Valence Virtual Orbitals: An Unambiguous ab Initio Quantification of the LUMO Concept

Many chemical concepts hinge on the notion of an orbital called the lowest unoccupied molecular orbital, or LUMO. This hypothetical orbital and the much more concrete highest occupied molecular orbital (HOMO) constitute the two frontier orbitals, which rationalize a great deal of chemistry. A viable LUMO candidate should have a sensible energy value, a realistic shape with amplitude on those atoms where electron attachment or reduction or excitation processes occur, and often an antibonding correspondence to one of the highest occupied MOs. Unfortunately, today's quantum chemistry calculations do not yield useful empty orbitals. Instead, the empty canonical orbitals form a large sea of orbitals, where the interesting valence antibonds are scrambled with the basis set's polarization and diffuse augmentations. The LUMO is thus lost within a continuum associated with a detached electron, as well as many Rydberg excited states. A suitable alternative to the canonical orbitals is proposed, namely, the valence virtual orbitals. VVOs are found by a simple algorithm based on singular value decomposition, which allows for the extraction of all valence-like orbitals from the large empty canonical orbital space. VVOs are found to be nearly independent of the working basis set. The utility of VVOs is demonstrated for construction of qualitative MO diagrams, for prediction of valence excited states, and as starting orbitals for more sophisticated calculations. This suggests that VVOs are a suitable realization of the LUMO, LUMO + 1, ... concept. VVO generation requires no expert knowledge, as the number of VVOs sought is found by counting s-block atoms as having only a valence s orbital, transition metals as having valence s and d, and main group atoms as being valence s and p elements. Closed shell, open shell, or multireference wave functions and elements up to xenon may be used in the present program.