Roothaan equations

The Roothaan equations are a set of integral equations that arise in the context of Hartree-Fock (HF) theory, which is a fundamental method in quantum chemistry for approximating the electronic structure of atoms and molecules. The Roothaan equations specifically provide a way to solve for molecular orbitals in a self-consistent field approximation. In essence, the Roothaan equations are derived from the variational principle applied to the Hartree-Fock method and can be written in matrix form.