 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
ironbased 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,
E_{xc},
is an integral over
all space with the
exchange correlation
energy density,
ε_{xc},
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, ε_{xc}[n(r),∇^{m}n
(r)],
that modify
the behavior at
large gradients in
such a way as to
preserve desired
properties. The most
widely used forms
for ε_{xc}
are the
ones proposed by
Becke [B88],
Perdew and Wang
[PW92], and Perdew,
Burke, and Enzerhof
[PBE]. 
Picture / Figure / Diagram:  
SFBLink:  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, WileyVCH, 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, 30983100 (1988); [PW92] J. P. Perdew and Y. Wang, Phys. Rev. B 45, 1324413249 (1992); J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 38653868 (1996) 

