### Abstract

A technique has been developed which in principle allows the determination of the full rotational-vibrational eigenspectrum of triatomic molecules by treating the important singularities present in the triatomic rotational-vibrational kinetic energy operator given in Jacobi coordinates and the R(1) embedding. The singular term related to the diatom-type coordinate, R(1), deemed to be unimportant for spectroscopic applications, is given no special attention. The work extends a previous [J. Chem. Phys., 2005, 122, 024101] vibration-only approach and employs a generalized finite basis representation (GFBR) resulting in a nonsymmetric Hamiltonian matrix [J. Chem. Phys., 2006, 124, 014110]. The basis set to be used is obtained by taking the direct product of a 1-D DVR basis, related to R(1), with a 5-D nondirect-product basis, the latter formed by coupling Bessel-DVR functions depending on the distance-type coordinate causing the singularity, associated Legendre polynomials depending on the Jacobi angle, and rotational functions depending on the three Euler angles. The robust implicitly restarted Arnoldi method within the ARPACK package is used for the determination of a number of eigenvalues of the nonsymmetric Hamiltonian matrix. The suitability of the proposed approach is shown by the determination of the rotational-vibrational energy levels of the ground electronic state of H(3)(+) somewhat above its barrier to linearity. Convergence of the eigenenergies is checked by an alternative approach, employing a Hamiltonian expressed in Radau coordinates, a standard direct-product basis, and no treatment of the singularities.

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

Pages (from-to) | 3407-3415 |

Number of pages | 9 |

Journal | Physical Chemistry Chemical Physics |

Volume | 9 |

Issue number | 26 |

DOIs | |

Publication status | Published - Jul 14 2007 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Physical Chemistry Chemical Physics*,

*9*(26), 3407-3415. https://doi.org/10.1039/b701911d

**Use of a nondirect-product basis for treating singularities in triatomic rotational-vibrational calculations.** / Czakó, G.; Furtenbacher, T.; Barletta, Paolo; Császár, A.; Szalay, V.; Sutcliffe, Brian T.

Research output: Contribution to journal › Article

*Physical Chemistry Chemical Physics*, vol. 9, no. 26, pp. 3407-3415. https://doi.org/10.1039/b701911d

}

TY - JOUR

T1 - Use of a nondirect-product basis for treating singularities in triatomic rotational-vibrational calculations.

AU - Czakó, G.

AU - Furtenbacher, T.

AU - Barletta, Paolo

AU - Császár, A.

AU - Szalay, V.

AU - Sutcliffe, Brian T.

PY - 2007/7/14

Y1 - 2007/7/14

N2 - A technique has been developed which in principle allows the determination of the full rotational-vibrational eigenspectrum of triatomic molecules by treating the important singularities present in the triatomic rotational-vibrational kinetic energy operator given in Jacobi coordinates and the R(1) embedding. The singular term related to the diatom-type coordinate, R(1), deemed to be unimportant for spectroscopic applications, is given no special attention. The work extends a previous [J. Chem. Phys., 2005, 122, 024101] vibration-only approach and employs a generalized finite basis representation (GFBR) resulting in a nonsymmetric Hamiltonian matrix [J. Chem. Phys., 2006, 124, 014110]. The basis set to be used is obtained by taking the direct product of a 1-D DVR basis, related to R(1), with a 5-D nondirect-product basis, the latter formed by coupling Bessel-DVR functions depending on the distance-type coordinate causing the singularity, associated Legendre polynomials depending on the Jacobi angle, and rotational functions depending on the three Euler angles. The robust implicitly restarted Arnoldi method within the ARPACK package is used for the determination of a number of eigenvalues of the nonsymmetric Hamiltonian matrix. The suitability of the proposed approach is shown by the determination of the rotational-vibrational energy levels of the ground electronic state of H(3)(+) somewhat above its barrier to linearity. Convergence of the eigenenergies is checked by an alternative approach, employing a Hamiltonian expressed in Radau coordinates, a standard direct-product basis, and no treatment of the singularities.

AB - A technique has been developed which in principle allows the determination of the full rotational-vibrational eigenspectrum of triatomic molecules by treating the important singularities present in the triatomic rotational-vibrational kinetic energy operator given in Jacobi coordinates and the R(1) embedding. The singular term related to the diatom-type coordinate, R(1), deemed to be unimportant for spectroscopic applications, is given no special attention. The work extends a previous [J. Chem. Phys., 2005, 122, 024101] vibration-only approach and employs a generalized finite basis representation (GFBR) resulting in a nonsymmetric Hamiltonian matrix [J. Chem. Phys., 2006, 124, 014110]. The basis set to be used is obtained by taking the direct product of a 1-D DVR basis, related to R(1), with a 5-D nondirect-product basis, the latter formed by coupling Bessel-DVR functions depending on the distance-type coordinate causing the singularity, associated Legendre polynomials depending on the Jacobi angle, and rotational functions depending on the three Euler angles. The robust implicitly restarted Arnoldi method within the ARPACK package is used for the determination of a number of eigenvalues of the nonsymmetric Hamiltonian matrix. The suitability of the proposed approach is shown by the determination of the rotational-vibrational energy levels of the ground electronic state of H(3)(+) somewhat above its barrier to linearity. Convergence of the eigenenergies is checked by an alternative approach, employing a Hamiltonian expressed in Radau coordinates, a standard direct-product basis, and no treatment of the singularities.

UR - http://www.scopus.com/inward/record.url?scp=34548694584&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34548694584&partnerID=8YFLogxK

U2 - 10.1039/b701911d

DO - 10.1039/b701911d

M3 - Article

C2 - 17664964

AN - SCOPUS:34548694584

VL - 9

SP - 3407

EP - 3415

JO - Physical Chemistry Chemical Physics

JF - Physical Chemistry Chemical Physics

SN - 1463-9076

IS - 26

ER -