Reciprocal polyhedra and the Euler relationship: cage hydrocarbons, C_nH_n and closo-boranes [B_xH_x]²⁻

Abstract

SummaryThe closo-boranes BxHx +2, or their corresponding anions [BxHx]2− (where x = 5 through 12) and polycycloalkanes CnHn (where n represents even numbers from 6 through 20) exhibit a complementary relationship whereby the structures of the corresponding molecules, e.g., [B6H6]2− and C8H8 (cubane), are based on reciprocal polyhedra. The vertices in the closo-boranes correspond to faces in its polycyclic hydrocarbon counterpart and vice versa. The different bonding patterns in the two series are described. Several of these hydrocarbons (cubane, pentagonal dodecahedrane and the trigonal and pentagonal prismanes) are known while others still remain elusive. Synthetic routes to the currently known CnHn highly symmetrical polyhedral species are briefly summarized and potential routes to those currently unknown are discussed. Finally, the syntheses of the heavier element analogues of cubane and the prismanes are described.

From [10]Paracyclophane to Ferrocenophanones: The Search for Molecular Machines and Bio‐Organometallic Anticancer Drugs

“…However, aromaticity is not limited to planar two‐dimensional π‐systems; there now exist a plethora of three‐dimensional aromatic species in which there is electron delocalization over a near‐spherical surface, as in boranes, carboranes, and transition metal clusters 74. Several carboranophanes incorporating an icosahedral B 10 C 2 core, such as 28 and 29 , have been reported,75 and one might envisage analogous cyclophanes based on metal clusters with globally delocalized electron density…”

Design and synthesis of novel bis-annulated caged polycycles via ring-closing metathesis: pushpakenediol

“…Caged polycyclic compounds draw the attention of synthetic organic chemists due to their unusual reactivity patterns as well as their strained nature [ 1 – 9 ]. Several pentacycloundecane (PCUD) related molecules were found to be key structural elements in various drugs [ 10 – 12 ], high-energy materials [ 13 – 15 ] and supramolecules [ 16 – 17 ].…”

Unification and Expansion of Wade-Mingos Rules with Elementary Number Theory

“…The method of calculating k value for lager clusters is the same. ,andB 6 H 6 2¯[ E=6x8 =48, V =6x3+6+2 =26, k = 11, code M-6-11-26, octahedral] 6 .In the case of transition metal carbonyl clusters, the same empirical formula will apply but E= will refer to the total 18 electron system of the 'skeletal' atoms and V= the total valence electrons of metal atoms and all the ligands and any embedded atoms involved. Take the examples, Mn 2 (CO) 10 [E =2x18 =36, V= 2x7+10x2 =34, k = ½ (36-34) = 1, M-2-1-34] 8 , Os 3 (CO) 12 18 2¯, octahedral] 9 is a capping process.…”