  In this work we undertake a comprehensive numerical study of the ground state
structures and optical absorption spectra of isomers of B$_{12}$ cluster.
Geometry optimization was performed at the coupled-cluster-singles-doubles
(CCSD) level of theory, employing cc-pVDZ extended basis sets. Once the
geometry of a given isomer was optimized, its ground state energy was
calculated more accurately at the coupled-cluster-singles-doubles along with
perturbative treatment of triples (CCSD(T)) level of theory, employing larger
cc-pVTZ basis sets. Thus, our computed values of binding energies of various
isomers are expected to be quite accurate. Our geometry optimization reveals
eleven distinct isomers, along with their point group, and electronic ground
state symmetries. We also performed vibrational frequency analysis on the three
lowest energy isomers, and found them to be stable. Therefore, we computed the
linear optical absorption spectra of these isomers of B$_{12}$, employing
large-scale multi-reference singles-doubles configuration-interaction (MRSDCI)
approach, and found a strong structure-property relationship. This implies that
the spectral fingerprints of the geometries can be utilized for optical
detection, and characterization, of various isomers of B$_{12}$. We also
explored the stability of the isomer with with the structure of a perfect
icosahedron, with $I_{h}$ symmetry. In bulk boron icosahedron is the basic
structural unit, but, our vibrational frequency analysis reveals that it is
unstable in the isolated form. We speculate that this instability could be due
to Jahn-Teller distortion because five-fold degenerate HOMO orbitals in $I_{h}$
structure are unfilled.
