Local Molecular Orbitals from a Projection onto Localized Centers.

A localization method for molecular orbitals is presented which exploits the locality of the eigenfunctions associated with the largest eigenvalues of the matrix representation of spatially localized functions. Local molecular orbitals are obtained by a projection of the canonical orbitals onto the set of the eigenvectors which correspond to the largest eigenvalues of these matrices. Two different types of spatially localized functions were chosen in this work, a two-parameter smooth-step-type function and the weight functions determined by a Hirshfeld partitioning of the molecular volume. It is shown that the method can provide fairly local occupied molecular orbitals if the positions of the set of local functions are set to the molecular bond centers. The method can also yield reasonably well-localized virtual molecular orbitals, but here, a sensible choice of the positions of the functions are the atomic sites and the locality then depends more strongly on the shape of the set of local functions. The method is tested for a range of polypeptide molecules in two different conformations, namely, a helical and a β-sheet conformation. Futhermore, it is shown that an adequate locality of the occupied and virtual orbitals can also be obtained for highly delocalized systems.