### 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 H_{2}CO, NH_{3}, and HOOH and the van der Waals cluster He_{2}Cl_{2} is discussed.

Original language | English |
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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.

Research output: Contribution to journal › Article

*Journal of Molecular Spectroscopy*, vol. 214, no. 1, pp. 11-20. https://doi.org/10.1006/jmsp.2002.8569

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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.

UR - http://www.scopus.com/inward/record.url?scp=0036069151&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036069151&partnerID=8YFLogxK

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 -