5.3.2 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.

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  Local Spin-Density Approximation (LSDA)

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    Slater: Slater-Dirac exchange functional (X$\alpha$ method with $\alpha =2/3$)²²⁰

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    SR_LSDA (BNL): Short-range version of the Slater-Dirac exchange functional²⁹³

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  Generalized Gradient Approximation (GGA)

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    PBE: Perdew, Burke, and Ernzerhof exchange functional⁷³²

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    B88: Becke exchange functional from 1988⁵³

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    revPBE: Zhang and Yang one-parameter modification of the PBE exchange functional¹¹⁰⁴

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    AK13: Armiento-Kümmel exchange functional from 2013²⁵

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    B86: Becke exchange functional (X$\alpha \beta \gamma$) from 1986⁵⁰

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    G96: Gill exchange functional from 1996³⁰¹

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    mB86: Becke “modified gradient correction” exchange functional from 1986⁵¹

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    mPW91: modified version (Adamo and Barone) of the 1991 Perdew-Wang exchange functional³

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    muB88 ($\mu$B88): Short-range version of the B88 exchange functional by Hirao and coworkers⁴¹³

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    muPBE ($\mu$PBE): Short-range version of the PBE exchange functional by Hirao and coworkers⁴¹³

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    srPBE: Short-range version of the PBE exchange functional by Goll and coworkers^{313, 312}

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    optB88: Refit version of the original B88 exchange functional (for use with vdW-DF-04) by Michaelides and coworkers⁴⁸⁷

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    OPTX: Two-parameter exchange functional by Handy and Cohen³⁴⁰

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    PBEsol: PBE exchange functional modified for solids⁷³⁶

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    PW86: Perdew-Wang exchange functional from 1986⁷⁴⁰

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    PW91: Perdew-Wang exchange functional from 1991⁷³³

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    RPBE: Hammer, Hansen, and Norskov exchange functional (modification of PBE)³³⁷

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    rPW86: Revised version (Murray et al.) of the 1986 Perdew-Wang exchange functional⁶⁷⁴

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    SOGGA: Second-order GGA functional by Zhao and Truhlar¹¹¹²

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    wPBE ($\omega$PBE): Henderson et al. model for the PBE GGA short-range exchange hole³⁷⁰

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  Meta-Generalized Gradient Approximation (meta-GGA)

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    TPSS: Tao, Perdew, Staroverov, and Scuseria exchange functional⁹⁵⁰

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    revTPSS: Revised version of the TPSS exchange functional⁷³⁵

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    BLOC: Minor modification of the TPSS exchange functional that works best with TPSSloc correlation (both by Della Sala and coworkers)¹⁷⁷

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    modTPSS: One-parameter version of the TPSS exchange functional⁷³⁷

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    oTPSS: TPSS exchange functional with 5 refit parameters (for use with oTPSS correlation) by Grimme and coworkers³⁰⁸

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    PBE-GX: First exchange functional based on a finite uniform electron gas (rather than an infinite UEG) by Pierre-François Loos⁶⁰⁷

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    PKZB: Perdew, Kurth, Zupan, and Blaha exchange functional⁷³⁴

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    regTPSS: Regularized (fixed order of limits issue) version of the TPSS exchange functional⁸³⁶

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    SCAN: Strongly Constrained and Appropriately Normed exchange functional⁹³⁶

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    TM: Tao-Mo exchange functional derived via an accurate modeling of the conventional exchange hole⁹⁴⁹