VALENCE ISOMERS OF BENZENE AND THEIR RELATIONSHIP TO ISOMERS OF ISOELECTRONIC-P6

We report the results of geometry optimized ab initio SCF MO calculations with 3-21G,4-31G*, and 6-31G* basis sets for neutral P6 in forms corresponding to the five valence isomers of benzene, (CH6), with which P6 is valence isoelectronic. At the 6-31G* level benzene, Dewar benzene, benzvalene, prismane, and bicyclopropenyl structures all correspond to real minima on the P6 energy surface. The order of energies of P6 structures is quite different from that for the (CH)6 isomers. For P6, benzvalene and prismane have low energies and the planar hexagon has the highest. Bond distances are easily classified as single, double, or aromatic. The energy of 2P6 lies only 30-35 kcal/mol above that of 3P4 and 60-100 kcal/mol below 6P2. Energies of the HOMO and the HOMO-LUMO gaps and values of Mulliken net atom populations appear to be normal for these P6 structures. Calculated energy changes of homodesmotic reactions involving P6 provide estimates of strain energies for the four nonhexagonal structures. These range from a high (50-55 kcal/mol) for prismane to a low (10-15 kcal/mol) for Dewar benzene. These values are remarkably low compared to strain energies for the same structures of (CH)6. Using calculated strain energies and resonance energies, we obtain an estimate of 84 kcal/mol for the P=P double bond energy. This is less than twice the energy of an unstrained P-P single bond, 55 kcal/mol. Based on these results, we present a model of benzene isomeric structures ordered in energy by the number of single bonds they contain. Prismane, with nine single bonds, would have the lowest energy, and the Kekule hexagon would be highest with only three single bonds. The order actually calculated for these structures already includes strain and resonance corrections. Large strain corrections for the (CH)6 structures raise the energies of those structures, while the resonance energy of the hexagon lowers the energy of benzene. The result is a considerable rearrangement of the basic single bond energy order for (CH)6. In contrast, the modest resonance energy of planar hexagonal P6 and the small strain energies of the other structures only slightly perturb the expected bond energy ordering of structural stabilities.