Screened exchange LDA

Fig. 7.18 Band structures calculated by Wolf and Herzig [150, 151] using screened-exchange LDA (sX-LDA) for hexagonal YH3 with space group (a) P3cl (b) PSZcm (c) P63. These band structure calculations...

Stampff C, Man ns tad t W, Asahi R, Freeman A Electronic stmetme and physical properties of early transition metal mononitrides density-functional theory LDA, GGA, and screened-exchange LDA FLAPW calculations, Phys Rev B 63(15) 155106, 2001. 

In practice, one only needs to input the value of the Flubbard parameter, U, that is, the Coulomb energy cost to place two electrons at the same site (Anisimov et al., 1991), and the screened exchange energy, J. Under this formalism, DFT - - U has been reported to improve the calculation of one-particle density of states (DOS) and the total energy of crystalline nickel oxide— an example of 3d-transition metal Mott insulator (Dudarev et al., 1998). On the other hand, rare earth materials such as Ce02 have also been modeled accurately by selecting appropriate values for the U and J parameters either in the LDA-F U (Andersson et al., 2007a) or in the GGA-F U formalism (Loschen et al., 2007 Scanlon et al., 2009). 

The LDA-fU theory may be regarded as an approximate GW method [37]. The screened Coulomb and exchange parameters U and J are usually estimated in a supercell approximation [39]. However, there is some arbitrariness in the choice of the localized orbitals when performing the partitioning of the Hamiltonian. A further step in the improvement of LDA-I-U consists in adding dynamical effects — frequency dependence in H r,r u). This may be performed using a DMFT-type approach (DMFT= Dynamical Mean Field Theory) [40] as part of the so-called LDA-b-1- approaches [41]. 

In this equation. Go is the Green s fimction of the uncorrelated reference system, whereas W denotes the screened Coulomb interaction. Commonly, Go is constructed from an LDA or LDA + U band structure, in which case, the reference system strictly speaking is not uncorrelated, but the potential due to correlation is the exchange-correlation potential, Vxc/ v hich is explicitly known and can be subtracted from E, namely E = E — Vxc r — r ). 

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