Clarifying the non-uniqueness in Polarization
For ionic and dielectric materials, the polarization (dipole moment per unit cell) is plagued with non-uniqueness. As a 1D example, consider a 1D line of alternating positive and negative charges. If we agree that the dipole is a vector from the negative to the positive charge, then we have two choices for the dipole. This is because every negative charge has two different positive charges in its immediate vicinity. The situation gets more complicated in higher dimensions.
