First-principles study of MoS₂ and MoSe₂ nanoclusters in the framework of evolutionary algorithm and density functional theory

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.