Computing Molecular Descriptors of Boron Icosahedral sheet

Boron, the element which is in close proximity with carbon in the periodic table has been hypothesized to produce diverse two-dimensional structures that differ from well-studied 2D materials. Icosahedron $B_{12}$, the monomers of which form the crystalline boron structure, appears as a recurring pattern in the chemistry of boron compounds, elemental boron and boron-rich materials, functions as a building block in a majority of boron allotropes. The topological study of the icosahedral sheets is a necessary field to be investigated for the effective analysis and characterization of its physico-chemical attributes without undertaking time-consuming experimental research. The topological descriptors being expressed as numerical values enable scientists to compare and correlate data, which can be applied to quantitative structure-activity relationships and quantitative structure-property relationships modeling. In this study, various degree based molecular descriptors of the crystal boron icosahedral $\alpha$ sheet $B_{\alpha }(a,b)$ has been formulated from a two-dimensional lattice perspective using the $𝕄$-polynomial approach. To establish the significance of these descriptors in the study of chemical attributes, an efficient linear regression modeling has also been performed, enabling the prediction of properties of several other boron sheets.