Local gradient-corrected exchange-correlation functional

The wave functions are expended in a plane wave basis set, and the effective potential of ions is described by ultrasoft pseudo potential. The generalized gradient approximation (GGA)-PW91, and local gradient-corrected exchange-correlation functional (LDA)-CAPZ are used for the exchange-correlation functional. 

Density functional calculations have become an increasingly popular method of computational molecular quantum chemistry during the last two decades. While density functional theory had been an established tool in solid state physics much earlier, its way into mainstream molecular quantum chemistry was paved by the advent of gradient-corrected exchange-correlation functionals. These functionals alleviate the problems the earlier local-density schemes have especially at the border of a finite molecular system and thus allowed... 

As a conclusion, the gradient-corrected exchange correlation functional affords significant improvement in the geometry compared to the local methods, but has little effect on the calculated force constants. The previous observation, that LDA/NL methods provide better frequencies than LDA methods, is mainly due to the improved reference geometry. Although in most cases the reference... 

The calculations were performed with the linear combination of Gaussian type orbital density functional theory (LCGTO-DFT) deMon2k (Koster et al. 2006) code. In O Fig. 16-1, the crosses refer to all-electron polarizabilities calculated with the local density approximation (LDA) employing the exchange functional from Dirac (1930) in combination with the correlation functional proposed by Vosko, Wilk and Nusair (VWN) (Vosko et al. 1980). The stars denote polarizabilities obtained with the gradient corrected exchange-correlation functional proposed by Perdew, Burke and Ernzerhof (PBE) (Perdew et al. 1996). 

The present authors own initial studies have focused on the J(P-P) coupling constants in a series of cis and tmns bis-phosphane complexes M(CO)4(PH3)2 (M = Cr, Mo, W). As shown in Figure 5, the computed coupling constants are rather sensitive to the nature of the local or gradient-corrected exchange-correlation functional employed. This is due to the above-mentioned sensitivity of the FC term, which dominates the couplings. The trends are reasonably well reproduced by... 

Three types of exchange/correlation functionals are presently in use (i) functionals based on the local spin density approximation, (ii) functionals based on the generalized gradient approximation, and (iii) functionals which employ the exact Hartree-Fock exchange as a component. The first of these are referred to as local density models, while the second two are collectively referred to as non-local models or alternatively as gradient-corrected models. 

The simplest exchange-correlation functionals, derived from the density alone, give reasonable results for many molecular properties. However, it has been found that adding terms proportional to the local gradient of the density in both the exchange and correlation integrands leads to much more accurate results. Most modern DFT computations use these so-called non-local or gradient-corrected functionals. 

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