5.13.3 Density Functional Approximations Available for Use with Complex Absorbing Potentials

Note:  All exchange functionals in this section can be invoked using the $rem variable EXCHANGE.

• $\circ$

  Local Spin-Density Approximation (LSDA)

  • $\bullet$

    cx_Slater: Slater-Dirac exchange functional (X$\alpha$ method with $\alpha =2/3$) ³²⁹ Dirac P. A. M.
    P. Camb. Philos. Soc.
    (1930), 26, pp. 376. Link

• $\circ$

  Generalized Gradient Approximation (GGA)

  • $\bullet$

    cx_B88: Becke exchange functional from 1988 ⁹⁵ Becke A. D.
    Phys. Rev. A
    (1988), 38, pp. 3098. Link

  • $\bullet$

    cx_PBE: Perdew, Burke, and Ernzerhof exchange functional ¹⁰⁶² Perdew J. P., Burke K., Ernzerhof M.
    Phys. Rev. Lett.
    (1996), 77, pp. 3865. Link

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

• $\circ$

  Local Spin-Density Approximation (LSDA)

  • $\bullet$

    cx_VWN5 / cx_VWN: Vosko-Wilk-Nusair parameterization of the LSDA correlation energy #5 ¹⁴¹⁰ Vosko S. H., Wilk L., Nusair M.
    Can. J. Phys.
    (1980), 58, pp. 1200. Link

  • $\bullet$

    cx_VWN1RPA: Vosko-Wilk-Nusair parameterization of the LSDA correlation energy #1 with RPA values ¹⁴¹⁰ Vosko S. H., Wilk L., Nusair M.
    Can. J. Phys.
    (1980), 58, pp. 1200. Link

• $\circ$

  Generalized Gradient Approximation

  • $\bullet$

    cx_PBE: Perdew, Burke, and Ernzerhof correlation functional ¹⁰⁶² Perdew J. P., Burke K., Ernzerhof M.
    Phys. Rev. Lett.
    (1996), 77, pp. 3865. Link

  • $\bullet$

    cx_LYP: Lee-Yang-Parr opposite-spin correlation functional ⁷⁸⁰ Lee C., Yang W., Parr R. G.
    Phys. Rev. B
    (1988), 37, pp. 785. Link

Note:  All exchange-correlation functionals in this section can be invoked using the $rem variable METHOD.

• $\circ$

  Local Spin-Density Approximation (LSDA)

  • $\bullet$

    cx_LDA / cx_SVWN5: Slater LSDA exchange + VWN5 LSDA correlation

• $\circ$

  Generalized Gradient Approximation (GGA)

  • $\bullet$

    cx_PBE: PBE GGA exchange + PBE GGA correlation

  • $\bullet$

    cx_BLYP: B88 GGA exchange + LYP GGA correlation

  • $\bullet$

    cx_BPBE: B88 GGA exchange + PBE GGA correlation

• $\circ$

  Global Hybrid Generalized Gradient Approximation (GH GGA)

  • $\bullet$

    cx_B1LYP: 25% HF exchange + 75% B88 GGA exchange + LYP GGA correlation ¹⁷ Adamo C., Barone V.
    Chem. Phys. Lett.
    (1997), 274, pp. 242. Link

  • $\bullet$

    cx_B3LYP: 20% HF exchange + 8% Slater LSDA exchange + 72% B88 GGA exchange + 19% VWN1RPA LSDA correlation + 81% LYP GGA correlation ⁹⁶ Becke A. D.
    J. Chem. Phys.
    (1993), 98, pp. 5648. Link ^{, 1309} Stephens P. J. et al.
    J. Phys. Chem.
    (1994), 98, pp. 11623. Link

  • $\bullet$

    cx_B3LYP5: 20% HF exchange + 8% Slater LSDA exchange + 72% B88 GGA exchange + 19% VWN5 LSDA correlation + 81% LYP GGA correlation ⁹⁶ Becke A. D.
    J. Chem. Phys.
    (1993), 98, pp. 5648. Link ^{, 1309} Stephens P. J. et al.
    J. Phys. Chem.
    (1994), 98, pp. 11623. Link

  • $\bullet$

    cx_B5050LYP: 50% HF exchange + 8% Slater LSDA exchange + 42% B88 GGA exchange + 19% VWN5 LSDA correlation + 81% LYP GGA correlation ¹²³⁹ Shao Y., Head-Gordon M., Krylov A. I.
    J. Chem. Phys.
    (2003), 118, pp. 4807. Link

  • $\bullet$

    cx_BHHLYP: 50% HF exchange + 50% B88 GGA exchange + LYP GGA correlation, sometimes called BH&H-LYP ⁴⁸⁴ Gray M., Mandal A., Herbert J. M.
    J. Phys. Chem. A
    (2025), 129, pp. 3969. Link

  • $\bullet$

    cx_HFLYP: 100% HF exchange + LYP GGA correlation

  • $\bullet$

    cx_PBE0: 25% HF exchange + 75% PBE GGA exchange + PBE GGA correlation ¹⁹ Adamo C., Barone V.
    J. Chem. Phys.
    (1999), 110, pp. 6158. Link

  • $\bullet$

    cx_PBE50: 50% HF exchange + 50% PBE GGA exchange + PBE GGA correlation ¹¹⁴ Bernard Y. A., Shao Y., Krylov A. I.
    J. Chem. Phys.
    (2012), 136, pp. 204103. Link