Using this expansion, the total photoelectron dipole matrix element is computed as a sum of the contributions from matrix elements determined at the individual centers. The dipole matrix elements are then computed using these atom-centered fragments of the Dyson orbital instead of the full molecular Dyson orbital. While this approach neglects coherences between the atomic centers, not all information about the molecular orbital is lost since the atomic centers retain some information about the bonding and polarization from the nearby atoms. The advantage of this approach is that it ensures orthogonality by placing the center of expansion of the photoelectron wave function on the corresponding atomic center.