Density functional theory DFT is a computational quantum mechanical modeling method used to investigate the electronic structure of many-body systems, such as atoms, molecules, and solids. In the context of comparing the electronic structure of a crystal of gold Au and a crystal of silver Ag , we can consider several factors such as the crystal structure, electronic configuration, and band structure.1. Crystal structure: Both gold and silver crystallize in the face-centered cubic FCC structure. This means that their crystal structures are similar, and the primary difference between them lies in their electronic properties.2. Electronic configuration: Gold has an electronic configuration of [Xe] 4f14 5d10 6s1, while silver has an electronic configuration of [Kr] 4d10 5s1. The primary difference between the two elements is the presence of the filled 4f orbitals in gold. These orbitals contribute to the relativistic effects, which significantly influence the electronic properties of gold.3. Band structure: In DFT calculations, the band structure represents the distribution of energy levels of electrons in a crystal. For both gold and silver, the valence band is primarily composed of d-orbitals, and the conduction band is composed of s-orbitals. However, due to the relativistic effects in gold, the 6s and 5d orbitals are closer in energy compared to the 5s and 4d orbitals in silver. This results in a smaller bandgap in gold, leading to its distinct electronic properties.In summary, the electronic structure of a crystal of gold differs from that of a crystal of silver primarily due to the relativistic effects in gold, which result in a smaller bandgap and distinct electronic properties. DFT calculations can provide detailed insights into these differences by analyzing the band structure and density of states of the two elements.