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Updated: Feb 25, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Exploring Unorthodox Dimensions for Two-Electron Atoms.

Dudley R Herschbach1,2, John G Loeser3, Wilton L Virgo1

  • 1Institute for Quantum Science and Engineering, Texas A&M University , College Station, Texas 77843, United States.

The Journal of Physical Chemistry. A
|August 1, 2017
PubMed
Summary
This summary is machine-generated.

Researchers developed a simple, accurate method for two-electron atoms by merging quantum and classical mechanics. This approach yields analytic formulas with high precision for helium, surpassing current density functional theory methods.

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Area of Science:

  • Physical Chemistry
  • Quantum Mechanics
  • Atomic Physics

Background:

  • Bridging quantum and classical mechanics is crucial for physical chemists seeking new insights and tools.
  • Accurate modeling of two-electron atoms is essential for understanding atomic and molecular behavior.

Purpose of the Study:

  • To present a novel, accurate, and simple analytical treatment for ground-state two-electron atoms.
  • To develop a method that combines quantum and classical mechanics principles for atomic systems.
  • To derive formulas applicable to D-dimensional two-electron atoms.

Main Methods:

  • Utilizing the dimensional dependence of the hydrogen atom, a quantum mechanical concept.
  • Incorporating the first-order perturbation value of electron-electron interaction, a quantum mechanical property.
  • Employing the D → ∞ limit, a classical mechanics concept.

Main Results:

  • An analytic formula for D-dimensional two-electron atoms (Z ≥ 2) was derived.
  • For D=3 helium, the method achieved accuracy better than 2 millihartrees, outperforming density functional theory.
  • A formula for correlation energy, when combined with Hartree-Fock energy, improved D=3 helium accuracy to better than 0.1 millihartrees.

Conclusions:

  • The presented method offers a surprisingly simple yet highly accurate approach to studying two-electron atoms.
  • This hybrid quantum-classical method provides a valuable tool for physical chemists and advances atomic physics.
  • The derived analytic formulas offer significant improvements in accuracy for atomic energy calculations.