GGA correlation functional

With respect to correlation functionals, corrections to the correlation energy density following Eq. (8.29) include B88, P86, and PW91 (which uses a different expression than Eq. (8.27) for the LDA correlation energy density and contains no empirical parameters). Another popular GGA correlation functional, LYP, does not correct the LDA expression but instead computes the correlation energy in toto. It contains four empirical parameters fit to the helium atom. Of all of the correlation functionals discussed, it is the only one tliat provides an exact cancellation of the self-interaction error in one-electron systems. 

Typically in the literature, a complete specification of the exchange and correlation functionals is accomplished by concatenating the two acronyms in that order. Thus, for instance, a BLYP calculation combines Becke s GGA exchange with the GGA correlation functional of Lee, Yang, and Parr. 

PW91 Perdew and Wang s (sic) 1991 GGA correlation functional. Perdew, J. P. 1991. In Electronic Structure of Solids 91, Ziesche, P. and Eschig, H., Eds., Akademie Verlag Berlin, 11. 

In a similar way, the local PW correlation functional of eqn (32) can be significantly improved by adding a gradient correction. The resulting GGA correlation functional is ... 

GGA correlation functionals are mainly classified into the density gradient approximation-types and the Colle-Salvetti (CS)-type functionals. 

In the CS-type correlation functionals, there are the Lap-series meta-GGA correlation functionals (see Sect. 5.4), among others. 

In this functional, two semiempirical parameters, D = 0.113 and tc = 0.804, are included. The PKZB correlation functional removes the self-interaction error (see Sect. 6.2) of the PBE-GGA correlation functional to reproduce the one-electron self-correlation energy in the case that electrons interact only with themselves (i.e.. 

For meta-GGA functionals, correlation functionals have been chiefly developed e.g., the Filatov-Thiel 1998 (FT98) (Filatov and Thiel 1998) and the Krieger-Chen-lafrate-Savin (KCIS) (Krieger et al. 1999) meta-GGA correlation functionals. 

The B3LYP hybrid functional (Becke 1993), the first hybrid functional, is the most frequently used functional (or method) in all functionals (or all theories) in quantum chemistry calculations. This functional uses three parameters as the mixing ratios to form the adiabatic connections between the Hartree-Fock exchange integral and the LDA exchange functional and between the LYP-GGA correlation functional and the LDA correlation functional, and to combine with the attenuated GGA term of the B88 exchange functional. 

Table 8.2 Fundamental conditions for the correlation energy and validity comparison of GGA correlation functionals ...

Commonly used GGA correlation functionals E. inclnde the Lee-Yang-Parr (LYP) functional, the Perdew 1986 correlation functional (P86 or Pc86), and the Perdew-Wang 1991 parameter-free correlation functional (PW91 or PWc91). 

Becke s B95 meta-GGA correlation functional, containing two parameters whose values were fitted to atomic correlation energy data, is often used. The TPSS (Tan, Perdew, Staroverov, Scuseria) meta-GGA functional has given good results for many properties. A reparametrization of TPSS gave the oTPSS functional, where o is for optimized [L. Goerigk and S. Grimme, J. Chem. Theory CompuL, 6,107 (2010)]. 

Dispersion Forces. The LDA and GGA also fail to reproduce dispersion forces (one type of van der Waals forces). In this case the problem is due to the short-ranged nature of the LDA/GGA correlation functional. In the LDA the correlation energy density is simply given by the energy density of the homogeneous electron gas (HEG), evaluated with the local density. 

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