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Abstract: 

Real-time time-dependent density functional theory (rt-TDDFT) offers a powerful framework for modeling electronic response in molecular and condensed-phase systems under time-dependent external fields.  In this talk, the focus is on the mathematical and computational aspects underpinning the stable propagation of the von Neumann equation for the density matrix using Magnus expansions.  Dr. Jakowski presents a systematic derivation of the propagator and discusses its formulation within the real-space multigrid (RMG) framework, emphasizing unitary time-evolution, energy conservation, and efficient matrix-matrix operations on massively parallel architectures.  The approach naturally incorporates fractional occupations and is applicable to both closed and open-shell systems.  This illustrates the results with benchmark simulations on systems ranging from small molecules to plasmonic nanostructures comprising 24,000 electrons.  The talk concludes with perspectives on generalizing this framework for non-Hermitian dynamics, spin propagation, and C0-semigroup.

Speaker’s Bio:

Dr. Jacek Jakowski was born in Poland.  He received his Ph.D. in theoretical chemistry from the University of Warsaw, Poland, in 2002. He pursued his postdoctoral research at the University of Utah, Indiana University, and Emory University.  In 2010 he became a research scientist at the Center for Nanophase Materials Sciences and the Joint Institute for Computational Sciences of the Oak Ridge National Laboratory and the University of Tennessee.  Since 2016, he has been a staff scientist at the Computational Sciences and Engineering Division of the Oak Ridge National Laboratory.  His research interests include the development and application of electronic structure and first-principles molecular and quantum dynamics methods and the effects of electronic excitation and quantum nuclei dynamics on the properties of materials.