Variationally optimized numerical orbitals for molecular calculations

The problem of variational optimization of the atomic orbitals used in molecular calculations is investigated. It is shown that the variational principle leads to an equation similar to the radial Schrodinger equation but containing an inhomogeneous term. As an example, the equations are solved for the minimum basis set orbitals for the methane molecule. The results show a substantial improvement over those of a previous calculation optimizing in a minimum basis of Slater orbitals.