Perspective: From the dipole of a crystallite to the polarization of a crystal

The quantum-mechanical expression for the polarization of a crystalline solid does not bear any resemblance to the (trivial) expression for the dipole of a bounded crystallite; and in fact it has been proved via a conceptually different path. Here I show how to alternatively define the dipole of a bounded sample in a somewhat unconventional way; from such formula, the crystalline polarization formula – as routinely implemented in electronic-structure codes – follows almost seamlessly.