5.3 Overview of Available Functionals

5.3.2 Exchange Functionals

(June 30, 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) 267 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 353 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 839 Perdew J. P., Burke K., Ernzerhof M.
      Phys. Rev. Lett.
      (1996), 77, pp. 3865.
      Link

    • B88: Becke exchange functional from 1988 75 Becke A. D.
      Phys. Rev. A
      (1988), 38, pp. 3098.
      Link

    • revPBE: Zhang and Yang one-parameter modification of the PBE exchange functional 1241 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 72 Becke A. D.
      J. Chem. Phys.
      (1986), 84, pp. 4524.
      Link

    • G96: Gill exchange functional from 1996 361 Gill P. M. W.
      Mol. Phys.
      (1996), 89, pp. 433.
      Link

    • mB86: Becke “modified gradient correction” exchange functional from 1986 73 Becke A. D.
      J. Chem. Phys.
      (1986), 85, pp. 7184.
      Link

    • mPW91: modified version (Adamo and Barone) of the 1991 Perdew-Wang exchange functional 19 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 484 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 484 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 374 Goll E., Werner H.-J., Stoll H.
      Phys. Chem. Chem. Phys.
      (2005), 7, pp. 3917.
      Link
      , 373 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 557 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 404 Handy N. C., Cohen A. J.
      Mol. Phys.
      (2001), 99, pp. 403.
      Link

    • PBEsol: PBE exchange functional modified for solids 844 Perdew J. P. et al.
      Phys. Rev. Lett.
      (2008), 100, pp. 136406.
      Link

    • PW86: Perdew-Wang exchange functional from 1986 849 Perdew J. P., Wang Y.
      Phys. Rev. B
      (1986), 33, pp. 8800.
      Link

    • PW91: Perdew-Wang exchange functional from 1991 840 Perdew J. P. et al.
      Phys. Rev. B
      (1992), 46, pp. 6671.
      Link

    • RPBE: Hammer, Hansen, and Norskov exchange functional (modification of PBE) 401 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 777 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 1249 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 439 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 1080 Tao J. et al.
      Phys. Rev. Lett.
      (2003), 91, pp. 146401.
      Link

    • revTPSS: Revised version of the TPSS exchange functional 843 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) 215 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 845 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 369 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 698 Loos P.-F.
      J. Chem. Phys.
      (2017), 146, pp. 114108.
      Link

    • PKZB: Perdew, Kurth, Zupan, and Blaha exchange functional 841 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 953 Ruzsinszky A. et al.
      J. Chem. Theory Comput.
      (2012), 8, pp. 2078.
      Link

    • SCAN: Strongly Constrained and Appropriately Normed exchange functional 1066 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 1079 Tao J., Mo Y.
      Phys. Rev. Lett.
      (2016), 117, pp. 073001.
      Link