Exchange-correlation functional, for

To perform excited-state calculations, one has to approximate the exchange-correlation potential. Local self-interaction-free approximate exchange-correlation potentials have been proposed for this purpose [73]. We can try to construct these functionals as orbital-dependent functionals. There are different exchange-correlation functionals for the different excited states, and we suppose that the difference between the excited-state functionals can be adequately modeled through the occupation numbers (i.e., the electron configuration). Both the OPM and the KLI methods have been generalized for degenerate excited states [37,40]. 

The exchange-correlation functional for the uniform electron gas is known to high precision for all values of the electron density, n. For some regimes, these results were determined from careful quantum Monte Carlo calculations, a computationally intensive technique that can converge to the exact solution of the Schrodinger equation. Practical LDA functionals use a continuous function that accurately fits the known values of gas(/i). Several different... 

Here, h is the one electron matrix in the non-orthogonal Gaussian basis and G (P ) is the two electron matrix for Hartree-Fock calculations, but for DFT it represents the Coulomb potential. The term Exc is the DFT exchange-correlation functional (for Hartree-Fock Exc = 0), while Vmn represents the nuclear repulsion energy. In the orthonormal basis, these matrices are h = etc., where the overlap... 

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. 

This leaves us with the exchange-correlation energy functional, ExciPo) (Eq. (7.15)) as the only term for which some method of calculation must be devised. Devising accurate exchange-correlation functionals for calculating this energy term from the electron density function is the main problem in DFT research. This is discussed in section 7.2.3.4. 

The additional information of the spin density p (r) can then be directly exploited in the exchange-correlation functionals. For open-shell systems, two different restrictions are possible when introducing the noninteracting reference system [109, 111]. We can require (i) that only the total electron density of the fully interacting and of the reference system agree or (ii) that, in addition, the spin densities of the two systems are exactly the same. The first condition leads to a spin-restricted Kohn-Sham DFT formulation, while for the latter a spin-unrestricted Kohn-Sham DFT framework is required [109]. 

T.W. Keal, T. Helgaker, P. Salek, D. Tozer, Choice of exchange-correlation functional for computing NMR indirect spin-spin couphng constants, J. Chem. Phys. Lett. 425 (2006) 163. 

Dev P, Agrawal S, English NJ (2012) Determining the appropriate exchange-correlation functional for time-dependent density functional theory studies of charge-transfer excitations in organic dyes. J Chem Phys 136 224301... 

The simplest approximation to solve the Eq.(2.50) is to assume that E / is a linear function in A, and use the EDA exchange-correlation functional for E. This approximation leads to the so-called half-and-half (HH) combination proposed by Becke [43], in which a 50% of exact exchange and a 50% of EDA exchange is included. 

Holland, J. R, 8c Green, J. C. (2010). Evaluation of exchange-correlation functionals for time-dependent density functional theory calculations on metal complexes. Journal of Computational Chemistry, 31,1008-1014. 

B. Santra, A. Michaelides, M. Fuchs, A. Tkatchenko, C. Filippi, M. Scheffler, On the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters. II. The water hexamer and Van der Waals interactions. J. Chem. Phys. 129(19), 194111 (2008)... 

References to recent work with SDFT include almost all practical DFT calculation SDFT is by far the most widely used form of DFT. In fact, SDFT has become synonymous with DFT to such an extent that often no distinction is made between the two, i.e. a calculation referred to as a DFT one is most often really a SDFT one Some recent work on SDFT is described in Ref [168]. A more detailed discussion of SDFT can be found in Refs., [7, 8, 85] and a particularly clear exposition of the construction of exchange-correlation functionals for SDFT is the contribution of Kurth and Perdew in Refs. [17,18]. 

---