  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.
