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

Peter Ludwig Rodríguez-Kessler

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.

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 BCa have been systematically investigated using density functional theory calculations. Extensive global basin-hopping searches identify a single-ring B 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 ring, leading to effective electronic stabilization without the involvement of transition-metal 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 BCa 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.
Paper Structure (8 sections, 6 figures, 2 tables)

This paper contains 8 sections, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Computational Details
  3. Results and Discussion
  4. Vibrational and Optical Properties
  5. Charge analysis
  6. Electron Density–Based Bonding Analysis
  7. Conclusions
  8. Acknowledgments

Figures (6)

  • Figure 1: Lowest energy structures for B$_{7}$Ca$_2$ cluster at PBE0/def2-TZVP.
  • Figure 2: IR spectra of B$_{7}$Ca$_2$ cluster.
  • Figure 3: Representative IR-active vibrational modes of the B$_7$Ca$_2$ cluster.
  • Figure 4: Simulated UV--Vis absorption spectrum of the B$_7$Ca$_2$ cluster calculated at the TD-DFT/TDA level. The spectrum is obtained from the excitation energies and oscillator strengths, applying Gaussian broadening ($\sigma = 0.05$ eV) to simulate a continuous absorption profile.
  • Figure 5: ELF 2D maps of the B$_{7}$Ca$_2$ cluster. Left: side view showing localized Ca-centered ELF maxima. Right: top view showing a continuous $\sigma$-delocalized network along the boron single ring.
  • ...and 1 more figures