Editing Rotational spectroscopy (section)

===Selection rules===
{{Main|selection rules}}

====Microwave and far-infrared spectra====
Transitions between rotational states can be observed in molecules with a permanent [[electric dipole moment]].<ref>{{harvnb|Hollas|1996|p=95}}</ref><ref group=notes>Such transitions are called electric dipole-allowed transitions. Other transitions involving quadrupoles, octupoles, hexadecapoles etc. may also be allowed but the spectral intensity is very much smaller, so these transitions are difficult to observe. Magnetic-dipole-allowed transitions can occur in [[paramagnetic]] molecules such as [[dioxygen]], {{chem|O|2}} and [[nitric oxide]], NO</ref> A consequence of this rule is that no microwave spectrum can be observed for centrosymmetric linear molecules such as {{chem|N|2}} ([[dinitrogen]]) or HCCH ([[ethyne]]), which are non-polar. Tetrahedral molecules such as {{chem|CH|4}} ([[methane]]), which have both a zero dipole moment and isotropic polarizability, would not have a pure rotation spectrum but for the effect of centrifugal distortion; when the molecule rotates about a 3-fold symmetry axis a small dipole moment is created, allowing a weak rotation spectrum to be observed by microwave spectroscopy.<ref>{{harvnb|Hollas|1996|p=104}} shows part of the observed rotational spectrum of [[silane]]</ref>

With symmetric tops, the selection rule for electric-dipole-allowed pure rotation transitions is {{nowrap|Δ''K'' {{=}} 0}}, {{nowrap|Δ''J'' {{=}} ±1}}. Since these transitions are due to absorption (or emission) of a single photon with a spin of one, [[conservation of angular momentum]] implies that the molecular angular momentum can change by at most one unit.<ref>{{harvnb|Atkins|de Paula|2006|p=447}}</ref> Moreover, the quantum number ''K'' is limited to have values between and including +''J'' to -''J''.<ref>{{harvnb|Banwell|McCash|1994|p=49}}</ref>

====Raman spectra====
For [[Raman spectroscopy|Raman spectra]] the molecules undergo transitions in which an ''incident'' photon is absorbed and another ''scattered'' photon is emitted. The general selection rule for such a transition to be allowed is that the molecular [[polarizability]] must be [[anisotropic]], which means that it is not the same in all directions.<ref>{{harvnb|Hollas|1996|p=111}}</ref> Polarizability is a 3-dimensional [[tensor]] that can be represented as an ellipsoid. The polarizability ellipsoid of spherical top molecules is in fact spherical so those molecules show no rotational Raman spectrum. For all other molecules both [[Stokes line|Stokes]] and anti-Stokes lines<ref group=notes>In Raman spectroscopy the photon energies for Stokes and anti-Stokes scattering are respectively less than and greater than the incident photon energy. See the energy-level diagram at [[Raman spectroscopy]].</ref> can be observed and they have similar intensities due to the fact that many rotational states are thermally populated. The selection rule for linear molecules is ΔJ = 0, ±2. The reason for the values ±2 is that the polarizability returns to the same value twice during a rotation.<ref>{{harvnb|Atkins|de Paula|2006|pp=474–5}}</ref> The value ΔJ = 0 does not correspond to a molecular transition but rather to [[Rayleigh scattering]] in which the incident photon merely changes direction.<ref name="Banwell 1994 loc=Section 4.2, p. 105, Pure Rotational Raman Spectra">{{harvnb|Banwell|McCash|1994|loc=Section 4.2, p. 105, ''Pure Rotational Raman Spectra''}}</ref>

The selection rule for symmetric top molecules is
: Δ''K'' = 0
: If ''K'' = 0, then Δ''J'' = ±2
: If ''K'' ≠ 0, then Δ''J'' = 0, ±1, ±2

Transitions with Δ''J'' = +1 are said to belong to the ''R'' series, whereas transitions with {{nowrap|Δ''J'' {{=}} +2}} belong to an ''S'' series.<ref name="Banwell 1994 loc=Section 4.2, p. 105, Pure Rotational Raman Spectra"/> Since Raman transitions involve two photons, it is possible for the molecular angular momentum to change by two units.