On the Viability of Small Endohedral Hydrocarbon Cage\nComplexes:  X@C₄H₄, X@C₈H₈, X@C₈H₁₄, X@C₁₀H₁₆, X@C₁₂H₁₂,\nand X@C₁₆H₁₆

Abstract

Small hydrocarbon complexes (X@cage) incorporating cage-centered endohedral atoms and\nions (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)\nhybrid HF/DFT level of theory. No tetrahedrane (C₄H₄, <i>T</i><i>_d</i>) endohedral complexes are minima, not even\nwith the very small hydrogen atom or beryllium dication. Cubane (C₈H₈, <i>O</i><i>_h</i>) and bicyclo[2.2.2]octane (C₈H₁₄,\n<i>D</i>₃<i>_h</i>) minima are limited to encapsulating species smaller than Ne and Na⁺. Despite its intermediate size,\nadamantane (C₁₀H₁₆, <i>T</i><i>_d</i>) can enclose a wide variety of endohedral atoms and ions including H, He, Ne,\nLi^0,+, Be^0,+,2+, Na^0,+, and Mg²⁺. In contrast, the truncated tetrahedrane (C₁₂H₁₂, <i>T</i><i>_d</i>) encapsulates fewer\nspecies, while the <i>D</i>₄<i>_d</i> symmetric C₁₆H₁₆ hydrocarbon cage (see Table of Contents graphic) encapsulates\nall but the larger Be, Mg, and Mg⁺ species. The host cages have more compact geometries when metal\natoms, rather than cations, are inside. This is due to electron donation from the endohedral metals into\nC−C bonding and C−H antibonding cage molecular orbitals. The relative stabilities of endohedral minima\nare evaluated by comparing their energies (<i>E</i>_endo) to the sum of their isolated components (<i>E</i>_inc = <i>E</i>_endo −\n<i>E</i>_cage − <i>E</i>_x) and to their exohedral isomer energies (<i>E</i>_isom = <i>E</i>_endo − <i>E</i>_exo). Although exohedral binding is\npreferred to endohedral encapsulation without exception (i.e., <i>E</i>_isom is always exothermic), Be²⁺@C₁₀H₁₆\n(<i>T</i><i>_d</i>; −235.5 kcal/mol), Li⁺@C₁₂H₁₂ (<i>T</i><i>_d</i>; 50.2 kcal/mol), Be²⁺@C₁₂H₁₂ (<i>T</i><i>_d</i>; −181.2 kcal/mol), Mg²⁺@C₁₂H₁₂\n(<i>T</i><i>_d</i>; −45.0 kcal/mol), Li⁺@C₁₆H₁₆ (<i>D</i>₄<i>_d</i>; 13.3 kcal/mol), Be⁺@C₁₆H₁₆ (<i>C</i>₄<i>_v</i>; 31.8 kcal/mol), Be²⁺@C₁₆H₁₆ (<i>D</i>₄<i>_d</i>;\n−239.2 kcal/mol), and Mg²⁺@C₁₆H₁₆ (<i>D</i>₄<i>_d</i>; −37.7 kcal/mol) are relatively stable as compared to experimentally\nknown He@C₂₀H₂₀ (<i>I</i><i>_h</i>), which has an <i>E</i>_inc = 37.9 kcal/mol and <i>E</i>_isom = −35.4 kcal/mol. Overall, endohedral\ncage complexes with low parent cage strain energies, large cage internal cavity volumes, and a small,\nhighly charged guest species are the most viable synthetic targets.