Uniform density limit exact constraints

We argue that the uniform density limit is an important theoretical constraint which should not be sacrificed in a functional that needs to be universal. The density functionals discussed here can be exact only for uniform densities. Approximations ought to be exact in those limits where they can be. Moreover, the unexpected success of LSD outside its formal domain of validity... 

Recent work [16,19-21] suggests that functionals which respect the uniform density limit and other exact constraints can still achieve high accuracy for molecules. Just as the empirical electron-ion pseudopotentials of the 1960 s have been replaced by non-empirical ones, we expect tiiat the empirical density functionals of the 1990 s will be replaced by ones that are fully or largely non-empirical. 

There are two answers to the seeming paradox of the previous paragraph. The first is that realistic electron densities are not very close to the slowly-varying limit (s -C 1, p/s exchange-correlation hole is the hole of a possible physical system, the uniform electron gas, and so satisfies many exact constraints, as discussed in Sect. 1.6.1. The second-order gradient expansion or GEA approximation to the hole is not, and does not. 

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