Lieb-Oxford limit

We see that PW86 includes both the correct uniform gas limit and the GEA by having the right s2 dependence. It still has curve-crossing problems, but not as severe as LM. It violates the Lieb-Oxford bound, Eq. (66), and the exact condition... 

Among others, three conditions are of particular importance. The first constraint is related to the behavior in the small x region, where the GGA exchange functional should reduce to in order to recover the correct uniform gas limit. The second condition was defined by Levy, who showed that some scaling properties can be satisfied if the asymptotic form of the functional for large x is x , where a > Vi [68,69]. The last condition is the so called "Lieb-Oxford bound" [70], which states that ... 

Finally, we want to satisfy the Lieb-Oxford bound of (1.120) and (1.122), which LSD respects. We can achieve this, and also recover the limit of (1.215), with the simple form... 

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