5.3.5 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.

• $\circ$

  Local Spin-Density Approximation (LSDA)

  • $\bullet$

    SPW92*: Slater LSDA exchange + PW92 LSDA correlation

  • $\bullet$

    LDA: Slater LSDA exchange + VWN5 LSDA correlation

  • $\bullet$

    SVWN5*: Slater LSDA exchange + VWN5 LSDA correlation

• $\circ$

  Generalized Gradient Approximation (GGA)

  • $\bullet$

    B97-D3(0): B97-D with a fitted DFT-D3(0) tail instead of the original DFT-D2 tail ⁴⁷⁰ Grimme S. et al.
    J. Chem. Phys.
    (2010), 132, pp. 154104. Link

  • $\bullet$

    B97-D: 9-parameter dispersion-corrected (DFT-D2) functional by Grimme ⁴⁷⁸ Grimme S.
    J. Comput. Chem.
    (2006), 27, pp. 1787. Link

  • $\bullet$

    PBE*: PBE GGA exchange + PBE GGA correlation

  • $\bullet$

    BLYP*: B88 GGA exchange + LYP GGA correlation

  • $\bullet$

    revPBE*: revPBE GGA exchange + PBE GGA correlation

  • $\bullet$

    BEEF-vdW: 31-parameter semi-empirical exchange functional developed via a Bayesian error estimation framework paired with PBE correlation and vdW-DF-10 NLC ¹³⁹⁶ Wellendorff J. et al.
    Phys. Rev. B
    (2012), 85, pp. 235149. Link

  • $\bullet$

    BOP: B88 GGA exchange + BOP “one-parameter progressive” GGA correlation ¹³³¹ Tsuneda T., Suzumura T., Hirao K.
    J. Chem. Phys.
    (1999), 110, pp. 10664. Link

  • $\bullet$

    BP86*: B88 GGA exchange + P86 GGA correlation

  • $\bullet$

    BP86VWN*: B88 GGA exchange + P86VWN5 GGA correlation

  • $\bullet$

    BPBE*: B88 GGA exchange + PBE GGA correlation

  • $\bullet$

    EDF1: Modification of BLYP to give good performance in the 6-31+G* basis set ²⁵ Adamson R. D., Gill P. M. W., Pople J. A.
    Chem. Phys. Lett.
    (1998), 284, pp. 6. Link

  • $\bullet$

    EDF2: Modification of B3LYP to give good performance in the cc-pVTZ basis set for frequencies ⁸⁰⁷ Lin C. Y., George M. W., Gill P. M. W.
    Aust. J. Chem.
    (2004), 57, pp. 365. Link

  • $\bullet$

    GAM: 21-parameter non-separable gradient approximation functional by Truhlar and coworkers ¹⁴⁷⁷ Yu H. S. et al.
    Phys. Chem. Chem. Phys.
    (2015), 17, pp. 12146. Link

  • $\bullet$

    HCTH93 (HCTH/93): 15-parameter functional trained on 93 systems by Handy and coworkers ⁵⁰⁰ Hamprecht F. A. et al.
    J. Chem. Phys.
    (1998), 109, pp. 6264. Link

  • $\bullet$

    HCTH120 (HCTH/120): 15-parameter functional trained on 120 systems by Boese et al. ¹³⁶ Boese A. D. et al.
    J. Chem. Phys.
    (2000), 112, pp. 1670. Link

  • $\bullet$

    HCTH147 (HCTH/147): 15-parameter functional trained on 147 systems by Boese et al. ¹³⁶ Boese A. D. et al.
    J. Chem. Phys.
    (2000), 112, pp. 1670. Link

  • $\bullet$

    HCTH407 (HCTH/407): 15-parameter functional trained on 407 systems by Boese and Handy ¹³⁷ Boese A. D., Handy N. C.
    J. Chem. Phys.
    (2001), 114, pp. 5497. Link

  • $\bullet$

    HLE16 – HCTH/407 exchange functional enhanced by a factor of 1.25 + HCTH/407 correlation functional enhanced by a factor of 0.5 ¹³⁵³ Verma P., Truhlar D. G.
    J. Phys. Chem. Lett.
    (2017), 8, pp. 380. Link

  • $\bullet$

    KT1: GGA functional designed specifically for shielding constant calculations ⁶⁵⁹ Keal T. W., Tozer D. J.
    J. Chem. Phys.
    (2003), 119, pp. 3015. Link

  • $\bullet$

    KT2: GGA functional designed specifically for shielding constant calculations ⁶⁵⁹ Keal T. W., Tozer D. J.
    J. Chem. Phys.
    (2003), 119, pp. 3015. Link

  • $\bullet$

    KT3: GGA functional with improved results for main-group nuclear magnetic resonance shielding constants ⁶⁶⁰ Keal T. W., Tozer D. J.
    J. Chem. Phys.
    (2004), 121, pp. 5654. Link

  • $\bullet$

    mPW91*: mPW91 GGA exchange + PW91 GGA correlation

  • $\bullet$

    N12: 21-parameter non-separable gradient approximation functional by Peverati and Truhlar ¹⁰⁴⁸ Peverati R., Truhlar D. G.
    J. Chem. Theory Comput.
    (2012), 8, pp. 2310. Link

  • $\bullet$

    OLYP*: OPTX GGA exchange + LYP GGA correlation

  • $\bullet$

    PBEOP: PBE GGA exchange + PBEOP “one-parameter progressive” GGA correlation ¹³³¹ Tsuneda T., Suzumura T., Hirao K.
    J. Chem. Phys.
    (1999), 110, pp. 10664. Link

  • $\bullet$

    PBEsol*: PBEsol GGA exchange + PBEsol GGA correlation

  • $\bullet$

    PW91*: PW91 GGA exchange + PW91 GGA correlation

  • $\bullet$

    RPBE*: RPBE GGA exchange + PBE GGA correlation

  • $\bullet$

    rVV10*: rPW86 GGA exchange + PBE GGA correlation + rVV10 non-local correlation ¹¹⁵³ Sabatini R., Gorni T., de Gironcoli S.
    Phys. Rev. B
    (2013), 87, pp. 041108. Link

  • $\bullet$

    SOGGA*: SOGGA GGA exchange + PBE GGA correlation

  • $\bullet$

    SOGGA11: 20-parameter functional by Peverati, Zhao, and Truhlar ¹⁰⁵¹ Peverati R., Zhao Y., Truhlar D. G.
    J. Phys. Chem. Lett.
    (2011), 2, pp. 1991. Link

  • $\bullet$

    VV10: rPW86 GGA exchange + PBE GGA correlation + VV10 non-local correlation ¹³⁶⁸ Vydrov O. A., Van Voorhis T.
    J. Chem. Phys.
    (2010), 133, pp. 244103. Link

• $\circ$

  Meta-Generalized Gradient Approximation (meta-GGA)

  • $\bullet$

    B97M-V: 12-parameter combinatorially-optimized, dispersion-corrected (VV10) functional by Mardirossian and Head-Gordon ⁸⁷⁷ Mardirossian N., Head-Gordon M.
    J. Chem. Phys.
    (2015), 142, pp. 074111. Link

  • $\bullet$

    B97M-rV*: B97M-V density functional with the VV10 NLC functional replaced by the rVV10 NLC functional ⁸⁸⁰ Mardirossian N. et al.
    J. Phys. Chem. Lett.
    (2017), 8, pp. 35. Link

  • $\bullet$

    M06-L: 34-parameter functional by Zhao and Truhlar ¹⁵⁰⁵ Zhao Y., Truhlar D. G.
    J. Chem. Phys.
    (2006), 125, pp. 194101. Link

  • $\bullet$

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

  • $\bullet$

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

  • $\bullet$

    B97MV-D3s(BJ): B97M-V density functional with the VV10 NLC functional replaced by DFT-D3s(BJ) (s6 = 1.0, s8 = 0.2641, a1 = 0.0, a2 = 5.4959)

  • $\bullet$

    B97MV-D4: B97M-V density functional with the VV10 NLC functional replaced by DFT-D4 (s6 = 1.0, s8 = 0.5093, s9 = 1.0, a1 = 0.0662, a2 = 5.4487)

  • $\bullet$

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

  • $\bullet$

    M11-L: 44-parameter dual-range functional by Peverati and Truhlar ¹⁰⁴⁷ Peverati R., Truhlar D. G.
    J. Phys. Chem. Lett.
    (2012), 3, pp. 117. Link

  • $\bullet$

    mBEEF: 64-parameter exchange functional paired with the PBEsol correlation functional ¹³⁹⁵ Wellendorff J. et al.
    J. Chem. Phys.
    (2014), 140, pp. 144107. Link

  • $\bullet$

    MGGA_MS0: MGGA_MS0 meta-GGA exchange + regTPSS GGA correlation ¹²⁸⁴ Sun J., Xiao B., Ruzsinszky A.
    J. Chem. Phys.
    (2012), 137, pp. 051101. Link

  • $\bullet$

    MGGA_MS1: MGGA_MS1 meta-GGA exchange + regTPSS GGA correlation ¹²⁸¹ Sun J. et al.
    J. Chem. Phys.
    (2013), 138, pp. 044113. Link

  • $\bullet$

    MGGA_MS2: MGGA_MS2 meta-GGA exchange + regTPSS GGA correlation ¹²⁸¹ Sun J. et al.
    J. Chem. Phys.
    (2013), 138, pp. 044113. Link

  • $\bullet$

    MGGA_MVS: MGGA_MVS meta-GGA exchange + regTPSS GGA correlation ¹²⁸² Sun J., Perdew J. P., Ruzsinszky A.
    Proc. Natl. Acad. Sci. USA
    (2015), 112, pp. 685. Link

  • $\bullet$

    MN12-L: 58-parameter meta-nonseparable gradient approximation functional by Peverati and Truhlar ¹⁰⁴⁹ Peverati R., Truhlar D. G.
    Phys. Chem. Chem. Phys.
    (2012), 14, pp. 13171. Link

  • $\bullet$

    MN15-L: 58-parameter meta-nonseparable gradient approximation functional by Yu, He, and Truhlar ¹⁴⁷⁶ Yu H. S., He X., Truhlar D. G.
    J. Chem. Theory Comput.
    (2016), 12, pp. 1280. Link

  • $\bullet$

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

  • $\bullet$

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

  • $\bullet$

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

  • $\bullet$

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

  • $\bullet$

    rSCAN: rSCAN exchange + rSCAN correltaion

  • $\bullet$

    r++SCAN: r++SCAN exchange + r++SCAN correlation

  • $\bullet$

    r2SCAN: r2SCAN exchange + r2SCAN correlation

  • $\bullet$

    r4SCAN: r4SCAN exchange + r2SCAN correlation

  • $\bullet$

    revSCAN: revSCAN exchange + revSCAN correlation

  • $\bullet$

    t-HCTH ($\tau$-HCTH): 16-parameter functional by Boese and Handy ¹³⁸ Boese A. D., Handy N. C.
    J. Chem. Phys.
    (2002), 116, pp. 9559. Link

  • $\bullet$

    TM*: TM meta-GGA exchange + TM meta-GGA correlation ¹²⁹⁹ Tao J., Mo Y.
    Phys. Rev. Lett.
    (2016), 117, pp. 073001. Link

  • $\bullet$

    revTM: revTM exchange + revTM correlation

  • $\bullet$

    regTM: regTM exchange + regTPSS correlation

  • $\bullet$

    rregTM: regTM exchange + rregTM correlation

  • $\bullet$

    TASK: TASK exchange + PW92 correlation

  • $\bullet$

    mTASK: mTASK exchange + PW92 correlation

  • $\bullet$

    VSXC: 21-parameter functional by Voorhis and Scuseria ¹³⁴⁶ Van Voorhis T., Scuseria G. E.
    J. Chem. Phys.
    (1998), 109, pp. 400. Link

• $\circ$

  Global Hybrid Generalized Gradient Approximation (GH GGA)

  • $\bullet$

    B3LYP: 20% HF exchange + 8% Slater LSDA exchange + 72% B88 GGA exchange + 19% VWN1RPA LSDA correlation + 81% LYP GGA correlation ⁹⁵ Becke A. D.
    J. Chem. Phys.
    (1993), 98, pp. 5648. Link ^{, 1265} Stephens P. J. et al.
    J. Phys. Chem.
    (1994), 98, pp. 11623. Link

  • $\bullet$

    PBE0: 25% HF exchange + 75% PBE GGA exchange + PBE GGA correlation ¹⁹ Adamo C., Barone V.
    J. Chem. Phys.
    (1999), 110, pp. 6158. Link

  • $\bullet$

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

  • $\bullet$

    B97: Becke’s original 10-parameter density functional with 19.43% HF exchange ⁹⁸ Becke A. D.
    J. Chem. Phys.
    (1997), 107, pp. 8554. Link

  • $\bullet$

    B1LYP: 25% HF exchange + 75% B88 GGA exchange + LYP GGA correlation ¹⁷ Adamo C., Barone V.
    Chem. Phys. Lett.
    (1997), 274, pp. 242. Link

  • $\bullet$

    B1PW91: 25% HF exchange + 75% B88 GGA exchange + PW91 GGA correlation ¹⁷ Adamo C., Barone V.
    Chem. Phys. Lett.
    (1997), 274, pp. 242. Link

  • $\bullet$

    B3LYP5: 20% HF exchange + 8% Slater LSDA exchange + 72% B88 GGA exchange + 19% VWN5 LSDA correlation + 81% LYP GGA correlation ⁹⁵ Becke A. D.
    J. Chem. Phys.
    (1993), 98, pp. 5648. Link ^{, 1265} Stephens P. J. et al.
    J. Phys. Chem.
    (1994), 98, pp. 11623. Link

  • $\bullet$

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

  • $\bullet$

    B1LYP: 25% HF exchange + 75% B88 GGA exchange + LYP GGA correlation ¹⁷ Adamo C., Barone V.
    Chem. Phys. Lett.
    (1997), 274, pp. 242. Link

  • $\bullet$

    B1PW91: 25% HF exchange + 75% B88 GGA exchange + PW91 GGA correlation ¹⁷ Adamo C., Barone V.
    Chem. Phys. Lett.
    (1997), 274, pp. 242. Link

  • $\bullet$

    B3LYP5: 20% HF exchange + 8% Slater LSDA exchange + 72% B88 GGA exchange + 19% VWN5 LSDA correlation + 81% LYP GGA correlation ⁹⁵ Becke A. D.
    J. Chem. Phys.
    (1993), 98, pp. 5648. Link ^{, 1265} Stephens P. J. et al.
    J. Phys. Chem.
    (1994), 98, pp. 11623. Link

  • $\bullet$

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

  • $\bullet$

    B3PW91: 20% HF exchange + 8% Slater LSDA exchange + 72% B88 GGA exchange+ 19% PW92 LSDA correlation + 81% PW91 GGA correlation ⁹⁵ Becke A. D.
    J. Chem. Phys.
    (1993), 98, pp. 5648. Link

  • $\bullet$

    B5050LYP: 50% HF exchange + 8% Slater LSDA exchange + 42% B88 GGA exchange + 19% VWN5 LSDA correlation + 81% LYP GGA correlation ¹¹⁹⁸ Shao Y., Head-Gordon M., Krylov A. I.
    J. Chem. Phys.
    (2003), 118, pp. 4807. Link

  • $\bullet$

    B97-1: Self-consistent parameterization of Becke’s B97 density functional with 21% HF exchange ⁵⁰⁰ Hamprecht F. A. et al.
    J. Chem. Phys.
    (1998), 109, pp. 6264. Link

  • $\bullet$

    B97-2: Re-parameterization of B97 by Tozer and coworkers with 21% HF exchange ¹⁴²⁴ Wilson P. J., Bradley T. J., Tozer D. J.
    J. Chem. Phys.
    (2001), 115, pp. 9233. Link

  • $\bullet$

    B97-3: 16-parameter version of B97 by Keal and Tozer with $\approx$ 26.93% HF exchange ⁶⁶¹ Keal T. W., Tozer D. J.
    J. Chem. Phys.
    (2005), 123, pp. 121103. Link

  • $\bullet$

    B97-K: Re-parameterization of B97 for kinetics by Boese and Martin with 42% HF exchange ¹³⁹ Boese A. D., Martin J. M. L.
    J. Chem. Phys.
    (2004), 121, pp. 3405. Link

  • $\bullet$

    BHHLYP: 50% HF exchange + 50% B88 GGA exchange + LYP GGA correlation, sometimes called BH&H-LYP ⁴⁶⁸ Gray M., Mandal A., Herbert J. M.
    J. Phys. Chem. A
    (2025), 129, pp. 3969. Link

  • $\bullet$

    HFLYP*: 100% HF exchange + LYP GGA correlation

  • $\bullet$

    MPW1K: 42.8% HF exchange + 57.2% mPW91 GGA exchange + PW91 GGA correlation ⁸⁴³ Lynch B. J. et al.
    J. Phys. Chem. A
    (2000), 104, pp. 4811. Link

  • $\bullet$

    MPW1LYP: 25% HF exchange + 75% mPW91 GGA exchange + LYP GGA correlation ¹⁸ Adamo C., Barone V.
    J. Chem. Phys.
    (1998), 108, pp. 664. Link

  • $\bullet$

    MPW1PBE: 25% HF exchange + 75% mPW91 GGA exchange + PBE GGA correlation ¹⁸ Adamo C., Barone V.
    J. Chem. Phys.
    (1998), 108, pp. 664. Link

  • $\bullet$

    MPW1PW91: 25% HF exchange + 75% mPW91 GGA exchange + PW91 GGA correlation ¹⁸ Adamo C., Barone V.
    J. Chem. Phys.
    (1998), 108, pp. 664. Link

  • $\bullet$

    O3LYP: 11.61% HF exchange + $\approx$ 7.1% Slater LSDA exchange + 81.33% OPTX GGA exchange + 19% VWN5 LSDA correlation + 81% LYP GGA correlation ⁵⁷⁰ Hoe W.-M., Cohen A. J., Handy N. C.
    Chem. Phys. Lett.
    (2001), 341, pp. 319. Link

  • $\bullet$

    PBEh-3c: Low-cost composite scheme of Grimme and coworkers for use with the def2-mSVP basis set only ⁴⁷¹ Grimme S. et al.
    J. Chem. Phys.
    (2015), 143, pp. 054107. Link

  • $\bullet$

    PBE50: 50% HF exchange + 50% PBE GGA exchange + PBE GGA correlation ¹¹³ Bernard Y. A., Shao Y., Krylov A. I.
    J. Chem. Phys.
    (2012), 136, pp. 204103. Link

  • $\bullet$

    SOGGA11-X: 21-parameter functional with 40.15% HF exchange by Peverati and Truhlar ¹⁰⁴⁵ Peverati R., Truhlar D. G.
    J. Chem. Phys.
    (2011), 135, pp. 191102. Link

  • $\bullet$

    WC04: Hybrid density functional optimized for the computation of ${}^{13}$C chemical shifts ¹⁴¹⁶ Wiitala K. W., Hoye T. R., Cramer C. J.
    J. Chem. Theory Comput.
    (2006), 2, pp. 1085. Link

  • $\bullet$

    WP04: Hybrid density functional optimized for the computation of ${}^1$H chemical shifts ¹⁴¹⁶ Wiitala K. W., Hoye T. R., Cramer C. J.
    J. Chem. Theory Comput.
    (2006), 2, pp. 1085. Link

  • $\bullet$

    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 correlation ¹⁴⁵² Xu X., Goddard III W. A.
    Proc. Natl. Acad. Sci. USA
    (2004), 101, pp. 2673. Link

• $\circ$

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

  • $\bullet$

    M06-2X: 29-parameter functional with 54% HF exchange by Zhao and Truhlar ¹⁵⁰⁹ Zhao Y., Truhlar D. G.
    Theor. Chem. Acc.
    (2008), 120, pp. 215. Link

  • $\bullet$

    M08-HX: 47-parameter functional with 52.23% HF exchange by Zhao and Truhlar ¹⁵⁰⁸ Zhao Y., Truhlar D. G.
    J. Chem. Theory Comput.
    (2007), 4, pp. 1849. Link

  • $\bullet$

    TPSSh: 10% HF exchange + 90% TPSS meta-GGA exchange + TPSS meta-GGA correlation ¹²⁵⁰ Staroverov V. N. et al.
    J. Chem. Phys.
    (2003), 119, pp. 12129. Link

  • $\bullet$

    revTPSSh: 10% HF exchange + 90% revTPSS meta-GGA exchange + revTPSS meta-GGA correlation ²⁸¹ Csonka G. I., Perdew J. P., Ruzsinszky A.
    J. Chem. Theory Comput.
    (2010), 6, pp. 3688. Link

  • $\bullet$

    B1B95: 28% HF exchange + 72% B88 GGA exchange + B95 meta-GGA correlation ⁹⁷ Becke A. D.
    J. Chem. Phys.
    (1996), 104, pp. 1040. Link

  • $\bullet$

    B3TLAP: 17.13% HF exchange + 9.66% Slater LSDA exchange + 72.6% B88 GGA exchange + PK06 meta-GGA correlation ¹⁰⁸⁷ Proynov E., Kong J.
    J. Chem. Theory Comput.
    (2007), 3, pp. 746. Link

  • $\bullet$

    BB1K: 42% HF exchange + 58% B88 GGA exchange + B95 meta-GGA correlation ¹⁵⁰⁰ Zhao Y., Lynch B. J., Truhlar D. G.
    J. Phys. Chem. A
    (2004), 108, pp. 2715. Link

  • $\bullet$

    BMK: Boese-Martin functional for kinetics with 42% HF exchange ¹³⁹ Boese A. D., Martin J. M. L.
    J. Chem. Phys.
    (2004), 121, pp. 3405. Link

  • $\bullet$

    dlDF: Dispersion-less density functional (based on the M05-2X functional form) by Szalewicz and coworkers ¹⁰⁴⁰ Pernal K. et al.
    Phys. Rev. Lett.
    (2009), 103, pp. 263201. Link

  • $\bullet$

    M05: 22-parameter functional with 28% HF exchange by Zhao, Schultz, and Truhlar ¹⁵⁰¹ Zhao Y., Schultz N. E., Truhlar D. G.
    J. Chem. Phys.
    (2005), 123, pp. 161103. Link

  • $\bullet$

    M05-2X: 19-parameter functional with 56% HF exchange by Zhao, Schultz, and Truhlar ¹⁵⁰² Zhao Y., Schultz N. E., Truhlar D. G.
    J. Chem. Theory Comput.
    (2006), 2, pp. 364. Link

  • $\bullet$

    M06: 33-parameter functional with 27% HF exchange by Zhao and Truhlar ¹⁵⁰⁹ Zhao Y., Truhlar D. G.
    Theor. Chem. Acc.
    (2008), 120, pp. 215. Link

  • $\bullet$

    M06-HF: 32-parameter functional with 100% HF exchange by Zhao and Truhlar ¹⁵⁰⁶ Zhao Y., Truhlar D. G.
    J. Phys. Chem. A
    (2006), 110, pp. 13126. Link

  • $\bullet$

    M08-SO: 44-parameter functional with 56.79% HF exchange by Zhao and Truhlar ¹⁵⁰⁸ Zhao Y., Truhlar D. G.
    J. Chem. Theory Comput.
    (2007), 4, pp. 1849. Link

  • $\bullet$

    MGGA_MS2h: 9% HF exchange + 91 % MGGA_MS2 meta-GGA exchange + regTPSS GGA correlation ¹²⁸¹ Sun J. et al.
    J. Chem. Phys.
    (2013), 138, pp. 044113. Link

  • $\bullet$

    MGGA_MVSh: 25% HF exchange + 75 % MGGA_MVS meta-GGA exchange + regTPSS GGA correlation ¹²⁸² Sun J., Perdew J. P., Ruzsinszky A.
    Proc. Natl. Acad. Sci. USA
    (2015), 112, pp. 685. Link

  • $\bullet$

    MN15: 59-parameter functional with 44% HF exchange by Truhlar and coworkers ¹⁴⁷⁵ Yu H. S. et al.
    Chem. Sci.
    (2016), 7, pp. 5032. Link

  • $\bullet$

    MPW1B95: 31% HF exchange + 69% mPW91 GGA exchange + B95 meta-GGA correlation ¹⁵⁰³ Zhao Y., Truhlar D. G.
    J. Phys. Chem. A
    (2004), 108, pp. 6908. Link

  • $\bullet$

    MPWB1K: 44% HF exchange + 56% mPW91 GGA exchange + B95 meta-GGA correlation ¹⁵⁰³ Zhao Y., Truhlar D. G.
    J. Phys. Chem. A
    (2004), 108, pp. 6908. Link

  • $\bullet$

    PW6B95: 6-parameter combination of 28 % HF exchange, 72 % optimized PW91 GGA exchange, and re-optimized B95 meta-GGA correlation by Zhao and Truhlar ¹⁵⁰⁴ Zhao Y., Truhlar D. G.
    J. Phys. Chem. A
    (2005), 109, pp. 5656. Link

  • $\bullet$

    PWB6K: 6-parameter combination of 46 % HF exchange, 54 % optimized PW91 GGA exchange, and re-optimized B95 meta-GGA correlation by Zhao and Truhlar ¹⁵⁰⁴ Zhao Y., Truhlar D. G.
    J. Phys. Chem. A
    (2005), 109, pp. 5656. Link

  • $\bullet$

    revM06: 32-parameter functional with 40.41% HF exchange ¹³⁸⁰ Wang Y. et al.
    Proc. Natl. Acad. Sci. USA
    (2018), 115, pp. 10257. Link

  • $\bullet$

    SCAN0: 25% HF exchange + 75% SCAN meta-GGA exchange + SCAN meta-GGA correlation ⁵⁸⁶ Hui K., Chai J.-D.
    J. Chem. Phys.
    (2016), 144, pp. 044114. Link

  • $\bullet$

    t-HCTHh ($\tau$-HCTHh): 17-parameter functional with 15% HF exchange by Boese and Handy ¹³⁸ Boese A. D., Handy N. C.
    J. Chem. Phys.
    (2002), 116, pp. 9559. Link

  • $\bullet$

    TPSS0: 25% HF exchange + 75% TPSS meta-GGA exchange + TPSS meta-GGA correlation ⁴⁷⁶ Grimme S.
    J. Phys. Chem. A
    (2005), 109, pp. 3067. Link

• $\circ$

  Range-Separated Hybrid Generalized Gradient Approximation (RSH GGA)

  • $\bullet$

    wB97X-V ($\omega$B97X-V): 10-parameter combinatorially-optimized, dispersion-corrected (VV10) functional with 16.7% SR HF exchange, 100% LR HF exchange, and $\omega =0.3$ ⁸⁷⁶ Mardirossian N., Head-Gordon M.
    Phys. Chem. Chem. Phys.
    (2014), 16, pp. 9904. Link

  • $\bullet$

    wB97XV-D3s(BJ) ($\omega$B97XV-D3s(BJ)): $\omega$B97X-V with the VV10 NLC functional replaced by DFT-D3s(BJ) (s6 = 1.0, s8 = 0.2641, a1 = 0.0, a2 = 5.4959)

  • $\bullet$

    wB97XV-D4 ($\omega$B97XV-D4): $\omega$B97X-V with the VV10 NLC functional replaced by DFT-D4 (s6 = 1.0, s8 = 0.5093, s9 = 1.0, a1 = 0.0662, a2 = 5.4487)

  • $\bullet$

    wB97X-D ($\omega$B97X-D): 15-parameter dispersion-corrected (DFT-CHG) functional with $\approx$ 22.2% SR HF exchange, 100% LR HF exchange, and $\omega =0.2$ ²¹⁹ Chai J.-D., Head-Gordon M.
    Phys. Chem. Chem. Phys.
    (2008), 10, pp. 6615. Link

  • $\bullet$

    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 $\omega =0.25$ ⁸¹¹ Lin Y.-S. et al.
    J. Chem. Theory Comput.
    (2013), 9, pp. 263. Link

  • $\bullet$

    KS-$\omega$B97X-D4 (see Example 5.6.3 for the usage): 10-parameter combinatorially-optimized, dispersion-corrected (D4) functional with $\approx$ 18.7% SR HF exchange, 100% LR HF exchange, and $\omega =0.3$ ⁷⁹⁴ Li S., Chai J.-D.
    J. Chem. Theory Comput.
    (2025), 21, pp. 9538. Link

  • $\bullet$

    CAM-B3LYP: Coulomb-attenuating method functional by Handy and coworkers ¹⁴⁵⁸ Yanai T., Tew D. P., Handy N. C.
    Chem. Phys. Lett.
    (2004), 393, pp. 51. Link

  • $\bullet$

    CAM-QTP00: Re-parameterized CAM-B3LYP designed to satisfy the IP-theorem for all occupied orbitals of the water molecule ¹³⁵² Verma P., Bartlett R. J.
    J. Chem. Phys.
    (2014), 140, pp. 18A534. Link

  • $\bullet$

    CAM-QTP01: Re-parameterized CAM-B3LYP optimized to satisfy the valence IPs of the water molecule, 34 excitation states, and G2-1 atomization energies ⁶²⁸ Jin Y., Bartlett R. J.
    J. Chem. Phys.
    (2016), 145, pp. 034107. Link

  • $\bullet$

    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 ⁷⁰⁵ Krukau A. V. et al.
    J. Chem. Phys.
    (2006), 125, pp. 224106. Link ^{, 538} Henderson T. M., Janesko B. G., Scuseria G. E.
    J. Chem. Phys.
    (2008), 128, pp. 194105. Link

  • $\bullet$

    LC-rVV10*: LC-VV10 density functional with the VV10 NLC functional replaced by the rVV10 NLC functional ⁸⁸⁰ Mardirossian N. et al.
    J. Phys. Chem. Lett.
    (2017), 8, pp. 35. Link

  • $\bullet$

    LC-VV10: 0% SR HF exchange + 100% LR HF exchange + $\omega$PBE GGA exchange + PBE GGA correlation + VV10 non-local correlation ($\omega$=0.45) ¹³⁶⁸ Vydrov O. A., Van Voorhis T.
    J. Chem. Phys.
    (2010), 133, pp. 244103. Link

  • $\bullet$

    LC-wPBE08 (LC-$\omega$PBE08): 0% SR HF exchange + 100% LR HF exchange + $\omega$PBE GGA exchange + PBE GGA correlation ($\omega$=0.45) ¹³⁹³ Weintraub E., Henderson T. M., Scuseria G. E.
    J. Chem. Theory Comput.
    (2009), 5, pp. 754. Link

  • $\bullet$

    LRC-BOP (LRC-$\mu$BOP): 0% SR HF exchange + 100% LR HF exchange + $\mu$B88 GGA exchange + BOP GGA correlation ($\omega$=0.47) ¹²⁴¹ Song J. W. et al.
    J. Chem. Phys.
    (2007), 126, pp. 154105. Link ^{, 1130} Richard R. M., Herbert J. M.
    J. Chem. Theory Comput.
    (2011), 7, pp. 1296. Link

  • $\bullet$

    LRC-wPBE (LRC-$\omega$PBE): 0% SR HF exchange + 100% LR HF exchange + $\omega$PBE GGA exchange + PBE GGA correlation ($\omega$=0.3) ¹¹³⁹ Rohrdanz M. A., Herbert J. M.
    J. Chem. Phys.
    (2008), 129, pp. 034107. Link

  • $\bullet$

    LRC-wPBEh (LRC-$\omega$PBEh): 20% SR HF exchange + 100% LR HF exchange + 80% $\omega$PBE GGA exchange + PBE GGA correlation ($\omega$=0.2) ¹¹⁴⁰ Rohrdanz M. A., Martins K. M., Herbert J. M.
    J. Chem. Phys.
    (2009), 130, pp. 054112. Link

  • $\bullet$

    N12-SX: 26-parameter non-separable GGA with 25% SR HF exchange, 0% LR HF exchange, and $\omega =0.11$ ¹⁰⁵⁰ Peverati R., Truhlar D. G.
    Phys. Chem. Chem. Phys.
    (2012), 14, pp. 16187. Link

  • $\bullet$

    rCAM-B3LYP: Re-fit CAM-B3LYP with the goal of minimizing many-electron self-interaction error ²⁵⁵ Cohen A. J., Mori-Sánchez P., Yang W.
    J. Chem. Phys.
    (2007), 126, pp. 191109. Link

  • $\bullet$

    wB97 ($\omega$B97): 13-parameter functional with 0% SR HF exchange, 100% LR HF exchange, and $\omega =0.4$ ²¹⁸ Chai J.-D., Head-Gordon M.
    J. Chem. Phys.
    (2008), 128, pp. 084106. Link

  • $\bullet$

    wB97X ($\omega$B97X): 14-parameter functional with $\approx$ 15.77% SR HF exchange, 100% LR HF exchange, and $\omega =0.3$ ²¹⁸ Chai J.-D., Head-Gordon M.
    J. Chem. Phys.
    (2008), 128, pp. 084106. Link

  • $\bullet$

    wB97X-rV* ($\omega$B97X-rV): $\omega$B97X-V density functional with the VV10 NLC functional replaced by the rVV10 NLC functional ⁸⁸⁰ Mardirossian N. et al.
    J. Phys. Chem. Lett.
    (2017), 8, pp. 35. Link

• $\circ$

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

  • $\bullet$

    wB97M-V ($\omega$B97M-V): 12-parameter combinatorially-optimized, dispersion-corrected (VV10) functional with 15% SR HF exchange, 100% LR HF exchange, and $\omega =0.3$ ⁸⁷⁸ Mardirossian N., Head-Gordon M.
    J. Chem. Phys.
    (2016), 144, pp. 214110. Link

  • $\bullet$

    wB97MV-D3s(BJ) ($\omega$B97M-D3s(BJ)): wB97M-V with the VV10 NLC functional replaced by DFT-D3s(BJ) (s6 = 1.0, s8 = 0.2641, a1 = 0.0, a2 = 5.4959)

  • $\bullet$

    wB97MV-D4 ($\omega$B97M-D4): wB97M-V with the VV10 NLC functional replaced by DFT-D4 (s6 = 1.0, s8 = 0.5093, s9 = 1.0, a1 = 0.0662, a2 = 5.4487)

  • $\bullet$

    M06-SX: local revM06-L functional with 33.5% SR HF exchange ¹³⁸¹ Wang Y. et al.
    Proc. Natl. Acad. Sci. USA
    (2020), 117, pp. 2294. Link

  • $\bullet$

    M11: 40-parameter functional with 42.8% SR HF exchange, 100% LR HF exchange, and $\omega =0.25$ ¹⁰⁴⁶ Peverati R., Truhlar D. G.
    J. Phys. Chem. Lett.
    (2011), 2, pp. 2810. Link

  • $\bullet$

    MN12-SX: 58-parameter non-separable meta-GGA with 25% SR HF exchange, 0% LR HF exchange, and $\omega =0.11$ ¹⁰⁵⁰ Peverati R., Truhlar D. G.
    Phys. Chem. Chem. Phys.
    (2012), 14, pp. 16187. Link

  • $\bullet$

    revM11: 22-parameter functional with 22.5% SR HF exchange, 100% LR HF exchange, and $\omega =0.4$ ¹³⁵⁴ Verma P. et al.
    J. Phys. Chem. A
    (2019), 123, pp. 2966. Link

  • $\bullet$

    wB97M-rV* ($\omega$B97X-rV): $\omega$B97M-V density functional with the VV10 NLC functional replaced by the rVV10 NLC functional ⁸⁸⁰ Mardirossian N. et al.
    J. Phys. Chem. Lett.
    (2017), 8, pp. 35. Link

  • $\bullet$

    wM05-D ($\omega$M05-D): 21-parameter dispersion-corrected (DFT-CHG) functional with $\approx$ 36.96% SR HF exchange, 100% LR HF exchange, and $\omega =0.2$ ⁸¹² Lin Y.-S. et al.
    J. Chem. Phys.
    (2012), 136, pp. 154109. Link

  • $\bullet$

    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 $\omega =0.3$ ⁸¹¹ Lin Y.-S. et al.
    J. Chem. Theory Comput.
    (2013), 9, pp. 263. Link

• $\circ$

  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_CORR

  • $\bullet$

    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 $\omega =0.3$ ²²⁰ Chai J.-D., Head-Gordon M.
    J. Chem. Phys.
    (2009), 131, pp. 174105. Link

  • $\bullet$

    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 $\omega =0.3$ ²²⁰ Chai J.-D., Head-Gordon M.
    J. Chem. Phys.
    (2009), 131, pp. 174105. Link

  • $\bullet$

    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) ¹⁴⁹³ Zhang Y., Xu X., Goddard III W. A.
    Proc. Natl. Acad. Sci. USA
    (2009), 106, pp. 4963. Link

  • $\bullet$

    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) ¹⁴⁸⁶ Zhang I. Y. et al.
    Proc. Natl. Acad. Sci. USA
    (2011), 108, pp. 19896. Link

  • $\bullet$

    wDSD72-PBEP86-D4 ($\omega$DSD72-PBEP86-D4): 0.72 HF range-separated exchange ($\omega$ = 0.13 bohr${}^{-1}$) + 0.28 PBE GGA exchange + 0.3425 P86 GGA correlation + 0.6904 OS MP2 correlation + 0.1343 SS MP2 correlation with DFT-D4 (s6 = 0.4685, s8 = 0, s9 = 1.0, a1 = 0.1884, a2 = 5.0101) ¹¹⁵⁷ Santra G., Cho M., Martin J. M. L.
    jcpa
    (2021), 125, pp. 4614. Link

  • $\bullet$

    xDSD75-PBEP86-D4: 0.75 HF exchange + 0.25 PBE GGA exchange + 0.3517 (1.0 during SCF cycles) P86 GGA correlation + 0.6623 OS MP2 correlation + 0.1168 SS MP2 correlation with DFT-D4 (s6 = 0.4246, s8 = 0, s9 = 1.0, a1 = 0.2828, a2 = 4.7204) ¹¹⁵⁷ Santra G., Cho M., Martin J. M. L.
    jcpa
    (2021), 125, pp. 4614. Link

  • $\bullet$

    revDOD-PBEP86-D4: 0.69 HF exchange + 0.31 PBE GGA exchange + 0.4301 P86 GGA correlation + 0.6131 OS MP2 correlation with DFT-D4 (s6 = 0.6158, s8 = 0, s9 = 1.0, a1 = 0.344, a2 = 4.2427) ¹¹⁵⁷ Santra G., Cho M., Martin J. M. L.
    jcpa
    (2021), 125, pp. 4614. Link

  • $\bullet$

    revDSD-PBEP86-D4: 0.69 HF exchange + 0.31 PBE GGA exchange + 0.4224 P86 GGA correlation + 0.5935 OS MP2 correlation + 0.0566 SS MP2 correlation with DFT-D4 (s6 = 0.5917, s8 = 0, s9 = 1.0, a1 = 0.371, a2 = 4.2014) ¹¹⁵⁷ Santra G., Cho M., Martin J. M. L.
    jcpa
    (2021), 125, pp. 4614. Link

  • $\bullet$

    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) tail ⁶⁹⁹ Kozuch S., Martin J. M. L.
    J. Comput. Chem.
    (2013), 34, pp. 2327. Link

  • $\bullet$

    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) tail ⁶⁹⁹ Kozuch S., Martin J. M. L.
    J. Comput. Chem.
    (2013), 34, pp. 2327. Link

  • $\bullet$

    B2-PLYP: 53% HF exchange + 47% B88 GGA exchange + 73% LYP GGA correlation + 27% MP2 correlation ⁴⁷⁷ Grimme S.
    J. Chem. Phys.
    (2006), 124, pp. 034108. Link

  • $\bullet$

    B2NC-PLYP: 0.81 HF exchange + 0.19 B88 GGA exchange + 0.45 LYP GGA correlation + 0.55 MP2 correlation ¹⁴⁷⁴ Yu F.
    J. Phys. Chem. A
    (2014), 118, pp. 3175. Link

  • $\bullet$

    mPW2-PLYP: 0.55 HF exchange + 0.45 mPW GGA exchange + 0.75 LYP GGA correlation + 0.25 MP2 correlation ¹¹⁷⁸ Schwabe T., Grimme S.
    Phys. Chem. Chem. Phys.
    (2006), 8, pp. 4398. Link

  • $\bullet$

    mPW2NC-PLYP: 0.67 HF exchange + 0.33 mPW GGA exchange + 0.51 LYP GGA correlation + 0.49 MP2 correlation ¹⁴⁷⁴ Yu F.
    J. Phys. Chem. A
    (2014), 118, pp. 3175. Link

  • $\bullet$

    B2GP-PLYP: 65% HF exchange + 35% B88 GGA exchange + 64% LYP GGA correlation + 36% MP2 correlation ⁶⁵⁴ Karton A. et al.
    J. Phys. Chem. A
    (2008), 112, pp. 12868. Link

  • $\bullet$

    LS1DH-PBE: 75% HF exchange + 25% PBE GGA exchange + 57.8125% PBE GGA correlation + 42.1875% MP2 correlation ¹³²¹ Toulouse J. et al.
    J. Chem. Phys.
    (2011), 135, pp. 101102. Link

  • $\bullet$

    PBE-QIDH: 69.3361% HF exchange + 30.6639% PBE GGA exchange + 66.6667% PBE GGA correlation + 33.3333% MP2 correlation ¹⁵⁵ Brémond É. et al.
    J. Chem. Phys.
    (2014), 141, pp. 031101. Link

  • $\bullet$

    PBE0-2: $\approx$ 79.37% HF exchange + $\approx$ 20.63% PBE GGA exchange + 50% PBE GGA correlation + 50% MP2 correlation ²²¹ Chai J.-D., Mao S.-P.
    Chem. Phys. Lett.
    (2012), 538, pp. 121. Link

  • $\bullet$

    PBE0-DH: 50% HF exchange + 50% PBE GGA exchange + 87.5% PBE GGA correlation + 12.5% MP2 correlation ¹⁵⁴ Brémond E., Adamo C.
    J. Chem. Phys.
    (2011), 135, pp. 024106. Link

  • $\bullet$

    SOS0-PBE0-2: 0.79 HF exchange + 0.21 PBE GGA exchange + 0.5 PBE GGA correlation + 0.66667 OS MP2 correlation

• $\circ$

  Double Hybrid Meta-Generalized Gradient Approximation (DH MGGA)

  • $\bullet$

    wB97M(2): 14-parameter functional form including MP2 correlation based on $\omega$B97M-V orbitals ⁸⁷⁹ Mardirossian N., Head-Gordon M.
    J. Chem. Phys.
    (2018), 148, pp. 241736. Link

  • $\bullet$

    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) tail ⁴⁴⁹ Goerigk L., Grimme S.
    J. Chem. Theory Comput.
    (2011), 7, pp. 291. Link

  • $\bullet$

    Pr2SCAN69-D4: 0.69 HF exchange + 0.31 r2SCAN meta-GGA exchange + 0.56 r2SCAN meta-GGA correlation + 0.592593 OS MP2 correlation with DFT-D4 (s6 = 0.7167, s8 = 0, s9 = 1.0, a1 = 0.4644, a2 = 5.2563) ¹⁴³⁰ Wittmann L. et al.
    J. Chem. Phys.
    (2023), 159, pp. 224103. Link

  • $\bullet$

    Pr2SCAN50-D4: 0.5 HF exchange + 0.5 r2SCAN meta-GGA exchange + 0.75 r2SCAN meta-GGA correlation + 0.333333 OS MP2 correlation with DFT-D4 (s6 = 0.7964, s8 = 0.3421, s9 = 1.0, a1 = 0.4663, a2 = 5.7916) ¹⁴³⁰ Wittmann L. et al.
    J. Chem. Phys.
    (2023), 159, pp. 224103. Link

  • $\bullet$

    wPr2SCAN50-D4 ($\omega$Pr2SCAN50-D4): 0.5 HF range-separated exchange ($\omega$ = 0.214 bohr${}^{-1}$) + 0.5 r2SCAN meta-GGA exchange + 0.65 r2SCAN meta-GGA correlation + 0.46667 OS MP2 correlation with DFT-D4 (s6 = 0.8143, s8 = 0.3842, s9 = 1.0, a1 = 0.4135, a2 = 5.8773) ¹⁴³⁰ Wittmann L. et al.
    J. Chem. Phys.
    (2023), 159, pp. 224103. Link

  • $\bullet$

    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) tail ⁶⁹⁹ Kozuch S., Martin J. M. L.
    J. Comput. Chem.
    (2013), 34, pp. 2327. Link

  • $\bullet$

    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) tail ⁴⁴⁹ Goerigk L., Grimme S.
    J. Chem. Theory Comput.
    (2011), 7, pp. 291. Link