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Although the scientific principles of anthropogenic climate change are well-established, existing calculations of the warming effect of carbon dioxide rely on spectral absorption databases, which obscures the physical foundations of the climate problem. Here, we show how CO₂radiative forcing can be expressed via a first-principles description of the molecule’s key vibrational-rotational transitions. Our analysis elucidates the dependence of carbon dioxide’s effectiveness as a greenhouse gas on the Fermi resonance between the symmetric stretch modeν₁and bending modeν₂. It is remarkable that an apparently accidental quantum resonance in an otherwise ordinary three-atom molecule has had such a large impact on our planet’s climate over geologic time, and will also help determine its future warming due to human activity. In addition to providing a simple explanation of CO₂radiative forcing on Earth, our results may have implications for understanding radiation and climate on other planets.