Rotational spectroscopy provides very accurate means of determining bond lengths in gas-phase molecules, because of the precision with which frequencies can be determined. Molecules only slightly more complicated require experiments to be done with isotopically labelled species. However, when I tried to do this calculation in class, I was unable to get reasonable answers. Apparently, I had made an error in reformulating the equations given in Atkins. Now the calculation is shown on the Mathcad pages, using equations directly in the form Atkins provides.
Group theory can easily tell which are infrared or Raman-active.