  A detailed and systematic density-functional theory (DFT) study of a series
of early transition-metal carbides (TMC's) in the NaCl structure is presented.
The focus is on the trends in the electronic structure and nature of bonding,
which are essential for the understanding of the reactivity of TMC's. The
employed approach is based on a thorough complementary analysis of the electron
density differences, the density of states (DOS), the band structure, and the
real-space wave functions to gain insight into the bonding of this class of
materials and get a more detailed picture of it than previously achieved, as
the trend study allows for a systematic identification of the bond character
along the different bands. Our approach confirms the presence of both the
well-known TM--C and TM--TM bonds and, more importantly, it shows the existence
and significance of direct C--C bonds in all investigated TMC's, which are
frequently neglected but have been recently identified in some cases [Solid
State Commun. 121, 411 (2002); Phys. Rev. B 75, 235438 (2007)]. New information
on the spatial extent of the bonds, their \textit{k}-space location within the
band structure, and their importance for the bulk cohesion is provided. Trends
in covalency and ionicity are presented. The resulting electron-structural
trends are analyzed and discussed within a two-level model.
