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

G. Czakó, T. Furtenbacher, Paolo Barletta, A. Császár, V. Szalay, Brian T. Sutcliffe

Research output: Contribution to journalArticle

8 Citations (Scopus)

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 languageEnglish
Pages (from-to)3407-3415
Number of pages9
JournalPhysical Chemistry Chemical Physics
Volume9
Issue number26
DOIs
Publication statusPublished - Jul 14 2007

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Hamiltonians
products
Bessel functions
Electronic states
Kinetic energy
triatomic molecules
Electron energy levels
Legendre functions
algae
Polynomials
embedding
linearity
Molecules
eigenvalues
kinetic energy
energy levels
operators
vibration
electronics

ASJC Scopus subject areas

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

Cite this

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.

In: Physical Chemistry Chemical Physics, Vol. 9, No. 26, 14.07.2007, p. 3407-3415.

Research output: Contribution to journalArticle

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