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New local "hybrid" functionals proposed by V. V. Karasiev in [J. Chem. Phys.{\bf 118}, 8567 (2003)] are benchmarked against nonlocal hybrid functionals.Their performance is tested on the total and high occupied orbital energies, aswell as the electric moments of selected diatomic molecules. The newfunctionals, along with the Hartree-Fock and non-hybrid functionals, areemployed for finite-difference calculations, which are basis-independent. Basisset errors in the total energy and electric moments are calculated for the6-311G, 6-311G++G(3df,3pd) and AUG-cc-pVnZ (n=3,4,6) basis sets used inconjunction with the Hartree-Fock and conventional density functional methods.A comparison between the results of the finite-difference local "hybrid" andbasis set nonlocal hybrid functional shows that total energies of local andnonlocal hybrid functionals agree to within the basis set error. Discrepanciesfor multipole moments are larger in magnitude when compared to the basis seterrors, but still reasonably small (smaller than errors produced by the 6-311Gbasis set). Thus, we recommend using the new local "hybrid" functionalswhenever the accuracy is expected to be sufficient, because they require asolution of just differential Kohn-Sham equations, instead ofintegro-differential ones in the case of hybrid functionals.

Numerical local "hybrid" functional treatment of selected diatomic  molecules: comparison of energies and multipole moments to conventional  hybrid functionals