5.3.4 Exchange-Correlation Functionals

Note:  All exchange-correlation functionals in this section can be invoked using the $rem variable METHOD. For backwards compatibility, all of the exchange-correlation functionals except for the ones marked with an asterisk can be used with 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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    SPW92*: Slater LSDA exchange + PW92 LSDA correlation

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    LDA: Slater LSDA exchange + VWN5 LSDA correlation

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    SVWN5*: Slater LSDA exchange + VWN5 LSDA correlation

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  Generalized Gradient Approximation (GGA)

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    B97-D3(0): B97-D with a fitted DFT-D3(0) tail instead of the original DFT-D2 tail³²¹

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    B97-D: 9-parameter dispersion-corrected (DFT-D2) functional by Grimme³²⁸

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    PBE*: PBE GGA exchange + PBE GGA correlation

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    BLYP*: B88 GGA exchange + LYP GGA correlation

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    revPBE*: revPBE GGA exchange + PBE GGA correlation

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    BEEF-vdW: 31-parameter semi-empirical exchange functional developed via a Bayesian error estimation framework paired with PBE correlation and vdW-DF-10 NLC¹⁰²⁶

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    BOP: B88 GGA exchange + BOP “one-parameter progressive” GGA correlation⁹⁷⁵

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    BP86*: B88 GGA exchange + P86 GGA correlation

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    BP86VWN*: B88 GGA exchange + P86VWN5 GGA correlation

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    BPBE*: B88 GGA exchange + PBE GGA correlation

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    EDF1: Modification of BLYP to give good performance in the 6-31+G* basis set¹⁰

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    EDF2: Modification of B3LYP to give good performance in the cc-pVTZ basis set for frequencies⁵⁸³

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    GAM: 21-parameter non-separable gradient approximation functional by Truhlar and coworkers¹⁰⁹³

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    HCTH93 (HCTH/93): 15-parameter functional trained on 93 systems by Handy and coworkers³³⁹

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    HCTH120 (HCTH/120): 15-parameter functional trained on 120 systems by Boese et al.⁸⁶

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    HCTH147 (HCTH/147): 15-parameter functional trained on 147 systems by Boese et al.⁸⁶

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    HCTH407 (HCTH/407): 15-parameter functional trained on 407 systems by Boese and Handy⁸⁷

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    HLE16 – HCTH/407 exchange functional enhanced by a factor of 1.25 + HCTH/407 correlation functional enhanced by a factor of 0.5⁹⁹⁵

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    KT1: GGA functional designed specifically for shielding constant calculations⁴⁶⁴

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    KT2: GGA functional designed specifically for shielding constant calculations⁴⁶⁴

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    KT3: GGA functional with improved results for main-group nuclear magnetic resonance shielding constants⁴⁶⁵

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    mPW91*: mPW91 GGA exchange + PW91 GGA correlation

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    N12: 21-parameter non-separable gradient approximation functional by Peverati and Truhlar⁷⁵¹

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    OLYP*: OPTX GGA exchange + LYP GGA correlation

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    PBEOP: PBE GGA exchange + PBEOP “one-parameter progressive” GGA correlation⁹⁷⁵

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    PBEsol*: PBEsol GGA exchange + PBEsol GGA correlation

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    PW91*: PW91 GGA exchange + PW91 GGA correlation

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    RPBE*: RPBE GGA exchange + PBE GGA correlation

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    rVV10*: rPW86 GGA exchange + PBE GGA correlation + rVV10 non-local correlation⁸³⁷

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    SOGGA*: SOGGA GGA exchange + PBE GGA correlation

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    SOGGA11: 20-parameter functional by Peverati, Zhao, and Truhlar⁷⁵⁴

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    VV10: rPW86 GGA exchange + PBE GGA correlation + VV10 non-local correlation¹⁰⁰⁶

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  Meta-Generalized Gradient Approximation (meta-GGA)

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    B97M-V: 12-parameter combinatorially-optimized, dispersion-corrected (VV10) functional by Mardirossian and Head-Gordon⁶²⁷

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    B97M-rV*: B97M-V density functional with the VV10 NLC functional replaced by the rVV10 NLC functional⁶³⁰

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    M06-L: 34-parameter functional by Zhao and Truhlar¹¹¹⁰

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    TPSS*: TPSS meta-GGA exchange + TPSS meta-GGA correlation

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    revTPSS*: revTPSS meta-GGA exchange + revTPSS meta-GGA correlation

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    BLOC*: BLOC meta-GGA exchange + TPSSloc meta-GGA correlation

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    M11-L: 44-parameter dual-range functional by Peverati and Truhlar⁷⁵⁰

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    mBEEF: 64-parameter exchange functional paired with the PBEsol correlation functional¹⁰²⁵

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    MGGA_MS0: MGGA_MS0 meta-GGA exchange + regTPSS GGA correlation⁹³⁷

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    MGGA_MS1: MGGA_MS1 meta-GGA exchange + regTPSS GGA correlation⁹³⁴

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    MGGA_MS2: MGGA_MS2 meta-GGA exchange + regTPSS GGA correlation⁹³⁴

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    MGGA_MVS: MGGA_MVS meta-GGA exchange + regTPSS GGA correlation⁹³⁵

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    MN12-L: 58-parameter meta-nonseparable gradient approximation functional by Peverati and Truhlar⁷⁵²

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    MN15-L: 58-parameter meta-nonseparable gradient approximation functional by Yu, He, and Truhlar¹⁰⁹²

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    oTPSS*: oTPSS meta-GGA exchange + oTPSS meta-GGA correlation

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    PKZB*: PKZB meta-GGA exchange + PKZB meta-GGA correlation

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    revM06-L: 31-parameter revised M06-L functional¹⁰¹³

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    SCAN*: SCAN meta-GGA exchange + SCAN meta-GGA correlation

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    t-HCTH ($\tau$-HCTH): 16-parameter functional by Boese and Handy⁸⁸

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    TM*: TM meta-GGA exchange + TM meta-GGA correlation⁹⁴⁹

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    VSXC: 21-parameter functional by Voorhis and Scuseria⁹⁸⁹

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  Global Hybrid Generalized Gradient Approximation (GH GGA)

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    B3LYP: 20% HF exchange + 8% Slater LSDA exchange + 72% B88 GGA exchange + 19% VWN1RPA LSDA correlation + 81% LYP GGA correlation^{54, 918}

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    PBE0: 25% HF exchange + 75% PBE GGA exchange + PBE GGA correlation⁴

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    revPBE0: 25% HF exchange + 75% revPBE GGA exchange + PBE GGA correlation

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    B97: Becke’s original 10-parameter density functional with 19.43% HF exchange⁵⁷

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    B1LYP: 25% HF exchange + 75% B88 GGA exchange + LYP GGA correlation²

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    B1PW91: 25% HF exchange + 75% B88 GGA exchange + PW91 GGA correlation²

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    B3LYP5: 20% HF exchange + 8% Slater LSDA exchange + 72% B88 GGA exchange + 19% VWN5 LSDA correlation + 81% LYP GGA correlation^{54, 918}

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    B3P86: 20% HF exchange + 8% Slater LSDA exchange + 72% B88 GGA exchange+ 19% VWN1RPA LSDA correlation + 81% P86 GGA correlation

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    B1LYP: 25% HF exchange + 75% B88 GGA exchange + LYP GGA correlation²

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    B1PW91: 25% HF exchange + 75% B88 GGA exchange + PW91 GGA correlation²

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    B3LYP5: 20% HF exchange + 8% Slater LSDA exchange + 72% B88 GGA exchange + 19% VWN5 LSDA correlation + 81% LYP GGA correlation^{54, 918}

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    B3P86: 20% HF exchange + 8% Slater LSDA exchange + 72% B88 GGA exchange+ 19% VWN1RPA LSDA correlation + 81% P86 GGA correlation

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    B3PW91: 20% HF exchange + 8% Slater LSDA exchange + 72% B88 GGA exchange+ 19% PW92 LSDA correlation + 81% PW91 GGA correlation⁵⁴

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    B5050LYP: 50% HF exchange + 8% Slater LSDA exchange + 42% B88 GGA exchange + 19% VWN5 LSDA correlation + 81% LYP GGA correlation⁸⁶⁹

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    B97-1: Self-consistent parameterization of Becke’s B97 density functional with 21% HF exchange³³⁹

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    B97-2: Re-parameterization of B97 by Tozer and coworkers with 21% HF exchange¹⁰⁵³

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    B97-3: 16-parameter version of B97 by Keal and Tozer with $\approx$ 26.93% HF exchange⁴⁶⁶

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    B97-K: Re-parameterization of B97 for kinetics by Boese and Martin with 42% HF exchange⁸⁹

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    BHHLYP: 50% HF exchange + 50% B88 GGA exchange + LYP GGA correlation

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    HFLYP*: 100% HF exchange + LYP GGA correlation

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    MPW1K: 42.8% HF exchange + 57.2% mPW91 GGA exchange + PW91 GGA correlation⁶¹¹

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    MPW1LYP: 25% HF exchange + 75% mPW91 GGA exchange + LYP GGA correlation³

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    MPW1PBE: 25% HF exchange + 75% mPW91 GGA exchange + PBE GGA correlation³

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    MPW1PW91: 25% HF exchange + 75% mPW91 GGA exchange + PW91 GGA correlation³

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    O3LYP: 11.61% HF exchange + $\approx$ 7.1% Slater LSDA exchange + 81.33% OPTX GGA exchange + 19% VWN5 LSDA correlation + 81% LYP GGA correlation³⁹⁰

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    PBEh-3c: Low-cost composite scheme of Grimme and coworkers for use with the def2-mSVP basis set only³²²

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    PBE50: 50% HF exchange + 50% PBE GGA exchange + PBE GGA correlation⁷⁰

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    SOGGA11-X: 21-parameter functional with 40.15% HF exchange by Peverati and Truhlar⁷⁴⁸

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    WC04: Hybrid density functional optimized for the computation of ${}^{13}$C chemical shifts¹⁰⁴⁶

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    WP04: Hybrid density functional optimized for the computation of ${}^1$H chemical shifts¹⁰⁴⁶

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    X3LYP: 21.8% HF exchange + 7.3% Slater LSDA exchange + $\approx$ 54.24% B88 GGA exchange + $\approx$ 16.66% PW91 GGA exchange + 12.9% VWN1RPA LSDA correlation + 87.1% LYP GGA correlation¹⁰⁷⁷

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  Global Hybrid Meta-Generalized Gradient Approximation (GH meta-GGA)

  • $\bullet$

    M06-2X: 29-parameter functional with 54% HF exchange by Zhao and Truhlar¹¹¹⁴

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    M08-HX: 47-parameter functional with 52.23% HF exchange by Zhao and Truhlar¹¹¹³

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    TPSSh: 10% HF exchange + 90% TPSS meta-GGA exchange + TPSS meta-GGA correlation⁹⁰⁷

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    revTPSSh: 10% HF exchange + 90% revTPSS meta-GGA exchange + revTPSS meta-GGA correlation¹⁹⁰

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    B1B95: 28% HF exchange + 72% B88 GGA exchange + B95 meta-GGA correlation⁵⁶

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    B3TLAP: 17.13% HF exchange + 9.66% Slater LSDA exchange + 72.6% B88 GGA exchange + PK06 meta-GGA correlation^{784, 785}

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    BB1K: 42% HF exchange + 58% B88 GGA exchange + B95 meta-GGA correlation¹¹⁰⁵

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    BMK: Boese-Martin functional for kinetics with 42% HF exchange⁸⁹

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    dlDF: Dispersion-less density functional (based on the M05-2X functional form) by Szalewicz and coworkers⁷⁴⁵

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    M05: 22-parameter functional with 28% HF exchange by Zhao, Schultz, and Truhlar¹¹⁰⁶

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    M05-2X: 19-parameter functional with 56% HF exchange by Zhao, Schultz, and Truhlar¹¹⁰⁷

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    M06: 33-parameter functional with 27% HF exchange by Zhao and Truhlar¹¹¹⁴

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    M06-HF: 32-parameter functional with 100% HF exchange by Zhao and Truhlar¹¹¹¹

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    M08-SO: 44-parameter functional with 56.79% HF exchange by Zhao and Truhlar¹¹¹³

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    MGGA_MS2h: 9% HF exchange + 91 % MGGA_MS2 meta-GGA exchange + regTPSS GGA correlation⁹³⁴

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    MGGA_MVSh: 25% HF exchange + 75 % MGGA_MVS meta-GGA exchange + regTPSS GGA correlation⁹³⁵

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    MN15: 59-parameter functional with 44% HF exchange by Truhlar and coworkers¹⁰⁹¹

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    MPW1B95: 31% HF exchange + 69% mPW91 GGA exchange + B95 meta-GGA correlation¹¹⁰⁸

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    MPWB1K: 44% HF exchange + 56% mPW91 GGA exchange + B95 meta-GGA correlation¹¹⁰⁸

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    PW6B95: 6-parameter combination of 28 % HF exchange, 72 % optimized PW91 GGA exchange, and re-optimized B95 meta-GGA correlation by Zhao and Truhlar¹¹⁰⁹

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    PWB6K: 6-parameter combination of 46 % HF exchange, 54 % optimized PW91 GGA exchange, and re-optimized B95 meta-GGA correlation by Zhao and Truhlar¹¹⁰⁹

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    revM06: 32-parameter functional with 40.41% HF exchange¹⁰¹⁴

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    SCAN0: 25% HF exchange + 75% SCAN meta-GGA exchange + SCAN meta-GGA correlation⁴⁰⁵

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    t-HCTHh ($\tau$-HCTHh): 17-parameter functional with 15% HF exchange by Boese and Handy⁸⁸

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    TPSS0: 25% HF exchange + 75% TPSS meta-GGA exchange + TPSS meta-GGA correlation³²⁶

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  Range-Separated Hybrid Generalized Gradient Approximation (RSH GGA)

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    wB97X-V ($\omega$B97X-V): 10-parameter combinatorially-optimized, dispersion-corrected (VV10) functional with 16.7% SR HF exchange, 100% LR HF exchange, and $\omega =0.3$⁶²⁶

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    wB97X-D3 ($\omega$B97X-D3): 16-parameter dispersion-corrected (DFT-D3(0)) functional with $\approx$ 19.57% SR HF exchange, 100% LR HF exchange, and $\omega =0.25$⁵⁸⁵

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    wB97X-D ($\omega$B97X-D): 15-parameter dispersion-corrected (DFT-CHG) functional with $\approx$ 22.2% SR HF exchange, 100% LR HF exchange, and $\omega =0.2$¹⁴⁷

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    CAM-B3LYP: Coulomb-attenuating method functional by Handy and coworkers¹⁰⁷⁹

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    CAM-QTP00: Re-parameterized CAM-B3LYP designed to satisfy the IP-theorem for all occupied orbitals of the water molecule⁹⁹⁴

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    CAM-QTP01: Re-parameterized CAM-B3LYP optimized to satisfy the valence IPs of the water molecule, 34 excitation states, and G2-1 atomization energies⁴³⁵

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    HSE-HJS: Screened-exchange “HSE06” functional with 25% SR HF exchange, 0% LR HF exchange, and $\omega$=0.11, using the updated HJS PBE exchange hole model^{504, 370}

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    LC-rVV10*: LC-VV10 density functional with the VV10 NLC functional replaced by the rVV10 NLC functional⁶³⁰

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    LC-VV10: 0% SR HF exchange + 100% LR HF exchange + $\omega$PBE GGA exchange + PBE GGA correlation + VV10 non-local correlation ($\omega$=0.45)¹⁰⁰⁶

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    LC-wPBE08 (LC-$\omega$PBE08): 0% SR HF exchange + 100% LR HF exchange + $\omega$PBE GGA exchange + PBE GGA correlation ($\omega$=0.45)¹⁰²⁴

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    LRC-BOP (LRC-$\mu$BOP): 0% SR HF exchange + 100% LR HF exchange + muB88 GGA exchange + BOP GGA correlation ($\omega$=0.47)⁹⁰⁰

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    LRC-wPBE (LRC-$\omega$PBE): 0% SR HF exchange + 100% LR HF exchange + $\omega$PBE GGA exchange + PBE GGA correlation ($\omega$=0.3)⁸²⁵

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    LRC-wPBEh (LRC-$\omega$PBEh): 20% SR HF exchange + 100% LR HF exchange + 80% $\omega$PBE GGA exchange + PBE GGA correlation ($\omega$=0.2)⁸²⁶

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    N12-SX: 26-parameter non-separable GGA with 25% SR HF exchange, 0% LR HF exchange, and $\omega =0.11$⁷⁵³

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    rCAM-B3LYP: Re-fit CAM-B3LYP with the goal of minimizing many-electron self-interaction error¹⁷⁴

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    wB97 ($\omega$B97): 13-parameter functional with 0% SR HF exchange, 100% LR HF exchange, and $\omega =0.4$¹⁴⁶

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    wB97X ($\omega$B97X): 14-parameter functional with $\approx$ 15.77% SR HF exchange, 100% LR HF exchange, and $\omega =0.3$¹⁴⁶

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    wB97X-rV* ($\omega$B97X-rV): $\omega$B97X-V density functional with the VV10 NLC functional replaced by the rVV10 NLC functional⁶³⁰

• $\circ$

  Range-Separated Hybrid Meta-Generalized Gradient Approximation (RSH meta-GGA)

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    wB97M-V ($\omega$B97M-V): 12-parameter combinatorially-optimized, dispersion-corrected (VV10) functional with 15% SR HF exchange, 100% LR HF exchange, and $\omega =0.3$⁶²⁸

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    M06-SX: local revM06-L functional with 33.5% SR HF exchange¹⁰¹⁵

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    M11: 40-parameter functional with 42.8% SR HF exchange, 100% LR HF exchange, and $\omega =0.25$⁷⁴⁹

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    MN12-SX: 58-parameter non-separable meta-GGA with 25% SR HF exchange, 0% LR HF exchange, and $\omega =0.11$⁷⁵³

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    revM11: 22-parameter functional with 22.5% SR HF exchange, 100% LR HF exchange, and $\omega =0.4$⁹⁹⁶

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    wB97M-rV* ($\omega$B97X-rV): $\omega$B97M-V density functional with the VV10 NLC functional replaced by the rVV10 NLC functional⁶³⁰

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    wM05-D ($\omega$M05-D): 21-parameter dispersion-corrected (DFT-CHG) functional with $\approx$ 36.96% SR HF exchange, 100% LR HF exchange, and $\omega =0.2$⁵⁸⁶

  • $\bullet$

    wM06-D3 ($\omega$M06-D3): 25-parameter dispersion-corrected [DFT-D3(0)] functional with $\approx$ 27.15% SR HF exchange, 100% LR HF exchange, and $\omega =0.3$⁵⁸⁵

• $\circ$

  Double Hybrid Generalized Gradient Approximation (DH GGA)

  Note:  In order to use the resolution-of-the-identity approximation for the MP2 component, specify an auxiliary basis set with the $rem variable AUX_BASIS

  • $\bullet$

    DSD-PBEPBE-D3: 68% HF exchange + 32% PBE GGA exchange + 49% PBE GGA correlation + 13% SS MP2 correlation + 55% OS MP2 correlation with DFT-D3(BJ) tail⁵⁰²

  • $\bullet$

    wB97X-2(LP) ($\omega$B97X-2(LP)): 13-parameter functional with $\approx$ 67.88% SR HF exchange, 100% LR HF exchange, $\approx$ 58.16% SS MP2 correlation, $\approx$ 47.80% OS MP2 correlation, and $\omega =0.3$¹⁴⁸

  • $\bullet$

    wB97X-2(TQZ) ($\omega$B97X-2(TQZ)): 13-parameter functional with $\approx$ 63.62% SR HF exchange, 100% LR HF exchange, $\approx$ 52.93% SS MP2 correlation, $\approx$ 44.71% OS MP2 correlation, and $\omega =0.3$¹⁴⁸

  • $\bullet$

    XYG3: 80.33% HF exchange - 1.4% Slater LSDA exchange + 21.07% B88 GGA exchange + 67.89% LYP GGA correlation + 32.11% MP2 correlation (evaluated with B3LYP orbitals)¹¹⁰³

  • $\bullet$

    XYGJ-OS: 77.31% HF exchange + 22.69% Slater LSDA exchange + 23.09% VWN1RPA LSDA correlation + 27.54% LYP GGA correlation + 43.64% OS MP2 correlation (evaluated with B3LYP orbitals)¹⁰⁹⁷

  • $\bullet$

    B2PLYP: 53% HF exchange + 47% B88 GGA exchange + 73% LYP GGA correlation + 27% MP2 correlation³²⁷

  • $\bullet$

    B2GPPLYP: 65% HF exchange + 35% B88 GGA exchange + 64% LYP GGA correlation + 36% MP2 correlation⁴⁶¹

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    DSD-PBEP86-D3: 69% HF exchange + 31% PBE GGA exchange + 44% P86 GGA correlation + 22% SS MP2 correlation + 52% OS MP2 correlation with DFT-D3(BJ) tail⁵⁰²

  • $\bullet$

    LS1DH-PBE: 75% HF exchange + 25% PBE GGA exchange + 57.8125% PBE GGA correlation + 42.1875% MP2 correlation⁹⁶⁷

  • $\bullet$

    PBE-QIDH: 69.3361% HF exchange + 30.6639% PBE GGA exchange + 66.6667% PBE GGA correlation + 33.3333% MP2 correlation¹⁰²

  • $\bullet$

    PBE0-2: $\approx$ 79.37% HF exchange + $\approx$ 20.63% PBE GGA exchange + 50% PBE GGA correlation + 50% MP2 correlation¹⁴⁹

  • $\bullet$

    PBE0-DH: 50% HF exchange + 50% PBE GGA exchange + 87.5% PBE GGA correlation + 12.5% MP2 correlation¹⁰¹

• $\circ$

  Double Hybrid Meta-Generalized Gradient Approximation (DH MGGA)

  • $\bullet$

    wB97M(2): 14-parameter functional form by wB97M-V + MP2 correlation.⁶²⁹

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    PTPSS-D3: 50% HF exchange + 50% Re-Fit TPSS meta-GGA exchange + 62.5% Re-Fit TPSS meta-GGA correlation + 37.5% OS MP2 correlation with DFT-D3(0) tail³⁰⁹

  • $\bullet$

    DSD-PBEB95-D3: 66% HF exchange + 34% PBE GGA exchange + 55% B95 GGA correlation + 9% SS MP2 correlation + 46% OS MP2 correlation with DFT-D3(BJ) tail⁵⁰²

  • $\bullet$

    PWPB95-D3: 50% HF exchange + 50% Re-Fit PW91 GGA exchange + 73.1% Re-Fit B95 meta-GGA correlation + 26.9% OS MP2 correlation with DFT-D3(0) tail³⁰⁹