Perdew and Wang

B3PW91 Becke exchange, Perdew and Wang correlation Hybrid... 

Similarly, there are local and gradient-corrected correlation functionals. For example, here is Perdew and Wang s formulation of the local part of their 1991 correlation functional ... 

In Equation 61, all of the arguments to G except tj are parameters chosen by Perdew and Wang to reproduce accurate calculations on uniform electron gases. The parameter sets differ for G when it is used to evaluate each of Ecfrj.O), EcCrj, ) and -ac(rs)-... 

A modified form for Ecjaijs) has been given by Perdew and Wang, and is used in comiection with tlie PW91 functional described in Section 6.2. 

Perdew and Wang (PW86) " proposed modifying the LSDA exchange expression to tliat shown in eq. (6.23), where x is a dimensionless gradient variable, and a, b and c being suitable constants (summation over equivalent expressions for the a and P densities is implicitly assumed). 

Perdew and Wang have proposed an exchange functional similar to B88 to be used in connection with the PW91 correlation functional given below (eq. (6.30)). 

This functional was later modified to the following form (also a correction to the LSDA energy) by Perdew and Wang in 1991 (PW91 or P91) ... 

We have investigated ground state properties on a first principles basis. Total energy as well as magnetic moment (for FeaNi) were determined with the FLAPW method and the GGA introduced by Perdew and Wang in 1992 by employing the WIEN95 code developed by Blaha et al. 

Functionals which are related to this approach include among others the recent FT97 functional of Filatov and Thiel, 1997, the PW91 exchange functional (Perdew, 1991, and Burke, Perdew, and Wang, 1998) and the CAM(A) and CAM(B) functionals developed by Handy and coworkers (Laming, Termath, and Handy, 1993). 

Perdew and Wang [40] and Becke [42] are available for the exchange terms. 

Thus it is of some interest to know if the Stoll ansatz is correct, especially since several other ansUtze have been developed and used as input to a spin-resolved pair correlation function. For example, Perdew and Wang (PW) [51,52] proposed a scaling relation... 

Table 2. Correlation energy of the uniform electron gas, comparing the highly-accurate parametrization of Perdew and Wang [4] with the LYP functional [10]...

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. 

The computation of the electronic structure for each Rc is by using the KS approach with a code designed to use Dirichlet boundary conditions. In this work, we use the Perdew and Wang exchange-correlation functional [33] within the local density approximation [34], Details about this code can be found in Ref. [9] and some applications are in Refs. [35-37],... 

The results presented here were obtained in the framework of DFT by using a modified version of deMon code [43], All calculations were performed within the nonlocal density approximation employing the gradient-corrected functional of Perdew [44] for correlation and that of Perdew and Wang [45] for exchange energy (PPW) respectively. For some species test calculations using the local potential [46] were carried out. 

The situation at present is that the nonlocal exchange functional suggested by Becke (B) in 198821 has been established as a standard expression in DFT calculations. The choice of the best correlation functional is less obvious than the choice of the exchange functional. The presently most popular correlation functionals are those of Perdew (P86)22, Lee et al. (LYP)23, Perdew and Wang (PW91)24 and Vosko et al. (VWN)25. 

The theoretical basis of CASTEP is the density functional theory (DFT) in the local density approximation (LDA) or gradient-corrected LDA version, as developed by Perdew and Wang (GGA).6-7 The DFT description of electron gas interactions is known to be sufficiently accurate in most cases, and it remains the only practical way of analyzing periodic systems. LDA is known to underestimate bond lengths in molecules and cell parameters in crystals, while GGA is typically more accurate to these optimized geometries. In the present calculations, we selected GGA, which is the default setting in CASTEP. 

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