Fascinating properties of Transition Metal Dichalcogenides, including Tungsten Disulfide, in lubricant, electronics, optoelectronics, and chemical aspects have resulted in a variety of applications in transistors and electronic devices, fuel cells and Li-ion batteries, jet engines and heavy industries as lubricant, flexible optoelectronic devices, etc. There is no comprehensive structure search on nano-clusters of Tungsten Disulfide in the literature; so the first part of this thesis is dedicated to this topic. This task is done by employing a modern structure search algorithm, namely, “Evolutionary Algorithm” which has a reliable performance in finding minima of potential energy surface, by using heredity, mutation, and permutation operators. Configurational space of (WS 2 ) n nano-clusters are scanned for n 10, and the lowest lying isomers are determined. By Comparing the results of different xc-functionals to that of the hybrid B3LYP functional, a suitable semi-local functional for investigation of small WS 2 clusters is proposed, and using that functional, the vibrational spectra of the ground state clusters are calculated and their dynamical stability is verified. At the next step, by determining the binding energy and second order difference in energy, relative stability of the clusters and magic numbers are studied at zero temperature. Calculation of Helmholtz vibrational free energy, made it possible to investigate the relative stability of the clusters at finite temperatures. HOMO-LUMO gaps are also computed using BLYP, PBE, and B3LYP, before and after GW correction, and are verified using ?SCF method of gap calculation. Exponential growth in computational cost of investigation of larger sizes, instigated the need for a fast and reliable method to do the calculations, so, the second part of the thesis is dedicated to this subject. To do this, by employing machine learning methods, especially neural networks, a
