Vladimir Bacic

• Exfoliation of graphene in 2004 initiated a tremendous interest (both theoretical as well as experimental) in the field of the two-dimensional (2D) materials. Such materials have typically layered structures, so the field of 2D materials is naturally related to the more general field of layered materials. A special (and relatively unexplored) class of such materials are the so-called misfit layered compounds (MLCs), which are made up of layers of 2D crystals whose lattice constant ratio is an irrational number. Moreover, with the ever growing interest in the chemistry and physics of new materials, there is a high demand for novel and improved theoretical and computational methods, especially for ones which offer accurate, ab-initio theoretical description of large systems (such as the aforementioned MLCs) with low computational costs. One of the methods that seems to meet these demands well is the density-functional based tight-binding. This thesis is a summary of my work on the above mentioned topics, including: i) development of new phonon calculation methods in the SCC-DFTB formalism ii) investigation of layered, intercalated PbNbS2 and misfit (PbS)1.14NbS2 compounds through Raman spectroscopy iii) investigation of a new family of layered materials, with the formula XY3 (X = group 14, Y = group 15 element)