Diatomic homonuclear molecules do not interact with electromagnetic radiation via electric dipole transitions at all since no vibrational or rotational change of state may induce an electric dipole in the molecule. Although such molecules may interact weakly with electromagnetic radiation in other ways, they are usually effectively considered to be radiatively inactive in terrestrial atmospheres since their weak absorptions are totally dominated by the electric dipole transitions of other molecules. However, the atmospheres of the giant planets are dominated by molecular hydrogen, which is just such a diatomic homonuclear molecule and in certain parts of the spectrum the more familiar electric dipole transitions of other molecules are
V] symmetric stretch V': bend (A) v; bend (B) v.i asymmetric stretch
themselves so negligible that it becomes necessary to consider in detail how such diatomic molecules may interact with electromagnetic radiation.
We saw earlier that, in addition to electric dipole transitions, there are a number of less likely, and thus weaker interaction mechanisms between a molecule and radiation. While diatomic homonuclear molecules may not engage in electric dipole transitions they may engage in the much weaker electric quadrupole transitions. For these electric quadrupole transitions the selection rules are AJ = ±2, and Av = ±1, ±2, ±3,... Thus, instead of having a P, Q, R-branch structure, electric quadrupole transitions are confined to the O-branch (AJ = —2) and S-branch (AJ = 2).
In the atmospheres of the giant planets, which are dominated by molecular hydrogen, the electric quadrupole lines of H2 are detectable for a number of vibra-tional transitions. In the far-infrared the S(0) and S(1) lines associated with the (1-0) vibrational transitions are observable where "S" means AJ = 2, and the numbers refer to the total angular momentum J of the lower state. At visible wavelengths the S(0) and S(1) transitions associated with the (3-0) and (4-0) vibrational energy changes are observable. Electric quadrupole transitions have similar linewidths to the electric dipole transitions described later in Section 6.3.7.
In the gas phase, collisions and interactions with other molecules can lead to transitory dipole moments being induced on homonuclear diatomic molecules that may then interact with IR light. Although the absorption is weak, the abundance of H2 in the giant planet atmospheres is so high that the far-IR spectra of the giant planets is dominated by H2-H2 and H2-He pressure-induced or collision-induced absorptions (CIA). Another example is N2-N2 and N2-CH4 collision-induced absorption in Titan's atmosphere. These pressure-induced dipole absorptions have AJ = 2 (i.e., S(0), S(1)) and are thus found near the wavelengths of the pure H2 quadrupole lines just discussed. However, temporarily induced dipoles have very short lifetimes, and thus from Heisenberg's uncertainty principle their line shape is extremely broad. For more detailed information on H2-H2 and H2-He collision-induced absorptions, the reader is referred to Birnbaum et al. (1996).
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