We present a simple tight-binding parametrization for TiC that is capable of giving qualitatively accurate results for a range of properties. The systematic procedure used to develop these parameters is described, and the transferability of the model is tested. We use the model to account for the existence of substoichiometric titanium carbide, and the variation of its lattice constant with vacancy concentration. We show that the unusual lattice constant trend arises from the fact that the lattice relaxation around a vacancy is highly localized. The physical origin of this localization is the strongly anisotropic strengthening of bonds around a vacancy, which follows from the quantum mechanical nature of the bonding.

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Single-Atom Catalysts (SACs), containing under-coordinated single metal atoms bound on the surface of supports, have recently emerged as promising heterogeneous catalysts due to their intrinsic catalytic properties and efficient utilization (high dispersion) of noble metal atoms. Strong Metal-Support Interactions (MSIs) present in these catalysts can dictate the physicochemical properties, activity, and stability of SACs, which are significantly different from the conventional supported nanoscale metal catalysts. Although SACs exhibit unique catalytic behavior, their stability under catalytic operation is questioned due to the tendency of metals to sinter (aggregation). An optimal MSI can avoid metal aggregation and tune the stability and catalytic activity of SACs. Herein, we investigate MSIs of a series of transition metal atoms (Au, Cu, Ag,

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The calculation of vacancy energy in TiC was carried out incorrectly. The curves of the vacancy formation energy as a function of concentration are incorrect, and should be as shown in figure 1. The most important consequence is that the vacancy formation is always positive, thus the earlier conclusion that vacancies should form spontaneously even at absolute zero is no longer valid. Additionally, the stated c/a ratio of the WC form of TiC predicted by the tight binding model was incorrect, as was the energy difference between the WC and NaCl structure types. These should be: optimum c/a = 0.67 and E (WC) - E (NaCl) = 0.21 eV/atom.   Figure 1.