CASUS Institute Seminar, Andreas Görling, Friedrich-Alexander University Erlangen-Nürnberg
Electronic structure methods using orbital-dependent exchange-correlation functionals within the Kohn-Sham (KS) formalism of density-functional theory are introduced. An approach to treat the KS exchange energy and potential exactly in the case of non-zero temperature is presented and applied to describe topological phase transitions in zinc-blende compounds [1,2]. The treatment of electron correlation based on the adiabatic-connection fluctuation-dissipation theorem is discussed [3,4] and a new class of correlation functionals, named sigma-functionals, is presented . Technically, sigma-functionals are very similar to functionals within the well-known random phase approximation and have similar computational demands. The accuracy of sigma-functionals, however, is substantially higher than that of functionals within the random-phase approximation. Indeed, reaction and transition state energies of molecules from various established test sets as well as Van-der-Waals binding energies from sigma-functionals are as accurate as those from high level quantum quemistry methods  that are computationally much more demanding and therefore quite limitied in their range of application. Sigma-functionals therefore open up new areas of application for KS methods in chemistry, physics, and materials science.
1. M. Greiner, P. Carrier, and A. Gorling, Phys. Rev. B 81, 155119 (2010).
2. E. Trushin and A. Gorling, Phys. Rev. Lett. 120, 146401 (2018).
3. J. Erhard, P. Bleizier, and A. Gorling, Phys. Rev. Lett. 117, 143002 (2016).
4. A. Gorling, Phys. Rev. B 99, 235120 (2019).
5. E. Trushin, A. Thierbach, A. Gorling, J. Chem. Phys. 154, 014104 (2021).