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Updated: Jun 17, 2026

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 in the electric-dipole approximation.

Jisu Ryu¹, David M Jonas¹

¹Department of Chemistry, University of Colorado, Boulder, Colorado 80309, USA.

The Journal of Chemical Physics

|June 16, 2026

Summary

This study derives quantum mechanical expressions for Einstein-coefficient spectra, establishing new generalized Einstein relations. These findings connect dipole-strength spectra to transition probabilities, clarifying equilibrium detailed balance and Stokes

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Published on: May 27, 2020

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Published on: July 27, 2018

Area of Science:

Quantum Optics
Spectroscopy
Physical Chemistry

Background:

Ryu et al. previously demonstrated that broadened bands obeying generalized Einstein relations exhibit detailed balance at equilibrium.
Existing frameworks for Einstein-coefficient spectra often rely on classical approximations or simplified models.

Purpose of the Study:

To derive quantum mechanical expressions for Einstein-coefficient spectra in isotropic, dispersive media.
To establish rigorous relationships between Einstein-coefficient spectra and dipole-strength spectra.
To develop new generalized Einstein relations applicable to broadband transitions.

Main Methods:

Utilized electric-dipole approximation and quantized field operators within an intramolecular Boltzmann distribution.
Defined dipole-strength spectra using conditional transition probabilities per unit time derived from electrodynamic relationships.
Analyzed transitions between two bands, focusing on the role of total dipole strength and underlying lineshapes.

Main Results:

Derived quantum mechanical formulas for dipole-strength spectra and new generalized Einstein relations.
Demonstrated that dipole-strength spectra depend on total dipole strength, chemical potential, and a single lineshape.
Specified the Stokes' shift at equilibrium and identified dependencies on material properties (refractive index, dielectric constant) but not its derivative.

Conclusions:

The derived relationships rigorously connect dipole-strength spectra with Einstein-coefficient spectra, validating detailed balance.
The new generalized Einstein relations offer a more comprehensive understanding of light-matter interactions in dispersive media.
These findings provide a quantum mechanical foundation for analyzing broadband spectroscopic phenomena and Stokes' shift.