Nuclear Magnetic Shielding in Alkali Halide Crystals

Abstract

The overlapping-ion model proposed by Kondo and Yamashita to explain the magnetic shielding of nuclei in alkali halides is extended to derive an expression for the shielding constant $\ensuremath{\sigma}$ in terms of all the important one- and two-center integrals in crystals with rocksalt structure. Using the results of Baron's pressure-dependence studies of the magnetic shielding in rubidium bromide in conjunction with our expression for $\ensuremath{\sigma}$, and using available Hartree-Fock wave functions for the ions, we have determined the average energy denominators ${\ensuremath{\Delta}}_{+}$ and ${\ensuremath{\Delta}}_{\ensuremath{-}}$ for the ${\mathrm{Rb}}^{+}$ and ${\mathrm{Br}}^{\ensuremath{-}}$ions. These values of ${\ensuremath{\Delta}}_{+}$ and ${\ensuremath{\Delta}}_{\ensuremath{-}}$ are then used to calculate the values of ${\ensuremath{\sigma}}_{\mathrm{Rb}}$ and ${\ensuremath{\sigma}}_{\mathrm{Br}}$ in the crystal with reference to the free ion. When these latter quantities are combined with the experimental values of the chemical shifts with reference to dilute aqueous solution of RbBr, one obtains ${{\ensuremath{\sigma}}_{\mathrm{Rb}}}^{\mathrm{aq}\ifmmode\cdot\else\textperiodcentered\fi{}}=0.63\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4} \mathrm{and} {{\ensuremath{\sigma}}_{\mathrm{Br}}}^{\mathrm{aq}\ifmmode\cdot\else\textperiodcentered\fi{}}=1.94\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ for the shielding constants in dilute solution relative to the free ions.