# Dresden 2017 – wissenschaftliches Programm

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# MM: Fachverband Metall- und Materialphysik

## MM 35: Electronic Structure Theory: New Concepts and Developments in Density Functional Theory and Beyond

### MM 35.4: Poster

### Dienstag, 21. März 2017, 18:30–20:30, P2-OG4

**Numerical improvements of Fermi-Löwdin orbital self-interaction correction** — •Lenz Fiedler, Torsten Hahn, Charlotte Vogelbusch, and Jens Kortus — TU Freiberg, Institute for Theoretical Physics, Germany

Electronic structure theory calculations based on density functional theory (DFT) using semilocal approximations for exchange and correlation are subjected to the self-interaction error. The recently proposed Fermi-Löwdin orbital method for self-interaction correction (FLOSIC) is based on sets of localized orbitals, that are a unitary invariant transformation of the Kohn-Sham orbitals [1,2]. The practical application of this method is however still numerically costly because one needs to determine the Fermi orbital descriptors that minimize the total energy. Numerical improvements to this optimization will drastically improve the performance of the whole FLOSIC DFT method.

We present the implementation of a preconditioned conjugate gradient [3] and a quasi-Newton L-BFGS algorithm [4] that draw on approximations of the analytical Hessian of the energy function. For a set of small molecules, benchmarks are done for different approximated Hessians. We here discuss the influence of different methods to approximate the Hessian and the usage of off-diagonal Hessian elements on the optimization performance.

[1] M. R. Pederson et al., J. Chem. Phys., vol. 140, 121103 (2014)

[2] J. Perdew, A. Zunger, Phys. Rev. B 23, 5048 (1981)

[3] D. Liu, J. Nocedal, Math. Prog. B 45, 503 (1989)

[4] W. Hager, H. Zhang, SIAM J. Optim., 16-1, 170 (2005)