  We present several results related to the instability of MoC and MoN in the
B1 (sodium chloride) structure. These compounds were proposed as potential
superconductors with moderately high transition temperatures. We show that the
elastic instability in B1-structure MoN, demonstrated several years ago,
persists at elevated pressures, thus offering little hope of stabilizing this
material without chemical doping. For MoC, another material for which
stoichiometric fabrication in the B1-structure has not proven possible, we find
that all of the cubic elastic constants are positive, indicating elastic
stability. Instead, we find X-point phonon instabilities in MoC (and in MoN as
well), further illustrating the rich behavior of carbo-nitride materials. We
also present additional electronic structure results for several transition
metal (Zr, Nb and Mo) carbo-nitride systems and discuss systematic trends in
the properties of these materials. Deviations from strict electron counting
dependencies are apparent.
