Density Functional Resonance Theory of Unbound Electronic Systems

TL;DR

Density Functional Resonance Theory (DFRT) extends DFT to unbound electronic systems, enabling calculation of resonance energies and lifetimes through a complex density formalism, with a Kohn-Sham approach for practical computations.

Contribution

This paper introduces DFRT, a novel complex-scaled DFT framework for unbound systems, including a Kohn-Sham scheme and analysis of correlation effects.

Findings

DFRT can compute resonance energies and lifetimes of metastable anions.

Neglecting complex correlation introduces errors comparable to standard scattering methods.

An exactly solvable model demonstrates the self-consistent DFRT approach.

Abstract

Density Functional Resonance Theory (DFRT) is a complex-scaled version of ground-state Density Functional Theory (DFT) that allows one to calculate the resonance energies and lifetimes of metastable anions. In this formalism, the exact energy and lifetime of the lowest-energy resonance of unbound systems is encoded into a complex "density" that can be obtained via complex-coordinate scaling. This complex density is used as the primary variable in a DFRT calculation just as the ground-state density would be used as the primary variable in DFT. As in DFT, there exists a mapping of the N-electron interacting system to a Kohn-Sham system of N non-interacting particles in DFRT. This mapping facilitates self consistent calculations with an initial guess for the complex density, as illustrated with an exactly-solvable model system. Whereas DFRT yields in principle the exact resonance energy and lifetime of the interacting system, we find that neglecting the complex-correlation contribution leads to errors of similar magnitude to those of standard scattering close-coupling calculations under the bound-state approximation.