The Manhattan exciton size: A physically tractable delocalization measure.

Area of Science:

• Chemical Physics
• Quantum Mechanics
• Materials Science

Background:

• Delocalized excitations, or excitons, are fundamental quasiparticles in chemical physics.
• Understanding exciton delocalization is key to characterizing their behavior in various systems.
• Common measures like the (inverse) participation ratio are widely used but have limitations.

Purpose of the Study:

• To revisit and analyze common delocalization measures for Frenkel-type excitons.
• To propose and validate a novel delocalization measure: the Manhattan exciton size.
• To demonstrate the advantages of the Manhattan exciton size, particularly for super-radiant states.

Main Methods:

• Revisiting and analyzing existing exciton delocalization measures.
• Introducing and defining the Manhattan exciton size.
• Comparing the Manhattan exciton size with the (inverse) participation ratio using linear aggregates.

Main Results:

• The Manhattan exciton size directly correlates with exciton oscillator strength.
• It provides a strict upper bound for oscillator strength in linear aggregates.
• This measure is more suitable for analyzing super-radiant states than the (inverse) participation ratio.

Conclusions:

• The Manhattan exciton size offers a valuable new perspective on exciton delocalization.
• It complements existing measures like the (inverse) participation ratio for a comprehensive understanding of exciton confinement.
• This approach enhances the characterization of excitons in systems exhibiting strong light-matter interactions.