Localized molecular orbitals for polyatomic molecules

Molecular wavefunctions have been generated by the PRDDO (Partial Retention of Diatomic Differential Overlap) method for the monocyclic aromatic rings containing six π-electrons (C₄H ₄ ^?2 , C₅H ₅ ^? , C₆H₆, C₇H ₇ ⁺ , and C₈H ₈ ⁺² ) and ten π-electron species (C₈H ₈ ^?2 , C₉H ₉ ^? , C₁₀H₁₀). The eigenvalue spectra of the canonical molecular orbitals are presented. Localized molecular orbitals (LMO's) generated using the Boys criterion are reported for localizations involving all occupied molecular orbitals (complete localizations) and localizations of the π orbitals only. We find evidence for σ-π separation in the complete localizations for some of these molecules even though the Boys criterion is often biased against such results. We demonstrate for C₆H₆ and find for the other molecules that the π-orbital localizations are indeterminate (i.e. there are an infinite number of equally satisfactory LMO structures between two limiting extremes). This result may be viewed as a corollary of Hückel's (4n+2) rule for aromaticity.