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Internet Electronic Journal of Molecular Design - IEJMD, ISSN 1538-6414, CODEN IEJMAT
ABSTRACT - Internet Electron. J. Mol. Des. May 2004, Volume 3, Number 5, 271-286

A New Perturbation-Theoretic Approach to the Rovibronic Transition Matrix Elements of Diatomics
Mahmoud Korek and Bassam Hamdoun
Internet Electron. J. Mol. Des. 2004, 3, 271-286

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Abstract:
The line intensities of the transitions vJ ↔ v'J' where |J' - J| ≥ 1 are proportional to the matrix elements RvJv'J' = <ΨvJ|f(r)|Ψv'J'>. In the conventional Rayleigh-Schrödinger perturbation theory these matrix elements are expressed in terms of the transition number m=(λ'-λ)/2 where λ = J(J+1) and λ' = J'(J'+1). In order to reduce the complexity in the calculation of these matrix elements for the high order corrections in the perturbation theory (because of the transition from λ and λ'- representations of ΨvJ and Ψv'J' to the m-representation of RvJv'J') the eigenvalue and the eigenfunction of the two states (vJ) and (v'J') are expanded in terms of one variable m as Evm = ΣEv(i)mi, Ψvm = Σφv(i)mi, Ev'm = ΣEv'(i)mi and Ψv'm = Σφv'(i)mi where the coefficients Ev(i), φv(i), Ev'(i) and φv'(i) are given by analytical expressions by using the canonical functions method. This new approach in the perturbation theory is valid for any transition (infrared, Raman, …), any operator f(r) and any potential function either empirical or of the RKR-type. The numerical application, in Raman transitions, to the ground state of the molecule CO shows that the values of Evm and Ψvm calculated by using the present formulation (up to sixth order) are in good agreement with those computed by a numerical direct method.

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