Gradient approximation

In two classic papers [18, 46], Calm and Flilliard developed a field theoretic extension of early theories of micleation by considering a spatially inliomogeneous system. Their free energy fiinctional, equations (A3.3.52). has already been discussed at length in section A3.3.3. They considered a two-component incompressible fluid. The square gradient approximation implied a slow variation of the concentration on the... 

Perdew J P, Burke K and Ernzerhof M 1996 Generaiized gradient approximation made simpie Phys. Rev. Lett. 77 3865... 

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 ... 

Philipsen, P.H.T. and Baerends, E.J. (2000) Relativistic calculations to assess the ability of the generalized gradient approximation to reproduce trends in cohesive properties of solids. Physical Review B - Condensed Matter, 61, 1773-1778. 

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. 

Patton, D. C., Pederson, M. R., 1997, Application of the Generalized-Gradient Approximation to Rare-Gas Dimers , Phys. Rev. A, 56, R2495. 

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

Over the range of Martinelli parameter of practical importance (0.1 Martinelli-Nelson correlation predicts a frictional pressure gradient approximately twice that predicted by the homogeneous model. 

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