Rotation-Vibration Transitions for a Perpendicular Band of a Symmetric Rotor
Rotation-Vibration Transitions for a Perpendicular Band of a Symmetric Rotor
This Demonstration shows the rotation-vibration energy level transitions that correspond to the lines observed in a rotationally resolved infrared spectrum of a perpendicular band of a symmetric rotor. The inherent degeneracy of the vibrational levels (since a symmetric rotor possesses a greater-than-twofold rotation axis) has been neglected in order to maintain clarity in this Demonstration. The transitions occur between nondegenerate vibrational energy levels, and the fundamental vibrational transition is accompanied by rotational transitions in which ←,←.
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K
″
K
′
J
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J
Symmetric rotors, such as benzene and ammonia, are molecules that possess a principal inertial axis with a unique moment of inertia and two other inertial axes with equal moments of inertia. A perpendicular band spectrum of a symmetric rotor results when the change in the dipole moment is perpendicular to the principal axis. The vibrational selection rule is for an absorption spectrum, and for a perpendicular band the rotational selection rules are , , and the allowed transitions are further restricted by .
Δv=+1
ΔK=±1
ΔJ=0,±1
J≥K
Because for a perpendicular band, rotation-vibration transitions can only occur between lower and excited state energy levels with different values of . The series of sub-bands corresponding to are the "positive" sub-bands and the series of sub-bands corresponding to are the "negative" sub-bands. As can be seen from the energy level diagram (top graphic), the transition energies for the lines in the "negative" sub-bands are smaller than the transition energies for the lines in the "positive" sub-bands, resulting in the "negative" sub-bands being shifted to lower wavenumbers in relation to the positions of the "positive" sub-bands in the simulated spectrum (bottom graphic). Each sub-band consists of a branch (), branch (), and branch (). There is no "negative" sub-band, and due to the restriction of , there is an increasing number of lines missing from the beginning of each branch as increases.
ΔK=±1
K
ΔK=+1
ΔK=-1
P
ΔJ=-1
Q
ΔJ=0
R
ΔJ=+1
K=0
J≥K
K
In this Demonstration, you can explore the energy level transitions within the "positive" and "negative" sub-bands of a particular value of , and the axis lower and upper boundary controls let you zoom in on any region of the spectrum. The color coding, transition labels, and transition energies can be found to the left and right within the controls area.
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