Phys.
      (1996), 89, pp. 433.
      Link

    • mB86: Becke “modified gradient correction” exchange functional from 1986 75 Becke A. D.
      J. Chem. Phys.
      (1986), 85, pp. 7184.
      Link

    • mPW91: modified version (Adamo and Barone) of the 1991 Perdew-Wang exchange functional 18 Adamo C., Barone V.
      J. Chem. Phys.
      (1998), 108, pp. 664.
      Link

    • muB88 (μB88): Short-range version of the B88 exchange functional by Hirao and coworkers 500 Iikura H. et al.
      J. Chem. Phys.
      (2001), 115, pp. 3540.
      Link

    • muPBE (μPBE): Short-range version of the PBE exchange functional by Hirao and coworkers 500 Iikura H. et al.
      J. Chem. Phys.
      (2001), 115, pp. 3540.
      Link

    • srPBE: Short-range version of the PBE exchange functional by Goll and coworkers 382 Goll E., Werner H.-J., Stoll H.
      Phys. Chem. Chem. Phys.
      (2005), 7, pp. 3917.
      Link
      , 381 Goll E. et al.
      Chem. Phys.
      (2006), 329, pp. 276.
      Link

    • optB88: Refit version of the original B88 exchange functional (for use with vdW-DF-04) by Michaelides and coworkers 574 Klimeš J., Bowler D. R., Michaelides A.
      J. Phys. Condens. Matter
      (2010), 22, pp. 022201.
      Link

    • OPTX: Two-parameter exchange functional by Handy and Cohen 415 Handy N. C., Cohen A. J.
      Mol. Phys.
      (2001), 99, pp. 403.
      Link

    • PBEsol: PBE exchange functional modified for solids 872 Perdew J. P. et al.
      Phys. Rev. Lett.
      (2008), 100, pp. 136406.
      Link

    • PW86: Perdew-Wang exchange functional from 1986 877 Perdew J. P., Wang Y.
      Phys. Rev. B
      (1986), 33, pp. 8800.
      Link

    • PW91: Perdew-Wang exchange functional from 1991 868 Perdew J. P. et al.
      Phys. Rev. B
      (1992), 46, pp. 6671.
      Link

    • RPBE: Hammer, Hansen, and Norskov exchange functional (modification of PBE) 413 Hammer B., Hansen L. B., Nørskov J. K.
      Phys. Rev. B
      (1999), 59, pp. 7413.
      Link

    • rPW86: Revised version (Murray et al.) of the 1986 Perdew-Wang exchange functional 799 Murray É. D., Lee K., Langreth D. C.
      J. Chem. Theory Comput.
      (2009), 5, pp. 2754.
      Link

    • SOGGA: Second-order GGA functional by Zhao and Truhlar 1284 Zhao Y., Truhlar D. G.
      J. Chem. Phys.
      (2006), 128, pp. 184109.
      Link

    • wPBE (ωPBE): Henderson et al. model for the PBE GGA short-range exchange hole 450 Henderson T. M., Janesko B. G., Scuseria G. E.
      J. Chem. Phys.
      (2008), 128, pp. 194105.
      Link

  • Meta-Generalized Gradient Approximation (meta-GGA)

    • TPSS: Tao, Perdew, Staroverov, and Scuseria exchange functional 1112 Tao J. et al.
      Phys. Rev. Lett.
      (2003), 91, pp. 146401.
      Link

    • revTPSS: Revised version of the TPSS exchange functional 871 Perdew J. P. et al.
      Phys. Rev. Lett.
      (2009), 103, pp. 026403.
      Link

    • BLOC: Minor modification of the TPSS exchange functional that works best with TPSSloc correlation (both by Della Sala and coworkers) 219 Constantin L. A., Fabiano E., Sala F. Della
      J. Chem. Theory Comput.
      (2013), 9, pp. 2256.
      Link

    • modTPSS: One-parameter version of the TPSS exchange functional 873 Perdew J. P. et al.
      Phys. Rev. A
      (2007), 76, pp. 042506.
      Link

    • oTPSS: TPSS exchange functional with 5 refit parameters (for use with oTPSS correlation) by Grimme and coworkers 377 Goerigk L., Grimme S.
      J. Chem. Theory Comput.
      (2010), 6, pp. 107.
      Link

    • PBE-GX: First exchange functional based on a finite uniform electron gas (rather than an infinite UEG) by Pierre-François Loos 719 Loos P.-F.
      J. Chem. Phys.
      (2017), 146, pp. 114108.
      Link

    • PKZB: Perdew, Kurth, Zupan, and Blaha exchange functional 869 Perdew J. P. et al.
      Phys. Rev. Lett.
      (1999), 82, pp. 2544.
      Link

    • regTPSS: Regularized (fixed order of limits issue) version of the TPSS exchange functional 984 Ruzsinszky A. et al.
      J. Chem. Theory Comput.
      (2012), 8, pp. 2078.
      Link

    • SCAN: Strongly Constrained and Appropriately Normed exchange functional 1098 Sun J., Ruzsinszky A., Perdew J. P.
      Phys. Rev. Lett.
      (2015), 115, pp. 036402.
      Link

    • TM: Tao-Mo exchange functional derived via an accurate modeling of the conventional exchange hole 1111 Tao J., Mo Y.
      Phys. Rev. Lett.
      (2016), 117, pp. 073001.
      Link