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

## TL;DR

This study compares the linear optical absorption spectra of two B12 cluster isomers, revealing how their distinct geometries influence their optical properties through both semi-empirical and ab initio calculations.

## Contribution

It provides a detailed analysis of how geometry affects optical absorption in B12 clusters using combined semi-empirical and ab initio methods, highlighting differences between isomers.

## Key findings

- Lower energy absorption in icosahedral B12
- Higher energy plasmon-like excitations in both isomers
- Good qualitative agreement between methods

## Abstract

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