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

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Exact ionization potentials from wavefunction asymptotics: the extended Koopmans' theorem, revisited.

Diederik Vanfleteren¹, Dimitri Van Neck, Paul W Ayers

¹Center for Molecular Modeling, Ghent University, Proeftuinstraat 86, B-9000 Gent, Belgium.

The Journal of Chemical Physics

|May 27, 2009

Summary

This summary is machine-generated.

The extended Koopmans' theorem (EKT) precisely calculates electron removal energy for many-body systems. This method yields exact ionization potentials and Dyson orbitals by targeting specific removal orbitals.

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Area of Science:

Quantum Chemistry
Many-Body Physics
Computational Physics

Background:

The extended Koopmans' theorem (EKT) is a theoretical framework used in quantum chemistry.
Accurate computation of ionization potentials and electron removal energies is crucial for understanding molecular and atomic systems.
Existing methods may face limitations in exactness for complex many-electron systems.

Purpose of the Study:

To provide a simple explanation for the exactness of the extended Koopmans' theorem (EKT).
To demonstrate EKT's applicability in calculating the removal energy of many-electron systems to the lowest-energy ground state ion.
To establish conditions for the validity of EKT for any state.

Main Methods:

Derivation of the exactness of EKT for computing removal energy.
Utilizing a
removal orbital
concentrated in the asymptotic region.
Analysis in terms of the third-order reduced density matrix.

Main Results:

The study explains the exactness of EKT for calculating ionization potentials and Dyson orbitals.
EKT is shown to be applicable beyond many-electron systems to any finite many-body system with vanishing interactions at large distances.
A necessary and sufficient condition for EKT's validity for any state is derived.

Conclusions:

The extended Koopmans' theorem offers an exact method for determining electron removal energies and Dyson orbitals.
The theorem's applicability is broader than initially assumed, extending to various many-body systems.
The derived condition provides a rigorous criterion for EKT's accurate application.