Structure, stability and optical absorption spectra of small Ti$_n$C$_x$ clusters: a first-principles approach

Titanium-carbide molecular clusters are thought to form in the circumstellar envelopes (CSEs) of carbon-rich Asymptotic Giant Branch stars (AGBs) but, to date, their detection has remained elusive. To facilitate the astrophysical identification of those clusters in AGBs and post-AGBs environments, the molecular structures and optical absorption spectra of small Ti$_n$C$_x$ clusters, with n = 1-4 and x = 1-4, and some selected larger clusters, Ti$_3$C$_8$, Ti$_4$C$_8$, Ti$_6$C$_{13}$, Ti$_7$C$_{13}$, Ti$_8$C$_{12}$, Ti$_9$C$_{15}$, and Ti$_{13}$C$_{22}$, have been calculated. The density functional formalism, within the B3LYP approximation for electronic exchange and correlation, was used to find the lowest energy structures. Except the clusters having a single Ti atom, the rest exhibit three-dimensional structures. Those are formed by a Ti fragment surrounded in general by carbon dimers. The optical spectra of Ti$_n$C$_x$, computed by time-dependent density functional theory, using the corrected CAM-B3LYP functional, show absorption features in the visible and near infrared regions which may help in the identification of these clusters in space. In addition, most of the clusters have sizable electric dipole moments, allowing their detection by radioastronomical observations.