Reports: DNI649599-DNI6: Density Functional Resonance Theory of Metastable Negative Ions

Adam Wasserman, PhD , Purdue University

We completed the development of Density Functional Resonance Theory (DFRT), 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 new 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. The 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 a DFT calculation. 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.

We illustrated the utility of the new formalism by solving a model system of interacting electrons. DFRT yields the exact resonance energy and lifetime of the interacting system, and we found 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.

My student Daniel Whitenack, supported by the grant, presented these results at the recent Gordon Research Conference in Time-dependent Density Functional Theory (Biddeford, ME, August 2011), and received one of the three ‘best poster’ awards. His poster was promoted to a short-talk.

Progress was also made on other two fronts: (1) Implementation of DFRT for the calculation of resonance lifetimes in molecular negative ions; and (2) Generalization of DFRT to zero-temperature ensembles, from which we generalized the Perdew-Parr-Levy-Balduz results of ground-state DFT to complex densities, allowing us to calculate derivative discontinuities of the XC-energy functional at the maximum number of bound electrons.  A paper with these results is almost ready for publication (our main DFRT results were accepted for publication in Phys.Rev.Lett.).

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