  The structural and electronic properties of hypothetical Ru$_x$Fe$_{1-x}$Se
and Ru$_x$Fe$_{1-x}$Te systems have been investigated from first principles
within the density functional theory (DFT). Reasonable values of lattice
parameters and chalcogen atomic positions in the tetragonal unit cell of iron
chalcogenides have been obtained with the use of norm-conserving
pseudopotentials. The well known discrepancies between experimental data and
DFT-calculated results for structural parameters of iron chalcogenides are
related to the semicore atomic states which were frozen in the used here
approach. Such an approach yields valid results of the electronic structures of
the investigated compounds. The Ru-based chalcogenides exhibit the same
topology of the Fermi surface (FS) as that of FeSe, differing only in subtle FS
nesting features. Our calculations predict that the ground states of RuSe and
RuTe are nonmagnetic, whereas those of the solid solutions Ru$_x$Fe$_{1-x}$Se
and Ru$_x$Fe$_{1-x}$Te become the single- and double-stripe antiferromagnetic,
respectively. However, the calculated stabilization energy values are
comparable for each system. The phase transitions between these magnetic
arrangements may be induced by slight changes of the chalcogen atom positions
and the lattice parameters $a$ in the unit cell of iron selenides and
tellurides. Since the superconductivity in iron chalcogenides is believed to be
mediated by the spin fluctuations in single-stripe magnetic phase, the
Ru$_x$Fe$_{1-x}$Se and Ru$_x$Fe$_{1-x}$Te systems are good candidates for new
superconducting iron-based materials.
