The design of new materials for solar cells, chemical catalysts, and novel electronic devices, will play a major role in the solutions to many pressing societal issues. Cheap and efficient solar cells will accelerate the transition away from fossil fuels, and energy efficient and toxin-free chemical catalysts will make the manufacture of fertilizers, plastics, and pharmaceuticals more sustainable. The engineering of these new materials requires an understanding of the structure and behavior of materials at the nano-scale. At the atomic level, materials are made of atomic nuclei surrounded by a cloud of electrons. Modern computers have made it possible to compute the structure of this cloud of electrons (known as the electronic structure) using physical principles. The computational technique known as density functional theory (DFT) has become ubiquitous in the calculation of electronic structure for materials design. Despite its success, DFT calculations are not exact, and refining the methodology to improve accuracy will allow DFT to address a wider range of problems. The goal of my research is to improve the accuracy of one major approximation in DFT known as the pseudopotential approximation.
In a DFT calculation, the behavior of each electron is calculated given its chemical environment. This environment is expressed mathematically with a potential function. When the potential function that describes the full system of electrons and nuclei is used, however, the DFT calculation is very computationally intensive. For large systems, this can make the calculation intractable even on the fastest super-computers. In materials design, typically only the outermost, or valence, electrons are of interest, and this fact makes possible a technique which drastically decreases the computational intensity of DFT. In this technique, the inner electrons are not included in the calculation explicitly, but their influence on the outer electrons is modeled implicitly through a modified potential function called a pseudopotential. This is the pseudopotential approximation, and though it is not exact, it has been used very successfully in materials design. There are many ways to design a pseudopotential to model the influence of the inner electrons, and new methods of pseudopotential design are still being developed.
The goal of my research is to design an algorithm that optimizes a set of parameters used in pseudopotential construction in order to improve the accuracy of pseudopotentials. This summer I was able to demonstrate that the algorithm I created successfully improved pseudopotentials for many types of atoms. There are, however, many types of atoms for which my algorithm did not produce improved pseudopotentials, so there remains work to be done to improve the algorithm.
Through this research experience, I have strengthened my research skills through close collaboration with Dr. Rappe and other experienced researchers in the lab. I have developed my ability to understand research articles in the field of DFT methodology, and I have begun writing my own research article about my personal research. I plan to pursue a PhD, and I believe this experience will be of great help in my PhD studies.