On the Viability of Small Endohedral Hydrocarbon Cage Complexes:  X@C₄H₄, X@C₈H₈, X@C₈H₁₄, X@C₁₀H₁₆, X@C₁₂H₁₂, and X@C₁₆H₁₆

Small hydrocarbon complexes (X@cage) incorporating cage-centered endohedral atoms and ions (X = H⁺, H, He, Ne, Ar, Li^0,+, Be^0,+,2+, Na^0,+, Mg^0,+,2+) have been studied at the B3LYP/6-31G(d) hybrid HF/DFT level of theory. No tetrahedrane (C₄H₄, T_d) endohedral complexes are minima, not even with the very small hydrogen atom or beryllium dication. Cubane (C₈H₈, O_h) and bicyclo[2.2.2]octane (C₈H₁₄, D_3h) minima are limited to encapsulating species smaller than Ne and Na⁺. Despite its intermediate size, adamantane (C₁₀H₁₆, T_d) can enclose a wide variety of endohedral atoms and ions including H, He, Ne, Li^0,+, Be^0,+,2+, Na^0,+, and Mg²⁺. In contrast, the truncated tetrahedrane (C₁₂H₁₂, T_d) encapsulates fewer species, while the D_4d symmetric C₁₆H₁₆ hydrocarbon cage (see Table of Contents graphic) encapsulates all but the larger Be, Mg, and Mg⁺ species. The host cages have more compact geometries when metal atoms, rather than cations, are inside. This is due to electron donation from the endohedral metals into C−C bonding and C−H antibonding cage molecular orbitals. The relative stabilities of endohedral minima are evaluated by comparing their energies (E_endo) to the sum of their isolated components (E_inc = E_endo − E_cage − E_x) and to their exohedral isomer energies (E_isom = E_endo − E_exo). Although exohedral binding is preferred to endohedral encapsulation without exception (i.e., E_isom is always exothermic), Be²⁺@C₁₀H₁₆ (T_d; −235.5 kcal/mol), Li⁺@C₁₂H₁₂ (T_d; 50.2 kcal/mol), Be²⁺@C₁₂H₁₂ (T_d; −181.2 kcal/mol), Mg²⁺@C₁₂H₁₂ (T_d; −45.0 kcal/mol), Li⁺@C₁₆H₁₆ (D_4d; 13.3 kcal/mol), Be⁺@C₁₆H₁₆ (C_4v; 31.8 kcal/mol), Be²⁺@C₁₆H₁₆ (D_4d; −239.2 kcal/mol), and Mg²⁺@C₁₆H₁₆ (D_4d; −37.7 kcal/mol) are relatively stable as compared to experimentally known He@C₂₀H₂₀ (I_h), which has an E_inc = 37.9 kcal/mol and E_isom = −35.4 kcal/mol. Overall, endohedral cage complexes with low parent cage strain energies, large cage internal cavity volumes, and a small, highly charged guest species are the most viable synthetic targets.