The Manhattan exciton size: A physically tractable delocalization measure

Abstract

Delocalized excitations, denoted excitons, play an important role in many systems in chemical physics. The characterization of their extent of delocalization is a crucial element in understanding these quasiparticles. In this paper, I will revisit the most common delocalization measures applied to Frenkel-type excitons. Based on this analysis, I propose to use a so-far ignored measure. The key advantage of this measure, which I will denote as the Manhattan exciton size, is that it directly connects with the oscillator strength of the excitons. It provides a strict upper bound on the oscillator strength of any given exciton for linear aggregates. Finally, I demonstrate that this exciton delocalization measure is more sensible for analyzing super-radiant states compared to, for example, the most commonly applied measure, i.e., the (inverse) participation ratio. However, these two measures together provide insight into the degree of exciton confinement.