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

TL;DR

This paper presents an alternative way to define the dipole of a bounded crystalline sample, linking it to the quantum-mechanical polarization formula used in electronic-structure calculations, thus clarifying their relationship.

Contribution

It introduces a novel definition of the dipole for bounded samples that naturally leads to the established polarization formula in electronic-structure methods.

Findings

New definition of the dipole for bounded samples

Clear derivation of polarization formula from the dipole definition

Bridges conceptual gap between classical dipole and quantum polarization

Abstract

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.