Generalised KS Schemes and Self-energy Models

We have seen that many-body-based methods provide an ab-initio way to treat the Coulomb correlation in an N electron system without the expensive cost of QMC calculations. However, they are computationally more demanding than routine LDA-KS calculations and, hence, the feasibility of their application to complex systems is unclear, especially in the context of ab-initio molecular dynamics calculations, where many total-energy evaluations are required. As described in Sect. 5.3, the main problem when constructing approximations to E c [n] is related to its inherent non-analytical character which is due to the specific way in which the KS mapping between the real and the fictitious systems is done. However, this is not the only possible realisation of DFT and recently, new DFT methods have been proposed [112,113]. In these generalised Kohn-Sham schemes (GKS) the actual electron system is mapped onto a fictitious one in which particles move in an effective non-local potential. As a result of this, it is possible to describe structmal properties at the same (or better) level than LDA/GGA but improving on its description of quasiparticle properties. 

Specifically, as shown in [63,64,65], pathologies of the exact KS functional such as the band-gap discontinuity and the xc field may be understood as arising when one transforms a MBPT description, with a non-pathological but non-local self-energy operator, into the KS system with its local potential. In this sense, a non-local xc potential should be more amenable to accmate approximation as an explicit functional of the density. 

The GKS approximation proposed by Sanchez-Friera and Godby [114] relies on the use of a jellium-like self-energy to describe the xc effects of inhomogeneous systems  

The total energy of the actual system is then approximated by 

---