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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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