Structure of Boranes Based on the Topology of Molecular Electron Density

Abstract

The Quantum Theory of Atoms in Molecules (QTAIM) is utilized in this computational study to characterize the structure of some representative borane molecules (closo-, nido-, and arachno- boranes). Being connectivity-rich but electron-deficient, these molecules exhibit nontraditional bonding patterns whose adequate classification require nontraditional bonding concepts.

Multi-center Molecular Orbitals (MO), equilibrium nuclear geometries and normal modes of vibrations are derived at the B3LYP/cc-pVTZ level of theory using the Gaussian-09 program package. Both the static (stationary) and dynamic one-electron densities (EDs) are analysed to access QTAIM descriptors, such as the value of the ED, and its principal curvatures at all critical points, the bond-path length and the topological graph. In term of these figures, we characterize and compare atomic interactions found in borane molecules and establish their structural stability. We observe chemically equivalent bonds to exhibit similar topology. All but the terminal B-H bonds are at the borderline of shared and closed-shell interactions. Certain distance-based atom-atom contacts suggested by experimental structures are however absent in the topological structure, though good agreement is found between the experimental and calculated geometry. Investigations of the Laplacian of the ED, (that identifies regions of local charge concentrations / depletions), lead to a general conclusion that the stability of the boron framework (including B-H-B bridges) is mainly a consequence of electron delocalization over three- and four-membered rings formed via week bonds. In a cage or ‘open-cage’ type structure the delocalization appears to fuse rings together even though they do not share a common plane. This finding seems to support the intuitive concept of 3D aromaticity invoked on the basis of the localized-MO model used to describe the structure of polyhedral boranes.

The QTAIM identifies a stable structure with a set of equivalent topological graphs corresponding to different nuclear configurations in the neighborhood of the stationary one. A strong support for the stability of these borane structures is gained, for the first time, from showing that their static and dynamic (averaged over nuclear displacements of harmonic vibrations) EDs are indeed topologically equivalent.