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Unformatted text preview: th having a s
g
the same sign angular momentum, 1Δ g , or opposite sign, 1 Σ + . g
A molecule may have multiple states corresponding to the same term; these are distinguished with letters in front of the term symbol. The ground state always €
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receives the letter X: e.g. the ground state of O2 would be written X 3Σ− . The letters g
denoting excited states are historical and follow no discernable pattern. B. ROTATION €
We now consider the motion of the nuclei in the Born
Oppenheimer approximation, i.e. treating the electronic wave function as evolving adiabatically as the nuclei move. The rotation of a closed
shell molecule involves the motion of the nuclei as well as the electrons. It can be treated to a first approximation like a rigid rotator (we will investigate vibration later). This gives rise to angular momentum quantum numbers J and M and an angular wave function ~YJM(θ,φ), with energy levels 2J(J+1)/2I, where I is the moment of inertia. The parity is (−1)J, in accordance with the parity of the spherical harmonic. Typical moments of inertia are ~few × 104 mea02, leading to energy levels in the microwave (~1011 Hz) for small J. A molecule with nonzero Λ or S exhibits more complicated behavior. In this case, one must distinguish several types of angular momentum: Angular momentum Total Projection on internuclear axis Electron orbital L Λ Electron spin S Σ Total orbital N Λ (No nuclear orbital a.m.  axis) Total orbital + spin J Ω We have already described the quantum numbers Λ and S. We also know that J is conserved. In order to identify the energy levels, however, we must consider two limiting cases: Hund Case (a): The precession of the electron spin around th...
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This document was uploaded on 03/08/2014 for the course AY 102 at Caltech.
 Winter '08
 Sargent,A

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