# Estimating the CCSD basis-set limit energy from small basis sets: basis-set extrapolations vs additivity schemes

## Abstract

Coupled cluster calculations with all single and double excitations (CCSD) converge exceedingly slowly with the size of the one-particle basis set. We assess the performance of a number of approaches for obtaining CCSD correlation energies close to the complete basis-set limit in conjunction with relatively small DZ and TZ basis sets. These include global and system-dependent extrapolations based on the A + B/L{sup α} two-point extrapolation formula, and the well-known additivity approach that uses an MP2-based basis-set-correction term. We show that the basis set convergence rate can change dramatically between different systems(e.g.it is slower for molecules with polar bonds and/or second-row elements). The system-dependent basis-set extrapolation scheme, in which unique basis-set extrapolation exponents for each system are obtained from lower-cost MP2 calculations, significantly accelerates the basis-set convergence relative to the global extrapolations. Nevertheless, we find that the simple MP2-based basis-set additivity scheme outperforms the extrapolation approaches. For example, the following root-mean-squared deviations are obtained for the 140 basis-set limit CCSD atomization energies in the W4-11 database: 9.1 (global extrapolation), 3.7 (system-dependent extrapolation), and 2.4 (additivity scheme) kJ mol{sup –1}. The CCSD energy in these approximations is obtained from basis sets of up to TZ quality and the latter two approachesmore »

- Authors:

- School of Chemistry and Biochemistry, The University of Western Australia, Perth, WA 6009 (Australia)

- Publication Date:

- OSTI Identifier:
- 22488587

- Resource Type:
- Journal Article

- Journal Name:
- AIP Advances

- Additional Journal Information:
- Journal Volume: 5; Journal Issue: 5; Other Information: (c) 2015 Author(s); Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 2158-3226

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; 36 MATERIALS SCIENCE; AMINO ACIDS; AROMATICS; ATOMIZATION; DNA; EXCITATION; EXTRAPOLATION; HYDROCARBONS; MOLECULES; PARTICLES; RNA

### Citation Formats

```
Spackman, Peter R., and Karton, Amir, E-mail: amir.karton@uwa.edu.au.
```*Estimating the CCSD basis-set limit energy from small basis sets: basis-set extrapolations vs additivity schemes*. United States: N. p., 2015.
Web. doi:10.1063/1.4921697.

```
Spackman, Peter R., & Karton, Amir, E-mail: amir.karton@uwa.edu.au.
```*Estimating the CCSD basis-set limit energy from small basis sets: basis-set extrapolations vs additivity schemes*. United States. doi:10.1063/1.4921697.

```
Spackman, Peter R., and Karton, Amir, E-mail: amir.karton@uwa.edu.au. Fri .
"Estimating the CCSD basis-set limit energy from small basis sets: basis-set extrapolations vs additivity schemes". United States. doi:10.1063/1.4921697.
```

```
@article{osti_22488587,
```

title = {Estimating the CCSD basis-set limit energy from small basis sets: basis-set extrapolations vs additivity schemes},

author = {Spackman, Peter R. and Karton, Amir, E-mail: amir.karton@uwa.edu.au},

abstractNote = {Coupled cluster calculations with all single and double excitations (CCSD) converge exceedingly slowly with the size of the one-particle basis set. We assess the performance of a number of approaches for obtaining CCSD correlation energies close to the complete basis-set limit in conjunction with relatively small DZ and TZ basis sets. These include global and system-dependent extrapolations based on the A + B/L{sup α} two-point extrapolation formula, and the well-known additivity approach that uses an MP2-based basis-set-correction term. We show that the basis set convergence rate can change dramatically between different systems(e.g.it is slower for molecules with polar bonds and/or second-row elements). The system-dependent basis-set extrapolation scheme, in which unique basis-set extrapolation exponents for each system are obtained from lower-cost MP2 calculations, significantly accelerates the basis-set convergence relative to the global extrapolations. Nevertheless, we find that the simple MP2-based basis-set additivity scheme outperforms the extrapolation approaches. For example, the following root-mean-squared deviations are obtained for the 140 basis-set limit CCSD atomization energies in the W4-11 database: 9.1 (global extrapolation), 3.7 (system-dependent extrapolation), and 2.4 (additivity scheme) kJ mol{sup –1}. The CCSD energy in these approximations is obtained from basis sets of up to TZ quality and the latter two approaches require additional MP2 calculations with basis sets of up to QZ quality. We also assess the performance of the basis-set extrapolations and additivity schemes for a set of 20 basis-set limit CCSD atomization energies of larger molecules including amino acids, DNA/RNA bases, aromatic compounds, and platonic hydrocarbon cages. We obtain the following RMSDs for the above methods: 10.2 (global extrapolation), 5.7 (system-dependent extrapolation), and 2.9 (additivity scheme) kJ mol{sup –1}.},

doi = {10.1063/1.4921697},

journal = {AIP Advances},

issn = {2158-3226},

number = 5,

volume = 5,

place = {United States},

year = {2015},

month = {5}

}