Second-order ladder approximation

Actually three-particle correlations such as that in Fig. 4(a) are introduced by the CSEs and ICSEs, even within a second-order ladder approximation. To understand why, consider the diagram in Fig. 4(d), which represents one of the terms in Within a second-order ladder approximation to A3, diagram 4(b) is included within diagram 4(d). Thus three- and higher-body effects are incorporated into the cumulants A3 and A4 by the CSEs or ICSEs, even when... 

Fig. 22. Neutron-scattering line width as a function of temperature for a Ce ion with Fy ground state, 7 = 5.5 K and the CF energies do = 50, 100, and 150 K from a self-consistent ladder approximation. Indicated are also experimental results for Ceo,7Lao.3Al2 (Loewenhaupt and Steglich 1977) and (as dashed line) the results of second-order perturbation theory (Maekawa et al. 1985c).

In order to make improvements over the LSDA, one has to assume that the density is not uniform. The approach that has been taken is to develop functionals that are dependent on not only the electron density but also derivatives of the density. This constitutes the generalized gradient approximation (GGA) and is the second rung on Jacob s Ladder. The third rung, meta-GGA functional, includes a dependence on the Laplacian of the density (V p) or on the orbital kinetic energy density (t). The fourth row, the hyper-GGA or hybrid functionals, includes a dependence on exact (HF) exchange. Finally, the fifth row incorporates the unoccupied Kohn-Sham orbitals. This is most widely accomplished within the so-called double hybrid functionals. 

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