  Recent advances in the high sensitivity spectroscopy have made it possible,
in combination with accurate theoretical predictions, to observe for the first
time very weak electric quadrupole transitions in a polar polyatomic molecule
of water. Here we present accurate theoretical predictions of the complete
quadrupole ro-vibrational spectrum of a non-polar molecule CO$_2$, important in
atmospheric and astrophysical applications. Our predictions are validated by
recent cavity enhanced absorption spectroscopy measurements and are used to
assign few weak features in the recent ExoMars ACS MIR spectroscopic
observations of the martian atmosphere. Predicted quadrupole transitions appear
in some of the mid-infrared CO$_2$ and water vapor transparency regions, making
them important for detection and characterization of the minor absorbers in
water- and CO$_2$-rich environments, such as present in the atmospheres of
Earth, Venus and Mars.
