Aromaticity in P₈ allotropes and (CH)₈ analogues: significance of their 40 valence electrons?

The currently unknown phosphorus allotrope P₈ is of interest since its 40 total valence electrons is a "magic number" corresponding to a filled 1S²1P⁶1D¹⁰1S²1F¹⁴2P⁶ shell such as found in the relatively stable main group element clusters Al₁₃^- and Ge₉^4-. However, P₈ still remains as an elusive structure not realized experimentally. The lowest energy P₈ structure by a margin of ∼9 kcal mol^-1 is shown by density functional theory to be a cuneane analogue with no PP double bonds and two each of P₅, P₄, and P₃ rings. Higher energy P₈ structures are polycyclic systems having at most a single PP double bond. These P₈ systems are not "carbon copies" of the corresponding (CH)₈ hydrocarbons with exactly one hydrogen atom bonded to each carbon atom. Thus the lowest energy (CH)₈ structure is cyclooctatetraene with four CC bonds followed by benzocyclobutene with three CC bonds. The cuneane (CH)₈ structure is a relatively high energy isomer lying ∼36 kcal mol^-1 above cyclooctatetraene. The cubane P₈ and (CH)₈ structures are even higher energy structures, lying ∼37 and ∼74 kcal mol^-1 in energy above the corresponding global minima. Our results demonstrate differences in medium sized aggregates of elemental phosphorus and isolobal hydrocarbon species.