  In this paper, we employ evolutionary algorithm along with the full-potential
density functional theory (DFT) computations to perform a comprehensive search
for the stable structures of stoichiometric (WS2)n nano-clusters (n=1-9),
within three different exchange-correlation functionals. Our results suggest
that n=3, 5, 8 are possible candidates for the low temperature magic sizes of
WS2 nano-clusters while at temperatures above 600 Kelvin, n=5 and 7 exhibit
higher relative stability among the studied systems. The electronic properties
and energy gap of the lowest energy isomers were computed within several
schemes, including semilocal PBE and BLYP functionals, hybrid B3LYP functional,
many body based DFT+GW approach, and time dependent DFT calculations.
Vibrational spectra of the lowest lying isomers, computed by the force constant
method, are used to address IR spectra and thermal free energy of the clusters.
Time dependent density functional calculation in real time domain is applied to
determine the full absorption spectra and optical gap of the lowest energy
isomers of the WS2 nano-clusters.
