A new method for the exact calculation of vibrational-rotational energy levels of triatomic molecules

Journal Article · Wed Aug 01 00:00:00 EDT 1979 · J. Chem. Phys.; (United States)

DOI:https://doi.org/10.1063/1.438450· OSTI ID:5022606

Shapiro, M ^[1]; Balint-Kurti, G G ^[2]

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1. Weizmann Institute of Science, Rehovot, Israel
2. Bristol, University, Bristol, England

A new method is presented for the calculation of the vibrational-rotational energy levels of a triatomic molecule. The method provides a means of solving Schroedinger's equation for the bound energy levels of a triatomic system as exactly as desired. The relative motion of the atoms is governed by a potential energy surface, which can be of arbitrary form, but must, naturally, be specified. The method utilizes the well developed techniques of molecular scattering theory and is formulated in a body-fixed reference frame. The bound state energies appear in the theory as first order poles of a specially constructed T-matrix element. Because the analytic behavior of these poles, as a function of the energy, is well defined, the exact bound state energies are easily found. The theory has been applied to the water molecule and results are presented for the lowest five vibrational-rotational energy levels corresponding to zero total angular momentum. These results agree well with previously published values.

• OSTI ID: 5022606
• Journal Information: J. Chem. Phys.; (United States), Vol. 71
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
MOLECULAR MODELS
MOLECULES
ENERGY LEVELS
WATER
DIFFERENTIAL EQUATIONS
NUMERICAL ANALYSIS
POTENTIAL ENERGY
ROTATIONAL STATES
S MATRIX
SCHROEDINGER EQUATION
VIBRATIONAL STATES
WAVE FUNCTIONS
ENERGY
EQUATIONS
EXCITED STATES
FUNCTIONS
HYDROGEN COMPOUNDS
MATHEMATICAL MODELS
MATHEMATICS
MATRICES
OXYGEN COMPOUNDS
PARTIAL DIFFERENTIAL EQUATIONS
WAVE EQUATIONS
640305* - Atomic
Molecular & Chemical Physics- Atomic & Molecular Theory- (-1987)