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.
