Exchange potential 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]. 

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. 

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. 

Similarly, as the case with response properties discussed in the previous section, imposing the correct asymptotic behavior of vxc improves the agreement between the numerical values of —sH0M0 and the experimental ionization potentials.85,90,91,94 For these reasons, the ionization potentials and electron affinities are usually obtained as energy differences (ASCF) in calculations using common approximations to the exchange-correlation functional. The discussed hereafter numerical values were obtained in this way. 

The asymptotic behavior of the exchange-correlation potential far from the molecule has been identified as the key factor determining the accuracy of the ionization potentials of anions and electron affinities of neutral molecules.5 Recently, Wu et al.91 proposed a variational method, which enforces the correct long-range behavior of vxc. Indeed, a noticeable improvement compared to the Kohn-Sham results derived using conventional approximations (LDA-, GGA-, and hybrid functionals) was reported for atoms (H, He, Li, Be, B, C, N, O, and F) and diatomics (BeH, CH, NH, OH, CN, BO, NO, OO, FO, and FF). The still significant discrepancies between the experimental and calculated ionization potentials (or electron affinities) were attributed to errors of the exchange-correlation potential in the molecular interior. 

Gisbergen, S.J.A. van, Osinga V.P., Gritsenko O.V., Leeuwen R. van, Snijders J.G. and Baerends E. J., Improved density functional theory results for frequency-dependent polarizabilities, by the use of an exchange-correlation potential with correct asymptotic behavior. J.Chem.Phys. (1996) 105 3142-3161. 

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