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

Density functional theory studies on the rhenatricarbaboranes C3Bn–4Hn–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.