From the metallurgy of the bronze age to the silicon semi-conductors driving the information age, every major step forward in human progress has been enabled by the arrival of new materials that expand the limits of human capability. Discovery of new materials has historically been achieved by diligent but expensive experimentation, but the advent of the computer changed this process. A rapid rise in computing power brings with it the possibility of simulating chemistry and physics to understand material processes at a microscopic level and to run programs that design new materials from the atoms up. In principle, such simulations are easy to formulate, as the equations of quantum mechanics that govern the constituent electrons can be written down on the back of an envelope. In practice, however, the equations become impossible to solve in all but the simplest situations, and the search for approximate models that are both accurate and efficient to compute is ongoing. Many of the most successful approximations to date fall into the class of "density-functional theory" (DFT), in which the complexity of the electronic quantum wave function is eschewed in favor of manipulating the simpler electron density function. This CAREER award supports basic research around density functional development, analyzing the fundamental quantum-mechanical nature of how electrons repel each other by interrogating the "exchange-correlation hole", a key object describing how finding an electron at one position reduces the chance of finding another electron elsewhere. The exchange-correlation hole will first be analyzed in some simple systems that challenge current DFT approximations, and this information will then be used to build more advanced DFT approximations. The resulting approximations will be tested in more complex systems relevant to technological applications. This research project will support, and be supported by, a high-school, undergraduate, and graduate education program that places importance on encouraging the participation of under-represented groups. The project's work and teaching will support outreach to community members in the New Orleans region who do not typically have access to high-quality opportunities for STEM mentorship.
A disconnect has emerged between applications of electronic-structure calculations and the underlying analyses that inform when and why a particular theory is successful. Of the many electronic-structure methods available, density-functional theory (DFT) has become the most popular. This project will analyse and improve approximations to the DFT exchange-correlation (XC) energy by modelling, interpreting, and visualizing the underlying XC hole, one of the most fundamental aspects of DFT. The results will be validated for a variety of molecules and solids, in particular transition-metal compounds. Whilst DFT is exact for the ground-state energy and electron density in principle, in practice the accuracy and efficiency are limited by the approximation of the XC energy, which can be formally defined by connection to the XC hole. Historically, developing an understanding of the XC hole has played a vital role in developing density-functional approximations and explaining their successes, though recent research into the XC hole has fallen behind the development of XC energy approximations. This has occurred for two reasons: 1) a practical DFT calculation needs only an XC energy approximation, resulting in developers overlooking XC holes in favor of energy densities and a gap in user understanding of XC holes, and 2) the formally defined XC hole is complicated to compute and only available for a few simple many-electron systems. This project will close the gap between users and developers as well as accelerating research in XC holes, and thus DFT generally, by i) accurately computing the formally defined XC holes for carefully chosen systems with interesting properties that are challenging to existing density-functional approximations, ii) reverse engineering holes for popular XC energy approximations and visualizing them against reference XC holes, iii) improving XC energy approximations using knowledge obtained from XC hole research, and iv) validating the existing and improved XC energy approximations on difficult systems with emphasis on transition-metal compounds.
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.
