Hybrid functionals and GW approximation in the FLAPW method

C. Friedrich, M. Betzinger, M. Schlipf, S. Blügel, A. Schindlmayr, Journal of Physics: Condensed Matter 24 (2012).

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We present recent advances in numerical implementations of hybrid functionals and the GW approximation within the full-potential linearized augmented-plane-wave (FLAPW) method. The former is an approximation for the exchange–correlation contribution to the total energy functional in density-functional theory, and the latter is an approximation for the electronic self-energy in the framework of many-body perturbation theory. All implementations employ the mixed product basis, which has evolved into a versatile basis for the products of wave functions, describing the incoming and outgoing states of an electron that is scattered by interacting with another electron. It can thus be used for representing the nonlocal potential in hybrid functionals as well as the screened interaction and related quantities in GW calculations. In particular, the six-dimensional space integrals of the Hamiltonian exchange matrix elements (and exchange self-energy) decompose into sums over vector–matrix–vector products, which can be evaluated easily. The correlation part of the GW self-energy, which contains a time or frequency dependence, is calculated on the imaginary frequency axis with a subsequent analytic continuation to the real axis or, alternatively, by a direct frequency convolution of the Green function G and the dynamically screened Coulomb interaction W along a contour integration path that avoids the poles of the Green function. Hybrid-functional and GW calculations are notoriously computationally expensive. We present a number of tricks that reduce the computational cost considerably, including the use of spatial and time-reversal symmetries, modifications of the mixed product basis with the aim to optimize it for the correlation self-energy and another modification that makes the Coulomb matrix sparse, analytic expansions of the interaction potentials around the point of divergence at k=0, and a nested density and density-matrix convergence scheme for hybrid-functional calculations. We show CPU timings for prototype semiconductors and illustrative results for GdN and ZnO.
Publishing Year
Journal Title
Journal of Physics: Condensed Matter
Volume
24
Issue
29
Article Number
293201
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Friedrich C, Betzinger M, Schlipf M, Blügel S, Schindlmayr A. Hybrid functionals and GW approximation in the FLAPW method. Journal of Physics: Condensed Matter. 2012;24(29). doi:10.1088/0953-8984/24/29/293201
Friedrich, C., Betzinger, M., Schlipf, M., Blügel, S., & Schindlmayr, A. (2012). Hybrid functionals and GW approximation in the FLAPW method. Journal of Physics: Condensed Matter, 24(29). https://doi.org/10.1088/0953-8984/24/29/293201
@article{Friedrich_Betzinger_Schlipf_Blügel_Schindlmayr_2012, title={Hybrid functionals and GW approximation in the FLAPW method}, volume={24}, DOI={10.1088/0953-8984/24/29/293201}, number={29293201}, journal={Journal of Physics: Condensed Matter}, publisher={IOP Publishing}, author={Friedrich, Christoph and Betzinger, Markus and Schlipf, Martin and Blügel, Stefan and Schindlmayr, Arno}, year={2012} }
Friedrich, Christoph, Markus Betzinger, Martin Schlipf, Stefan Blügel, and Arno Schindlmayr. “Hybrid Functionals and GW Approximation in the FLAPW Method.” Journal of Physics: Condensed Matter 24, no. 29 (2012). https://doi.org/10.1088/0953-8984/24/29/293201.
C. Friedrich, M. Betzinger, M. Schlipf, S. Blügel, and A. Schindlmayr, “Hybrid functionals and GW approximation in the FLAPW method,” Journal of Physics: Condensed Matter, vol. 24, no. 29, 2012.
Friedrich, Christoph, et al. “Hybrid Functionals and GW Approximation in the FLAPW Method.” Journal of Physics: Condensed Matter, vol. 24, no. 29, 293201, IOP Publishing, 2012, doi:10.1088/0953-8984/24/29/293201.
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