2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/28237The Born effective charge, Z*, that describes the polarization created by collective atomic displacements, can be computed from first-principles by different techniques. Its band-by-band decomposition appeared recently as a powerful tool for the microscopic characterisation of the bonding in solids. We describe the connections between the different expressions used for the computation of Z*, and analyze the possible associated band-by-band decompositions. We show that unlike for the full Z*, the different band-by-band values are not equal, and emphasize that one of them has an interesting physical meaning.11 pages, 1 table, LaTeXCondensed Mattertext