5.3 Overview of Available Functionals

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.

  • Local Spin-Density Approximation (LSDA)

    • SPW92*: Slater LSDA exchange + PW92 LSDA correlation

    • LDA: Slater LSDA exchange + VWN5 LSDA correlation

    • SVWN5*: Slater LSDA exchange + VWN5 LSDA correlation

  • Generalized Gradient Approximation (GGA)

    • B97-D3(0): B97-D with a fitted DFT-D3(0) tail instead of the original DFT-D2 tail324

    • B97-D: 9-parameter dispersion-corrected (DFT-D2) functional by Grimme331

    • PBE*: PBE GGA exchange + PBE GGA correlation

    • BLYP*: B88 GGA exchange + LYP GGA correlation

    • revPBE*: revPBE GGA exchange + PBE GGA correlation

    • BEEF-vdW: 31-parameter semi-empirical exchange functional developed via a Bayesian error estimation framework paired with PBE correlation and vdW-DF-10 NLC969

    • BOP: B88 GGA exchange + BOP “one-parameter progressive” GGA correlation925

    • BP86*: B88 GGA exchange + P86 GGA correlation

    • BP86VWN*: B88 GGA exchange + P86VWN5 GGA correlation

    • BPBE*: B88 GGA exchange + PBE GGA correlation

    • EDF1: Modification of BLYP to give good performance in the 6-31+G* basis set27

    • EDF2: Modification of B3LYP to give good performance in the cc-pVTZ basis set for frequencies569

    • GAM: 21-parameter non-separable gradient approximation functional by Truhlar and coworkers1031

    • HCTH93 (HCTH/93): 15-parameter functional trained on 93 systems by Handy and coworkers337

    • HCTH120 (HCTH/120): 15-parameter functional trained on 120 systems by Boese et al.101

    • HCTH147 (HCTH/147): 15-parameter functional trained on 147 systems by Boese et al.101

    • HCTH407 (HCTH/407): 15-parameter functional trained on 407 systems by Boese and Handy102

    • HLE16 – HCTH/407 exchange functional enhanced by a factor of 1.25 + HCTH/407 correlation functional enhanced by a factor of 0.5942

    • KT1: GGA functional designed specifically for shielding constant calculations456

    • KT2: GGA functional designed specifically for shielding constant calculations456

    • KT3: GGA functional with improved results for main-group nuclear magnetic resonance shielding constants457

    • mPW91*: mPW91 GGA exchange + PW91 GGA correlation

    • N12: 21-parameter non-separable gradient approximation functional by Peverati and Truhlar718

    • OLYP*: OPTX GGA exchange + LYP GGA correlation

    • PBEOP: PBE GGA exchange + PBEOP “one-parameter progressive” GGA correlation925

    • PBEsol*: PBEsol GGA exchange + PBEsol GGA correlation

    • PW91*: PW91 GGA exchange + PW91 GGA correlation

    • RPBE*: RPBE GGA exchange + PBE GGA correlation

    • rVV10*: rPW86 GGA exchange + PBE GGA correlation + rVV10 non-local correlation799

    • SOGGA*: SOGGA GGA exchange + PBE GGA correlation

    • SOGGA11: 20-parameter functional by Peverati, Zhao, and Truhlar721

    • VV10: rPW86 GGA exchange + PBE GGA correlation + VV10 non-local correlation952

  • Meta-Generalized Gradient Approximation (meta-GGA)

    • B97M-V: 12-parameter combinatorially-optimized, dispersion-corrected (VV10) functional by Mardirossian and Head-Gordon607

    • B97M-rV*: B97M-V density functional with the VV10 NLC functional replaced by the rVV10 NLC functional609

    • M06-L: 34-parameter functional by Zhao and Truhlar1048

    • revM06-L: 31-parameter functional

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

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

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

    • M11-L: 44-parameter dual-range functional by Peverati and Truhlar717

    • mBEEF: 64-parameter exchange functional paired with the PBEsol correlation functional968

    • MGGA_MS0: MGGA_MS0 meta-GGA exchange + regTPSS GGA correlation892

    • MGGA_MS1: MGGA_MS1 meta-GGA exchange + regTPSS GGA correlation889

    • MGGA_MS2: MGGA_MS2 meta-GGA exchange + regTPSS GGA correlation889

    • MGGA_MVS: MGGA_MVS meta-GGA exchange + regTPSS GGA correlation890

    • MN12-L: 58-parameter meta-nonseparable gradient approximation functional by Peverati and Truhlar719

    • MN15-L: 58-parameter meta-nonseparable gradient approximation functional by Yu, He, and Truhlar1030

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

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

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

    • t-HCTH (τ-HCTH): 16-parameter functional by Boese and Handy103

    • TM*: TM meta-GGA exchange + TM meta-GGA correlation902

    • VSXC: 21-parameter functional by Voorhis and Scuseria938

  • Global Hybrid Generalized Gradient Approximation (GH GGA)

    • B3LYP: 20% HF exchange + 8% Slater LSDA exchange + 72% B88 GGA exchange + 19% VWN1RPA LSDA correlation + 81% LYP GGA correlation68, 873

    • PBE0: 25% HF exchange + 75% PBE GGA exchange + PBE GGA correlation21

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

    • B97: Becke’s original 10-parameter density functional with 19.43% HF exchange71

    • B1LYP: 25% HF exchange + 75% B88 GGA exchange + LYP GGA correlation19

    • B1PW91: 25% HF exchange + 75% B88 GGA exchange + PW91 GGA correlation19

    • B3LYP5: 20% HF exchange + 8% Slater LSDA exchange + 72% B88 GGA exchange + 19% VWN5 LSDA correlation + 81% LYP GGA correlation68, 873

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

    • B1LYP: 25% HF exchange + 75% B88 GGA exchange + LYP GGA correlation19

    • B1PW91: 25% HF exchange + 75% B88 GGA exchange + PW91 GGA correlation19

    • B3LYP5: 20% HF exchange + 8% Slater LSDA exchange + 72% B88 GGA exchange + 19% VWN5 LSDA correlation + 81% LYP GGA correlation68, 873

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

    • B3PW91: 20% HF exchange + 8% Slater LSDA exchange + 72% B88 GGA exchange+ 19% PW92 LSDA correlation + 81% PW91 GGA correlation68

    • B5050LYP: 50% HF exchange + 8% Slater LSDA exchange + 42% B88 GGA exchange + 19% VWN5 LSDA correlation + 81% LYP GGA correlation828

    • B97-1: Self-consistent parameterization of Becke’s B97 density functional with 21% HF exchange337

    • B97-2: Re-parameterization of B97 by Tozer and coworkers with 21% HF exchange993

    • B97-3: 16-parameter version of B97 by Keal and Tozer with 26.93% HF exchange458

    • B97-K: Re-parameterization of B97 for kinetics by Boese and Martin with 42% HF exchange104

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

    • HFLYP*: 100% HF exchange + LYP GGA correlation

    • MPW1K: 42.8% HF exchange + 57.2% mPW91 GGA exchange + PW91 GGA correlation594

    • MPW1LYP: 25% HF exchange + 75% mPW91 GGA exchange + LYP GGA correlation20

    • MPW1PBE: 25% HF exchange + 75% mPW91 GGA exchange + PBE GGA correlation20

    • MPW1PW91: 25% HF exchange + 75% mPW91 GGA exchange + PW91 GGA correlation20

    • O3LYP: 11.61% HF exchange + 7.1% Slater LSDA exchange + 81.33% OPTX GGA exchange + 19% VWN5 LSDA correlation + 81% LYP GGA correlation383

    • PBEh-3c: Low-cost composite scheme of Grimme and coworkers for use with the def2-mSVP basis set only325

    • PBE50: 50% HF exchange + 50% PBE GGA exchange + PBE GGA correlation84

    • SOGGA11-X: 21-parameter functional with 40.15% HF exchange by Peverati and Truhlar715

    • WC04: Hybrid density functional optimized for the computation of 13C chemical shifts986

    • WP04: Hybrid density functional optimized for the computation of 1H chemical shifts986

    • X3LYP: 21.8% HF exchange + 7.3% Slater LSDA exchange + 54.24% B88 GGA exchange + 16.66% PW91 GGA exchange + 12.9% VWN1RPA LSDA correlation + 87.1% LYP GGA correlation1018

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

    • M06-2X: 29-parameter functional with 54% HF exchange by Zhao and Truhlar1052

    • M08-HX: 47-parameter functional with 52.23% HF exchange by Zhao and Truhlar1051

    • TPSSh: 10% HF exchange + 90% TPSS meta-GGA exchange + TPSS meta-GGA correlation863

    • revTPSSh: 10% HF exchange + 90% revTPSS meta-GGA exchange + revTPSS meta-GGA correlation198

    • B1B95: 28% HF exchange + 72% B88 GGA exchange + B95 meta-GGA correlation70

    • B3TLAP: 17.13% HF exchange + 9.66% Slater LSDA exchange + 72.6% B88 GGA exchange + PK06 meta-GGA correlation748, 749

    • BB1K: 42% HF exchange + 58% B88 GGA exchange + B95 meta-GGA correlation1043

    • BMK: Boese-Martin functional for kinetics with 42% HF exchange104

    • dlDF: Dispersion-less density functional (based on the M05-2X functional form) by Szalewicz and coworkers713

    • M05: 22-parameter functional with 28% HF exchange by Zhao, Schultz, and Truhlar1044

    • M05-2X: 19-parameter functional with 56% HF exchange by Zhao, Schultz, and Truhlar1045

    • M06: 33-parameter functional with 27% HF exchange by Zhao and Truhlar1052

    • revM06: 32-parameter functional with 40.41% HF exchange959

    • M06-HF: 32-parameter functional with 100% HF exchange by Zhao and Truhlar1049

    • M08-SO: 44-parameter functional with 56.79% HF exchange by Zhao and Truhlar1051

    • MGGA_MS2h: 9% HF exchange + 91 % MGGA_MS2 meta-GGA exchange + regTPSS GGA correlation889

    • MGGA_MVSh: 25% HF exchange + 75 % MGGA_MVS meta-GGA exchange + regTPSS GGA correlation890

    • MN15: 59-parameter functional with 44% HF exchange by Truhlar and coworkers1029

    • MPW1B95: 31% HF exchange + 69% mPW91 GGA exchange + B95 meta-GGA correlation1046

    • MPWB1K: 44% HF exchange + 56% mPW91 GGA exchange + B95 meta-GGA correlation1046

    • PW6B95: 6-parameter combination of 28 % HF exchange, 72 % optimized PW91 GGA exchange, and re-optimized B95 meta-GGA correlation by Zhao and Truhlar1047

    • PWB6K: 6-parameter combination of 46 % HF exchange, 54 % optimized PW91 GGA exchange, and re-optimized B95 meta-GGA correlation by Zhao and Truhlar1047

    • SCAN0: 25% HF exchange + 75% SCAN meta-GGA exchange + SCAN meta-GGA correlation398

    • t-HCTHh (τ-HCTHh): 17-parameter functional with 15% HF exchange by Boese and Handy103

    • TPSS0: 25% HF exchange + 75% TPSS meta-GGA exchange + TPSS meta-GGA correlation329

  • Range-Separated Hybrid Generalized Gradient Approximation (RSH GGA)

    • wB97X-V (ωB97X-V): 10-parameter combinatorially-optimized, dispersion-corrected (VV10) functional with 16.7% SR HF exchange, 100% LR HF exchange, and ω=0.3606

    • wB97X-D3 (ωB97X-D3): 16-parameter dispersion-corrected (DFT-D3(0)) functional with 19.57% SR HF exchange, 100% LR HF exchange, and ω=0.25571

    • wB97X-D (ωB97X-D): 15-parameter dispersion-corrected (DFT-CHG) functional with 22.2% SR HF exchange, 100% LR HF exchange, and ω=0.2159

    • CAM-B3LYP: Coulomb-attenuating method functional by Handy and coworkers1020

    • CAM-QTP00: Re-parameterized CAM-B3LYP designed to satisfy the IP-theorem for all occupied orbitals of the water molecule941

    • CAM-QTP01: Re-parameterized CAM-B3LYP optimized to satisfy the valence IPs of the water molecule, 34 excitation states, and G2-1 atomization energies427

    • HSE-HJS: Screened-exchange “HSE06” functional with 25% SR HF exchange, 0% LR HF exchange, and ω=0.11, using the updated HJS PBE exchange hole model492, 364

    • LC-rVV10*: LC-VV10 density functional with the VV10 NLC functional replaced by the rVV10 NLC functional609

    • LC-VV10: 0% SR HF exchange + 100% LR HF exchange + ωPBE GGA exchange + PBE GGA correlation + VV10 non-local correlation (ω=0.45)952

    • LC-wPBE08 (LC-ωPBE08): 0% SR HF exchange + 100% LR HF exchange + ωPBE GGA exchange + PBE GGA correlation (ω=0.45)967

    • LRC-BOP (LRC-μBOP): 0% SR HF exchange + 100% LR HF exchange + muB88 GGA exchange + BOP GGA correlation (ω=0.47)856

    • LRC-wPBE (LRC-ωPBE): 0% SR HF exchange + 100% LR HF exchange + ωPBE GGA exchange + PBE GGA correlation (ω=0.3)788

    • LRC-wPBEh (LRC-ωPBEh): 20% SR HF exchange + 100% LR HF exchange + 80% ωPBE GGA exchange + PBE GGA correlation (ω=0.2)789

    • N12-SX: 26-parameter non-separable GGA with 25% SR HF exchange, 0% LR HF exchange, and ω=0.11720

    • rCAM-B3LYP: Re-fit CAM-B3LYP with the goal of minimizing many-electron self-interaction error182

    • wB97 (ωB97): 13-parameter functional with 0% SR HF exchange, 100% LR HF exchange, and ω=0.4158

    • wB97X (ωB97X): 14-parameter functional with 15.77% SR HF exchange, 100% LR HF exchange, and ω=0.3158

    • wB97X-rV* (ωB97X-rV): ωB97X-V density functional with the VV10 NLC functional replaced by the rVV10 NLC functional609

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

    • wB97M-V (ωB97M-V): 12-parameter combinatorially-optimized, dispersion-corrected (VV10) functional with 15% SR HF exchange, 100% LR HF exchange, and ω=0.3608

    • M11: 40-parameter functional with 42.8% SR HF exchange, 100% LR HF exchange, and ω=0.25716

    • revM11: 22-parameter functional with 22.5% SR HF exchange, 100% LR HF exchange, and ω=0.4943

    • MN12-SX: 58-parameter non-separable meta-GGA with 25% SR HF exchange, 0% LR HF exchange, and ω=0.11720

    • wB97M-rV* (ωB97X-rV): ωB97M-V density functional with the VV10 NLC functional replaced by the rVV10 NLC functional609

    • wM05-D (ωM05-D): 21-parameter dispersion-corrected (DFT-CHG) functional with 36.96% SR HF exchange, 100% LR HF exchange, and ω=0.2572

    • wM06-D3 (ωM06-D3): 25-parameter dispersion-corrected [DFT-D3(0)] functional with 27.15% SR HF exchange, 100% LR HF exchange, and ω=0.3571

  • 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

    • 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) tail490

    • wB97X-2(LP) (ωB97X-2(LP)): 13-parameter functional with 67.88% SR HF exchange, 100% LR HF exchange, 58.16% SS MP2 correlation, 47.80% OS MP2 correlation, and ω=0.3160

    • wB97X-2(TQZ) (ωB97X-2(TQZ)): 13-parameter functional with 63.62% SR HF exchange, 100% LR HF exchange, 52.93% SS MP2 correlation, 44.71% OS MP2 correlation, and ω=0.3160

    • 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)1041

    • 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)1035

    • B2PLYP: 53% HF exchange + 47% B88 GGA exchange + 73% LYP GGA correlation + 27% MP2 correlation330

    • B2GPPLYP: 65% HF exchange + 35% B88 GGA exchange + 64% LYP GGA correlation + 36% MP2 correlation453

    • 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) tail490

    • LS1DH-PBE: 75% HF exchange + 25% PBE GGA exchange + 57.8125% PBE GGA correlation + 42.1875% MP2 correlation918

    • PBE-QIDH: 69.3361% HF exchange + 30.6639% PBE GGA exchange + 66.6667% PBE GGA correlation + 33.3333% MP2 correlation117

    • PBE0-2: 79.37% HF exchange + 20.63% PBE GGA exchange + 50% PBE GGA correlation + 50% MP2 correlation161

    • PBE0-DH: 50% HF exchange + 50% PBE GGA exchange + 87.5% PBE GGA correlation + 12.5% MP2 correlation116

  • Double Hybrid Meta-Generalized Gradient Approximation (DH MGGA)

    • 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) tail312

    • 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) tail490

    • 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) tail312