Orbitals and Electronic Band Structures (Part 5, p Orbital Bands in a 1D System)

To understand molecular bonding and electronic structure Chemists utilize orbital models, while Physicists often use the so-called k-vector to construct electronic structure band diagrams for solid state systems. The connection of orbitals to k-space diagrams can be difficult to visualize. These tutorials are presented at a level accessible to a materials science undergraduate in an attempt to provide that intuition and understanding.
In the 5th video we see how a linear chain of p-orbitals yields crystal orbitals derived from sigma and pi overlaps. In the final band diagram, the energy of the sigma p orbitals increases with the value of the k-vector, while the energies of the pi derived p-orbitals (and the s-band) increase with k.
Content is based on seminal papers by Roald Hoffmann recommended to those seeking a more extensive treatment: e.g., “How Chemistry and Physics Meet in the Solid State”, Angew. Chem. Int. Ed. Engl. 26, [1987], 846-87.