A density functional method for general excited states in atoms

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. It is well-known that DFT has been one of the most powerful and successful tools for electronic structure calculation of atoms, molecules, solids in the past two decades. While it has witnessed diverse spectacular applications for ground states, the same for excited states, unfortunately, has come rather lately and remains somehow less conspicuous relatively. 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. In summary, we have presented an accurate, simple, general DFT method for description of arbitrary excited states of atoms and ions.