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Density functional theory of complex transition densities.

Matthias Ernzerhof¹

¹Département de Chimie, Université de Montréal, C.P. 6128 Succursale A, Montréal, Québec H3C 3J7, Canada. matthias.ernzerhof@umontreal.ca

The Journal of Chemical Physics

|October 4, 2006

Summary

This study extends Hohenberg-Kohn-Sham density functional theory to complex potentials and densities, enabling calculations for resonance states and scattering problems. It establishes a connection between complex potentials and densities for non-Hermitian systems.

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Area of Science:

Quantum Chemistry
Condensed Matter Physics
Computational Physics

Background:

Hohenberg-Kohn-Sham density functional theory (DFT) is a cornerstone for electronic structure calculations.
Standard DFT typically deals with real potentials and electron densities.
Resonance states and scattering phenomena involve complex energy eigenvalues and non-Hermitian Hamiltonians.

Purpose of the Study:

To extend Hohenberg-Kohn-Sham density functional theory to incorporate complex local potentials and complex electron densities.
To establish a theoretical framework for studying resonance states and scattering problems within DFT.
To investigate the behavior of exchange-correlation functionals in the complex domain.

Main Methods:

Development of a complex extension of Hohenberg-Kohn-Sham DFT.
Mathematical formulation for non-Hermitian Hamiltonians with complex local potentials.
Analytic continuation of exchange-correlation functionals from real to complex domains.

Main Results:

Established a one-to-one correspondence between complex local potentials and complex electron densities under specific conditions.
Demonstrated that complex energy eigenvalues of non-Hermitian Hamiltonians can be related to system lifetimes.
Showed that exchange-correlation functionals can be analytically continued to the complex domain.

Conclusions:

The extended DFT approach is applicable to resonance states and transport problems.
Exchange-correlation effects on resonance lifetimes can be derived from ground-state theory functionals.
This work provides a new avenue for theoretical investigations of complex quantum systems.