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Updated: Jun 27, 2026

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

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Published on: May 27, 2020

Rydberg energies using excited state density functional theory.

Chiao-Lun Cheng¹, Qin Wu, Troy Van Voorhis

¹Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139, USA.

The Journal of Chemical Physics

|December 3, 2008

Summary

Excited state density functional theory (eDFT) accurately calculates Rydberg energies in atoms, outperforming time-dependent DFT. This method uses excited state densities for accurate Kohn-Sham potentials, offering a rigorous approach for specific quantum systems.

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Area of Science:

Quantum Chemistry
Computational Physics
Theoretical Chemistry

Background:

Accurate calculation of atomic Rydberg states is crucial for understanding electronic structure.
Traditional time-dependent density functional theory (TDDFT) often fails for Rydberg states.
Excited state density functional theory (eDFT) presents an alternative computational approach.

Purpose of the Study:

To investigate the efficacy of excited state density functional theory (eDFT) for calculating Rydberg states in atoms.
To compare eDFT performance against time-dependent density functional theory (TDDFT).
To explore the theoretical underpinnings and limitations of eDFT for these systems.

Main Methods:

Utilized excited state density functional theory (eDFT) with semilocal functionals.
Employed analytical and numerical methods to study Rydberg energies.
Applied optimized effective potential (OEP) techniques to analyze density v-representability.

Main Results:

eDFT, using semilocal functionals, yielded accurate Rydberg energies, succeeding where TDDFT failed.
The Kohn-Sham potential in eDFT, derived from excited state densities, exhibits polynomial decay, enabling Rydberg series.
eDFT solutions are rigorous when the excited state density minimizes non-interacting kinetic energy.

Conclusions:

eDFT provides a robust and accurate method for studying atomic Rydberg states.
The success of eDFT stems from its use of state-specific potentials derived from excited state densities.
eDFT complements constrained DFT, offering a rigorous framework for non-ground-state densities.