Scaling exchange-correlation

Correlation Energies from Scaled Exchange-Correlation Kernels Importance of Spatial vs. Temporal Nonlocality. 

This fitting does not reduce the formal scaling, since the exchange-correlation term already is of order M. ... 

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]. 

Goh, S. K., Gallant, R. T., St-Amant, A., 1998, Towards Linear Scaling for the Fits of the Exchange-Correlation Terms in the LCGTO-DF Method via a Divide-and-Conquer Approach , Int. J. Quant. Chem., 69, 405. 

Stratmann, R. E., Scuseria, G. E., Frisch, M. J., 1996, Achieving Linear Scaling in Exchange-Correlation Density Functional Quadratures , Chem. Phys. Lett., 257, 213. 

As mentioned above, LSD yields a reasonable description of the exchange-correlation hole, because it satisfies several exact conditions. However, since the correlation hole satisfies a zero sum rule, the scale of the hole must be set by its value at some value of . The local approximation is most accurate at points near the electron. In fact, while not exact at m = 0, LSD is highly accurate there. Thus the on-top hole provides the missing link between the uniform electron gas and real atoms and molecules [18]. 

Because of different scaling properties, the exchange-correlation energy density functional (XCEDF) can be further decomposed into separate exchange and correlation components, ... 

An exact expression for Exc is obtained by scaling the electron-electron interaction with a factor A and varying A between 1 (real system) and 0 (noninteracting system). The exchange-correlation functional Exc is then given by (3) ... 

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