Gradient expansion approximation GEA

To improve upon this, from a chemical point of view rather crude assumption, the most widely employed corrections are based on using not only the density, but also its gradient. These corrections form the so-called generalized gradient approximation, GGA, or gradient expansion approximation (GEA) methods ... 

For the kinetic energy functional, regular gradient expansion approximation (GEA)74 takes the following form ... 

The main issue involved in using DFT and the KS scheme pertains to construction of expressions for the XC functional, Exc[n], containing the many-body aspects of the problems (1.38). The main approaches to this issue are (a) local functionals the Thomas Fermi (TF) and LDA, (b)semilocal or gradient-dependent functionals the gradient-expansion approximation (GEA) and generalized gradient approximation (GGA), and (c) nonlocal functionals hybrids, orbital functionals, and SIC. For detailed discussions the reader is referred to the reviews [257,260-272]. 

There are approximations that go beyond the LDA. They consider that the dependence ExcLp] may be non-local i.e., E c may depend on p at a given point (locality), but also on p nearby (non-locality). When we are at a point, what happens further off depends not only on p at that point, but also the gradient of p at the point, etc. This is how the idea of the gradient expansion approximation (GEA) appeared... 

There is no systematic treatment of other contributions to the ground-state energy of the RHEG. This remark also pertains to the construction of gradient expansion approximations (GEA), which in the x-only limit involves,... 

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