TY  - JOUR
AU  - Friedrich, C.
AU  - Betzinger, M.
AU  - Schlipf, M.
AU  - Blügel, S.
AU  - Schindlmayr, A.
TI  - Hybrid functionals and GW approximation in the FLAPW method
JO  - Journal of physics / Condensed matter
VL  - 24
SN  - 0953-8984
CY  - Bristol
PB  - IOP Publ.
M1  - PreJuSER-21969
SP  - 293201
PY  - 2012
N1  - We gratefully acknowledge valuable discussions with Marjana Lezaic, Gustav Bihlmayer, Mathias C. Muller, and Georg Kresse, as well as financial funding by the Young Investigators Group Programme of the Helmholtz Association (Computational Nanoferronics Laboratory', contract VH-NG-409) and by the Deutsche Forschungsgemeinschaft through the Priority Program 1145.
AB  - 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.
KW  - J (WoSType)
LB  - PUB:(DE-HGF)16
C6  - pmid:22773268
UR  - <Go to ISI:>//WOS:000306270700001
DO  - DOI:10.1088/0953-8984/24/29/293201
UR  - https://juser.fz-juelich.de/record/21969
ER  -