being 𝐶 𝑙𝜇 the matrix of the coefficients of the molecular orbitals and the Gaussian 𝜁 𝑙 (𝑥)AOs. These are created as an orthogonal set of vectors, which have components in each atomic orbital of a given molecule. The 𝑆 𝑖𝑗 overlap matrix is then defined by the set of AOs 𝜁 𝑙 (𝑥), which forms a set of non-orthogonal bases :