NSF Award
2426275
NONTECHNICAL ABSRACT<br/>This award supports theoretical and computational research and education to advance Kohn-Sham density functional theory. This theory provides a computationally efficient and usefully accurate description of the electronic properties of materials enabling molecules, chemicals, and materials to be modeled. The aim of this project is to develop more accurate computer models of materials. To do this, the PI will focus on the “glue” that binds one atom to another to form molecules and materials: the exchange-correlation energy. In this research, the PI will develop even more accurate approximations for this “glue” that still permit efficient simulation on computers. Kohn-Sham density functional theory is widely used in physics, chemistry, and materials science to predict what atoms, molecules, and materials can exist and with what properties. Starting from the first principles of quantum mechanics, this theory constructs the ground-state energy and electron density of a many-electron system from an auxiliary system of non-interacting electrons including the contribution from the "glue", facilitating practical computation. The exact exchange-correlation energy must be approximated. Widely predictive approximations should themselves be based upon first principles and be accurate enough to predict the small energy differences between competing states in complex materials and systems. The strategy of this project is to achieve more accurate but computable general-purpose approximations by incorporating more of the mathematical properties of the exact universal density functional for the exchange-correlation energy. Exact constraints and appropriate norms, non-bonded systems for which the approximations can be exact or very accurate, guide the construction of functionals that reliably predict bonds without being fitted to bonds. <br/>Kohn-Sham density functional theory also provides guidance and input to machine-learning approaches to materials theory. Progress in the improvement of the functionals has been relentless but slow, requiring rigorous theory, intuition, and persistence. Since 1965, there has been great progress from the original local spin density approximation to generalized gradient approximations (GGAs), meta-GGAs, and their exact-exchange hybrid or self-interaction corrections. It is hard to get everything right, but worth the effort. The goals of the proposed research are to advance understanding of this theory, and to improve its useful approximations in order to better understand and predict interesting materials.<br/>Broader impacts will include more reliable predictions for the existence and properties of new materials the education of graduate students and postdoctoral fellows, and research experiences for undergraduates, high-school students, and middle-school students.<br/><br/>TECHNICAL ABSTRACT<br/>This award supports theoretical and computational research and education to advance Kohn-Sham density functional theory. While the appropriate norms used to construct non-empirical density functionals for the exchange-correlation energy are normally correlated, the approximations that employ only occupied orbitals, especially the higher-level ones, can often describe strong-correlation effects on the energy through symmetry breaking. The principal investigator and his research group have recently found a proper and possibly general-purpose Perdew-Zunger self-interaction to the local spin density approximation, locally scaled down in many-electron regions and called LSIC alpha. They are investigating an interpolation between LSIC alpha and the advanced r2SCAN meta-generalized gradient approximation (meta-GGA), each dominating in its appropriate region of space. They plan to use these improved functionals to explore how reliably symmetry breaking can simulate strong correlation. They will also investigate the degeneracies at the non-interacting-electron level that create strong correlation, and the physical interpretation of excited-state solutions to the Kohn-Sham equations. Evaluating a non-self-interaction-corrected functional on the too-localized Hartree-Fock density instead of its own self-consistent density often leads to higher accuracy, due to an unconventional but understandable error cancellation. The principal investigator and collaborators will test this idea on materials problems such as the formation and reaction energies of transition-metal oxides that are currently treated with a +U correction. They will search for violations of their conjectured tight lower bound on the exchange energy. They will use an accurate inversion of an accurate electron density to investigate how reliably the exact Kohn-Sham orbital energies approximate all the vertical ionization energies. Since the r2SCAN meta-GGA is already too non-local for metals, especially magnetic ones, they will develop a constraint-satisfying GGA for metals, and a local indicator of metallicity that will permit an interpolation between it and r2SCAN or functionals beyond r2SCAN. They will investigate how the derivative discontinuity evolves from a smooth energy surface as an open system moves away from its electron reservoir. They will revisit the sd transfer errors of approximate functionals, including modern ones. They will generalize r2SCAN to ground states with non-zero current densities, study the distribution of dimensionless meta-GGA ingredients over real systems, investigate the exchange-correlation-corrected screening by a uniform electron gas in position space and time, delve into an atom-cluster phase transition in jellium spheres, find and test an improved self-interaction correction to the random phase approximation (RPA), and extract an RPA-based long-range van der Waals correction to improved functionals that need one.<br/>Broader impacts will include more reliable predictions for the existence and properties of new materials, the education of graduate students and postdoctoral fellows, and research experiences for undergraduates, high-school students, and middle-school students.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
