Coordination-Driven Classification and Energetic Scaling of Boron Fullerenes and Borophene

TL;DR

This study uses first-principles calculations to classify boron nanostructures based on atomic coordination, revealing energetic scaling laws, structural correspondences with borophenes, and properties that inform future design of boron materials.

Contribution

It introduces a coordination-based classification and a universal energetic scaling relation for boron nanostructures, linking 0D cages with 2D borophenes and providing a predictive design framework.

Findings

Identified clear trends in stability, electronic properties, and magnetism based on local coordination.

Established energetic scaling laws that describe convergence of fullerene energies to 2D boron phases.

Linked specific boron cages to experimentally observed borophenes, validating the classification.

Abstract

We present a comprehensive first-principles investigation of boron fullerenes and two-dimensional boron sheets, unified under a coordination-based framework. By classifying over a dozen boron nanostructures, including B$_{12}$, B$_{40}$, B$_{38}$, B$_{65}$, B$_{80}$, and B$_{92}$, according to their local atomic environments (4-, 5-, and 6-fold coordination), we identify clear trends in structural stability, electronic properties, and magnetism. A universal energetic scaling relation $E_c(n) = -a/n^b + E_c^{\mathrm{sheet}}$, with $b = 0.4$ or $b = 0.9$ depending on the coordination family, captures the convergence of fullerene cohesive energies toward those of 2D boron phases. Notably, we establish one-to-one structural correspondences between select cages and experimentally accessible borophenes: B$_{40}$ mirrors the $\chi^3$-sheet, B$_{65}$ the $\beta_{12}$-sheet, B$_{80}$ the $\alpha$-sheet, and B$_{92}$ the $bt$-sheet. Our analysis reveals two distinct families of boron nanostructures based on the scaling exponent: one with $b = 0.9$, comprising structures with significant 6-fold coordination, and another with $b = 0.4$, which includes B$_{40}$, B$_{38}$, and two experimentally observed borophenes. These clusters also exhibit large HOMO--LUMO gaps (e.g., $E_g = 1.78$~eV for B$_{40}$, 1.14~eV for B$_{92}$), contrasting with the metallicity of their 2D counterparts and, in the case of B$_{65}$, spontaneous spin polarization ($M = 3\mu_B$). Our findings provide a predictive strategy for designing boron nanostructures by leveraging coordination fingerprints, and are further validated by the recent experimental synthesis of the B$_{80}$ cage. This work bridges zero- and two-dimensional boron chemistry, offering a roadmap for the future synthesis and application of boron-based materials.