The diagonal elements can be seen as the interaction of an atom with itself and are essentially a polynomial fit of the atomic energies to the nuclear charge Z. The off-diagonal elements represent the Coulomb repulsion between nuclei i and j. The exponents in the diagonal entries correspond to a polynomial fit relating the atomic number to the total energies of the free atoms; the off-diagonal entries describe Coulomb's law like repulsions between the bare nuclei . Ewald sum matrix can be viewed as a logical extension of the Coulomb matrix for periodic systems, as it models the interaction between atoms in a periodic crystal through electrostatic interaction. However, to calculate the Coulomb interaction between the atomic cores in a periodic crystal, the Ewald summation technique has to be used together with a uniform neutralizing background charge. This term does however not correspond to the correct Ewald energy, as seen in the case of two interacting atoms, one of which has no charge: