LDA theory

QM theory has been applied to studies of several other oxide surfaces in recent years. The structure of the low index surfaces of AI2O3 has been computed within PW-LDA theory (Manassidis and Gillan, 1994), which predicts a very large relaxation of the basal plane surface (0001). Studies of this surface have been extended to the adsorption of niobium atoms (Kruse et al., 1994) and of complex organic molecules (Frank et al., 1995). 

Further discussion on LDA theory and different modes of operation may be found in the classic texts of Durst et al. (1976) and Watrasiewics and Rudd (1976). 

Transition structures are more dihicult to describe than equilibrium geometries. As such, lower levels of theory such as semiempirical methods, DFT using a local density approximation (LDA), and ah initio methods with small basis sets do not generally describe transition structures as accurately as they describe equilibrium geometries. There are, of course, exceptions to this, but they must be identihed on a case-by-case basis. As a general rule of thumb, methods that are empirically dehned, such as semiempirical methods or the G1 and G2 methods, describe transition structures more poorly than completely ah initio methods do. 

The exchange-correlation energy density can be split into two parts exchange component Ex n) and correlation component e Cn). The explicit expression for the exchange component is known from Hartree-Fock theory but the correlation component is known only numerically. Several parametrisations exist for the exchange-correlation energy and potential of a homogeneous gas system which can be used for the LDA calculations within DFT. 

Table 1. Optimized Lattice Parameters a, b, c (in Angstroms) and a, fi, y (in degrees) of CsMgBr, Obtained at the LDA and GGA DFT Levels of Theory, Together with the Experimental X-ray Diffraction Data (exp.)...

Table 2. Optimized Local Structure Around the Eu2+ Impurity Embedded in CsMgBr3 for the Ground 4f7 (GC) and Excited 4f65dl (EC) Electron Configurations of Eu2+ Obtained at the LDA and GGA DFT Levels of Theory"...

Andzelm and Wimmer, 1992, published one of the first comprehensive studies on the performance of approximate density functional theory in which optimized molecular geometries were reported. These authors computed the geometries of several organic species containing the atoms C, N, O, H, and F at the local SVWN level, using a polarized double-zeta basis set optimized for LDA computations. Some trends have been discerned... 

Generally, all band theoretical calculations of momentum densities are based on the local-density approximation (LDA) [1] of density functional theory (DFT) [2], The LDA-based band theory can explain qualitatively the characteristics of overall shape and fine structures of the observed Compton profiles (CPs). However, the LDA calculation yields CPs which are higher than the experimental CPs at small momenta and lower at large momenta. Furthermore, the LDA computation always produces more pronounced fine structures which originate in the Fermi surface geometry and higher momentum components than those found in the experiments [3-5]. 

---