# Explicitly correlated ring-coupled-cluster-doubles theory

## Abstract

The connection between the random-phase approximation and the ring-coupled-cluster-doubles method bridges the gap between density-functional and wave-function theories and the importance of the random-phase approximation lies in both its broad applicability and this linking role in electronic-structure theory. In this contribution, we present an explicitly correlated approach to the random-phase approximation, based on the direct ring-coupled-cluster-doubles ansatz, which overcomes the problem of slow basis-set convergence, inherent to the random-phase approximation. Benchmark results for a test set of 106 molecules and a selection of 10 organic complexes from the S22 test set demonstrate that convergence to within 99% of the basis-set limit is reached for triple-zeta basis sets for atomisation energies, while quadruple-zeta basis sets are required for interaction energies. Corrections due to single excitations into the complementary auxiliary space reduce the basis-set incompleteness error by one order of magnitude, while contributions due to the coupling of conventional and geminal amplitudes are in general negligible. We find that a non-iterative explicitly correlated correction to first order in perturbation theory exhibits the best ratio of accuracy to computational cost.

- Authors:

- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 2, D-76131 Karlsruhe (Germany)
- School of Chemistry, University of Bristol, Bristol BSB 1TS (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 22415788

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 142; Journal Issue: 19; 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; BENCHMARKS; CONVERGENCE; CORRECTIONS; COUPLING; DENSITY FUNCTIONAL METHOD; ELECTRONIC STRUCTURE; EXCITATION; ITERATIVE METHODS; PERTURBATION THEORY; RANDOM PHASE APPROXIMATION; WAVE FUNCTIONS

### Citation Formats

```
Hehn, Anna-Sophia, Klopper, Wim, and Tew, David P.
```*Explicitly correlated ring-coupled-cluster-doubles theory*. United States: N. p., 2015.
Web. doi:10.1063/1.4921256.

```
Hehn, Anna-Sophia, Klopper, Wim, & Tew, David P.
```*Explicitly correlated ring-coupled-cluster-doubles theory*. United States. doi:10.1063/1.4921256.

```
Hehn, Anna-Sophia, Klopper, Wim, and Tew, David P. Thu .
"Explicitly correlated ring-coupled-cluster-doubles theory". United States. doi:10.1063/1.4921256.
```

```
@article{osti_22415788,
```

title = {Explicitly correlated ring-coupled-cluster-doubles theory},

author = {Hehn, Anna-Sophia and Klopper, Wim and Tew, David P.},

abstractNote = {The connection between the random-phase approximation and the ring-coupled-cluster-doubles method bridges the gap between density-functional and wave-function theories and the importance of the random-phase approximation lies in both its broad applicability and this linking role in electronic-structure theory. In this contribution, we present an explicitly correlated approach to the random-phase approximation, based on the direct ring-coupled-cluster-doubles ansatz, which overcomes the problem of slow basis-set convergence, inherent to the random-phase approximation. Benchmark results for a test set of 106 molecules and a selection of 10 organic complexes from the S22 test set demonstrate that convergence to within 99% of the basis-set limit is reached for triple-zeta basis sets for atomisation energies, while quadruple-zeta basis sets are required for interaction energies. Corrections due to single excitations into the complementary auxiliary space reduce the basis-set incompleteness error by one order of magnitude, while contributions due to the coupling of conventional and geminal amplitudes are in general negligible. We find that a non-iterative explicitly correlated correction to first order in perturbation theory exhibits the best ratio of accuracy to computational cost.},

doi = {10.1063/1.4921256},

journal = {Journal of Chemical Physics},

issn = {0021-9606},

number = 19,

volume = 142,

place = {United States},

year = {2015},

month = {5}

}