Exchange-correlation energy Gunnarsson-Lundqvist

There are a number of model exchange-correlation functionals for the ground-state. How do they perform for ensemble states Recently, several local density functional approximations have been tested [24]. The Gunnarsson-Lundqvist-Wilkins (GLW) [26], the von Barth-Hedin (VBH)[25] and Ceperley-Alder [27] local density approximations parametrized by Perdew and Zunger [28] and Vosko, Wilk and Nusair (VWN) [29] are applied to calculate the first excitation energies of atoms. 

Thus, the many-body problem is reduced to a set of effective one-electron equations of the form of eq. (4), with an orbital-independent potential if the exchange-correlation potential is known. Approximate expressions for and have been derived by many authors (see e.g. Kohn and Sham 1965, Gunnarsson and Lundqvist 1976, Moruzzi et al. 1978, Mackintosh and Andersen 1979, Koelling 1981, Kohn and Vashista 1983, Hedin and Lundqvist 1971, von Barth and Hedin 1972). In particular, the local density approximation (LDA) uses for [n] the exchange and correlation energy of a uniform electron gas at the same local density. The exchange and correlation potential is then local. 

The early suggestion of Gunnarsson and Lundqvist to use a symmetry-dependent exchange-correlation functional to calculate the lowest-energy excited state of each symmetry class has been implemented approximately by von Barth, but suffers from lack of knowledge of the symmetry dependence of the functional. More recent work on this dependence is provided in Ref [87]. 

In this section, the ground state properties of the lanthanides are studied with a first principles all-electron total energy band structure method. The LMTO method is employed within the local density (LDA) and local spin density (LSD) functional approximations (Hohenberg and Kohn 1964, Kohn and Sham 1965, Gunnarsson and Lundqvist 1976). The von Barth-Hedin (1972) interpolation formula is used for the exchange and correlation potential with the parameters of Hedin and Lundqvist (1971) and RPA scaling (Janak 1978). 

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