Deviations from the Most Spherical Deltahedra in Rhenatricarbaboranes Having 2n + 2 Wadean Skeletal Electrons

Density functional theory studies on the rhenatricarbaboranes C₃B_n-4H_n-1Re(CO)₃ (n = 7-12) show that the lowest energy polyhedra for n-vertex metallaboranes having 2n + 2 skeletal electrons and sufficiently dissimilar vertex atoms can deviate from the most spherical closo deltahedra predicted by application of the Wade-Mingos rules. Furthermore, the lowest energy structures of these rhenatricarbaboranes are found to avoid C-C edges and have carbon atoms located at degree 4 rather than degree 5 vertices. The lowest energy structures for the 7-vertex C₃B₃H₆Re(CO)₃ system all have a central C₃B₃Re closo deltahedron, namely the pentagonal bipyramid with the rhenium atom at a degree 5 axial vertex and all three carbon atoms at degree 4 equatorial vertices. However, the lowest energy structure for the 8-vertex C₃B₄H₇Re(CO)₃ is not the most spherical closo 8-vertex deltahedron, namely the bisdisphenoid, but instead a central C₃B₄Re hexagonal bipyramid with mutually nonadjacent degree 4 vertices for the carbon atoms. Similarly, the lowest energy 10-vertex C₃B₆H₉Re(CO)₃ structures are derived from isocloso deltahedra having three degree 4 vertices for all three carbon atoms rather than from the most spherical 10-vertex closo deltahedron, namely the bicapped square antiprism with only two degree 4 vertices. However, for the 9-vertex C₃B₅H₈Re(CO)₃ system, the most spherical closo deltahedron, namely the tricapped trigonal prism, has three mutually nonadjacent degree 4 vertices, which is ideal for the three carbon atoms and thus is the preferred deltahedron. The preferred deltahedron for the 11-vertex C₃B₇H₁₀Re(CO)₃ remains the most spherical closo deltahedron despite having only two degree 4 vertices for the carbon atoms. Furthermore, the six lowest energy 12-vertex C₃B₈H₁₁Re(CO)₃ structures are all based on the regular icosahedron generally favored in polyhedral borane chemistry despite its complete lack of degree 4 vertices for the carbon atoms.