  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 CO2 radiative 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 mode $\nu_1$ and bending mode $\nu_2$. 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 CO2 radiative forcing on Earth,
our results may have implications for understanding radiation and climate on
other planets.
