Extensions of the Second Order Functional

Random Phase Approximation. The most straightforward approach to go beyond the second order functional is a resummation of certain classes of diagrams. Starting from the exact representation (2.77) of Exc, one could, for example, resum the ring diagrams [19,20] (random phase approximation -RPA), which are known to form the most important class for the description of metals, 

The basic idea of the ISI is to obtain Wg in the interesting regime t 1 fi-om an interpolation between the weak ( C 1) and the strong ( 1) interaction limit. The former limit is well-known by now For a weak interaction one can expand xc in powers of the coupling constant g which automatically yields a corresponding expansion for Wg, 

The strong interaction limit requires a new concept. However, for g — oo the electrostatic forces completely dominate over kinetic effects, so that a simple model system ( point charge plus continuum model ) is sufficient to extract Wg [65]. In this way one finds the two leading orders of the expansion of Wg in powers of 1/y/g, 

Equations (2.99) and (2.100) should be understood as an effective resummation of the KS perturbation series. The correlation part of E is obtained by subtraction of the exact Ex from (2.99). 

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