Donghyung Lee

Condition on the Kohn-Sham kinetic energy and modern parametrization of the Thomas-Fermi density.

We study the asymptotic expansion of the neutral-atom energy as the atomic number Z-->infinity, presenting a new method to extract the coefficients from oscillating numerical data. Recovery of the correct expansion yields a condition on the Kohn-Sham kinetic energy that is important for the accuracy of approximate kinetic energy functionals for atoms, molecules, and solids. For example, this determines the small gradient limit of any generalized gradient approximation and conflicts somewhat with the standard gradient expansion. Tests are performed on atoms, molecules, and jellium clusters using densities constructed from Kohn-Sham orbitals. We also give a modern, highly accurate parametrization of the Thomas-Fermi density of neutral atoms.

Electronic structure via potential functional approximations

The universal functional of Hohenberg-Kohn is given as a coupling-constant integral over the density as a functional of the potential. Conditions are derived under which potential-functional approximations are variational. Construction via this method and imposition of these conditions are shown to greatly improve the accuracy of the noninteracting kinetic energy needed for orbital-free Kohn-Sham calculations.

Leading corrections to local approximations

For the kinetic energy of one-dimensional model finite systems the leading corrections to local approximations as a functional of the potential are derived using semiclassical methods. The corrections are simple, nonlocal functionals of the potential. Turning points produce quantum oscillations leading to energy corrections, which are completely different from the gradient corrections that occur in bulk systems with slowly varying densities. Approximations that include quantum corrections are typically much more accurate than their local analogs. The consequences for density functional theory are discussed.

Finding electron affinities with approximate density functionals

There has been a long discussion about the reliability of approximate density functionals for atomic anions. It is well known that the extra electron produces a strong self-interaction error, so strong that the extra electron is unbound. Despite this, electron affinities have been calculated using finite basis sets and very good results have been reported by Schaefer and others. We recently suggested how to resolve the contradicting viewpoints between theory and calculation. We calculate electron affinities using Hartree–Fock or exact exchange DFT densities which bind the extra electron correctly and show excellent results with well-defined basis-set limit. Here we give further data in support of our argument, and explain further how and why accurate densities and total energies of anions may be obtained from approximate density functional theory, despite positive HOMO energies.

Corrections to Thomas-Fermi Densities at Turning Points and Beyond

Uniform semiclassical approximations for the number and kinetic-energy densities are derived for many noninteracting fermions in one-dimensional potentials with two turning points. The resulting simple, closed-form expressions contain the leading corrections to Thomas-Fermi theory, involve neither sums nor derivatives, are spatially uniform approximations, and are exceedingly accurate.