What is it about?
(Uploaded 2018-04-18). The present paper should be seen in continuation of our previous "Vibronic Energy Levels of Linear Triatomic Molecule in a Degenerate Electronic State: a Unified Treatment of the Renner-Teller Effect." Adv. Chem. Phys. 1982, 52, p117-180 DOI: 10.1002/9780470142769.ch2 There we used more modern terminology to resurrect Renner's original approach. Allowing only for the bending vibration, Renner assumed the two Born-Oppenheimer (BO-) potentials to be harmonic and fairly close to each other. We did, however, emphasize that his approach is so that it dictates how to obtain ab initio expressions for the parameters in an effective Hamiltonian which also allow for the remaining degrees of freedom. Among these we only considered the important spin-orbit interaction, which affects the energy levels as much as the Renner-Teller effect itself. We did, however, demonstrate the efficiency of our more modern approach by showing that only a modest effort is necessary to repeat Renner's original second order perturbation calculation and continue it through the order four. Now we furthermore allow for stretching vibrations and include the effects cubic and quartic anharmonicities also in the two potentials for stretching.
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Why is it important?
To prepare for inclusion of cubic and quartic anharmonicities in the two Born-Oppenheimer potentials we first collect the familiar results for a molecule with only one. And we briefly recapitalize Renner's approach to an effective Hamiltonian as resurrected by us. One reason that the results for the so-called vibronic energy levels are rather more complicate is the strong influence of spin-orbit interaction due to the last electron. We do, however, believe that all parameters found by us are necessary if we want a fit to a vibronic spectrum like the more familiar fit to a vibrational spectrum in case of a non-degenerate electronic state.
Perspectives
The vibration-rotation Hamiltonian for a linear tri-atomic molecule in non-degenerate electronic state has been known for a very long time. And so have the energy levels determined by perturbation theory. Our ultimate aim of our resurrection of Renner's original work has been to reach the same level of understanding also in case of a twice degenerate electronic state. In the present work we have only reached the formulas for the vibronic levels, i.e, those which correspond to the levels of the vibration Hamiltonian. There is still a way to go before we also have formulas for the rovibronic levels where also end-over-end rotation is included.
Dr Flemming Jørgensen
Nygårdsvej 43, 4700 Næstved http://www.naestved-gym.dk/
Read the Original
This page is a summary of: Anharmonic corrections for linear triatomic molecules subject to the Rennet-Teller effect, Molecular Physics, December 1982, Taylor & Francis,
DOI: 10.1080/00268978200100782.
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