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

Hua Gen Yu, James Muckerman

Research output: Contribution to journalArticle

67 Citations (Scopus)

Abstract

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
Volume214
Issue number1
DOIs
Publication statusPublished - 2002

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Electron energy levels
Hamiltonians
energy levels
Molecules
molecules
Potential energy
operators
Mathematical operators
products
Atoms
eigenvalues
potential energy
grids
evaluation
approximation
atoms

ASJC Scopus subject areas

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

Cite this

A general variational algorithm to calculate vibrational energy levels of tetraatomic molecules. / Yu, Hua Gen; Muckerman, James.

In: Journal of Molecular Spectroscopy, Vol. 214, No. 1, 2002, p. 11-20.

Research output: Contribution to journalArticle

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