A minimal model for excitons within TDDFT
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A minimal model for excitons within TDDFT Carsten A. Ullrich, University of Missouri-Columbia, DMR 1005651.

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A minimal model for excitons within TDDFTCarsten A. Ullrich, University of Missouri-Columbia, DMR 1005651

Time-dependent density-functional theory (TDDFT) is a universal approach to electronic dynamics and excitations. One of the major challenges of TDDFT, describing excitons, has now been accomplished for many materials, but the basic mechanisms of exciton formation in TDDFT have remained poorly understood.

We have developed a minimal model for excitons in TDDFT, and applied it to a one-dimensional Kronig-Penney model. This work shows that very simple exchange-correlation functionals produce excitonic binding (figure a), but an excitonic Rydberg series requires nonadiabatic functionals. We also show that

the effective electron-hole interaction in TDDFT is nonlocal (figure b). These findings are significant because the open up new systematic ways to calculate optical properties in materials.

Z.Yang, Y. Li, and C. A. Ullrich, J. Chem. Phys. 137, 014513 (2012)




(a) Excitonic spectrum in a 1D Kronig-Penney model

(b) Effective nonlocal electron-hole interaction in TDDFT

A minimal model for excitons within TDDFTCarsten A. Ullrich, University of Missouri-Columbia, DMR 1005651

The broader impact of the project is in various forms of course development, teaching, and student mentoring.

● Developed an undergraduate course at MU, “Modern condensed-matter physics”, and taught a graduate course on theoretical materials science, incorporating elements of modern research on electronic excitations.

● Organized a tutorial on DFT at the APS March Meeting 2012.

● Taught a 2-week intensive course on excitation in materials at UFABC, Santo Andre, Brazil (July 2012). Lectured at the TDDFT winter school in Benasque, Spain (January 2012).

● Published a textbook on TDDFT.