Structural, Bonding, and Optical Properties of B$_{18}$Ca$_2$ Clusters: Double-Ring Forms

The structural and electronic properties of the doubly calcium-doped boron cluster B$_{18}$Ca$_2$ have been systematically investigated using density functional theory calculations. Basin-hopping searches reveal that B$_{18}$Ca$_2$ adopts a double-ring geometry as its global minimum, consisting of two fused B$_9$ rings symmetrically stabilized by calcium atoms located above and below the boron framework. Vibrational frequency calculations verify the dynamical stability of the low-lying structures, while infrared and UV-Vis spectra highlight strong Ca--B coupling and pronounced electronic delocalization within the boron scaffold. Atomic dipole-corrected Hirshfeld charge analysis indicates substantial charge transfer from Ca to the electron-deficient boron framework, with the donated electrons uniformly delocalized over the B$_{18}$ skeleton. Real-space bonding analyses based on the electron localization function (ELF), Interaction Region Indicator (IRI), and the Laplacian of the electron density reveal an extended multicenter bonding network characterized by global $\sigma$-delocalization and Ca-induced polarization effects rather than localized two-center Ca--B bonds. Together, these results establish B$_{18}$Ca$_2$ as a prototypical boron toroidal cluster and provide fundamental insights into the role of alkaline-earth doping in stabilizing complex boron nanostructures.