Charge, Bonding, and Optical Properties of the B$_7$Ca$_2$ Cluster: An Alkaline-Earth Dimer Stabilized by a Single Boron Ring

Abstract

The charge, bonding, and optical properties of the calcium-doped boron cluster B$_7$Ca$_2$ have been systematically investigated using density functional theory calculations. Extensive global basin-hopping searches identify a single-ring B$_7$ geometry stabilized by two calcium atoms symmetrically located on opposite sides of the boron ring as the global minimum. Electronic structure analysis reveals pronounced charge redistribution and strong Ca--B interactions that promote electron delocalization over the boron framework. Hirshfeld charge analysis indicates substantial electron donation from the electropositive calcium atoms to the electron-deficient B$_7$ ring, leading to effective electronic stabilization without the involvement of transition-metal $d$ orbitals. Optical absorption spectra further reflect the delocalized nature of the frontier electronic states. Real-space bonding analyses based on the electron localization function (ELF), Interaction Region Indicator (IRI), and the Laplacian of the electron density reveal a multicenter bonding pattern dominated by electron delocalization within the boron ring, with calcium acting primarily as an electrostatic and charge-donating stabilizer rather than forming localized two-center Ca--B bonds. These results establish B$_7$Ca$_2$ as a prototypical example of an alkaline-earth-metal-stabilized boron ring and highlight the ability of non-transition metals to stabilize aromatic boron clusters through charge transfer and multicenter bonding.