Functional gradient approximation

Massobrio C, Pasquarello A and Corso A D 1998 Structural and electronic properties of small Cu clusters using generalized-gradient approximations within density functional theory J. Chem. Phys. 109 6626... 

The local density approximation is highly successful and has been used in density functional calculations for many years now. There were several difficulties in implementing better approximations, but in 1991 Perdew et al. successfully parametrised a potential known as the generalised gradient approximation (GGA) which expresses the exchange and correlation potential as a function of both the local density and its gradient ... 

When the two phases separate the distribution of the solvent molecules is inhomogeneous at the interface this gives rise to an additional contribution to the free energy, which Henderson and Schmickler treated in the square gradient approximation [36]. Using simple trial functions, they calculated the density profiles at the interface for a number of system parameters. The results show the same qualitative behavior as those obtained by Monte Carlo simulations for the lattice gas the lower the interfacial tension, the wider is the interfacial region in which the two solvents mix (see Table 3). 

Burke, K., Perdew, J. R, Wang, Y., 1998, Derivation of a Generahzed Gradient Approximation The PW91 Density Functional , in Electronic Density Functional Theory. Recent Progress and New Directions, Dobson, J. F., Vignale, G., Das, M. P. (eds.), Plenum Press, New York. 

Filatov, M., Thiel, W., 1998, Exchange-Correlation Density Functional Beyond the Gradient Approximation , Phys. Rev. A, SI, 189. 

Gritsenko, O. V., Schipper, P. R. T., Baerends, E. J., 1997, Exchange and Correlation Energy in Density Functional Theory. Comparison of Accurate DFT Quantities With Traditional Hartree-Fock Based Ones and Generalized Gradient Approximations for the Molecules Li2, N2, F2 , J. Chem. Phys., 107, 5007. 

Perdew, J. P., Wang, Y., 1986, Accurate and Simple Density Functional for the Electronic Exchange Energy Generalized Gradient Approximation , Phys. Rev. B, 33, 8800. 

Local exchange-correlation functionals such as generalized gradient approximations (GGA) are continuum approximations, which can, at best, average over the discontinuity. In regions where the HOMO and LUMO are significant, they provide an approximate average description [39—41] ... 

If the main limitations of HF theory are overcome by the introduction of electron correlation, those of density functional theory are expanded by the use of more accurate functionals. These functionals, that improve the uniform gas description of the LDA approach, are labeled as non-local or Generalize Gradient Approximation (GGA). 

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 density functional calculations were performed using the Vienna Ab Initio Simulation Package (VASP). ° The spin-polarized generalized gradient approximation, Perdue—Wang exchange correlation function, and ultrasoft pseudopotentials were used. ... 

Recently, a new class of functionals, called general gradient approximations (GGA s) [6-14], has been developed. These take the general form... 

Perdew JP, Burke K, Wang Y, Real space cutoff construction of a generalized gradient approximation derivation of the PW91 functional, submitted to Phys Rev B... 

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