Projection between basis sets: A means of defining the electronic structure of functional subunits

The general problem of the transfer of the representation of a set of orthonormal functions from one basis to a different, nonequivalent one is considered and specialized to a matrix formulation convenient for use in molecular electronic structure calculations. A procedure is suggested for treating problems where the transfer of representation breaks into a subset of most interest and one of less interest as for example the occupied and virtual orbitals of a Hartree-Fock SCF calculation. These techniques are then applied to obtain a representation of a methyl group from an SCF wave function for methane.