Molecular geometry from molecular tensegrity: A case study of gas-phase MX₂ compounds

We define a tensegrity factor, ${\mathrm{t}}_{00}^{\underset{-}{+}}$, for X–M–X linkages of gas-phase MXn compounds (X is an atom of an insulating element) that is a measure of the matching of 'ideal' 1,2-(single-bonded) M–X distance, ${\mathrm{d}}_{\mathrm{M}\mathrm{X}}^{00}$, to the 'ideal' (non-bonded) 1,3-X---X distances, ${\mathrm{d}}_{\mathrm{M}\mathrm{X}}^{00}$. The actually observed 1,3-distance, dXX is given (within 1% error) by 2CR(X)/FS, where FS ($\left({=2-1.41}_{00}^{\underset{-}{+}}\right)$) is shown to be an ab initio quantity with no adjustable parameter, no dependence on actual M–X distance or bond order and with 2CR(X) depending only on whether M is an atom of an insulating element (2CR(X) ≡ ${\mathrm{d}}_{\mathrm{X}\mathrm{X}}^{00}$) or whether M is metallic (2CR(X) = ${1.1\mathrm{d}}_{\mathrm{X}\mathrm{X}}^{00}$). This is illustrated for gas-phase MX₂ compounds.