Non-local approximations NLDA

There are approximations that go beyond the LDA. They consider that the dependence xcip] may be non-local, i.e. Exc 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 

A breakthrough in the quality of results is represented by the following proposition of Perdew and Wang  

If you do it this way - satisfaction is (almost) guaranteed, your results will agree very well with raperiment. 

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