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.

• some vibrations, that introduce a time-dependent dipole moment
• high rotational speeds that cause some distortion of an originally spherical symmetry. A (weak) dipole moment emerges.

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 = µr2.

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) + DJ2(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(3J2+ 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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