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.
This project stems from the use of quantum Monte Carlo methods to measure and understand the correlations of electrons in materials. Understanding in detail the interactions between electrons and how these affect material structures like chemical bonds is particularly important for developing and improving practical computational methods for determining the electronic structure of materials and nanostructures. A key goal is to improve the description of electron correlations in density functional theory, an approach to the prediction of the electronic structure and properties of a material in terms of the average electron density at the atomic scale. This is perhaps the most effective and versatile method currently available for making electronic structure predictions and as such, it is a starting point for many other computational simulations such as the simulation of nanoscale electronic devices, where detail at the level of individual atoms and molecules come into play. Such tools are a crucial component for making advances in nanotechnology, where key properties of devices are atomic in scale and hard to characterize experimentally, but may be readily investigated computationally by atomistic simulations. This project has involved the development, implementation and testing of new density functional models built upon the Laplacian of density and inspired by recent Monte Carlo calculations of electron correlations in the silicon crystal at Georgia Tech. The Laplacian is a mathematical transformation that highlights "hilltop" and "valley" features of a function and can be used to distinguish, e.g., between covalent and ionic bonds. The Laplacian proves to be a key to understanding the effects of inhomogeneity on electron energy -- electrons in hilltop regions have naturally different interaction energies than those in valleys or elsewhere, and these differences prove to be the same from material to material. Our approach has allowed us to use this insight to reimagine a basic form of density functional theory in terms of this quantity, one that has been largely unexplored in the past, and has led to a deeper understanding of the fundamental issues that govern the theory. Our main outcome is a functional which combines the benefits of the Laplacian of the density and the much more frequently used gradient of the density, while avoiding several known defects of each. Just as in biology, hybridization of two complementary approaches combines the best features of each and avoids the worst. We have tested our model both for atoms, the building blocks of all materials, and a novel artificial atom, the jellium droplet, which mimics some of the behaviors of metal clusters, and for which exact results exist. Techniques developed in the course of this project will be of use in other contexts, notably in developing orbital-free density functionals. These attempt to make electronic structure predicitions without knowledge of the individual quantum orbitals occupied by individual electrons, a short-cut which could greatly speed up electronic structure calculations and open up much larger systems to atomistic simulation. We have also contributed to testing and error-correcting of online databases of atomic potentials used for electronic structure calculations. Another area of research has been the visualization of the Laplacian of the density and other quantities important for density functional theory, for a representative set of molecules typically used in assessing the quality of new density functionals. Visualization of the chemical bond and other chemical structures is an important qualitative tool in quantum chemistry. Similar to GPS mapping of the earth used to learn about the presence of, say, oil reserves or archeological sites by using appropriate probes of the earth's surface, measuring different mathematical quantities associated with the electron density can reveal interesting new features and shed new light into character of electronic bonding. Shown in the accompanying figure are six different such maps of the propyne molecule, illustrating the difference between a single bond and triple bond between two carbons (the bonds between the second and third and fourth atoms shown.) The Laplacian (c) highlights the triple bond with a distinctive butterfly-wing pattern. The broader impacts of the project have included training for a number of students pursuing careers in STEM areas, including chemistry, mathematics and physics majors, some of whom have gone on to pursue doctoral work at national universities. It provides East Central Indiana, which is trying to retool after a disastrous decline of the auto industry in the area, with a regional center of expertise, software and educational resources in computational materials science. It builds upon and supports existing Ball State initiatives for revitalizing the ECI region, including an initiative to become a regional center of excellence in computational science, particularly nanoscience, as well as theoretical support for local experimental initiatives in device fabrication and medical physics.
