### Abstract

In this study, an early-working algorithm is designed to evaluate derivatives of electron repulsion integrals (DERIs) for heavy-element systems. The algorithm is constructed to extend the accompanying coordinate expansion and transferred recurrence relation (ACE-TRR) method, which was developed for rapid evaluation of electron repulsion integrals (ERIs) in our previous article (M. Hayami, J. Seino, and H. Nakai, J. Chem. Phys. 2015, 142, 204110). The algorithm was formulated using the Gaussian derivative rule to decompose a DERI of two ERIs with the same sets of exponents, different sets of contraction coefficients, and different angular momenta. The algorithms designed for segmented and general contraction basis sets are presented as well. Numerical assessments of the central processing unit time of gradients for molecules were conducted to demonstrate the high efficiency of the ACE-TRR method for systems containing heavy elements. These heavy elements may include a metal complex and metal clusters, whose basis sets contain functions with long contractions and high angular momenta.

Original language | English |
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Journal | International Journal of Quantum Chemistry |

DOIs | |

Publication status | Accepted/In press - 2018 Jan 1 |

### Fingerprint

### Keywords

- Accompanying coordinate expansion and transferred recurrence relation
- Derivative of electron repulsion integral
- General contraction
- High angular momentum
- Long contraction

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Condensed Matter Physics
- Physical and Theoretical Chemistry

### Cite this

*International Journal of Quantum Chemistry*. https://doi.org/10.1002/qua.25640

**Derivative of electron repulsion integral using accompanying coordinate expansion and transferred recurrence relation method for long contraction and high angular momentum.** / Hayami, Masao; Seino, Junji; Nakai, Hiromi.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Derivative of electron repulsion integral using accompanying coordinate expansion and transferred recurrence relation method for long contraction and high angular momentum

AU - Hayami, Masao

AU - Seino, Junji

AU - Nakai, Hiromi

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In this study, an early-working algorithm is designed to evaluate derivatives of electron repulsion integrals (DERIs) for heavy-element systems. The algorithm is constructed to extend the accompanying coordinate expansion and transferred recurrence relation (ACE-TRR) method, which was developed for rapid evaluation of electron repulsion integrals (ERIs) in our previous article (M. Hayami, J. Seino, and H. Nakai, J. Chem. Phys. 2015, 142, 204110). The algorithm was formulated using the Gaussian derivative rule to decompose a DERI of two ERIs with the same sets of exponents, different sets of contraction coefficients, and different angular momenta. The algorithms designed for segmented and general contraction basis sets are presented as well. Numerical assessments of the central processing unit time of gradients for molecules were conducted to demonstrate the high efficiency of the ACE-TRR method for systems containing heavy elements. These heavy elements may include a metal complex and metal clusters, whose basis sets contain functions with long contractions and high angular momenta.

AB - In this study, an early-working algorithm is designed to evaluate derivatives of electron repulsion integrals (DERIs) for heavy-element systems. The algorithm is constructed to extend the accompanying coordinate expansion and transferred recurrence relation (ACE-TRR) method, which was developed for rapid evaluation of electron repulsion integrals (ERIs) in our previous article (M. Hayami, J. Seino, and H. Nakai, J. Chem. Phys. 2015, 142, 204110). The algorithm was formulated using the Gaussian derivative rule to decompose a DERI of two ERIs with the same sets of exponents, different sets of contraction coefficients, and different angular momenta. The algorithms designed for segmented and general contraction basis sets are presented as well. Numerical assessments of the central processing unit time of gradients for molecules were conducted to demonstrate the high efficiency of the ACE-TRR method for systems containing heavy elements. These heavy elements may include a metal complex and metal clusters, whose basis sets contain functions with long contractions and high angular momenta.

KW - Accompanying coordinate expansion and transferred recurrence relation

KW - Derivative of electron repulsion integral

KW - General contraction

KW - High angular momentum

KW - Long contraction

UR - http://www.scopus.com/inward/record.url?scp=85045736259&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85045736259&partnerID=8YFLogxK

U2 - 10.1002/qua.25640

DO - 10.1002/qua.25640

M3 - Article

JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

SN - 0020-7608

ER -