### Abstract

Electronic resonance state energies and photoionization cross sections of atoms and molecules are calculated with the complex basis function method by using mixture of appropriate complex basis functions representing one-electron continuum orbitals and the usual real basis functions for the remaining bound state orbitals. The choice of complex basis functions has long been a central difficulty in such calculations. To address this challenge, we constructed complex Slater-type orbital represented by N-term Gaussian-type orbitals (cSTO-NG) basis sets using the method of least squares. Three expansion schemes are tested: (1) expansion in complex Gaussian-type orbitals, (2) expansion in real Gaussian-type orbitals, and (3) expansion in even-tempered real Gaussian-type orbitals. By extending the Shavitt–Karplus integral transform expression to cSTO functions, we have established a mathematical foundation for these expansions. To demonstrate the efficacy of this approach, we have applied these basis sets to the calculation of the lowest Feshbach resonance of H_{2} and the photoionization cross section of the He atom including autoionization features due to doubly excited states. These calculations produce acceptably accurate results compared with past calculations and experimental data in all cases examined here.

Original language | English |
---|---|

Article number | 1521 |

Pages (from-to) | 1-12 |

Number of pages | 12 |

Journal | Theoretical Chemistry Accounts |

Volume | 133 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2014 Sep 1 |

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### Keywords

- Autoionization
- Complex basis function method
- Feshbach resonance
- Gaussian-type orbital
- Least squares fitting
- Slater-type orbital

### ASJC Scopus subject areas

- Physical and Theoretical Chemistry

### Cite this

*Theoretical Chemistry Accounts*,

*133*(9), 1-12. [1521]. https://doi.org/10.1007/s00214-014-1521-6

**Construction of complex STO-NG basis sets by the method of least squares and their applications.** / Matsuzaki, Rei; Asai, Shigeko; McCurdy, C. William; Yabushita, Satoshi.

Research output: Contribution to journal › Article

*Theoretical Chemistry Accounts*, vol. 133, no. 9, 1521, pp. 1-12. https://doi.org/10.1007/s00214-014-1521-6

}

TY - JOUR

T1 - Construction of complex STO-NG basis sets by the method of least squares and their applications

AU - Matsuzaki, Rei

AU - Asai, Shigeko

AU - McCurdy, C. William

AU - Yabushita, Satoshi

PY - 2014/9/1

Y1 - 2014/9/1

N2 - Electronic resonance state energies and photoionization cross sections of atoms and molecules are calculated with the complex basis function method by using mixture of appropriate complex basis functions representing one-electron continuum orbitals and the usual real basis functions for the remaining bound state orbitals. The choice of complex basis functions has long been a central difficulty in such calculations. To address this challenge, we constructed complex Slater-type orbital represented by N-term Gaussian-type orbitals (cSTO-NG) basis sets using the method of least squares. Three expansion schemes are tested: (1) expansion in complex Gaussian-type orbitals, (2) expansion in real Gaussian-type orbitals, and (3) expansion in even-tempered real Gaussian-type orbitals. By extending the Shavitt–Karplus integral transform expression to cSTO functions, we have established a mathematical foundation for these expansions. To demonstrate the efficacy of this approach, we have applied these basis sets to the calculation of the lowest Feshbach resonance of H2 and the photoionization cross section of the He atom including autoionization features due to doubly excited states. These calculations produce acceptably accurate results compared with past calculations and experimental data in all cases examined here.

AB - Electronic resonance state energies and photoionization cross sections of atoms and molecules are calculated with the complex basis function method by using mixture of appropriate complex basis functions representing one-electron continuum orbitals and the usual real basis functions for the remaining bound state orbitals. The choice of complex basis functions has long been a central difficulty in such calculations. To address this challenge, we constructed complex Slater-type orbital represented by N-term Gaussian-type orbitals (cSTO-NG) basis sets using the method of least squares. Three expansion schemes are tested: (1) expansion in complex Gaussian-type orbitals, (2) expansion in real Gaussian-type orbitals, and (3) expansion in even-tempered real Gaussian-type orbitals. By extending the Shavitt–Karplus integral transform expression to cSTO functions, we have established a mathematical foundation for these expansions. To demonstrate the efficacy of this approach, we have applied these basis sets to the calculation of the lowest Feshbach resonance of H2 and the photoionization cross section of the He atom including autoionization features due to doubly excited states. These calculations produce acceptably accurate results compared with past calculations and experimental data in all cases examined here.

KW - Autoionization

KW - Complex basis function method

KW - Feshbach resonance

KW - Gaussian-type orbital

KW - Least squares fitting

KW - Slater-type orbital

UR - http://www.scopus.com/inward/record.url?scp=84923765282&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84923765282&partnerID=8YFLogxK

U2 - 10.1007/s00214-014-1521-6

DO - 10.1007/s00214-014-1521-6

M3 - Article

AN - SCOPUS:84923765282

VL - 133

SP - 1

EP - 12

JO - Theoretical Chemistry Accounts

JF - Theoretical Chemistry Accounts

SN - 1432-881X

IS - 9

M1 - 1521

ER -