A General Variational Algorithm to Calculate Vibrational Energy Levels of Tetraatomic Molecules
✍ Scribed by Hua-Gen Yu; James T. Muckerman
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 192 KB
- Volume
- 214
- Category
- Article
- ISSN
- 0022-2852
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✦ Synopsis
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 bodyfixed 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.