Spectral-moment constraints on electride-electron locations in the crystalline electride [Cs(18-crown-6)2]

The inverse-first moment and the first moment of the observed optical-absorption spectrum of the crystalline electride [Cs(18-crown-6${)}_2$] [where (18-crown-6) is (${\mathrm{CH}}_2$ ${\mathrm{CH}}_2$O${)}_6$] are used to determine rigorous upper and lower bounds for the absolute maximum of the single-particle probability density of a typical constituent electride electron. These bounds sufficiently bracket the contact densitites that are determined from magic-angle-spinning ${}_{}{}^{133}{}_{}{}^{}\mathrm{NMR}$ spectra of the pure electride and of its mix-crystals with the isomorphous sodide, [Cs(18-crown-6${)}_2$Na], to indicate that the distribution of the electron most likely is located in the immediate vicinity of a cesium nucleus. Limitations on the number of ${}_{}{}^{133}{}_{}{}^{}\mathrm{NMR}$ absorptions in sodide-electride mix-crystals are shown to support such a location.