For the metal-edge of pure NbS 2 catalyst mixed with Mo and promoted with V, Fe, Co, and Ni, density functional theory and first-principles surface thermodynamics calculations at hydrodesulfurization conditions have been performed. It was found that V, Co, and Ni promoters impart stabilization to the catalyst surfaces whereas Fe produces an opposite effect and renders the catalysts less stable. Catalyst structures corresponding to the fully Ni-promoted edge of the mixed Mo−Nb sulfide with a Mo 3 Nb 2 S 10 composition and to the NbS 2 V-promoted with 50% sulfur coverage forming S dimers are by far the most stable structures. The nature of the hydrodesulfurization active sites of both most stable monolayers were studied using reactivity predictors such as the electrostatic potential, the electronic localization function, and the Laplacian of the electronic density.

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We examine the validity of the first Hohenberg‐Kohn theorem, namely, the one‐to‐one relationship between an external potential and the 1‐particle density, when it is applied to finite subspaces and consider the stability of these subspaces with respect to external potentials. This is done by analysing the DFT description of some simple atoms (eg, H, He, Li, and Be) provided by the solution of the Kohn‐Sham equation in a finite Gaussian basis set. We show that in the finite subspace generated from the finite basis set, it is possible to construct external potentials that differ from one another by more than a constant but which associate with the same 1‐particle density. We carry out the specific construction of these potentials for the above atoms using the wave functions resulting from the application of the B3LYP functional. We comment on the fact that these instability potentials seem to be prominent only in the outer region of the atom where the density tends to zero. We also discuss the implications that the instability potentials have in relation to the Kohn‐Sham formalism and equations.