Saha, Amartyajyoti2025-01-072025-01-072023-12https://hdl.handle.net/11299/269233University of Minnesota Ph.D. dissertation. December 2023. Major: Physics. Advisor: Turan Birol. 1 computer file (PDF); xxvii, 192 pages.Understanding the crystal structure and symmetry is essential for gaining insights into the fundamental physical and chemical properties of a material, as well as its macroscopic behavior. Recent advancements in computational power and the development of advanced and reproducible density functional theory-based methods provide us with a powerful arsenal to explore crystal structures. This thesis involves a first-principles computational study of structural instabilities, phase transitions, and various electronic and thermal properties in four distinct families of materials. I use group-theoretical analysis to study the evolution of octahedral rotation and ferroelectric instabilities in Pnma perovskite oxides for multiple compounds under different strains. I explore the stability of the tetrahedral rotation and tilt in orthovanadates with palmierite structure, and the resulting phase transitions. In layered 112 compounds with 2D square nets, I study the instability of the square-net as well as its novel electronic properties. I also investigate the electronic and thermal properties of metallic delafossite, which show remarkable agreement with experiments. For each class of compounds, I use a combination of first-principles methods and group-theoretical analysis to explore the evolution of various instabilities and the resulting changes in structure and symmetry via lattice vibrations.enDelafossiteDensity Functional TheoryDFTFirst-principlesOrthovanadatePerovskiteThesis or Dissertation