Phosphorus Analogues of Diazonium Ions. 2. Protonation of N₂, PN, and P₂

The potential energy surfaces of protonated N ₂ , P ₂ , and PN are explored at RHF, MP2, and CISD levels. Stationary structures were not only optimized but also characterized by computation of their vibrational frequencies at each of these levels. Model dependencies of potential energy surface characteristics, geometries, vibrational frequencies, relative isomer stabilities, and proton affinities are studied in a systematic fashion. The potential energy surface of HP ₂ ⁺ exhibits dramatic model dependencies and it is clarified by a scan of the potential energy surface as a function of the H-P-P angle at the CISD level. Geometries and vibrational frequencies of the most stable isomers also are reported at the CISD(full)/6-311G(df,p) level. Accurate scale factors for bond lengths and vibrational frequencies determined for the neutral diatomics X≡X can be applied successfully to the protonated species as well. End-on protonation of N ₂ , edge-on protonation of P ₂ , and N-protonation of PN are favored, and our best estimates for the proton affinities are 116.3, 161.2, and 194.2 kcal/mol, respectively. Proton affinities parallel the increase of the polarizabilities (N ₂ < NP < P ₂ ) but the polarizabilities perpendicular to the bond axis, α _perp , are significantly small than α _para and their ratio α _para /α _perp is not related to the isomer preference energies. For protonated N ₂ and P ₂ , the isomer preference is closely related to the X ₂ bond length per se and the structural preferences of the protonated systems thus reflect the same factors that also determine the X≡X bond lengths in the neutral diatomics. The proton is atypically electrophilic compared to carbenium ions and the carbenium ion affinities of N ₂ , P ₂ , and PN are generally much smaller than proton affinities. While the potential energy surfaces of protonated and methylated N ₂ and PN are qualitatively similar, the respective derivatives of P ₂ differ significantly.