A variational method for the calculation of vibrational energy levels of triatomic molecules using a Hamiltonian in hyperspherical coordinates
- 15 December 1990
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 93 (12) , 8902-8914
- https://doi.org/10.1063/1.459229
Abstract
A full variational procedure is presented which is particularly suited to the calculation of vibrational (J=0) energy levels of triatomic potentials with large amplitude motions and also allows for high permutational symmetries. Starting from simple basis functions reflecting the structure of the kinetic energy operator, an optimized basis set is derived by a step‐wise contraction scheme. The method is applied to H+3 and Na+3 (D3h) and to model potentials for H2O+ (C2v) and HLiH− (D∞h). The results for H+3 are shown to be superior to all previous calculations, in particular for those energy levels that lie above 20 000 cm−1. A new ab initio potential is presented for Na+3, for which converged energy levels are calculated up to 3500 cm−1. For H2O+ and HLiH−, the calculated energy levels agree with those obtained from a variational procedure in internal valence coordinates.Keywords
This publication has 29 references indexed in Scilit:
- Highly excited rovibrational states using a discrete variable representation: The H+3 molecular ionThe Journal of Chemical Physics, 1989
- Benchmark calculations of first principles rotational and ro-vibrational line strenghtsComputer Physics Communications, 1989
- Efficient pointwise representations for vibrational wave functions: Eigenfunctions of H+3The Journal of Chemical Physics, 1989
- A variational method for the determination of the vibrational (J = 0) energy levels of acetylene, using a Hamiltonian in internal coordinatesComputer Physics Communications, 1988
- The calculation of the ground state energy of weakly bound van der waals trimers using the method of hyperspherical harmonics I. The Born—Oppenheimer and adiabatic approximationsChemical Physics, 1985
- A variational description of the vibrational states of triatomic molecules using numerical wavefunctionsMolecular Physics, 1984
- A variational method for the calculation of ro-vibronic levels of any orbitally degenerate (Renner-Teller) triatomic moleculeMolecular Physics, 1984
- Variational Approaches to Vibration‐Rotation Spectroscopy for Polyatomic MoleculesAdvances in Chemical Physics, 1978
- A Symmetric Representation for Three-Body Problems. I. Motion in a PlaneJournal of Mathematical Physics, 1962
- The electronic absorption spectra of NH2and ND2Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1959