Expected Microwave Absorption Coefficients of Water and Related Molecules

The microwave absorption of water and related molecules is of interest for practical and theoretical reasons. Since these molecules are asymmetric rotors, the occurrence of lines is a matter of chance and the calculation of their intensities is rather difficult. The line strengths of all transitions of ${\mathrm{H}}_2$O up to $J=6\mathrm{}$ have been calculated exactly and the transformation matrices are given explicitly. Van Vleck has shown that the observed intensity of the $6_{16}$-$6_{23}$ radar line can be accounted for theoretically, by use of the calculated value of the line strength. The microwave absorption of HDO and ${\mathrm{D}}_2$O is also predicted with the use of the dipole moment and half-width of ${\mathrm{H}}_2$O which are presumably the same in the isotopic molecules. In addition, it is pointed out that HDO has components along both the least and intermediate axes of inertia. The selection rules for the former are quite different from the latter (obtaining in ${\mathrm{H}}_2$O, ${\mathrm{D}}_2$O), and give rise to transitions between levels which are components of doubly degenerate levels in the limiting case of the symmetric rotor. This splitting varies in magnitude so that lines of HDO should appear throughout the radio and microwave regions. One of these lines has been discovered at 0.7441 ${\mathrm{cm}}^{-1\mathrm{}}$, and is interpreted as the $5_{33}$-$5_{32}$ transition predicted at 0.79 ${\mathrm{cm}}^{-1\mathrm{}}$. The calculated absorption coefficient is 26×${10}^{-6\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$ which is in excellent agreement with the observed value of 30×${10}^{-6\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$. The microwave absorption of ${\mathrm{H}}_2$S and ${\mathrm{H}}_2$Se is discussed, and it is pointed out that HDS and HDSe will also have many lines in this region.