Exchange asymptotic behavior

A common problem for both methods lies in the use of potentials that do not possess the correct net attractiveness. This can have the consequence that continuum feamres appear shifted in energy. In particular, there is evidence that the LB94 exchange-correlation potential currently used for the B-spline calculations, although possessing the correct asymptotic behavior for ion plus electron, is too attractive, and near threshold features can then disappear below the ionization threshold. An empirical correction can be made, offsetting the energy scale, but this can mean that dynamics within a few electronvolts of threshold get an inadequate description or are lost. There is limited scope to tune the Xa potential, principally by adjustment of the assumed a parameter, but for the B-spline method a preferable alternative for the future may well be use of the SAOP functional that also has correct asymptotic behavior, but appears to be better calibrated for such problems [79]. 

Becke, A. D., 1988b, Density-Functional Exchange-Energy Approximation With Correct Asymptotic Behavior , Phys. Rev. A, 38, 3098. 

Chermette, H., Lembarki, A., Razafinjanahary, H., Rogemond, 1998, Gradient-Corrected Exchange Potential Functional With the Correct Asymptotic Behavior , Adv. Quant. Chem., 33, 105. 

Lembarki, A., F. Regemont, and H. Chermette. 1995. Gradient-corrected exchange potential with the correct asymptotic behavior and the corresponding exchange-energy functional obtained from virial theorem. Phys. Rev. A 52, 3704. 

Glossman, M. D., L. C. Baibas, A. Rubio, and I. A. Alonso. 1994. Nonlocal Exchange and Kinetic Energy Density Functionals with Correct Asymptotic Behavior for Electronic Systems. Int. I. Q. Chem. 49, 171. 

Glossman, M. D., Baibas, L. C., Rubio, A. and Alonso, J. A. Nonlocal exchange and kinetic energy density functionals with correct asymptotic behavior for electronic systems, Int.J. Quantum ( hem., 49 (1994), 171-184... 

DPT schemes, which allow to calculate the electron affinities of atoms are based on the exact [59,60] and generalized (local) [61,62] exchange self-interaction-corrected (SIC) density functionals, treating the correlation separately in some approximation. Having better asymptotic behavior than GGA s, like in the improved SIC-LSD methods, one should obtain more... 

Density Functional Theory (DFT) has become a powerful tool for ab-initio electronic structure calculations of atoms, molecules and solids [1, 2, 3]. The success of DFT relies on the availability of accurate approximations for the exchange-correlation (xc) energy functional Exc or, equivalently, for the xc potential vxc. Though these quantities are not known exactly, a number of properties of the exact xc potential vxc(r) are well-known and may serve as valuable criteria for the investigation of approximate xc functionals. In this contribution, we want to focus on one particular property, namely the asymptotic behavior of the xc potential For finite systems, the exact xc potential vxc(r) is known to decrease like — 1/r as r —oo, reflecting also the proper cancellation of spurious self-interaction effects induced by the Hartree potential. 

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