Perdew-Burke-Emzerhof

B. Hammer, L. B. Hansen, and J. K. Nprskov, Improved adsorption energetics within density-functional theory using Perdew-Burke-Emzerhof functionals, Phys. Rev. B 59,7413-7421 (1999). 

Emzerhof, M., Scuseria, G. E., 1999a, Assessment of the Perdew-Burke-Emzerhof Exchange-Correlation Functional , J. Chem. Phys., 110, 5029. 

Ernzerhof M, ScuseriaGE( 1999) Assessment of the Perdew-Burke-Emzerhof exchange-correlation functional, J Chem Phys, 110, 5029-5036... 

We use the DFT SIESTA code [13], which implements the generalized gradient approximation (GGA), Perdew-Burke-Emzerhof (PBE) density functional [14], norm-conserving pseudopotentials and periodic boundary conditions. A localized double- polarized (DZP) basis set was used for valence electrons. 

T= 13 K experiment of 37.5 A ). Previously we remarked that Catti et a/. [62] reported a double minimum at cell volumes of 36.5 A and 36.9 A, separated in energy by only about 100 (w 2.7 meV) per formula unit. For gradient-dependent DFT approximations less has been reported but the Perdew-Burke-Emzerhof (PBE) GDA [96] gives Q = 39.42 A versus PW91 [97] Q - 40.19 AI Catti et al. also report a double minimum for the empirical hybrid B3LYP [98] DFT model Q = 37.9 A and 38.5 A ... 

PBEN Perdew-Burke-Emzerhof (functional), modified by Norskov et al. PC point charge... 

To calculate the charge of the surface oxygen and titanium atoms (Mulliken charges) we have performed plane wave pseudopotential density functional theory (DFT) calculations, using the gradient corrected exchange-correlation functional of Perdew-Burke-Emzerhof [10]. 

The Perdew-Burke-Emzerhof (PBE) exchange and correlation functional has no empirical parameters [Phys. Rev. Lett.,11,2865 (19%)]. 

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 (PW) functional [15] and the Perdew-Burke-Emzerhof (PBE) functional [16]. Because GGA functionals include more physical ingredients than the LDA functional, it is often assumed that GGA functionals should be more accurate than the LDA. This is quite often true, but there are exceptions. One example of such a situation is in the calculation of the surface energy of transition metals and oxides. 

In contrast to the scarce knowledge on hardness and elastic properties of intermetallic clathrates, there is an enormous amount of data on Einstein and Debye temperatures available in the literature. The exceptional vibrational features of these cage compounds were extensively smdied in recent years and will be discussed in the frame of this work. Needless to say that DPT calculations of electron and phonon density of states, of thermoelectric properties and of elastic properties have greatly supported clathrate research. In this context attention should be drawn to a recent work of Karttunen et al. [29], who employed the Perdew-Burke-Emzerhof hybrid density functional with localized atomic basis sets composed of Gaussian-type functions, to calculate the elastic properties of 14 different types of clathrate frameworks (for elemental structures of C, Si, Ge, Sn) predicting bulk and Young s moduli comparing them with their diamond-like, dense so called ot-phases. 

There are several other composite approaches, for example, complete basis set (CBS) models [56], focal-point analysis [57], multi-coefficient correlation methods [58], high-accuracy extrapolated ab initio thermo-chemistry (HEAT) [59] and the Weizmann-4 theory [60]. Hansen et al. [61] have employed the so-caUed MP2 DFT [193] scheme for analysing benzene ethylation over H-ZSM-5. Density functional calculations applying periodic boundary conditions [Perdew-Burke-Emzerhof (PBE) functional] were combined with MP2 energy calculations on a series of... 

F. 6.2 Band structure and total and partial densities of states for ZnMo04 crystal with the Perdew-Burke-Emzerhof (PBE) functional calculation... 

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