A variational localized representation calculation of the vibrational levels of the water molecule up to 27 000 cm-1

Zlatko Bacic, D. Watt, J. C. Light

Research output: Contribution to journalArticle

Abstract

We have calculated variationally highly excited vibrational (J = 0) levels of the water molecule up to ∼ 27 000 cm-1 (relative to the minimum of the potential surface), for a global Sorbie-Murrell-type potential surface. The calculation has been performed in Radau coordinates, using the recently developed DVR-DGB variational approach [Z. Bačić and J. C. Light, J. Chem. Phys. 85, 4594 (1986); 86, 3065 (1987)]. 110 symmetric and 77 antisymmetric vibrational levels have been determined accurately, requiring diagonalization of relatively small Hamiltonian matrices of dimension ∼600. Many of the calculated levels correspond to large amplitude bending vibrations. Nearest neighbor level spacing statistics for the calculated levels above 18 000-20 000 cm-1 conform closely to a Wigner distribution, suggesting classically chaotic behavior in this energy range. Convergence rates of these variational calculations for H2O are comparable to those seen earlier for LiCN/LiNC and HCN/HNC. The DVR-based vibrationally adiabatic approach introduced by Light and Bačić [J. Chem. Phys. 87, 4008 (1987)] has also been tested here. Perturbative inclusion of the nonadiabatic corrections has allowed reliable identification of vibrational (J = 0) levels of H 2O up to 18 000-20 000 cm-1. With this model potential energy surface, reasonable agreement (∼1%) is obtained with experimentally known vibrational states to ∼20 000 cm-1.

Original languageEnglish (US)
Pages (from-to)947-955
Number of pages9
JournalThe Journal of chemical physics
Volume89
Issue number2
StatePublished - 1988

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Hamiltonians
Potential energy surfaces
Molecules
Water
water
molecules
Statistics
bending vibration
vibrational states
potential energy
spacing
statistics
inclusions
energy

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

A variational localized representation calculation of the vibrational levels of the water molecule up to 27 000 cm-1 . / Bacic, Zlatko; Watt, D.; Light, J. C.

In: The Journal of chemical physics, Vol. 89, No. 2, 1988, p. 947-955.

Research output: Contribution to journalArticle

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abstract = "We have calculated variationally highly excited vibrational (J = 0) levels of the water molecule up to ∼ 27 000 cm-1 (relative to the minimum of the potential surface), for a global Sorbie-Murrell-type potential surface. The calculation has been performed in Radau coordinates, using the recently developed DVR-DGB variational approach [Z. Bačić and J. C. Light, J. Chem. Phys. 85, 4594 (1986); 86, 3065 (1987)]. 110 symmetric and 77 antisymmetric vibrational levels have been determined accurately, requiring diagonalization of relatively small Hamiltonian matrices of dimension ∼600. Many of the calculated levels correspond to large amplitude bending vibrations. Nearest neighbor level spacing statistics for the calculated levels above 18 000-20 000 cm-1 conform closely to a Wigner distribution, suggesting classically chaotic behavior in this energy range. Convergence rates of these variational calculations for H2O are comparable to those seen earlier for LiCN/LiNC and HCN/HNC. The DVR-based vibrationally adiabatic approach introduced by Light and Bačić [J. Chem. Phys. 87, 4008 (1987)] has also been tested here. Perturbative inclusion of the nonadiabatic corrections has allowed reliable identification of vibrational (J = 0) levels of H 2O up to 18 000-20 000 cm-1. With this model potential energy surface, reasonable agreement (∼1{\%}) is obtained with experimentally known vibrational states to ∼20 000 cm-1.",
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