The qualitative notion of frontier molecular orbitals, particularly the HOMO and LUMO, is extremely useful in chemistry. While the HOMO is easy to identify in a Hartree-Fock or Density Functional Approximation calculation, the LUMO is a more nebulous concept. Klaus Ruedenberg, honored at this 59th Sanibel Symposium, found a way to easily separate the valence subspace from the remainder of the virtual function space of such calculations, using Singular Value Decomposition1. Canonicalization within this valence subspace yields orbitals called the Valence Virtual Orbitals. Practical uses for these VVOs are to quantify the LUMO, to allow construction of polyatomic MO diagrams with semi- -‐quantitative accuracy, to predict the orbital shapes involved in valence excited states, and to provide starting orbitals for multi–‐reference calculations2. The separation of the empty orbitals into valence and external subspaces allows different calculational procedures for the correlation energy in these two spaces. One such Hybrid Correlation Energy scheme3 can approach the accuracy of triples–‐corrected coupled cluster theory, with a much lower formal scaling. Finally, the localization of all the occupied orbitals together with all the VVOs leads to atomic centered orbitals (namely, the AOs after optimal distortion into the molecular environment), which may be used for decompositions of the molecular binding energy4.