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Updated: Mar 26, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Self-consistent second-order Green's function perturbation theory for periodic systems.

Alexander A Rusakov1, Dominika Zgid1

  • 1Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA.

The Journal of Chemical Physics
|February 8, 2016
PubMed
Summary

A new periodic Green's function (GF2) method quantitatively treats electron correlation in extended systems. This computational approach successfully recovers metallic, band insulating, and Mott insulating phases in a hydrogen lattice.

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Area of Science:

  • Computational physics
  • Quantum chemistry
  • Materials science

Background:

  • Electron correlation in extended systems is computationally challenging.
  • Green's function methods offer systematic improvable descriptions of electronic correlations.
  • Previous methods struggled with quantitative accuracy for both weak and strong correlations.

Purpose of the Study:

  • To present a periodic, self-consistent, temperature-dependent 2nd-order Green's function (GF2) method.
  • To evaluate the self-energy in an atomic orbital basis for computational feasibility.
  • To apply the GF2 method to a model crystalline system.

Main Methods:

  • Periodic implementation of the self-consistent 2nd-order Green's function (GF2) method.
  • Evaluation of the self-energy in the atomic orbital basis.
  • Solving the Dyson equation in k-space for a computationally feasible algorithm.

Main Results:

  • The GF2 method was applied to a one-dimensional hydrogen lattice.
  • Analysis of spectral functions, natural occupations, and self-energies.
  • Successful recovery of metallic, band insulating, and Mott insulating regimes.

Conclusions:

  • The periodic GF2 method provides a computationally feasible approach for electron correlation in extended systems.
  • GF2 qualitatively captures strong correlation effects, including Mott insulating behavior.
  • The iterative nature of GF2 is crucial for describing metallic and Mott phases.