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A general treatment of vibration‐rotation coordinates for triatomic molecules
Author(s) -
Sutcliffe Brian T.,
Tennyson Jonathan
Publication year - 1991
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560390208
Subject(s) - triatomic molecule , hamiltonian (control theory) , classical mechanics , coordinate system , gravitational singularity , physics , hamiltonian system , generalized coordinates , elliptic coordinate system , scattering , mathematical physics , quantum mechanics , molecule , spherical coordinate system , geometry , mathematics , mathematical optimization
An exact, within the Born–Oppenheimer approximation, body‐fixed Hamiltonian for the nuclear motions of a triatomic system is presented. This Hamiltonian is expressed in terms of two arbitrarily defined internal distances and the angle between them. The body‐fixed axis system is related to these coordinates in a general fashion. Problems with singularities and the domain of the Hamiltonian are discussed using specific examples of axis embedding. A number of commonly used coordinate systems including Jacobi, bond‐length‐bond‐angle, and Radau coordinates are special cases of this Hamiltonian. Sample calculations on the H 2 S molecule are presented using all these and other coordinate systems. The possibility of using this Hamiltonian for reactive scattering calculations is also discussed.