To make this approach practically useful, another approximation is needed. The (unknown) molecular orbitals are expanded in a set of known basis functions. This is called the basis set approximation or the linear combination of atomic orbitals (LCAO) to give molecular orbitals (MO). The HF equations then transform into matrix equations (Roothaan-Hall equations, eq. 2.10) which are much easier for a computer to solve. Here, the matrix 𝑪 contains all coefficients of the basis functions for every molecular orbital while 𝑺 contains the overlap between the different basis functions.