RUI: Empirical Density Functional Theory Using the Laplacian of the Density

Ball State University, Muncie IN

Investigators

Abstract

TECHNICAL SUMMARY: This award supports research and education on Density Functional Theory. The work develops a series of improvements in the theory based on insights gained from modeling exchange-correlation holes and energy densities in Si crystal and other systems. The approach focuses on using the Laplacian of the density. The change in density about an electron?s position due to Pauli exclusion and Coulomb correlations and the change in the local energy due to the existence of the hole are key theoretical inputs to this approach at enhancing density functional theory (DFT). The research employs a growing body of data comparing Quantum Monte Carlo simulations of the exchange-correlation holes and energy density in realistic systems with those from density functional theories, such as the local density approximation (LDA). The PI and others previously showed a strong linear correlation of the error of the hole with the local Laplacian of the density. In this research, the correlation is quantified with a model transferable to a number of different systems. This research effort incorporates the essential physics revealed by these studies into preexisting, widely used DFT?s with only minor changes. The research implements a series of changes to current DFT models based on the model and data previously acquired. The activities include developing a test-bed of basic solid-state and molecular systems to test the performance of these models with respect to energies and ground-state structures. As a result, this research improves DFT predictions for semiconductor structures and facilitates extensions to include other properties of the energy functional known to depend on the Laplacian of the density. The work has broader impact beyond the specific research investigations including education and relevance to growing device technologies. The work adds a deeper understanding of the key inputs of existing DFT models. The result is a more robust description of exchange-correlation potentials and ground-state structural properties without a significant increase in computational cost. Scientific impact follows from the fact that Density Functional Theory is the most important computational tool for electronic structure in materials science and quantum chemistry. Thus an improvement in the predictive power accomplished under this award has a potentially significant impact on a wide range of applications and fields. The broader impact extends to economic development. The PI's institution, Ball State University, is the major institution of higher education in the region, with a mission of technology development and transfer supporting a transition from heavy industry. Initiatives associated with this mission include a Center of Computational Nanoscience in the department of Physics, with collaborators from Purdue University, Ohio University and others, and a push to computation-based research and education focused on high performance computing. The proposed project makes a substantive contribution in these initiatives by enhancement of theoretical methods of immediate relevance to computer modeling of nanoscale electronic systems. The development undertaken also helps to educate researchers and educators in the use of modern atomistic modeling techniques, developing educational tools in solid-state physics and nanoscience, and providing graduates with excellent training in materials modeling and excellent preparation for industry and graduate school. NONTECHNICAL SUMMARY: This award supports research and education on Density Functional Theory, the current predominant tool for calculating electronic properties in chemistry and materials. The work develops a series of improvements in the theory based on insights gained from comparisons with quasi-exact but less flexible methods such a Quantum Monte Carlo. Quantum Monte Carlo simulations give reliable details about the local arrangement of electrons relative to one another as they undergo movement according to the laws of quantum physics. Studying these correlations of the positions of electrons in molecules and materials, the PI and others previously established a strong connection between the error of the predictions of Density Functional Theory and Quantum Monte Carlo. The error is found connected with regions where the overall electronic density was changing in a nonlinear fashion. This research describes these connections mathematically and appropriately incorporates the essential laws of physics. It is so able to identify enhancements to widely used variants of Density Functional Theory with only minor changes in the computations. The research activities include developing a test-bed of basic solid-state and molecular systems to evaluate the performance of these models with respect to predicting energies and structures. As a result, this research improves DFT predictions for semiconductor structures and facilitates extensions to include other properties of materials. The broader impact extends to economic development. The PI's institution, Ball State University, is the major institution of higher education in the region, with a mission of technology development and transfer supporting a transition from heavy industry. Initiatives associated with this mission include a Center of Computational Nanoscience in the department of Physics, with collaborators from Purdue University, Ohio University and others, and a push to computation-based research and education focused on high performance computing. The proposed project makes a substantive contribution in these initiatives by enhancement of theoretical methods of immediate relevance to computer modeling of nanoscale electronic systems. The development undertaken also helps to educate researchers and educators in the use of modern atomistic modeling techniques, developing educational tools in solid-state physics and nanoscience, and providing graduates with excellent training in materials modeling and excellent preparation for industry and graduate school.