![]() ![]() This repulsive interaction primarily arises due to electron – electron repulsion between two closed shell atoms. However, for the stability of a crystal, apart from the attractive Coulomb forces, short range repulsive interactions are required to prevent the collapse of the structure to a point. 11,12 Hence, this problem is generally tackled numerically in computational chemistry through the Ewald's summation technique that gives excellent convergence with increase in the size/periodicity of the system. ![]() Series summation method for the calculation of Madelung constant (M) for simple crystals is imprecise since such series are only conditionally convergent though numerically reasonable convergence is attainable. 9,10 Even within the point charge model, the number of ions in the crystal being of the order of N A (Avogadro's number), a proper summation of all charges across the lattice is an involved task. This apparent simplicity is deceptive because Coulomb potential is a slowly decaying function and hence contributions from higher order multipole interactions need to be taken into consideration. Hence, the description of their ground state energies (and thus the structure, following the variation theorem) is exact within the point charge model. From an atomistic picture, ionic crystals are probably the simplest system to understand since the interactions among the ions are purely electrostatic in origin. ![]()
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