Atoms-in-molecules and electron localization function study of the phosphoryl bond

Calculations at the B3LYP/6-311+G(d,p)//B3LYP/6-311+G(d,p) level involving the atoms-in-molecules (AIM) and electron localization function (ELF) methods have been carried out for a variety of PO-bond-containing molecules in an effort to further characterize the phosphoryl bond. One cannot distinguish the phosphoryl bond from a conventional PO double bond by comparing bond distances. Both the bond breaking energies and delocalization indices do divide into the three classes of single, double, and phosphoryl and tend to parallel each other. On the basis of the PO bond in HPO having a reference bond order of 2.0, the phosphoryl bond has a bond order of about 1.3. Examination of localized orbitals confirm our ideas that the phosphoryl bond is highly polar as, indeed, are the other PO bonds. What sets the phosphoryl bond apart is the high degree of back-bonding that contributes to the delocalization index (and covalent bond order) and provides for its stronger-than-single-bond character and short bond distance.