Semi-local functionals

There are exceptions from this trend. A noted example is the polarizability of sodium clusters significantly underestimated by semi-local functionals.73... 

Table 1.1 MAEs (in kcal/mol) in atomization energies, barrier heights, and noncovalent binding energies of the global hybrids based on various local or semi-local functionals. The value of the mixing parameter ao for each case is also reported. The MAEs of the original local or semi-local functionals are given in parenthesis...

Four different Fock/Kohn-Sham operators have been applied to obtain the orbitals, which are subsequently localized by the standard Foster-Boys procedure. In addition to the local/semi-local functionals LDA and PBE, the range-separated hybrid RSHLDA [37, 56] with a range-separation parameter of /r = 0.5 a.u. as well as the standard restricted Hartree-Fock (RHF) method were used. The notations LDA[M] and LDA[0] refer to the procedure applied to obtain the matrix elanents either by the matrix algebra [M] or by the operator algebra [O] method. All calculations were done with the aug-cc-pVTZ basis set, using the MOLPRO quantum chemical program package [57]. The matrix elements were obtained by the MATROP facility of MOLPRO [57] the Cg coefficients were calculated by Mathematica. 

Since the localized orbitals satisfy local Brillouin theorem, we finally obtain for the matrix elements of the fock operator with multiphcative potential (typically Kohn-Sham operator with local or semi-local functionals) between two oscillator orbitals ... 

Kristyan, S., Pulay, P., 1994, Can (Semi)Local Density Functional Theory Account for the London Dispersion Forces , Chem. Phys. Lett., 229, 175. 

The description of bonding at transition metal surfaces presented here has been based on a combination of detailed experiments and quantitative theoretical treatments. Adsorption of simple molecules on transition metal surfaces has been extremely well characterized experimentally both in terms of geometrical structure, vibrational properties, electronic structure, kinetics, and thermo-chemistry [1-3]. The wealth of high-quality experimental data forms a unique basis for the testing of theoretical methods, and it has become clear that density functional theory calculations, using a semi-local description of exchange and correlation effects, can provide a semi-quantitative description of surface adsorption phenomena [4-6]. Given that the DFT calculations describe reality semi-quantitatively, we can use them as a basis for the analysis of catalytic processes at surfaces. 

The complexity of the functional form for Cc0Te increases from equation (67) to equation (71). To remove the necessity of accepting any particular predetermined functional form Kahn and Goddard29 evaluated a semi-local potential by making use of... 

The term non-local is used sometimes in die literature in association with gradient-dependent (GGA) functionals. This nomenclature is not applied in this work. The LDA-, GGA-, and meta-GGA functionals are referred to as semi-local as they do not account for any long-range non-locality of the exchange-correlation energy density excseim local(r) = exc(p(r), Vp(r), V2p(r), r(r)) whereas... 

Kristyan S, Pulay P (1994) Can (semi)local density-functional theory account for London dispersion forces, Chem Phys Lett, 229 175-180... 

For semi-local xc functionals such as the local density approximation, general gradient approximations or meta functionals using the kinetic energy density, the xc energy can, using (18) and (19), be written as... 

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