  Equilibrium atomic configuration and electronic structure of the (001)
surface of IV-VI semiconductors PbTe, PbSe, SnTe and SnSe, is studied using the
density functional theory (DFT) methods. At surfaces of all those compounds,
the displacements of ions from their perfect lattice sites reveal two features
characteristic of the rock salt crystals. First, the ionic displacements occur
only along the direction perpendicular to the surface, and they exhibit the
rumpling effect, i.e., the vertical shifts of cations and anions differ.
Second, the interlayer spacing of the first few monolayers at the surface
oscillates. Our results are in good agreement with the previous X-ray
experimental data and theoretical results where available. They also are
consistent with the presence of two {110} mirror planes at the (001) surface of
the rock salt. One the other hand, experiments preformed for the topological
Pb$_{1-x}$Sn$_x$ Se alloy indicate breaking of the mirror symmetry due to a
large 0.3 {\AA} relative displacement of the cation and anion sublattices at
the surface, which induces the opening of the gap of the Dirac cones. Our
results for Pb$_{1-x}$Sn$_x$Se including the simulated STM images, are in
contradiction with these findings, since surface reconstructions with broken
symmetry are never the ground state configurations. The impact of the
theoretically determined surface configurations and of the chemical disorder on
the surface states is analyzed.
