Also when making rotational transition a molecule (at least for a moment)
should have dipole which vibrates with frequency of electromagnetic field. The
polar molecule has an alternative dipole moment when rotating and
transition dipole moment can't be equal to 0.
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Example HCl |
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symmetric vibrations |
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bending vibrations | ![]() |
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antisymmetric vibrations | ![]() |
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High rotation changes the initial spherical symmetry and therefore there is a (weak) dipole moment. |
Homonuclear diatomic molecules don't have rotational spectra at all;
the same is true for spherical tops. It's clear one can find vibrating dipole
when molecule is vibrating, that leads to the interaction by using
electromagnetic field. High rotations can be met also in spherical tops which
have dipole moments but these moments are quite weak, however. The conservation
of kinetic moment gives us the following selection rules for a linear molecule:
ΔJ = ± 1 | ΔMJ = 0, ± 1 |
The dipole moment for a symmetric top lays always parallel to molecular axis;
and so it's not possible to change rotation around molecular axis:
ΔK = 0 |
For absorption spectrum, J + 1 ← J one will have:
n [cm-1] = B(J + 1)(J + 2) - BJ(J + 1)
n= 2B(J + 1) where J = 0, 1, 2...
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The separation between two lines is the same, Dn = n(J) -n(J − 1) = 2B. One can obtain the binding length r from it since I = µr2. The centrifugal expansion when having high rotations gives the following:
n = B(J + 1)(J + 2) - D(J + 1)2(J + 2)2 - BJ(J + 1) + DJ2(J + 1)2
n = 2B(J + 1) - 4D(J + 1)3
Dn = 2B - 4D(3J2 + 9J + 7)
The centrifugal constant D is connected with vibration (wavenumber nS of vibration) for diatomic molecules by using the following expression:
The transition intensity depends certainly on the dipole moment transition
value and the amount of occupied electronic states of initial and resultant
states.