Force Balance Approach for Advanced Approximations in Density Functional Theories

Journal of Chemical Physics 151, 154107 (2019)

Force Balance Approach for Advanced Approximations in Density Functional Theories

Mary-Leena M. Tchenkoue, Markus Penz, Iris Theophilou, Michael Ruggenthaler, Angel Rubio

We propose a systematic and constructive way to determine the exchange-correlation potentials of density-functional theories including vector potentials. The approach does not rely on energy or action functionals. Instead it is based on equations of motion of current quantities (force balance equations) and is feasible both in the ground-state and the time-dependent setting. This avoids, besides differentiability and causality issues, the optimized-effective-potential procedure of orbital-dependent functionals. We provide straightforward exchange-type approximations for different density functional theories that for a homogeneous system and no external vector potential reduce to the exchange-only local-density and Slater Xα approximations.

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We express our gratitude for helpful comments from Andre Laestadius on an earlier draft and for insightful discussions with Florian Eich. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 694097), as well as from the Deutsche Forschungsgemeinschaft (DFG) Sonderforschungsbereich 925 “Light-induced dynamics and control of correlated quantum systems” (Project No. A4) and the DFG Cluster of Excellence “Advanced Imaging of Matter” (EXC 2056, Project ID 390715994). M.P. acknowledges support by the Erwin Schrödinger Fellowship J 4107-N27 of the FWF (Austrian Science Fund).

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