  Evolutionary algorithm is combined with full-potential ab-initio calculations
to investigate conformational space of (MoS$_2$)$_n$ and (MoSe$_2$)$_n$
(n=1-10) nanoclusters and to identify the lowest energy structural isomers of
these systems. It is argued that within both BLYP and PBE functionals, these
nanoclusters favor sandwiched planar configurations, similar to their ideal
planar sheets. The second order difference in total energy ($\Delta_2$E) of the
lowest energy isomers are computed to estimate the abundance of the clusters at
different sizes and to determine the magic sizes of (MoS$_2$)$_n$ and
(MoSe$_2$)$_n$ nanoclusters. In order to investigate the electronic properties
of nanoclusters, their energy gap is calculated by several methods, including
hybrid functionals (B3LYP and PBE0), GW approach, and $\Delta$scf method. At
the end, the vibrational modes of the lowest lying isomers are calculated by
using the force constants method and the IR active modes of the systems are
identified. The vibrational spectra are used to calculate the Helmholtz free
energy of the systems and then to investigate abundance of the nanoclusters at
finite temperatures.
