Exchange-Correlation Functionals Available

The following exchange-correlation functionals are available for all four modules (DSCF, GRAD, RIDFT, and RDGRAD):

• The Slater-Dirac exchange functional only (S) [44,45].

• The 1980 correlation functional (functional V in the paper) of Vosko, Wilk, and Nusair only (VWN) [46].

• A combination of the Slater-Dirac exchange and Vosko, Wilk, and Nusair 1980 (functional V) correlation functionals (S-VWN) [44,45,46].

• The S-VWN functional with VWN functional III in the paper. This is the same functional form as available in the Gaussian program [44,45,46].

• A combination of the Slater-Dirac exchange and Perdew-Wang (1992) correlation functionals [44,45,47].

• A combination of the Slater-Dirac exchange and Becke's 1988 exchange functionals (B88) [44,45,48].

• Lee, Yang, and Parr's correlation functional (LYP) [49].

• The B-LYP exchange-correlation functional (B88 exchange and LYP correlation functionals) [44,45,48,49].

• The B-VWN exchange-correlation functional (B88 exchange and VWN (V) correlation functionals) [44,45,48,46].

• The B-P86 exchange-correlation functional (B88 exchange, VWN(V) and
  Perdew's 1986 correlation functionals) [44,45,48,46,50].

• The Perdew, Burke, and Ernzerhof (PBE) exchange-correlation functional [44,45,47,51].

• The Tao, Perdew, Staroverov, and Scuseria functional (Slater-Dirac, TPSS exchange and Perdew-Wang (1992) and TPSS correlation functionals) [44,45,47,52].

Additionally, for all four modules (DSCF, GRAD, RIDFT, and RDGRAD) following hybrid functionals are available (a mixture of Hartree-Fock exchange with DFT exchange-correlation functionals):

• The BH-LYP exchange-correlation functional (Becke's half-and-half exchange in a combination with the LYP correlation functional) [44,45,48,49,53].

• The B3-LYP exchange-correlation functional (Becke's three-parameter
  functional) with the form,

  $$0.8S + 0.72B88 + 0.2HF + 0.19VWN(V) + 0.81LYP$$ (4.3)

  
  
  where HF denotes the Hartree-Fock exchange [44,45,48,49,54].

• The B3-LYP exchange-correlation functional with VWN functional V in the paper. This is the same functional form as available in the Gaussian program.

• The 1996 hybrid functional of Perdew, Burke, and Ernzerhof, with the form,

  $$0.75(S + PBE(X)) + 0.25HF + PW + PBE(C)$$ (4.4)

  
  
  where PBE(X) and PBE(C) are the Perdew-Burke-Ernzerhof exchange and correlation functionals and PW is the Perdew-Wang correlation functional [44,45,47,51,55].

• The TPSSH exchange-correlation functional of Staroverov, Scuseria, Tao and Perdew with the form,

  $$0. (S + TPSS(X)) + 0.1 HF + PW + TPSS(C)$$ (4.5)

  
  
  where HF denotes the Hartree-Fock exchange [44,45,47,52,56].
• The localized Hartree-Fock method (LHF) to obtain an effective exact exchange Kohn-Sham potential [57,58] (module DSCFonly).