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Related Experiment Video

Updated: Jun 14, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Generalized Einstein relations between absorption and emission spectra at thermodynamic equilibrium.

Jisu Ryu¹, Sarang Yeola², David M Jonas^1,3

¹Department of Chemistry, University of Colorado, Boulder, CO 80309-0215.

Proceedings of the National Academy of Sciences of the United States of America

|September 3, 2024

Summary

This study introduces generalized Einstein relations for overlapping energy bands, revealing four spectra that govern transitions and predict equilibrium Stokes

Keywords:

Einstein coefficients Stokes’ shift free energy line broadening luminescence

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Area of Science:

Quantum Optics
Spectroscopy
Chemical Physics

Background:

Traditional Einstein relations describe transitions between distinct spectral lines.
Overlapping energy bands in molecules allow for complex absorption and emission processes.
Understanding these transitions is crucial for accurately modeling light-matter interactions.

Purpose of the Study:

To derive generalized Einstein relations for overlapping energy bands.
To introduce Einstein coefficient spectra replacing traditional coefficients.
To explore the implications for spontaneous and stimulated emission.

Main Methods:

Detailed-balance derivation of generalized Einstein relations.
Analysis of Einstein coefficient spectra for broadened, overlapping levels.
Application of molecular quantum statistics (Boltzmann statistics).

Main Results:

Four Einstein coefficient spectra replace the three traditional coefficients for overlapping bands.
These spectra obey specific pairwise relationships at equilibrium, with one lineshape generating all four.
The theory predicts equilibrium Stokes' shifts and incorporates formal chemical potentials for bands.

Conclusions:

Generalized Einstein relations accurately describe transitions between overlapping energy bands.
The framework accounts for non-purely absorptive or emissive transitions.
This work provides a foundation for understanding complex spectral phenomena in various physical systems.