# Accompanying coordinate expansion and recurrence relation method using a transfer relation scheme for electron repulsion integrals with high angular momenta and long contractions

## Abstract

An efficient algorithm for the rapid evaluation of electron repulsion integrals is proposed. The present method, denoted by accompanying coordinate expansion and transferred recurrence relation (ACE-TRR), is constructed using a transfer relation scheme based on the accompanying coordinate expansion and recurrence relation method. Furthermore, the ACE-TRR algorithm is extended for the general-contraction basis sets. Numerical assessments clarify the efficiency of the ACE-TRR method for the systems including heavy elements, whose orbitals have long contractions and high angular momenta, such as f- and g-orbitals.

- Authors:

- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo 169-8555 (Japan)
- Research Institute for Science and Engineering, Waseda University, Tokyo 169-8555 (Japan)
- (Japan)
- (ESICB), Kyoto University, Katsura, Kyoto 615-8520 (Japan)

- Publication Date:

- OSTI Identifier:
- 22415863

- 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; ALGORITHMS; ANGULAR MOMENTUM; CALCULATION METHODS; CONTRACTION; COORDINATES; EFFICIENCY; ELECTRONS; EVALUATION; EXPANSION; INTEGRALS; RECURSION RELATIONS

### Citation Formats

```
Hayami, Masao, Seino, Junji, Nakai, Hiromi, E-mail: nakai@waseda.jp, Research Institute for Science and Engineering, Waseda University, Tokyo 169-8555, CREST, Japan Science and Technology Agency, Saitama 332-0012, and Elements Strategy Initiative for Catalysts and Batteries.
```*Accompanying coordinate expansion and recurrence relation method using a transfer relation scheme for electron repulsion integrals with high angular momenta and long contractions*. United States: N. p., 2015.
Web. doi:10.1063/1.4921541.

```
Hayami, Masao, Seino, Junji, Nakai, Hiromi, E-mail: nakai@waseda.jp, Research Institute for Science and Engineering, Waseda University, Tokyo 169-8555, CREST, Japan Science and Technology Agency, Saitama 332-0012, & Elements Strategy Initiative for Catalysts and Batteries.
```*Accompanying coordinate expansion and recurrence relation method using a transfer relation scheme for electron repulsion integrals with high angular momenta and long contractions*. United States. doi:10.1063/1.4921541.

```
Hayami, Masao, Seino, Junji, Nakai, Hiromi, E-mail: nakai@waseda.jp, Research Institute for Science and Engineering, Waseda University, Tokyo 169-8555, CREST, Japan Science and Technology Agency, Saitama 332-0012, and Elements Strategy Initiative for Catalysts and Batteries. Thu .
"Accompanying coordinate expansion and recurrence relation method using a transfer relation scheme for electron repulsion integrals with high angular momenta and long contractions". United States. doi:10.1063/1.4921541.
```

```
@article{osti_22415863,
```

title = {Accompanying coordinate expansion and recurrence relation method using a transfer relation scheme for electron repulsion integrals with high angular momenta and long contractions},

author = {Hayami, Masao and Seino, Junji and Nakai, Hiromi, E-mail: nakai@waseda.jp and Research Institute for Science and Engineering, Waseda University, Tokyo 169-8555 and CREST, Japan Science and Technology Agency, Saitama 332-0012 and Elements Strategy Initiative for Catalysts and Batteries},

abstractNote = {An efficient algorithm for the rapid evaluation of electron repulsion integrals is proposed. The present method, denoted by accompanying coordinate expansion and transferred recurrence relation (ACE-TRR), is constructed using a transfer relation scheme based on the accompanying coordinate expansion and recurrence relation method. Furthermore, the ACE-TRR algorithm is extended for the general-contraction basis sets. Numerical assessments clarify the efficiency of the ACE-TRR method for the systems including heavy elements, whose orbitals have long contractions and high angular momenta, such as f- and g-orbitals.},

doi = {10.1063/1.4921541},

journal = {Journal of Chemical Physics},

issn = {0021-9606},

number = 20,

volume = 142,

place = {United States},

year = {2015},

month = {5}

}

DOI: 10.1063/1.4921541

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