Charge Distribution and Nuclear Quadrupole Interactions in Ionic Crystals

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Abstract
A general expression for the electric field gradient (EFG) at the positive ion nucleus in an ionic crystal with polyatomic negative ions has been derived in the frameworks of the LCAO–MO approximation and the multipole expansion theorem of the electrostatic potential. The contribution to the field gradient in the present treatment is analyzed in terms of the multipole moments well defined in molecular orbital theory; the expression for the field gradient due to the atomic charges located on each atom of the polyatomic ion provides just what Bersohn derived on the assumption of the point‐charge model, and the contribution due to higher multipole moments describes a deviation from it. The expression derived on the basis of this type of point‐multipole model has been applied to the evaluation of the field gradient at the 23Na nucleus in a single crystal of sodium nitrite (NaNO2), and the results have been used to make clear the underlying assumptions and the limitations of the simple point‐charge model. The conclusions derived from the present calculation are: (1) the field gradient in an ionic crystal depends too sensitively on the electron charge distribution of the polyatomic ions adjacent to the nucleus under study to be predicted by the point‐multipole model, and so (2) the evaluation of the field gradient needs a careful treatment of the charge distribution of the closest ions including overlap and covalent bonding effects.

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