Calculation of chemical shifts of X-ray-emission spectra of niobium in niobium(V) oxides relative to metal

Chemical shifts of the $K_{\alpha1}$ and $K_{\beta1}$ lines of X-ray-emission spectra of niobium in oxides $(\mathrm{Nb}_{2}\mathrm{O}_{5})_{n}$, $n=1-4$, relative to metal $\mathrm{Nb}$ have been calculated. Stoichiometric clusters $(\mathrm{Nb}_{2}\mathrm{O}_{5})_{n}$ the electronic structure of which was calculated using accurate relativistic pseudopotentials and two-component version of the density functional theory are considered as prototypes for modeling different crystal forms of niobium(V) oxide. The chemical shifts were calculated using the method based on using the property of approximate proportionality of valence spinors in the core region of the heavy atom [11]. Corrections to values of chemical shifts have been determined with allowance for deviations from the abovementioned proportionality. Rapid convergence of results with respect to the size of the niobium oxide cluster has been demonstrated.