This dissertation explores the fundamental principles of quantum mechanics and their application to periodic structures, with a particular focus on density functional theory (DFT) and its performance in predicting lattice constants of bulk solids. This will focus on foundational concepts of quantum mechanics, the wave-particle duality, Schrödinger equation, and quantum mechanical operators. It provides a theoretical framework for understanding the behaviour of electrons in atoms and molecules. This also looks into crystal structures and the basic classes of lattices along with the application of periodic structures. Following this will be the focus on density functional theory (DFT), a powerful theoretical framework for studying the electronic structure of materials. The main objective of the thesis is the assessment of the performance of DFT in predicting lattice constants of bulk solids. Through a comparative analysis of various density functional approximations (DFAs), such as LDA, PBE, and hybrid functionals, this chapter evaluates the accuracy and reliability of different functionals in reproducing experimental results.
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