A density functional method for general excited states in atoms

TL;DR

This paper introduces a density functional theory method for accurately calculating a wide range of excited states in atoms, including complex resonances, with results comparable to Hartree-Fock and experimental data.

Contribution

A novel DFT-based approach using a work-function exchange potential and gradient-corrected correlation functional for general excited states in atoms.

Findings

Exchange-only results are Hartree-Fock quality.

Including correlation yields excellent agreement with experimental data.

Method successfully predicts many states for the first time.

Abstract

This chapter presents the development of a density functional theory (DFT)-based method for accurate, reliable treatment of various resonances in atoms. Many of these are known to be notorious for their strong correlation, proximity to more than one thresholds, degeneracy with more than one minima. Therefore these pose unusual challenges to both theoreticians and experimentalists. Our method uses a work-function-based exchange potential in conjunction with the popular gradient-corrected Lee-Yang-Parr correlation functional. The resulting Kohn-Sham equation, in the non-relativistic framework, is numerically solved accurately and efficiently by means of a generalized pseudospectral method through a non-uniform, optimal spatial discretization. This has been applied to a variety of excited states, such as low and high states; single, double, triple as well as multiple excitations; valence and core excitations; autoionizing states; satellites; hollow and doubly-hollow states; very high-lying Rydberg resonances; etc., of atoms and ions, with remarkable success. A thorough and systematic comparison with literature data reveals that, for all these systems, the exchange-only results are practically of Hartree-Fock quality; while with inclusion of correlation, this offers excellent agreement with available experimental data as well as those obtained from other sophisticated theoretical methods. Properties such as individual state energies, excitation energies, radial densities as well as various expectation values are studied. This helps us in predicting many states for the first time.