5.3.3 Exchange Functionals

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.

• $\circ$

  Local Spin-Density Approximation (LSDA)

  • $\bullet$

    Slater: Slater-Dirac exchange functional (X$\alpha$ method with $\alpha =2/3$) ²⁸⁵ Dirac P. A. M.
    P. Camb. Philos. Soc.
    (1930), 26, pp. 376. Link

  • $\bullet$

    SR_LSDA (BNL): Short-range version of the Slater-Dirac exchange functional ³⁸² Gill P. M. W., Adamson R. D., Pople J. A.
    Mol. Phys.
    (1996), 88, pp. 1005. Link

• $\circ$

  Generalized Gradient Approximation (GGA)

  • $\bullet$

    PBE: Perdew, Burke, and Ernzerhof exchange functional ⁹²³ Perdew J. P., Burke K., Ernzerhof M.
    Phys. Rev. Lett.
    (1996), 77, pp. 3865. Link

  • $\bullet$

    B88: Becke exchange functional from 1988 ⁸¹ Becke A. D.
    Phys. Rev. A
    (1988), 38, pp. 3098. Link

  • $\bullet$

    revPBE: Zhang and Yang one-parameter modification of the PBE exchange functional ¹³⁴⁵ Zhang Y., Yang W.
    Phys. Rev. Lett.
    (1998), 80, pp. 890. Link

  • $\bullet$

    AK13: Armiento-Kümmel exchange functional from 2013 ⁴⁵ Armiento R., Kümmel S.
    Phys. Rev. Lett.
    (2013), 111, pp. 036402. Link

  • $\bullet$

    B86: Becke exchange functional (X$\alpha \beta \gamma$) from 1986 ⁷⁸ Becke A. D.
    J. Chem. Phys.
    (1986), 84, pp. 4524. Link

  • $\bullet$

    G96: Gill exchange functional from 1996 ³⁹¹ Gill P. M. W.
    Mol. Phys.
    (1996), 89, pp. 433. Link

  • $\bullet$

    mB86: Becke “modified gradient correction” exchange functional from 1986 ⁷⁹ Becke A. D.
    J. Chem. Phys.
    (1986), 85, pp. 7184. Link

  • $\bullet$

    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

  • $\bullet$

    muB88 ($\mu$B88): Short-range version of the B88 exchange functional by Hirao and coworkers ⁵²⁹ Iikura H. et al.
    J. Chem. Phys.
    (2001), 115, pp. 3540. Link

  • $\bullet$

    muPBE ($\mu$PBE): Short-range version of the PBE exchange functional by Hirao and coworkers ⁵²⁹ Iikura H. et al.
    J. Chem. Phys.
    (2001), 115, pp. 3540. Link

  • $\bullet$

    srPBE: Short-range version of the PBE exchange functional by Goll and coworkers ⁴⁰⁵ Goll E., Werner H.-J., Stoll H.
    Phys. Chem. Chem. Phys.
    (2005), 7, pp. 3917. Link ^{, 404} Goll E. et al.
    Chem. Phys.
    (2006), 329, pp. 276. Link

  • $\bullet$

    optB88: Refit version of the original B88 exchange functional (for use with vdW-DF-04) by Michaelides and coworkers ⁶¹⁰ Klimeš J., Bowler D. R., Michaelides A.
    J. Phys. Condens. Matter
    (2010), 22, pp. 022201. Link

  • $\bullet$

    OPTX: Two-parameter exchange functional by Handy and Cohen ⁴⁴¹ Handy N. C., Cohen A. J.
    Mol. Phys.
    (2001), 99, pp. 403. Link

  • $\bullet$

    PBEsol: PBE exchange functional modified for solids ⁹²⁸ Perdew J. P. et al.
    Phys. Rev. Lett.
    (2008), 100, pp. 136406. Link

  • $\bullet$

    PW86: Perdew-Wang exchange functional from 1986 ⁹³⁴ Perdew J. P., Wang Y.
    Phys. Rev. B
    (1986), 33, pp. 8800. Link

  • $\bullet$

    PW91: Perdew-Wang exchange functional from 1991 ⁹²⁴ Perdew J. P. et al.
    Phys. Rev. B
    (1992), 46, pp. 6671. Link

  • $\bullet$

    RPBE: Hammer, Hansen, and Norskov exchange functional (modification of PBE) ⁴³⁹ Hammer B., Hansen L. B., Nørskov J. K.
    Phys. Rev. B
    (1999), 59, pp. 7413. Link

  • $\bullet$

    rPW86: Revised version (Murray et al.) of the 1986 Perdew-Wang exchange functional ⁸⁴³ Murray É. D., Lee K., Langreth D. C.
    J. Chem. Theory Comput.
    (2009), 5, pp. 2754. Link

  • $\bullet$

    SOGGA: Second-order GGA functional by Zhao and Truhlar ¹³⁵⁴ Zhao Y., Truhlar D. G.
    J. Chem. Phys.
    (2006), 128, pp. 184109. Link

  • $\bullet$

    wPBE ($\omega$PBE): Henderson et al. model for the PBE GGA short-range exchange hole ⁴⁷⁷ Henderson T. M., Janesko B. G., Scuseria G. E.
    J. Chem. Phys.
    (2008), 128, pp. 194105. Link

• $\circ$

  Meta-Generalized Gradient Approximation (meta-GGA)

  • $\bullet$

    TPSS: Tao, Perdew, Staroverov, and Scuseria exchange functional ¹¹⁷⁸ Tao J. et al.
    Phys. Rev. Lett.
    (2003), 91, pp. 146401. Link

  • $\bullet$

    revTPSS: Revised version of the TPSS exchange functional ⁹²⁷ Perdew J. P. et al.
    Phys. Rev. Lett.
    (2009), 103, pp. 026403. Link

  • $\bullet$

    BLOC: Minor modification of the TPSS exchange functional that works best with TPSSloc correlation (both by Della Sala and coworkers) ²²⁹ Constantin L. A., Fabiano E., Sala F. Della
    J. Chem. Theory Comput.
    (2013), 9, pp. 2256. Link

  • $\bullet$

    modTPSS: One-parameter version of the TPSS exchange functional ⁹³⁰ Perdew J. P. et al.
    Phys. Rev. A
    (2007), 76, pp. 042506. Link

  • $\bullet$

    oTPSS: TPSS exchange functional with 5 refit parameters (for use with oTPSS correlation) by Grimme and coworkers ³⁹⁹ Goerigk L., Grimme S.
    J. Chem. Theory Comput.
    (2010), 6, pp. 107. Link

  • $\bullet$

    PBE-GX: First exchange functional based on a finite uniform electron gas (rather than an infinite UEG) by Pierre-François Loos ⁷⁵⁷ Loos P.-F.
    J. Chem. Phys.
    (2017), 146, pp. 114108. Link

  • $\bullet$

    PKZB: Perdew, Kurth, Zupan, and Blaha exchange functional ⁹²⁵ Perdew J. P. et al.
    Phys. Rev. Lett.
    (1999), 82, pp. 2544. Link

  • $\bullet$

    regTPSS: Regularized (fixed order of limits issue) version of the TPSS exchange functional ¹⁰⁴⁵ Ruzsinszky A. et al.
    J. Chem. Theory Comput.
    (2012), 8, pp. 2078. Link

  • $\bullet$

    SCAN: Strongly Constrained and Appropriately Normed exchange functional ¹¹⁶⁴ Sun J., Ruzsinszky A., Perdew J. P.
    Phys. Rev. Lett.
    (2015), 115, pp. 036402. Link

  • $\bullet$

    rSCAN: Regularized SCAN exchange ⁷¹ Bartok A. P., Yates J. R.
    J. Chem. Phys.
    (2019), 150, pp. 161101. Link ^{, 361} Furness J. W. et al.
    J. Chem. Phys.
    (2022), 156, pp. 034109. Link

  • $\bullet$

    r++SCAN: Regularized SCAN with uniform density limit and coordinate scaling behavior ³⁶¹ Furness J. W. et al.
    J. Chem. Phys.
    (2022), 156, pp. 034109. Link

  • $\bullet$

    r2SCAN: Re-Regularized SCAN exchange ³⁵⁹ Furness J. W. et al.
    J. Phys. Chem. Lett.
    (2020), 11, pp. 8208. Link ^{, 360} Furness J. W. et al.
    J. Phys. Chem. Lett.
    (2020), 11, pp. 9248. Link ^{, 361} Furness J. W. et al.
    J. Chem. Phys.
    (2022), 156, pp. 034109. Link

  • $\bullet$

    r4SCAN: Regularized SCAN with exact constraints obeyed by SCAN ³⁶¹ Furness J. W. et al.
    J. Chem. Phys.
    (2022), 156, pp. 034109. Link

  • $\bullet$

    revSCAN: Revised SCAN exchange ⁸²¹ Mezei P. D., Csonka G. I., Kállay M.
    J. Chem. Theory Comput.
    (2018), 14, pp. 2469. Link

  • $\bullet$

    TM: Tao-Mo exchange functional derived via an accurate modeling of the conventional exchange hole ¹¹⁷⁷ Tao J., Mo Y.
    Phys. Rev. Lett.
    (2016), 117, pp. 073001. Link

  • $\bullet$

    regTM: Regularized TM exchange ⁹⁰⁹ Patra A., Jana S., Samal P.
    J. Chem. Phys.
    (2020), 153, pp. 184112. Link

  • $\bullet$

    revTM: Revised TM exchange ⁵⁴⁵ Jana S., Sharma K., Samal P.
    J. Phys. Chem. A
    (2019), 123, pp. 6356. Link

  • $\bullet$

    TASK: TASK exchange functional ⁴⁶ Aschebrock T., Kümmel S.
    Phys. Rev. Research
    (2019), 1, pp. 033082. Link

  • $\bullet$

    mTASK: Modified TASK exchange functional ⁸⁶¹ Neupane B. et al.
    Phys. Rev. Materials
    (2021), 5, pp. 063803. Link