  A combinatorial approach is employed to investigate the atomic and electronic
structures of a metal vacancy in titanium carbide. It turns out that the usual
relaxed geometry of the vacancy is just a metastable state representing a local
energy minimum. Using ab initio calculations and by systematically searching
through the configurational space of a Ti monovacancy, we identify a multitude
of local minima with reconstructed geometry that are lower in energy. Among
them, there is a planar configuration with two displaced carbons forming a
dimer inside the vacancy. This structure has the optimal number and order of
C-C bonds making it the global minimum. Further calculations show that this
reconstructed geometry is also the ground state of metal vacancies in other
carbides such as ZrC, HfC, and VC. The reconstructed metal vacancies are
characterized by localized electron states due to the relatively short C-C
bonds. The defect states lie just below the upper and lower valence bands. The
existence of reconstructed vacancy configurations is essential for
understanding the mechanism of metal self-diffusion in transition-metal
carbides.
