This Materials World Network (MWN) award supports a joint research project between Cornell University and Universitat Erlangen-Nurnberg to use quantum Monte Carlo (QMC) methods to answer the longstanding question of the size of the difference of the Kohn-Sham band gap and the true fundamental band gap of a semiconductors and insulators. This difference is the so called derivative discontinuity -- the discontinuity of the exchange-correlation energy at integer electron numbers. This is a question that is not only of great fundamental importance in density functional theory (DFT) but also of great practical significance for band-gap engineering of materials. For example, accurate predictions of the bandgaps of inorganic semiconductors and of inexpensive organic semiconductors is important for designing photovoltaic cells. Another goal of this proposal is to determine nearly exact exchange-correlation potentials for a number of materials that would constitute a reference in the development of new density functionals. Such a reference, so far, is missing for periodic systems.
This project involves training US and the German graduate students and visits by the students and faculty to their partner institutions as well as exchanges at international conferences. Both the US and the German graduate students will receive a thorough grounding in state of the art QMC and DFT methods. The German graduate student will be a member of the newly founded Graduate School for Molecular Science at the University Erlangen-Nuremberg and the US graduate student will have the opportunity to attend summer and winter schools offered there. There will also be exchanges with faculty and graduate students at the University of Paris. The computed nearly exact DFT quantities will be dissminated widely via the web.
Electronic structure calculations allow one to predict the properties of materials that are important for various technological applications. The most commonly used method density functional theory (DFT) is sufficiently accurate for some materials but not for others. Another method, quantum Monte Carlo (QMC) is more accurate but also considerably more expensive and therefore applicable only to relatively small systems. A major goal of this project was to use QMC to gain insights into the successes and failures of DFT with the goal of improving the functionals used in DFT. The Materials World Network award allowed the US team (expert in QMC) to collaborate with the German team (expert in DFT). In addition to these two teams other researchers in Paris, Amsterdam, Cambridge (England) and Duke University, contributed greatly to the research. Most density functional calculations employ a variety of approximate exchange-correlation functionals. However, it is possible to calculate essentially exac t density functional quantities as follows. First an accurate density is calculated using QMC methods. Then the potential that yields this density in a sin gle-particle approach is calculated. This is by definition the exact effective potential. By subtracting out the known external and Hartree potentials one can also get the exact exchange-correlation potentials. Knowing the exact density functional effective potential one can calculate the exact orbitals and th eir eigenvalues. By doing this we were able to answer one of the long-standing questions in DFT -- how much of the underestimate of the band gaps computed using commonly used approximate density functionals is due to the approximate nature of the functionals and how much due to the derivative discontinuity? Calculations of excited states are typically more difficult than those of ground states. These calculations employ both the exchange-correlation potential and the exchange-correlation kernel. In one of our project we showed the importance of using exact-exchange rather than approximate exchange-correlation potentials for calculating excited states and that further improvements can be achieved by including also the exact correlation potential. In another project, we helped researchers in Amsterdam develop an approximate density functional that is appropriate for systems such as negative ions, where an accurate description of correlation is essential. We have also help researchers at Duke elucidate the details of the zigzag quantum phase transition in quantum wires and the localization of electrons in constricted wires. The student involved in the project received broad training in computational science methods and is now exployed at one of the two top management consulting firms in the US. His educational and cultural experience was enhanced by two trips to Europe, one of the being the 58th Annual Meeting of Nobel Laureates in Lindau, Germany. This is a unique program that allows students from all over the world to hear lectures by Nobel Laureates and to have small group discussions with them.
