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GGA

GGA: Generalized Gradient Approximation
Definition:A method to approximate both the exchange and correlation energy in density functional methods and represent a further development of local density approximation (→LDA).
Explanation:The need to use approximations in density functional theory (→DFT) to calculate exchange and correlation energies is described in the item, LDA.

LDA suffers from the fact that it requires an infinitely slow variation of electron densities in the crystal in principle. The GGA method was developed to overcome such a shortcoming of LDA by additionally taking into account of the density gradient. Both methods show advantages and disadvantages in different materials and the physical properties to be calculated; therefore, they are employed depending on their application. For iron-based alloys, GGA is better since LDA is shown to be even uncapable of predicting the correct ground state of iron.

In a comparison with LDA, the GGA is a higher level approximation of the exchange correlation energy functional where the exchange correlation energy, Exc, is an integral over all space with the exchange correlation energy density, εxc, depending on both the local electronic density and its gradient as shown in the equation below.

The term, GGA, denotes a variety of ways proposed for functions, εxc[n(r),|∇mn (r)|], that modify the behavior at large gradients in such a way as to preserve desired properties. The most widely used forms for εxc are the ones proposed by Becke [B88], Perdew and Wang [PW92], and Perdew, Burke, and Enzerhof [PBE].
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SFB-Link:The GGA method, mainly in the parametrization of Perdew, Burke, and Ernzerhof [PBE], is used in all SFB projects performing DFT calculations (projects A1, A2, C3, and T4).
References:R. Dronskowski, Computational Chemistry of Solid State Materials, Wiley-VCH, Weinheim, 2005.
[PBE] J. P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 1996, 77, 3865.
R. M. Martin, Electronic Structure: Basic Theory and Practical Methods, Cambridge University Press, 2004;
[B88] A. D. Becke, Phys. Rev. A 38, 3098-3100 (1988);
[PW92] J. P. Perdew and Y. Wang, Phys. Rev. B 45, 13244-13249 (1992);
J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865-3868 (1996)