5.3.4 Correlation Functionals

Note:  All correlation functionals in this section can be invoked using the $rem variable CORRELATION. 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)

  • $\bullet$

    PW92: Perdew-Wang parameterization of the LSDA correlation energy from 1992 ¹⁰⁰⁰ Perdew J. P., Wang Y.
    Phys. Rev. B
    (1992), 45, pp. 13244. Link

  • $\bullet$

    VWN5 (VWN): Vosko-Wilk-Nusair parameterization of the LSDA correlation energy #5 ¹³¹⁴ Vosko S. H., Wilk L., Nusair M.
    Can. J. Phys.
    (1980), 58, pp. 1200. Link

  • $\bullet$

    srVWN: Short-range version of the VWN correlation functional by Toulouse and coworkers ¹²⁷³ Toulouse J., Savin A., Flad H.-J.
    Int. J. Quantum Chem.
    (2004), 100, pp. 1047. Link

  • $\bullet$

    Liu-Parr: Liu-Parr ${\rho }^{1/3}$ model from the functional expansion formulation ⁸⁰² Liu S., Parr R. G.
    J. Mol. Struct. (Theochem)
    (2000), 501, pp. 29. Link

  • $\bullet$

    PK09: Proynov-Kong parameterization of the LSDA correlation energy from 2009 ¹⁰⁵² Proynov E., Kong J.
    Phys. Rev. A
    (2009), 79, pp. 014103. Link

  • $\bullet$

    PW92RPA: Perdew-Wang parameterization of the LSDA correlation energy from 1992 with RPA values ¹⁰⁰⁰ Perdew J. P., Wang Y.
    Phys. Rev. B
    (1992), 45, pp. 13244. Link

  • $\bullet$

    srPW92: Short-range version of the PW92 correlation functional by Paziani and coworkers ⁹⁸² Paziani S. et al.
    Phys. Rev. B
    (2006), 73, pp. 155111. Link

  • $\bullet$

    PZ81: Perdew-Zunger parameterization of the LSDA correlation energy from 1981 ¹⁰⁰¹ Perdew J. P., Zunger A.
    Phys. Rev. B
    (1981), 23, pp. 5048. Link

  • $\bullet$

    VWN1: Vosko-Wilk-Nusair parameterization of the LSDA correlation energy #1 ¹³¹⁴ Vosko S. H., Wilk L., Nusair M.
    Can. J. Phys.
    (1980), 58, pp. 1200. Link

  • $\bullet$

    VWN1RPA: Vosko-Wilk-Nusair parameterization of the LSDA correlation energy #1 with RPA values ¹³¹⁴ Vosko S. H., Wilk L., Nusair M.
    Can. J. Phys.
    (1980), 58, pp. 1200. Link

  • $\bullet$

    VWN2: Vosko-Wilk-Nusair parameterization of the LSDA correlation energy #2 ¹³¹⁴ Vosko S. H., Wilk L., Nusair M.
    Can. J. Phys.
    (1980), 58, pp. 1200. Link

  • $\bullet$

    VWN3: Vosko-Wilk-Nusair parameterization of the LSDA correlation energy #3 ¹³¹⁴ Vosko S. H., Wilk L., Nusair M.
    Can. J. Phys.
    (1980), 58, pp. 1200. Link

  • $\bullet$

    VWN4: Vosko-Wilk-Nusair parameterization of the LSDA correlation energy #4 ¹³¹⁴ Vosko S. H., Wilk L., Nusair M.
    Can. J. Phys.
    (1980), 58, pp. 1200. Link

  • $\bullet$

    Wigner:Wigner correlation functional (simplification of LYP) ¹³⁶⁴ Wigner E. P.
    Trans. Faraday Soc.
    (1938), 34, pp. 678. Link ^{, 1225} Stewart P. A., Gill P. M. W.
    J. Chem. Soc. Faraday Trans.
    (1995), 91, pp. 4337. Link

• $\circ$

  Generalized Gradient Approximation (GGA)

  • $\bullet$

    BOP: “one-parameter progressive” correlation functional with parameters appropriate for B88 exchange ¹²⁸⁴ Tsuneda T., Suzumura T., Hirao K.
    J. Chem. Phys.
    (1999), 110, pp. 10664. Link

  • $\bullet$

    PBE: Perdew, Burke, and Ernzerhof correlation functional ⁹⁸⁸ Perdew J. P., Burke K., Ernzerhof M.
    Phys. Rev. Lett.
    (1996), 77, pp. 3865. Link

  • $\bullet$

    LYP: Lee-Yang-Parr opposite-spin correlation functional ⁷³⁷ Lee C., Yang W., Parr R. G.
    Phys. Rev. B
    (1988), 37, pp. 785. Link

  • $\bullet$

    P86: Perdew-Wang correlation functional from 1986 based on the PZ81 LSDA functional ¹⁰⁰² Perdew J. P.
    Phys. Rev. B
    (1986), 33, pp. 8822. Link

  • $\bullet$

    P86VWN5: Perdew-Wang correlation functional from 1986 based on the VWN5 LSDA functional ¹⁰⁰² Perdew J. P.
    Phys. Rev. B
    (1986), 33, pp. 8822. Link

  • $\bullet$

    PBEloc: PBE correlation functional with a modified beta term by Della Sala and coworkers

  • $\bullet$

    PBEBOP: “one-parameter progressive” correlation functional with parameters appropriate for PBE exchange ¹²⁸⁴ Tsuneda T., Suzumura T., Hirao K.
    J. Chem. Phys.
    (1999), 110, pp. 10664. Link

  • $\bullet$

    PBEsol: PBE correlation functional modified for solids ⁹⁹³ Perdew J. P. et al.
    Phys. Rev. Lett.
    (2008), 100, pp. 136406. Link

  • $\bullet$

    srPBE: Short-range version of the PBE correlation functional by Goll and coworkers ⁴³⁶ Goll E., Werner H.-J., Stoll H.
    Phys. Chem. Chem. Phys.
    (2005), 7, pp. 3917. Link ^{, 435} Goll E. et al.
    Chem. Phys.
    (2006), 329, pp. 276. Link

  • $\bullet$

    PW91: Perdew-Wang correlation functional from 1991 ⁹⁸⁹ Perdew J. P. et al.
    Phys. Rev. B
    (1992), 46, pp. 6671. Link

  • $\bullet$

    regTPSS: Slight modification of the PBE correlation functional (also called vPBEc) ¹¹¹³ Ruzsinszky A. et al.
    J. Chem. Theory Comput.
    (2012), 8, pp. 2078. Link

• $\circ$

  Meta-Generalized Gradient Approximation (meta-GGA)

  • $\bullet$

    TPSS:Tao, Perdew, Staroverov, and Scuseria correlation functional ¹²⁵⁶ Tao J. et al.
    Phys. Rev. Lett.
    (2003), 91, pp. 146401. Link

  • $\bullet$

    revTPSS: Revised version of the TPSS correlation functional ⁹⁹² Perdew J. P. et al.
    Phys. Rev. Lett.
    (2009), 103, pp. 026403. Link

  • $\bullet$

    B95: Becke’s two-parameter correlation functional from 1995 ⁹¹ Becke A. D.
    J. Chem. Phys.
    (1996), 104, pp. 1040. Link

  • $\bullet$

    oTPSS: TPSS correlation functional with 2 refit parameters (for use with oTPSS exchange) by Grimme and coworkers ⁴³⁰ Goerigk L., Grimme S.
    J. Chem. Theory Comput.
    (2010), 6, pp. 107. Link

  • $\bullet$

    PK06: Proynov-Kong “tLap” functional with $\tau$ and Laplacian dependence ¹⁰⁵⁰ Proynov E., Kong J.
    J. Chem. Theory Comput.
    (2007), 3, pp. 746. Link

  • $\bullet$

    PKZB: Perdew, Kurth, Zupan, and Blaha correlation functional ⁹⁹⁰ Perdew J. P. et al.
    Phys. Rev. Lett.
    (1999), 82, pp. 2544. Link

  • $\bullet$

    SCAN: Strongly Constrained and Appropriately Normed correlation functional ¹²³⁹ Sun J., Ruzsinszky A., Perdew J. P.
    Phys. Rev. Lett.
    (2015), 115, pp. 036402. Link

  • $\bullet$

    rSCAN: Regularized SCAN correlation ⁷⁶ Bartok A. P., Yates J. R.
    J. Chem. Phys.
    (2019), 150, pp. 161101. Link ^{, 390} 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 ³⁹⁰ Furness J. W. et al.
    J. Chem. Phys.
    (2022), 156, pp. 034109. Link

  • $\bullet$

    r2SCAN: Re-Regularized SCAN correlation ³⁸⁸ Furness J. W. et al.
    J. Phys. Chem. Lett.
    (2020), 11, pp. 8208. Link ^{, 389} Furness J. W. et al.
    J. Phys. Chem. Lett.
    (2020), 11, pp. 9248. Link ^{, 390} Furness J. W. et al.
    J. Chem. Phys.
    (2022), 156, pp. 034109. Link

  • $\bullet$

    revSCAN: Revised SCAN correlation ⁸⁸³ Mezei P. D., Csonka G. I., Kállay M.
    J. Chem. Theory Comput.
    (2018), 14, pp. 2469. Link

  • $\bullet$

    TM: Tao-Mo correlation functional, representing a minor modification to the TPSS correlation functional ¹²⁵⁵ Tao J., Mo Y.
    Phys. Rev. Lett.
    (2016), 117, pp. 073001. Link

  • $\bullet$

    revTM: Revised TM correlation ⁵⁹¹ Jana S., Sharma K., Samal P.
    J. Phys. Chem. A
    (2019), 123, pp. 6356. Link

  • $\bullet$

    rregTM: Revised regularized TM correlation ⁵⁸⁸ Jana S. et al.
    J. Chem. Phys.
    (2021), 155, pp. 024103. Link

  • $\bullet$

    TPSSloc: The TPSS correlation functional with the PBE component replaced by the PBEloc correlation functional