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Why does B$_{12}$H$_{12}$-icosahedron need two electrons to be stable: A first-principles electron-correlated investigation of B$_{12}$H$_{n}$ ($n=$6,12) clusters

In this work, we present large-scale electron-correlated computations on various conformers of B$_{12}$H$_{12}$ and B$_{12}$H$_{6}$ clusters, to understand the reasons behind the high stability of di-anion icosahedron ($I_{h}$) and cage-like B$_{12}$H$_{6}$ geometries. Although the B$_{12}$-icosahedron is the basic building block in some structures of bulk boron, it is unstable in its free form. Furthermore, its H-passivated entity, i.e., B$_{12}$H$_{12}$ icosahedron is also unstable in free form. However, dianion B$_{12}$H$_{12}$ has been predicted to be stable as a perfect icosahedron in the free-standing form. In order to capture the correct picture for the stability of B$_{12}$H$_{12}^{-2}$ and B$_{12}$H$_{6}$ clusters, we optimized these structures by employing the coupled-cluster singles-doubles (CCSD) approach and cc-pVDZ basis set. We also performed vibrational frequency analysis of the isomers of these clusters, using the same level of theory to ensure the stability of the structures. For all the stable geometries obtained from the vibrational frequency analysis, we additionally computed their optical absorption spectra using the time-dependent density functional theory (TDDFT) approach, at the the B3LYP/6-31G{*} level of theory. Our calculated absorption spectra could be probed in future experiments on these clusters.