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Analytic expression of the rotation‐vibration eigenfunction of any electronic potential of a diatomic molecule
Author(s) -
Kobeissi Hafez,
Dagher Mounzer
Publication year - 2009
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.560160818
Subject(s) - diatomic molecule , eigenfunction , physics , boundary value problem , wave function , mathematics , mathematical analysis , quantum mechanics , molecule , eigenvalues and eigenvectors
Any electronic potential can be represented (or approximated) by a numerical potential defined by the coordinates of the turning points of the rotationless potential and by suitable polynomial interpolations (and extrapolations). We reduce the determination of the wavefunction ψ vj of such a potential to that of the canonical functions α vj and β vj related by ψ vj ( r ) = ψ vj ( a )α vj ( r ) + ψ vj ( a ) × β vj (r) , with the initial values α vj (a) = 1, α vj (a) = 0, β vj (a) = 0, β vj (a) = 1, and the boundary conditionsWe give the exact analytic expressions of α vj (r) and β vj (r); thus the values of ψ vj (a) and ψ vj (a) are deduced from those of the canonical functions by using the boundary conditions. The numerical applications show that, at any point, the value obtained by our analytic expression is the limit of that computed by a numerical method when the numerical error approaches zero.