The electronic band structure of a material represents the range of energy levels that electrons can occupy within the material. It is a key factor in determining the electrical, optical, and thermal properties of the material. Density functional theory DFT is a widely used computational method to study the electronic structure of materials, including the effects of external pressure.When external pressure is applied to a material, the atomic positions and interatomic distances change, leading to a modification in the electronic structure. This can result in changes to the electronic band structure, which can be predicted by DFT calculations. Here are some general trends observed in the electronic band structure of materials under varying external pressure:1. Bandgap change: The bandgap is the energy difference between the valence band maximum and the conduction band minimum. With increasing pressure, the bandgap can either increase or decrease, depending on the material. For example, in some semiconductors, the bandgap increases with pressure, leading to a blue shift in the optical absorption edge. In contrast, some materials may undergo a semiconductor-to-metal transition under high pressure, where the bandgap closes completely.2. Bandwidth modification: The bandwidth, which is the energy range of a specific band, can also change with pressure. As pressure increases, the interatomic distances decrease, leading to stronger interactions between atomic orbitals and a broader bandwidth. This can affect the material's electrical conductivity and other properties.3. Band overlap: In some cases, increasing pressure can cause previously non-overlapping bands to overlap, leading to new electronic states and modified properties. This can result in changes in the material's electrical and optical behavior.4. Structural phase transitions: High pressure can induce structural phase transitions in materials, leading to significant changes in the electronic band structure. For example, a material might transition from a low-symmetry crystal structure to a high-symmetry one, which can have a profound impact on the band structure and the material's properties.5. Changes in the density of states: The density of states DOS represents the number of electronic states per energy interval. With varying pressure, the DOS can change, affecting the material's properties such as electrical conductivity, optical absorption, and thermoelectric performance.In summary, the electronic band structure of a material can change significantly with varying external pressure, as predicted by density functional theory calculations. These changes can lead to modifications in the material's electrical, optical, and thermal properties, making the study of pressure-dependent electronic structure an important aspect of materials science and condensed matter physics.