Electronic polarization in quasilinear chains

TL;DR

This paper explores the concept of electronic polarization in quasilinear chains, clarifying various definitions, introducing a new formulation, and analyzing the effects of chain termination on polarization properties.

Contribution

It relates different polarization definitions, derives expressions for infinite chains, and introduces a new single particle formulation for polarization in quasilinear chains.

Findings

Traditional sawtooth polarization misses intercellular contributions.

Intracellular and intercellular polarization are independent of chain termination.

The new formulation aligns with the modern theory of polarization.

Abstract

Starting with a finite $k$-mesh version of a well-known equation by Blount, we show how various definitions proposed for the polarization of long chains are related. Expressions used for infinite periodic chains in the 'modern theory of polarization' are thereby obtained along with a new single particle formulation. Separate intracellular and intercellular contributions to the polarization are identified and, in application to infinite chains, the traditional sawtooth definition is found to be missing the latter. For a finite open chain the dipole moment depends upon how the chain is terminated, but the intracellular and intercellular polarization do not. All of these results are illustrated through calculations with a simple H\"uckel-like model.