# Linear-scaling implementation of the direct random-phase approximation

## Abstract

We report the linear-scaling implementation of the direct random-phase approximation (dRPA) for closed-shell molecular systems. As a bonus, linear-scaling algorithms are also presented for the second-order screened exchange extension of dRPA as well as for the second-order Møller–Plesset (MP2) method and its spin-scaled variants. Our approach is based on an incremental scheme which is an extension of our previous local correlation method [Rolik et al., J. Chem. Phys. 139, 094105 (2013)]. The approach extensively uses local natural orbitals to reduce the size of the molecular orbital basis of local correlation domains. In addition, we also demonstrate that using natural auxiliary functions [M. Kállay, J. Chem. Phys. 141, 244113 (2014)], the size of the auxiliary basis of the domains and thus that of the three-center Coulomb integral lists can be reduced by an order of magnitude, which results in significant savings in computation time. The new approach is validated by extensive test calculations for energies and energy differences. Our benchmark calculations also demonstrate that the new method enables dRPA calculations for molecules with more than 1000 atoms and 10 000 basis functions on a single processor.

- Authors:

- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest (Hungary)

- Publication Date:

- OSTI Identifier:
- 22415859

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 142; Journal Issue: 20; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ALGORITHMS; ATOMS; BENCHMARKS; CORRELATIONS; INTEGRALS; MOLECULAR ORBITAL METHOD; MOLECULES; RANDOM PHASE APPROXIMATION; SPIN

### Citation Formats

```
Kállay, Mihály, E-mail: kallay@mail.bme.hu.
```*Linear-scaling implementation of the direct random-phase approximation*. United States: N. p., 2015.
Web. doi:10.1063/1.4921542.

```
Kállay, Mihály, E-mail: kallay@mail.bme.hu.
```*Linear-scaling implementation of the direct random-phase approximation*. United States. doi:10.1063/1.4921542.

```
Kállay, Mihály, E-mail: kallay@mail.bme.hu. Thu .
"Linear-scaling implementation of the direct random-phase approximation". United States. doi:10.1063/1.4921542.
```

```
@article{osti_22415859,
```

title = {Linear-scaling implementation of the direct random-phase approximation},

author = {Kállay, Mihály, E-mail: kallay@mail.bme.hu},

abstractNote = {We report the linear-scaling implementation of the direct random-phase approximation (dRPA) for closed-shell molecular systems. As a bonus, linear-scaling algorithms are also presented for the second-order screened exchange extension of dRPA as well as for the second-order Møller–Plesset (MP2) method and its spin-scaled variants. Our approach is based on an incremental scheme which is an extension of our previous local correlation method [Rolik et al., J. Chem. Phys. 139, 094105 (2013)]. The approach extensively uses local natural orbitals to reduce the size of the molecular orbital basis of local correlation domains. In addition, we also demonstrate that using natural auxiliary functions [M. Kállay, J. Chem. Phys. 141, 244113 (2014)], the size of the auxiliary basis of the domains and thus that of the three-center Coulomb integral lists can be reduced by an order of magnitude, which results in significant savings in computation time. The new approach is validated by extensive test calculations for energies and energy differences. Our benchmark calculations also demonstrate that the new method enables dRPA calculations for molecules with more than 1000 atoms and 10 000 basis functions on a single processor.},

doi = {10.1063/1.4921542},

journal = {Journal of Chemical Physics},

issn = {0021-9606},

number = 20,

volume = 142,

place = {United States},

year = {2015},

month = {5}

}