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5.3 Overview of Available Functionals

5.3.3 Exchange Functionals

(May 21, 2025)

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) 320 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 426 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 1013 Perdew J. P., Burke K., Ernzerhof M.
      Phys. Rev. Lett.
      (1996), 77, pp. 3865.
      Link

    • B88: Becke exchange functional from 1988 93 Becke A. D.
      Phys. Rev. A
      (1988), 38, pp. 3098.
      Link

    • revPBE: Zhang and Yang one-parameter modification of the PBE exchange functional 1477 Zhang Y., Yang W.
      Phys. Rev. Lett.
      (1998), 80, pp. 890.
      Link

    • AK13: Armiento-Kümmel exchange functional from 2013 51 Armiento R., Kümmel S.
      Phys. Rev. Lett.
      (2013), 111, pp. 036402.
      Link

    • B86: Becke exchange functional (Xαβγ) from 1986 90 Becke A. D.
      J. Chem. Phys.
      (1986), 84, pp. 4524.
      Link

    • G96: Gill exchange functional from 1996 435 Gill P. M. W.
      Mol. Phys.
      (1996), 89, pp. 433.
      Link

    • mB86: Becke “modified gradient correction” exchange functional from 1986 91 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 590 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 590 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 450 Goll E., Werner H.-J., Stoll H.
      Phys. Chem. Chem. Phys.
      (2005), 7, pp. 3917.
      Link
      , 449 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 677 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 497 Handy N. C., Cohen A. J.
      Mol. Phys.
      (2001), 99, pp. 403.
      Link

    • PBEsol: PBE exchange functional modified for solids 1018 Perdew J. P. et al.
      Phys. Rev. Lett.
      (2008), 100, pp. 136406.
      Link

    • PW86: Perdew-Wang exchange functional from 1986 1024 Perdew J. P., Wang Y.
      Phys. Rev. B
      (1986), 33, pp. 8800.
      Link

    • PW91: Perdew-Wang exchange functional from 1991 1014 Perdew J. P. et al.
      Phys. Rev. B
      (1992), 46, pp. 6671.
      Link

    • RPBE: Hammer, Hansen, and Norskov exchange functional (modification of PBE) 494 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 931 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 1488 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 534 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 1287 Tao J. et al.
      Phys. Rev. Lett.
      (2003), 91, pp. 146401.
      Link

    • revTPSS: Revised version of the TPSS exchange functional 1017 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) 257 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 1020 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 444 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 831 Loos P.-F.
      J. Chem. Phys.
      (2017), 146, pp. 114108.
      Link

    • PKZB: Perdew, Kurth, Zupan, and Blaha exchange functional 1015 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 1141 Ruzsinszky A. et al.
      J. Chem. Theory Comput.
      (2012), 8, pp. 2078.
      Link

    • SCAN: Strongly Constrained and Appropriately Normed exchange functional 1270 Sun J., Ruzsinszky A., Perdew J. P.
      Phys. Rev. Lett.
      (2015), 115, pp. 036402.
      Link

    • rSCAN: Regularized SCAN exchange 81 Bartok A. P., Yates J. R.
      J. Chem. Phys.
      (2019), 150, pp. 161101.
      Link
      , 404 Furness J. W. et al.
      J. Chem. Phys.
      (2022), 156, pp. 034109.
      Link

    • r++SCAN: Regularized SCAN with uniform density limit and coordinate scaling behavior 404 Furness J. W. et al.
      J. Chem. Phys.
      (2022), 156, pp. 034109.
      Link

    • r2SCAN: Re-Regularized SCAN exchange 402 Furness J. W. et al.
      J. Phys. Chem. Lett.
      (2020), 11, pp. 8208.
      Link
      , 403 Furness J. W. et al.
      J. Phys. Chem. Lett.
      (2020), 11, pp. 9248.
      Link
      , 404 Furness J. W. et al.
      J. Chem. Phys.
      (2022), 156, pp. 034109.
      Link

    • r4SCAN: Regularized SCAN with exact constraints obeyed by SCAN 404 Furness J. W. et al.
      J. Chem. Phys.
      (2022), 156, pp. 034109.
      Link

    • revSCAN: Revised SCAN exchange 908 Mezei P. D., Csonka G. I., Kállay M.
      J. Chem. Theory Comput.
      (2018), 14, pp. 2469.
      Link

    • TM: Tao-Mo exchange functional derived via an accurate modeling of the conventional exchange hole 1286 Tao J., Mo Y.
      Phys. Rev. Lett.
      (2016), 117, pp. 073001.
      Link

    • regTM: Regularized TM exchange 998 Patra A., Jana S., Samal P.
      J. Chem. Phys.
      (2020), 153, pp. 184112.
      Link

    • revTM: Revised TM exchange 609 Jana S., Sharma K., Samal P.
      J. Phys. Chem. A
      (2019), 123, pp. 6356.
      Link

    • TASK: TASK exchange functional 52 Aschebrock T., Kümmel S.
      Phys. Rev. Research
      (2019), 1, pp. 033082.
      Link

    • mTASK: Modified TASK exchange functional 949 Neupane B. et al.
      Phys. Rev. Materials
      (2021), 5, pp. 063803.
      Link