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. 

The core electrons of all atoms were treated via ultra-soft pseudo potentials [10,11] with a cut-off of 25 Ry for wave function, and 240 for electronic density. The PBE gradient-corrected exchange-correlation function was used in self-consistent DFT calculations. The geometry optimization was performed using a lxlxl /c-point mesh. Because of the natural paired electron occupancies of the adsorbates, spin polarization effects were not considered to be important and were not treated explicitly in this study. 

It can be shown, essentially by dimensional analysis (9), that the lowest order gradient-corrected exchange-correlation functional has the form... 

To calculate the charge of the surface oxygen and titanium atoms (Mulliken charges) we have performed plane wave pseudopotential density functional theory (DFT) calculations, using the gradient corrected exchange-correlation functional of Perdew-Burke-Emzerhof [10]. 

DFT-Based Pseudopotentials. - The model potentials and shape-consistent pseudopotentials as introduced in the previous two sections can be characterized by a Hartree-Fock/Dirac-Hartree-Fock modelling of core-valence interactions and relativistic effects. Now, Hartree-Fock has never been popular in solid-state theory - the method of choice always was density-functional theory (DFT). With the advent of gradient-corrected exchange-correlation functionals, DFT has found a wide application also in molecular physics and quantum chemistry. The question seems natural, therefore Why not base pseudopotentials on DFT rather than HF theory ... 

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... 

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