There are many codes that can be used to calculate the electronic band structure of three-dimensional crystals. Some of them are found in the Wikipedia list of quantum chemistry and solid-state physics software. There are free software packages as well as commercial packages. Commonly used packages to calculate band structures are VASP, Quantum Espresso, FHI-AIMS, and ABINIT. These codes are used to calculate the electronic, magnetic, optical, mechanical, and thermodynamic properties of materials based on the arrangement of the atoms in the crystal. All of them have some limitations. It is advisable to follow a course on band structure calculations or to work with someone experienced with band structure calculations before you start using them.

Many band structure calculations have already been performed. A simple internet search of the form 'electronic band structure ' will probably retrieve the band structure of the crystal you are interested in. The Materials Project is a database with many electron dispersion relations and densities of states.

A common strategy for calculating band structures is to guess a form for the wave function that contains some adjustable parameters. This form for the wavefunction is inserted into the Schrödinger equation, which results in some algebraic equations involving the adjustable parameters and the energy. The combination of parameters that minimizes the energy is the best solution for the wavefunction that is possible for the form of the initial guess. To illustrate how this works, two band structure methods, the plane wave method and tight binding, will be described.