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 language | English |
|---|---|
| Pages (from-to) | 11-20 |
| Number of pages | 10 |
| Journal | Journal of Molecular Spectroscopy |
| Volume | 214 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2002 |
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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 journal › Article
}
TY - JOUR
T1 - A general variational algorithm to calculate vibrational energy levels of tetraatomic molecules
AU - Yu, Hua Gen
AU - Muckerman, James
PY - 2002
Y1 - 2002
N2 - 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.
AB - 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.
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U2 - 10.1006/jmsp.2002.8569
DO - 10.1006/jmsp.2002.8569
M3 - Article
VL - 214
SP - 11
EP - 20
JO - Journal of Molecular Spectroscopy
JF - Journal of Molecular Spectroscopy
SN - 0022-2852
IS - 1
ER -