  The approximate atomic self-interaction corrections (ASIC) method to density
functional theory is put to the test by calculating the exchange interaction
for a number of prototypical materials, critical to local exchange and
correlation functionals. ASIC total energy calculations are mapped onto an
Heisenberg pair-wise interaction and the exchange constants J are compared to
those obtained with other methods. In general the ASIC scheme drastically
improves the bandstructure, which for almost all the cases investigated
resemble closely available photo-emission data. In contrast the results for the
exchange parameters are less satisfactory. Although ASIC performs reasonably
well for systems where the magnetism originates from half-filled bands, it
suffers from similar problems than those of LDA for other situations. In
particular the exchange constants are still overestimated. This reflects a
subtle interplay between exchange and correlation energy, not captured by the
ASIC.
