Density Gradient Corrections

Philipsen P H T, te Velde G and Baerends E J 1994 The effect of density-gradient corrections for a molecule-surface potential energy surface. Slab calculations on Cu(100)c(2x2)-C0 Chem. Phys. Lett. 226 583... 

Nonlocal density gradient corrections (GC)-local spin density (LDA) approximation. 

Why Density-Gradient Corrections Improve Atomization Energies... 

The short-range form of the correlation potential has been considered in DFT primarily in terms of density-gradient corrections to the LDA [6,7]. The correlation energy functional given by Eq.(7) here is not expressed explicitly as a functional of the electronic density, but is a formally exact expression which could be used to calibrate proposed functionals in particular cases where an accurate Cl expansion of a correlated ground-state wave function is known. When occupied orbital functions are expressed in a localized representation,... 

Density Gradient Corrections.—Mucci and March50 have discussed the corrections expected to the result (84) of the simplest density description. As they emphasize, three steps are involving in deriving equations (116) and (84) for molecules at equilibrium ... 

Since one expects, for bound molecules, that the chemical potential p will be negative, the fact that J(Vp)2jp dr is a positive quantity shows from equation(120) that deviations from relation (84) of the simplest density treatment can, in principle, be of either sign, depending on the relative magnitudes of the chemical potential and density gradient corrections. We shall discuss numerical values for the deviation from equation (84) in Section 16 below, in the light of equation (120). But before doing this it is of interest to re-examine the theoretical basis of Walsh s rules. 

It is worth noting that no overbinding seems to occur in the local density description of alkali chemisorption on nickel clusters, in contrast to findings for carbon transition metal bonds (23,27,28). At present, it would be premature to correlate this difference with the character of the various bonds (covalent vs. ionic). Clearly, density gradient corrections to the energy functional (31) would be highly useful in deciding this question. 

Somewhat similar results emerged from a comparable study of Pu02 [85]. Spin-orbit corrections, density gradient corrections, and spin-polarization each contribute a lattice parameter increase in the range 0.1 - 0.2 au and a decrease in 5 of order 15-30 GPa. The combined effect is to move the estimated lattice parameter to 10.30 au (experiment 10.20 au) and estimated 5 to 175 GPa (experiment 379 GPa) relative to scalar relativistic, LDA, non-spin-polarized values of 9.83 au and 246 GPa respectively. 

Progress beyond this point becomes more difficult. The original expectation of Perdew was that c should be a number close to zero. Part of the motivation for this expectation was that the dependence of p upon R had been found extremely weak in variational density functional calculations using model electron densities [6,13]. Those variational calculations used an approximate form for the kinetic energy of the electrons the local Thomas-Fermi term plus the first density gradient correction (sec Ref. [14] for details)... 

Considerable improvement of molecular calculation was given by Becke s density gradient correction of the local spin density (or Slater exchange) approximation of the exchange energy [180] ... 

Therefore, the effect of the density Laplacian is included implicitly in the kinetic energy density. It is natural that the next step in density gradient correction is the kinetic energy density correction on Jacob s ladder (see Sect. 5.1). Major meta-GGA functionals include the van Voorhis-Scuseria 1998 (VS98) meta-GGA exchange-correlation (van Voorhis and Scuseria 1998), the Perdew-Kurt-Zupan-Blaha (PKZB) meta-GGA exchange-correlation (Perdew et al. 1999), and the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA exchange-correlation (Tao et al. 2003) functionals. 

More specifically, we list bellow some nonlocal correlation density functionals in the low density (gradient corrections over LDA) regime ... 

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