Abstract

The bonding in carboranes has been a subject of interest for scientists due to the number of atoms in close radial proximity of each other in the molecules despite being deficient of valence electrons. A three-center-two-electron bond has been hypothesized to explain the boron atom’s ability to form more than three bonds within a molecule and several papers have been written supporting the existence of this bonding arrangement within carboranes10-11. This study utilized computational chemistry techniques including DFT and the QTAIM method, the Laplacian scalars, charge values, basin paths, Poincare-Hopf algebra, and specifically, a B3LYP DFT method with an ab initio MP2 level of theory, and a 6-311+G(2d,p) basis set to produce a geometric optimization of two closo-carboranes. The computational results determined that there is no three-center-two-electron bonding in these molecules due to the satisfaction of the Poincare-Hopf theorem and because all the structures bond critical points connecting to ring critical points and to atoms. The smaller difference between the bond critical points and their corresponding ring critical points in the two axial positions of both molecules indicates they are the weakest and would break first. The breaking of the first axial bond would lead to the nido structure and subsequent breaking of the second the arachno structure, which supports Wade’s Rules characterizing the cluster tightness of the closo structure from the nido and arachno structures. The structural characterization of carboranes is, therefore, more accurately described by Wade’s Rules. The charge values and Laplacian scalars results show electron densities that indicate fragment behavior, like ligand behavior, between the boron and carbon atoms and their corresponding hydrogens. A more accurate theory for describing the bonding in carboranes would include steric proximity and ligand/fragment coordination to overcome the electron deficiency, combined with Wade’s Rules for the characterization of structure.

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