# Accurate localized resolution of identity approach for linear-scaling hybrid density functionals and for many-body perturbation theory,

Research output: Contribution to journal › Article

### Standard

**Accurate localized resolution of identity approach for linear-scaling hybrid density functionals and for many-body perturbation theory,** / Ihrig, A.C.; Wieferink, J.; Zhang, I.Y.; Ropo, M.; Ren, X.; Rinke, P.; Scheffler, M.; Blum, V.

Research output: Contribution to journal › Article

### Harvard

*New Journal of Physics*, vol. 17, no. 9, 093020, pp. 1-20. https://doi.org/10.1088/1367-2630/17/9/093020

### APA

*New Journal of Physics*,

*17*(9), 1-20. [093020]. https://doi.org/10.1088/1367-2630/17/9/093020

### Vancouver

### Author

### Bibtex - Download

}

### RIS - Download

TY - JOUR

T1 - Accurate localized resolution of identity approach for linear-scaling hybrid density functionals and for many-body perturbation theory,

AU - Ihrig, A.C.

AU - Wieferink, J.

AU - Zhang, I.Y.

AU - Ropo, M.

AU - Ren, X.

AU - Rinke, P.

AU - Scheffler, M.

AU - Blum, V.

PY - 2015

Y1 - 2015

N2 - A key component in calculations of exchange and correlation energies is the Coulomb operator, which requires the evaluation of two-electron integrals. For localized basis sets, these four-center integrals are most efficiently evaluated with the resolution of identity (RI) technique, which expands basis-function products in an auxiliary basis. In this work 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 Hartree–Fock calculations, for the PBE0 hybrid density functional, as well as for RPA and MP2 perturbation theory. Molecular test sets used include the S22 set of weakly interacting molecules, the G3 test set, as well as the G2–1 and BH76 test sets, and heavy elements including titanium dioxide, copper and gold clusters. Our RI-LVL implementation paves the way for linear-scaling RI-based hybrid functional calculations for large systems and for all-electron many-body perturbation theory with significantly reduced computational and memory cost.

AB - A key component in calculations of exchange and correlation energies is the Coulomb operator, which requires the evaluation of two-electron integrals. For localized basis sets, these four-center integrals are most efficiently evaluated with the resolution of identity (RI) technique, which expands basis-function products in an auxiliary basis. In this work 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 Hartree–Fock calculations, for the PBE0 hybrid density functional, as well as for RPA and MP2 perturbation theory. Molecular test sets used include the S22 set of weakly interacting molecules, the G3 test set, as well as the G2–1 and BH76 test sets, and heavy elements including titanium dioxide, copper and gold clusters. Our RI-LVL implementation paves the way for linear-scaling RI-based hybrid functional calculations for large systems and for all-electron many-body perturbation theory with significantly reduced computational and memory cost.

KW - electronic structure

KW - exact exchange

KW - hybrid functionals

KW - linear scaling

KW - many-body perturbation theory

KW - resolution of identity

KW - electronic structure

KW - exact exchange

KW - hybrid functionals

KW - linear scaling

KW - many-body perturbation theory

KW - resolution of identity

KW - electronic structure

KW - exact exchange

KW - hybrid functionals

KW - linear scaling

KW - many-body perturbation theory

KW - resolution of identity

UR - http://stacks.iop.org/1367-2630/17/i

U2 - 10.1088/1367-2630/17/9/093020

DO - 10.1088/1367-2630/17/9/093020

M3 - Article

VL - 17

SP - 1

EP - 20

JO - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

IS - 9

M1 - 093020

ER -

ID: 1975937