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On the diatomic vibration–rotation eigenvalue equation: Highly accurate results for high levels
Author(s) -
Dagher Mounzer,
Kobeissi Hafez
Publication year - 1984
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540050611
Subject(s) - eigenvalues and eigenvectors , eigenfunction , diatomic molecule , vibration , mathematics , dissociation (chemistry) , rotation (mathematics) , mathematical analysis , physics , quantum mechanics , chemistry , geometry , molecule
Accurate vibration–rotation eigenvalues E vJ are sought for very high levels (up to dissociation) of a diatomic potential. The method used is the recent “eigenvalue equation” method [Kobeissi et al., J. Comput. Chem. , 4 , 218 (1983)] which dissociates the determination of the eigenvalue from that of the eigenfunction. A new mathematical formulation for any numerical potential is presented, which reduces the problem to the use of a single recurrent formula. A numerical application to the model potential used by Cashion [ J. Chem. Phys. , 39 , 1872 (1963)], up to v = 23, gives results equal to the exact eigenvalues to approximately 10 −14 cm −1 . Another application to the model potential used by Johnson [ J. Chem. Phys. , 67 , 4086 (1977)], up to v = 60, gives similar results.