  The electronic structure of $\sigma$-phase Fe$_{100-x}$V$_x$ compounds with
33.3 $\le x \le 60.0$ was calculated from the charge self-consistent
Korringa-Kohn-Rostoker method. For the first time, charge densities $\rho_A(0)$
and electric field gradients were determined at Fe nuclei, that occupy five
nonequivalent lattice sites. The highest $\rho_A(0)$ values were found on sites
A and D, and the lowest one on site B, the difference ranging between 0.162 and
0.174 $\it s$-like electrons per Fe atom for $x = 33.3$ and $x = 60$,
respectively. The calculated quantities combined with experimentally determined
site occupancies were successfully applied to analyze $^{57}$Fe M\"ossbauer
spectra recorded on a series of 8 samples in a paramagnetic state.
