Selection rules for pure rotational spectra
A molecule must have a transitional dipole moment that is in resonance with an electromagnetic
field for rotational spectroscopy to be used. Polar molecules have a dipole moment. A transitional dipole
moment not equal to zero is possible.
z. B. HCl |
symmetric stretch mode | ||
bending mode | ||
antisymmetric stretch mode |
With high rotational speed, an originally spherical symmetry of a molecule is distorted. |
In contrast, no rotational spectra are displayed by homonuclear diatomics; the same is true for spherical tops. Nevertheless, certain states of a such molecules allow unexpected interactions with the electromagnetic field; i.e.
ΔJ = ± 1 | ΔM_{J} = 0, ± 1 |
For a symmetric top, an existing dipole moment is always parallel to the
molecule's axis. Thus, with respect to this axis, no changes of the rotational
state occur.
ΔK = 0 |
For transitions J + 1 ← J, an equation of the following kind rules the wavenumbers of absorbances to occur.
ν = B(J + 1)(J + 2) - BJ(J +
1)
ν = 2B(J + 1)
with J = 0, 1, 2...
The distance between two lines is constant. Δν = ν(J) −ν(J−1) = 2B. We are then able to determine the bond's length r as I = µr^{2}. |
For high rotational speeds and centrifugal forces that stretch a molecule, a more accurate equation for ν is
ν = B(J+1)(J+2) - D(J+1)^{2}(J+2)^{2} - BJ(J+1) + DJ^{2}(J+1)^{2} |
ν = 2B(J + 1) - 4D(J + 1)^{3} |
i.e., the distance between the lines
Δν = ν(J) - ν (J − 1) |
Δν = 2B - 4D(3J^{2}+ 9J + 7) |
decreases with J. Thus, the centrifugal constant D for diatomic molecules is in connection with the wavenumber ν_{S} that corresponds with the molecule's vibration.
Conversely, D provides information on ν_{s}. Of course, the intensity
of an absorption is dependent on the transitional dipole moment and on the
occupancy of the initial and the final state.
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