Vibrational spectra and electronic structure of 11-vertex boron-containing clusters: a comparative study of [B11H11](2-), [CB10H11](-), and C2B9H11

Vibrational spectroscopy studies of 11-vertex boron-containing clusters [B11H11](2-)(1), [2-CB10H11](-) (2), and 2,3-C2B9H11 (3) revealed two low-frequency large-amplitude modes in their spectra and, therefore, structural nonrigidity of these polyhedra in contrast to related 12-, 10-, and 6-vertex closo-clusters. The nonrigidity originates from specific features of the electron density distribution. According to calculations within the framework of the Atoms in Molecule (AIM) theory, these polyhedra are characterized by the lack of many bond paths localized on corresponding edges, in particular, between boron atoms with coordination numbers of 6 and 5 (6k and 5k). Consequently, these polyhedra are composed of not only trigonal faces, i.e., formally do not have the closo-structure that was traditionally ascribed to them based on formal count of (2n + 2) valence electrons. According to calculations of three-center delocalization indices, the absence of bond paths is not equivalent to the lack of interaction between corresponding atoms since this interaction occurs through open three-center bonds. The mechanism and reasons for signal averaging observed in B-11 NMR spectra of compounds 1 and 2 in contrast to 3 are analyzed.