# Dresden 2014 – wissenschaftliches Programm

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# HL: Fachverband Halbleiterphysik

## HL 77: Frontiers of electronic structure theory - Non-equilibrium phenomena at the nano-scale V (organized by O)

### HL 77.4a: Vortrag

### Mittwoch, 2. April 2014, 17:15–17:30, TRE Ma

**Localized Resolution of Identity: Accurate and efficient evaluation of the coulomb operator for advanced functionals** — •Arvid Conrad Ihrig, Jürgen Wieferink, Igor Ying Zhang, Sergey Levchenko, Matti Ropo, Patrick Rinke, Volker Blum, and Matthias Scheffler — Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin, Germany

A key component for high-level correlation methods is the Coulomb operator, which requires the evaluation of four-center Coulomb integrals. For numeric atom-centered orbitals, as used in the all-electron code FHI-aims [1], the four-center integrals are most efficiently evaluated with the “Resolution of Identity” (RI), which expands basis-function products in an auxiliary basis. In this contribution we show the practical applicability of a localized RI-variant (“RI-LVL”), which expands products of basis functions only in the subset of those auxiliary basis functions which are located at the same atoms as the basis functions. We demonstrate the accuracy of RI-LVL for exact exchange in HF and PBE0, and also for correlation methods like MP2 and RPA for the S22 test set[2] of weakly interacting dimers. The error relative to the established RI can be converged in a systematic way by augmenting the auxiliary basis set with additional basis functions of increasing angular momentum. We also show that RI-LVL exhibits a superior scaling with system size, both in terms of computational time and memory requirements.

[1] V. Blum *et al.*, Comput. Phys. Commun. **180**, 2175 (2009)

[2] P. Jurecka *et al.*, Phys. Chem. Chem. Phys **8**, 1985 (2006)