Perdew-Burke-Ernzerhof density

Nonempirical GGA functionals satisfy the uniform density limit. In addition, they satisfy several known, exact properties of the exchange-correlation hole. Two widely used nonempirical functionals that satisfy these properties are the Perdew-Wang 91 (PW91) functional and the Perdew-Burke-Ernzerhof (PBE) functional. Because GGA functionals include more physical ingredients than the LDA functional, it is often assumed that nonempirical GGA functionals should be more accurate than the LDA. This is quite often true, but there are exceptions. One example is in the calculation of the surface energy of transition metals and oxides. 

Hammer B, Hansen LB, Nprskov JK (1999) Improved adsorption energetics within density-functional theory using revised Perdew-Burke-Ernzerhof functionals, Phys Rev B, 59 7413-7421... 

Adamo C, Barone V (2002) Physically motivated density functionals with improved performances The modified Perdew-Burke-Ernzerhof model, J. Chem. Phys, 116 5933-5940... 

A common feature of all pseudopotential methods is that the parameters depend on the employed method, i.e. the potential derived for e.g. the Local Spin Density Approximation (LSDA) functional (Section 6.5.1) is different from that derived from a generalized gradient functional such as Perdew-Burke-Ernzerhof (PBE) (Section 6.5.2). In practice, the difference is relatively small and pseudopotentials optimized for one functional are often used for other functionals without re-optimization. 

The calculations reported in this work are performed by the all-electron density functional theory DMoP code. - Double numerical polarized (DNP) basis set that includes all occupied atomic orbitals plus a second set of valence orbitals plus polarized d-valence orbitals is used. Atom element-dependent cutoff radii with a medium size of 8.0 A are applied. Perdew-Burke-Ernzerhof (PBE) exchange-correlation potential is used. DMoP PBE calculations have been demonstrated to give a very successful account of reaction enthalpies of molecules in the gas phase. A sufficient level of convergence for the COSMO solvent accessible surface (SAS) is reached using a 110-point scheme for all atoms except hydrogen, where the 50-point scheme is used. 

Burke K, Perdew JP, Ernzerhof M, Accuracy of density functionals and system-averaged exchange-correlation holes, in preparation for Phys Rev Lett... 

Perdew JP, Ernzerhof M, Burke K, Savin A. On-top pair-density interpretation of spin-density functional theory, with applications to magnetism to appear in Int. J. Quantum Chem. 

Ernzerhof, M., Perdew, J. P., Burke, K. Density Functionals Where Do They Come From, Why Do They Work 190, 1-30(1996). 

M. Ernzerhof, J.P. Perdew and K. Burke, in Density Functional Theory, eds. R. Nalewajski, Springer, Berlin (1996). 

The local spin density approximation (LSD) for the exchange-correlation energy, (1.11), was proposed in the original work of Kohn and Sham [6], and has proved to be remarkably accurate, useful, and hard to improve upon. The generalized gradient approximation (GGA) of (1.12), a kind of simple extension of LSD, is now more widely used in quantum chemistry, but LSD remains the most popular way to do electronic-structure calculations in solid state physics. Tables 1.1 and 1.2 provide a summary of typical errors for LSD and GGA, while Tables 1.3 and 1.4 make this comparison for a few specific atoms and molecules. The LSD is parametrized as in Sect. 1.5, while the GGA is the non-empirical one of Perdew, Burke, and Ernzerhof [20], to be presented later. 

Fig. 1.1. The enhancement factor iTc of (1.217) for the GGA of Perdew, Burke, and Ernzerhof [20], as a function of the reduced density gradient s of (1.183), for C = 0. The local density parameter Vs and the relative spin polarization C are defined in (1.133) and (1.149), respectively...

The calculations were performed with the linear combination of Gaussian type orbital density functional theory (LCGTO-DFT) deMon2k (Koster et al. 2006) code. In O Fig. 16-1, the crosses refer to all-electron polarizabilities calculated with the local density approximation (LDA) employing the exchange functional from Dirac (1930) in combination with the correlation functional proposed by Vosko, Wilk and Nusair (VWN) (Vosko et al. 1980). The stars denote polarizabilities obtained with the gradient corrected exchange-correlation functional proposed by Perdew, Burke and Ernzerhof (PBE) (Perdew et al. 1996). 

---