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Boron clusters have been widely studied theoretically for their geometricalproperties and electronic structure using a variety of methodologies. Animportant cluster of boron is the B$_{12}$ cluster whose two main isomers havedistinct geometries, namely, icosahedral ($I_{h}$) and quasi planar ($C_{3v}$).In this paper we investigate the linear optical absorption spectrum of thesetwo B$_{12}$ structures with the aim of examining the role of geometry on theoptical properties of clusters. The optical absorption calculations areperformed using both the semi-empirical and the ab initio approaches. Thesemi-empirical approach uses a wave function methodology employing the INDOmodel Hamiltonian, coupled with large-scale configuration interaction (CI)calculations, to account for the electron-correlation effects. The \emph{abinitio} calculations are performed within atime-dependent-density-functional-theory (TDDFT) methodology. The results forthe two approaches are in very good qualitative agreement with each other.Quantitatively speaking, results agree with each other in the lower energyregion, while in the higher energy region, features predicted by the TDDFTapproach are red-shifted as compared to the INDO-CI results. Both theapproaches predict that the optical absorption begins at much lower energies inthe icosahedral cluster as compared to the planar one, a fact which can beutilized in experiments to distinguish between the two geometries. At higherenergies, both the isomers exhibit plasmon-like excitations. 73,1 4%

Theory of Linear Optical Absorption in B_12 Clusters: Role of the geometry