A general variational algorithm to calculate vibrational energy levels of tetraatomic molecules

Hua Gen Yu, James T. Muckerman

Research output: Contribution to journalArticlepeer-review

73 Citations (Scopus)


A general variational method for calculating vibrational energy levels of tetraatomic molecules is presented. The quantum mechanical Hamiltonian of the system is expressed in a set of coordinates defined by three orthogonalized vectors in the body-fixed frame without any dynamical approximation. The eigenvalue problem is solved by a Lanczos iterative diagonalization algorithm, which requires the evaluation of the action of the Hamiltonian operator on a vector. The Lanczos recursion is carried out in a mixed grid/basis set, i.e., a direct product discrete variable representation (DVR) for the radial coordinates and a nondirect product finite basis representation (FBR) for the angular coordinates. The action of the potential energy operator on a vector is accomplished via a pseudo-spectral transform method. Six types of orthogonal coordinates are implemented in this algorithm, which is capable of describing most four-atom systems with small and/or large amplitude vibrational motions. Its application to the molecules H2CO, NH3, and HOOH and the van der Waals cluster He2Cl2 is discussed.

Original languageEnglish
Pages (from-to)11-20
Number of pages10
JournalJournal of Molecular Spectroscopy
Issue number1
Publication statusPublished - Jan 1 2002

ASJC Scopus subject areas

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

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