Limited occurrence of isocloso deltahedra with 9 to 12 vertices in low-energy hypoelectronic diferradicarbaborane structures

Theoretical studies show that the 10-vertex system Cp(2)Fe(2)C(2)B(6)H(8) is the only one of the 2n skeletal electron Cp(2)Fe(2)C(2)B(n-4)H(n-2) systems (n = 9, 10, 11, 12) for which a true isocloso deltahedron having a single degree 6 vertex is highly favored over alternative structures. This is demonstrated by the occurrence of only the 10-vertex isocloso deltahedron as the central Fe(2)C(2)B(6) polyhedron in all nine of the Cp(2)Fe(2)C(2)B(6)H(8) structures within 8 kcal/mol of the global minimum. Low energy isocloso structures are also observed for the 11-vertex Cp(2)Fe(2)C(2)B(7)H(9). However, interspersed with these isocloso structures are Cp(2)Fe(2)C(2)B(7)H(9) structures based on deltahedra having two or more degree 6 vertices. For the 12-vertex Cp(2)Fe(2)C(2)B(8)H(10), the six lowest energy structures all have central Fe(2)C(2)B(8) deltahedra with two degree 6 vertices, one for each iron atom. The Cp(2)Fe(2)C(2)B(8)H(10) structures having a central Fe(2)C(2)B(8) icosahedron with all degree 5 vertices lie at significantly higher energies, starting at 17.8 kcal/mol above the global minimum. The 9-vertex Cp(2)Fe(2)C(2)B(5)H(7) system appears to be too small for isocloso structures to be favorable, although three such structures are found at energies between 5.5 and 8.0 kcal/mol above the global minimum. Five Cp(2)Fe(2)C(2)B(5)H(7) structures based on the tricapped trigonal prism lie in an energy below the lowest energy isocloso structure. The lowest energy Cp(2)Fe(2)C(2)B(5)H(7) structure and two higher energy structures within 8.0 kcal/mol of the global minimum have central Fe(2)C(2)B(5) deltahedra with a degree 6 vertex for each iron atom.