Perturbation‐Theoretical Model Calculation of the Lattice Mechanics of Ionic Crystals in the Point‐Dipole Approximation

A perturbation‐theoretic model calculation is developed in the point‐dipole approximation for the study of ionic crystals from a knowledge of the Hartree‐Fock wave functions of the free ions that constitute the solid. The salient features of the present calculation are that it a) provides a method for calculating the different lattice static and dynamic properties of a crystal directly from the free ion wave functions without using any crystal property; b) clearly gives an empirical justification for the major assumption of the phenomenological shell model; c) develops a new method for evaluating the Coulomb overlap interaction; d) suggests a modified short‐range polarisation mechanism; and lastly e) shows how far actually the free ion wave functions are realistic as a starting point. The method is applied to calculate a number of lattice mechanical properties of the two ionic crystals namely, NaCl and KCl. Despite the simplicity of the approach the agreement, with observation for both the crystals is quite impressive. The source of the remaining discrepancy is discussed.