Generalized gradient approximation local hybrid

The quantity ffffr.r. a ) is the frequency-dependent XC kernel for which common approximations are applied frequency-independent (adiabatic) local density approximations (LDA), adiabatic generalized gradient approximations (GGA), hybrid-DFT variants such as the popular functionals B3LYP and PBEO in which Kxc contains an admixture of Hartree-Fock ( exact ) exchange X,... 

The main issue involved in using DFT and the KS scheme pertains to construction of expressions for the XC functional, Exc[n], containing the many-body aspects of the problems (1.38). The main approaches to this issue are (a) local functionals the Thomas Fermi (TF) and LDA, (b)semilocal or gradient-dependent functionals the gradient-expansion approximation (GEA) and generalized gradient approximation (GGA), and (c) nonlocal functionals hybrids, orbital functionals, and SIC. For detailed discussions the reader is referred to the reviews [257,260-272]. 

Table 4 Calculated and experimental distances (in A) between the actinides and the fluorine atoms in UF<, NpFg, and PuF6. HF denotes Hartree-Fock results, and LDA, GGA, and hybrid marks results from density-functional calculations with a local-density approximation, a generalized-gradient approximation, and a hybrid method. The results are taken from ref 33...

Exchange-correlation functionals, which determine the reliability of Kohn-Sham calculations, are compared in terms of the basic concepts in their development, and for their features and problems, in Chap. 5. This chapter uses as examples the major local density approximation (LDA) and generalized gradient approximation (GGA) exchange-correlation functionals and meta-GGA, hybrid GGA, and semi-empirical functionals to enhance the degree of approximation in terms of their concepts, applicabilities, and problems. 

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