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

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