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lecture notes6

We may consider three types of transitions rotational

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Unformatted text preview: s for bonds between two metal atoms. In diatomic molecules, vibration has no effect on the symmetry properties, etc. The above discussion presumes a harmonic potential for vibrations. In reality, the molecule has a dissociation energy, and as it is approached the vibration becomes anharmonic, with energy levels spaced closer than ω. A similar result occurs for rotation. In particular, the finite dissociation energy means that a molecule has a finite number of rotation ­vibration levels in any electronic state. D. NUCLEAR SPIN Nuclear spin has a tiny effect on molecular energy levels and may lead to hyperfine spitting (e.g. in the ground state of 16O1H). But it can have a much more profound effect on homonuclear molecules because nuclei obey wave function antisymmetrization or symmetrization depending on their spin. As an extreme example, consider a closed ­shell homonuclear molecule such as H2. In this case, swapping the spatial positions of the nuclei introduces a (−1)J into the wave function. Correspondingly the proton spins for H2 must be symmetric (I=1) for odd J and antisymmetric (I=0) for even J. Thus there are two different types of H2: para H2 (even J) and ortho H2 (odd J). They can only interconvert by swapping protons or flipping a nuclear spin. Moreover, they have different statistical weights: ortho ­H2 has three nuclear spin states while para ­H2 has only one. An even more extreme realization of the same facts occurs for molecules such as 4He2+ (ground term: 2 Σ + ; Case b), where the nuclei have spin 0. In this case, g wave function symmetrization implies the spatial wave function must be symmetric. Thus the odd ­N levels of the ground electronic state of 4He2+ simply do not exist! € 3. Radiatio...
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