Complete wave equation of a nonlinear polyatomic molecule

Journal Article · Tue Sep 01 04:00:00 EDT 1981 · J. Chem. Phys.; (United States)

DOI:https://doi.org/10.1063/1.442293· OSTI ID:6293493

Webster, F; Huang, M; Wolfsberg, M

The complete nonrelativistic wave equation of a nonlinear polyatomic molecule, including the electronic motion, is formulated in molecule fixed coordinates. The method is an extension of that used by Pickett to obtain the molecular rotation--vibration wave equation. Both the choice of rotating axes and the choice of internal vibrational coordinates are general. The transformation to quantum mechanics is undertaken after the rotating axes and the vibrational coordinates have been introduced. The total molecular wave function, after elimination of the motion of the center of mass, is written as a sum of products of eignfunctions of the rigid symmetric top Hamiltonian and of functions of the internal molecular (vibrational and electronic) coordinates. The coupled wave equations for the functions of internal coordinates are derived. Application is made to a nonlinear triatomic molecule and the result is compared with a previous formulation. By contrast to the present formulation, the transformation to quantum mechanics in the previous formulation had been carried out for the Hamiltonian in space fixed coordinates.

• Research Organization: Department of Chemistry, University of California, Irvine, California 92717
• OSTI ID: 6293493
• Journal Information: J. Chem. Phys.; (United States), Journal Name: J. Chem. Phys.; (United States) Vol. 75:5; ISSN JCPSA
• Country of Publication: United States
• Language: English

Related Subjects

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Molecular & Chemical Physics-- Atomic & Molecular Theory-- (-1987)
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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
COORDINATES
DIFFERENTIAL EQUATIONS
ELECTRON MOBILITY
EQUATIONS
HAMILTONIANS
MATHEMATICAL OPERATORS
MECHANICS
MOBILITY
MOLECULES
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MOBILITY
POLYATOMIC MOLECULES
QUANTUM MECHANICS
QUANTUM OPERATORS
TRANSFORMATIONS
WAVE EQUATIONS