Aromaticity in P allotropes and (CH) analogues: significance of their 40 valence electrons?

The currently unknown phosphorus allotrope P is of interest since its 40 total valence electrons is a "magic number" corresponding to a filled 1S1P1D1S1F2P shell such as found in the relatively stable main group element clusters Al and Ge. However, P still remains as an elusive structure not realized experimentally. The lowest energy P structure by a margin of ∼9 kcal mol is shown by density functional theory to be a cuneane analogue with no PP double bonds and two each of P, P, and P rings. Higher energy P structures are polycyclic systems having at most a single PP double bond. These P systems are not "carbon copies" of the corresponding (CH) hydrocarbons with exactly one hydrogen atom bonded to each carbon atom. Thus the lowest energy (CH) structure is cyclooctatetraene with four CC bonds followed by benzocyclobutene with three CC bonds. The cuneane (CH) structure is a relatively high energy isomer lying ∼36 kcal mol above cyclooctatetraene. The cubane P and (CH) structures are even higher energy structures, lying ∼37 and ∼74 kcal mol in energy above the corresponding global minima. Our results demonstrate differences in medium sized aggregates of elemental phosphorus and isolobal hydrocarbon species.