Density Functional Theory of Electronic Structure

Tulane University, New Orleans LA

Investigators

Abstract

This award supports theoretical research and education motivated in part by the desire to improve the accuracy of density functional theory as practiced in condensed matter physics and quantum chemistry. The PI describes a "ladder" of approximations for the exchange-correlation functional in which the first rung is the local spin density approximation and the second rung is the generalized gradient approximation (GGA). These standard approximations do not enable electronic structure calculations with chemical accuracy. In particular, they do not accurately describe strongly correlated or strongly spatially inhomogeneous densities, polarizabilities of long-chain molecules, or highly excited states. The PI proposes to address these problems through work on several projects: (1) Develop and test approximations for the exchange-correlation functional that correspond to the third and fourth rungs of the "ladder" of approximations. The meta-GGA would be developed as a controlled interpolation between the slowly varying and iso-orbital density limits. The hyper-GGA uses the exact exchange energy density to achieve freedom from self-interaction error and a correct non-uniform scaling behavior. (2) The uniform electron gas will be explored using a modified pair density functional method with a self-consistent electron-electron interaction. An energy interpolation between exact high- and low-density limits will be used to explore the spin-polarized electron gas. The results will be compared with much more computationally expensive diffusion Monte Carlo calculations. (3) Diffusion Monte Carlo, density-functional theory, and RPA studies of the jellium surface energy will be carried out in parallel to resolve the apparent discrepancy between surface energies calculated using diffusion Monte Carlo and other methods. (4) Calculations for real solids will test a new analytic equation of state and will construct a Kohn-Sham potential for the orbital-dependent meta-GGA and hyper-GGA energy functionals. (5) A Laplacian-level meta-GGA will be constructed non-empirically for the orbital kinetic energy. This project also contributes directly to the education of undergraduate and graduate students, and to the professional development of postdoctoral researchers. This award supports fundamental theoretical research with an aim to improve the accuracy of density-functional based theories of materials. Analytical and numerical methods will be used. Density functional theory is widely used to predict a variety of materials properties, such as crystal structures, electron spin densities, and phonon modes. Another component of the PI's research would study fundamental problems associated with the electron gas and improved approximations for the kinetic energy. The homogeneous electron gas plays a fundamental role in the practical application of density functional theory. This award also supports education at the undergraduate, graduate, and postdoctoral levels.