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Ideas of Quantum Chemistry P28

Ideas of Quantum Chemistry P28 shows how quantum mechanics is applied to chemistry to give it a theoretical foundation. The structure of the book (a TREE-form) emphasizes the logical relationships between various topics, facts and methods. It shows the reader which parts of the text are needed for understanding specific aspects of the subject matter. Interspersed throughout the text are short biographies of key scientists and their contributions to the development of the field. | 236 6. Separation of Electronic and Nuclear Motions for the harmonic oscillator. The corresponding wave functions also resemble those for the harmonic oscillator. Higher-energy vibrational levels are getting closer and closer as for the Morse potential. This is a consequence of the anharmonicity of the potential - we are just approaching the dissociation limit where the Uk R curves differ qualitatively from the harmonic potential. 6.6.2 ROTATIONAL STRUCTURE What would happen if we took J 1 instead of J 0 This corresponds to the potential energy curves VkJ R Uk R J J 1 h2 2 R2 in our case Vki R Uk R 1 1 1 h2 2 R2 Uk R h2 pR2 for k 0 1 2. The new curves therefore represent the old curves plus the term h2 R2 which is the same for all the curves. This corresponds to a small modification of the curves for large R and a larger modification for small R. The potential energy curves just go up a little bit on the left.19 Of course this is why the solution of eq. 6.24 for these new curves will be similar to that which we had before but this tiny shift upwards will result in a tiny shift upwards of all the computed vibrational levels. Therefore the levels Ekv1 for v 0 1 2 . will be a little higher than the corresponding Ekv0 for v 0 1 2 . this pertains to k 0 2 there will be no vibrational states for rotational k 1 . This means that each vibrational level v will have its own rotational structure structure corresponding to J 0 1 2 . Increasing J means that the potential energy curve becomes shallower.20 It may happen that after a high-energy rotational excitation to a large J the potential energy curve will be so shallow that no vibrational energy level will be possible. This means that the molecule will undergo dissociation due to the excessive centrifugal force. At some lower J s the molecule may accommodate all or part of the vibrational levels that exist for J 0. Example Let us try this. An ideal experimental range for us would be a molecule with a Morse-like potential .