Time-dependent exciton dynamics : insights from 1- and 2-dimensional model systems
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Time-Dependent Density-Functional Theory (TDDFT) has become a promising alternative to the Bethe-Salpeter Equation (BSE) in terms of the calculation of optical spectra, including excitoinic features, due to its significantly lower computational cost. TDDFT brings with it the advantage of, in principle, access to the Time-Dependent (TD) exciton wave function and the ability to study ultra-fast TD phenomena. One promising family of Exchange & Correlation (XC) functionals for capturing excitonic effects in TDDFT are the Long-Range Corrected (LRC) functionals. In order to test the LRC functionals, we have written programs to do calculations in both a One-Dimensional (1D) and Two-Dimensional (2D) model systems. We used the 1D model system to explore avenues of TD exciton wave function visualization to facilitate the study and understanding of the TD dynamics of excitons. Likewise, we used the 2D model system to study various methods of correction to the LRC in hopes of better capturing excitonic effects and improving stability for Real-Time (RT) calculations. We show examples of exciton wave functions visualized with various techniques, including waterfall plots and heat maps. We have also used our 1D model system to explore how RT calculations performed using TDDFT can be used to gain insight into novel systems, as exemplified by our study of charge-transfer excitations. Using our 2D model system we have explored two possible avenues of correction to the LRC: adding a 'counter' term to the XC functional and 'generalizing' the differential equation which defines the LRC. The first avenue we explored is the addition of a new term to the XC potential, explicitly constructed to cancel out the error produced by the LRC's violation of the zero-force theorem, leading to the introduction of spurious, nonphysical, internal forces. This approach, in the end, does not seem to make a substantial impact on the optical absorption spectra or the stability of the LRC. The second avenue, using the so-called "Proca" equation, adds terms to the equation of motion in order to stabilize the calculations-again with limited success. We have successfully demonstrated in our model systems that the RT methods for TDDFT are promising tools for the exploration of TD phenomena in electronic systems. We have also explored these techniques using some illustrative situations and avenues for improving the accuracy and stability of these calculations.
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Ph. D.