  The magnetic moments per Fe atom in high-$T{_\textrm{c}}$ iron-based
superconducting compounds, BaFe$_{2}$As$_{2}$ and LaFeAsO obtained from the
first-principles calculation with local-spin-density approximation are much
larger than those obtained from experiments. To resolve the contradictory
results between theory and experiment we employed the so-called LDA$+ U$ (or
more exactly GGA$+ U$) technique with negative \emph{U} in the first-principles
calculation. The calculated values with negative \emph{U}, $- 0.09$ Ry and $-
0.10$ Ry for BaFe$_{2}$As$_{2}$ and LaFeAsO, respectively, are in excellent
agreement with the experimental ones. By comparing the differences in
\emph{d}-orbital occupation numbers and spin densities calculated by using a
simple GGA and GGA$+ U$ with negative $U$, the magnetic moments of the two
compounds are found to be similar to the case of low-spin state of metamagnetic
Fe$_{3}$Al alloy.
