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.
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