Beyond the PBE functional

In order to simplify the following discussion, we separate correlation and exchange contributions, i.e. 

Even if this is the most common representation of Exc, the distinction between different contributions is somewhat artificial in the context of DFT. Furthermore it can be misleading because there is some error compensation between both partners and combination of exchange and correlation functionals issuing from different sources could be dangerous. Anyway the separation between these two terms considerably simplifies the discussion and in the following we adopt this distinction. 

Some efforts have been done to improve the numerical performances of the PBE exchange functional without modifying its theoretical background. 

Among all the PBE conditions, the fulfillment of the Lieb-Oxford (LO) bound [35], 

In the construction of the revPBE functional [29], Zhang and Yang pointed out that, for a given electron density, fuljBllment of equation (6), which may be considered a local LO limit, is a sufficient, but not a necessary requirement for the fidfiUment of the true, integrated LO bound  

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