and obtained by summing over all atoms X of the unit cell. The integration interval [ ω ω 0 , ω ω 1 ] is chosen in such a way that it encompasses all the phonon states relevant for the specific study. The integral at the denominator of the definition of C M A is the contribution of the atom A to the states in the frequency range [ ω ω 0 , ω ω 1 ] ; we call such quantity the phonicity of the A atom in that specific frequency range. The phonicity of an atom then represents the amount of phonon states that such atom contributes to form; in this respect, it can be regarded as the phonon counterpart of the atomic valence, that is the number of electrons with which an atom participates to form the electronic states of the system, counted as the integral of the atom-projected electronic density of states.