This award supports theoretical and computational research and education to study optical excitation processes in extended systems, with a particular emphasis on excitonic effects in bulk semiconductors and organic chains. The PI will use time-dependent density-functional theory. Exchange-correlation functionals with a long spatial range are required to capture excitonic effects, and only a few of these are available. The primary goal is to develop and test exchange-correlation functionals which produce excitonic binding in the frequency-dependent linear-response domain and in the nonlinear real-time domain.
The PI will use time-dependent density-functional theory in the linear-response domain to calculate excitonic binding energies in bulk semiconductors and insulators. A two-band model, demonstrated to produce excitonic binding for various simple exchange-correlation kernels, will be extended to include additional bands. Various long-range exchange-correlation kernels will be implemented and tested, and singlet-triplet exciton splittings will be calculated using a spin-dependent formalism.
The PI will apply real-time time-dependent density-functional theory to simulate short-time exciton dynamics in organic chain molecules. The exchange-correlation functionals required for excitonic binding will be carried over from the frequency-dependent linear-response regime into the real-time domain. A new computational tool to visualize exciton dynamics, the time-dependent transition density matrix, will be developed. Real-time simulations will be carried out for simple polymer chains to study how localized excitations spread out along the chains and connect to neighboring units.
An accurate time-dependent density-functional theory description of excitons will be relevant and applicable for a wide range of materials, from bulk inorganic semiconductors to polymers and organic heterojunctions. The latter systems will be explored in real-time calculations, to test the time-dependent transition density matrix. Developing these methodologies may have impact on organic optoelectronics and photovoltaics.
An undergraduate condensed-matter physics course developed under prior NSF support will be broadened in scope so as to address a wider audience. A new graduate course in theoretical materials science will be developed with the goal to introduce students to a variety of topics in materials theory and simulation, including hands-on computational exercises.
NON-TECHNICAL SUMMARY This award supports theoretical and computational research and education to develop new theoretical and computational methods to describe the optical properties of materials, specifically semiconductors with particular emphasis on semiconductor materials made of long chain-like molecules called polymers. An accurate and computationally efficient approach to simulate the optical properties of these materials will provide important assistance for understanding and designing novel solar cell and optoelectronic devices.
The PI will further develop and use a computationally efficient method to describe the fundamental processes that take place during the interaction of semiconductor materials with light. The method known as time-dependent density functional theory has successfully described the response of electrons in molecules to time varying electric fields. This theory will be used to simulate and visualize in real time the basic steps involving the interaction of the electrons in polymer semiconductors with light.
An undergraduate condensed-matter physics course developed under prior NSF support will be broadened in scope so as to address a wider audience. A new graduate course in theoretical materials science will be developed with the goal to introduce students to a variety of topics in materials theory and simulation, including hands-on computational exercises.
The scientific goal of this project was the study and development of new theoretical and computational approaches to treat excitonic effects in materials. Excitons are an important feature in the optical response of insulators and semiconductors, as well as large organic molecules: they consist of bound electron-hole pairs which arise during optical absorption. Excitons dominate the photophysics of materials close to the band gap; they play a crucial role in photovoltaic processes. Accurate and computationally efficient tools to predict excitonic properties are important for a fundamental understanding and for the development of new materials for optoelectronics and solar cell applications. In this project, excitonic effects were treated using time-dependent density-functional theory (TDDFT); this is a universal theory for electronic excitations, which is very widely used in chemistry, physics and materials science. TDDFT is both accurate and computationally efficient, and works very well for many molecular applications. However, excitons are difficult to capture with TDDFT and require specialized, non-standard approximations to treat the so-called exchange-correlation (XC) effects. The intellectual merit of the project outcomes is twofold. First, we developed a new TDDFT approach to calculate exciton binding energies in bulk solids and insulators. This approach allows computational researchers to test the accuracy of approximations to treat XC effects. We have tested several such approximations and found, by and large, that their accuracy is less than that of other approaches based on so-called Green’s function techniques (these methods are computationally much more expensive, so TDDFT would be preferable). However, we found that so-called ``hybrid functionals’’ may provide a promising way forward towards the accurate description of excitonic effects with TDDFT. The second aspect of intellectual merit is that we developed a novel method to visualize excitations in organic molecules, in particular so-called charge-transfer excitons, using a ``particle-hole map’’. This map provides spatially resolved information about where electrons are coming from and going to, during an excitation process. Figure 1 gives an illustration of what such a map looks like, for a one-dimensional model molecule. The horizontal and vertical coordinates indicate where electrons and holes come from and where they are going to, during an excitation. The two panels show examples of a localized excitation and of an excitation that has significant charge-transfer character. The broader impact of this research is that it will provide a wide community of researchers with new theoretical and computational tools to study excitonic effects. This can help in the development of new materials for application in optoelectronics and photovoltaics. This project also has had broader impact in the area of education. During the project period, several undergraduate and graduate courses in condensed-matter physics and materials science were developed, a graduate textbook on TDDFT was published, and tutorials and courses on the subject of TDDFT were given, aimed at students and nonexperts.
