### 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 - Jan 1 2002 |

### ASJC Scopus subject areas

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