  The nuclear quadrupole moment of the I=3/2- excited nuclear state of 57Fe at
14.41 keV, important in M\"ossbauer spectroscopy, is determined from the
large-scale nuclear shell-model calculations for 57Fe and also from the
electronic ab initio and density functional theory calculations including solid
state and electron correlation effects for the molecules Fe(CO)_5 and Fe(C_5
H_5)_2. Both independent methods yield very similar results. The recommended
value is 0.16(1) eb. The NQM of the isomeric 10+ in 54Fe has also been
calculated. The new value (0.5 eb), consistent with the perturbed angular
distribution data, is by a factor of two larger than the currently recommended
value.
