Gradient-corrected DFT functional

One major source of error in Eq. (7) or AGf is the calculation of the O2 molecule using single determinant theories of electronic structure (such as DFT and Hartree-Fock) [80,81]. In general, gradient-corrected DFT functionals overestimate formation and binding energies and it is estimated that these are accurate for O2 to less than 0.5 eV [48]. It is fortunate however that many studies of stirface stability are not sensitive even to this magnitude of discrepancy in po, as is clear in the examples discussed below. 

Pure DFT methods are defined by pairing an exchange functional with a correlation functional. For example, the well-known BLYP functional pairs Becke s gradient-corrected exchange functional with the gradient-corrected correlation functional of Lee, Yang and Parr. 

Berghold, G., Hutter, J., Parrinello, M.,1998, Grid-Free DFT Implementation of Local and Gradient-Corrected XC Functionals , Theor. Chem. Acc., 99, 344. 

Currently, the density functional theory (DFT) method has become the method of choice for the study of reaction mechanism with transition-metals involved. Gradient corrected DFT methods are of particular value for the computational modeling of catalytic cycles. They have been demonstrated in numerous applications for several elementary processes, to be able to provide quantitative information of high accuracy concerning structural and energetic properties of the involved key species and also to be capable of treating large model systems.30... 

As it is now very well known, accurate studies of the water-water interaction by means of ab-initio techniques require the use of larger and flexible basis sets and methods which consider correlation effects [85,94-96], Since high level ab-initio post-Hartree-Fock calculations are unfeasible because of their high computational cost for systems with many degrees of freedom, Density Functional Theory, more economical from the computational point of view, is being more and more considered as a viable alternative. Recently, we have presented [97] results of structural parameters and vibrational frequencies for the water clusters (H20) , n=2 to 8, using the DFT method with gradient corrected density functionals. 

Iq this study the B3LYP hybrid method proposed by Becke [31] and included in the Gaussian 98 [30] package was used. This method includes a mixture of Hartree-Fock and DFT exchange terms associated with the gradient corrected correlation functional of Lee et al [32], In all the calculations the metal cluster geometry was kept frozen. 

Currently, research in our laboratory continues on real-space models of exchange and correlation hole functions in inhomogeneous systems. We anticipate that this work will ultimately generate completely non-empirical parameter-free beyond-LDA density functional theories. The quality of molecular dissociation energies and related properties obtainable with existing semi-empirical gradient-corrected DFTs approaches chemical accuracy, and we hope these future theoretical developments will continue this trend. 

Dynamical electron correlation effects are intrinsically included in DFT methods via the local and gradient-corrected correlation functionals. Most importantly, the nondynamlcal electron correlation effects have been partially accounted for via the exchange functionals (33,34). As a consequence, the multiconfiguration characters that often show up in traditional ab initio calculations using Hartree-Fock references could be sUghtly reduced in DFT methods. In other words, for approximating the true electronic stmctures of many-electron atoms and molecules... 

Recently, Becke has derived theoretically the need to include part of the Hartree-Fock exact exchange (i.e. non-local effects) in the exchange functional to improve the predictions of the gradient-corrected DFT methods (16,17). Becke (17) proposed the functional... 

Here j SDA timkind of accurate pure DFT LSDA non-gradient-corrected exchange functional alluded to in section 7.2.3.4b, is the KS-orbital-based HF exchange energy functional of Eq. (7.30), is the Becke 88 exchange functional mentioned above, is the Vosko, Wilk, Nusair function (VWN, or Slater VWN, SVWN... 

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