Fig. 2. Energies and displacement vectors for the translations, rotations and vibrations of the CO₂ molecule, obtained by diagonalising the dynamical matrix D defined in eqn (1), from DFT calculations (see ESI,† for details). The energies are obtained by taking the square root of the eigenvalues ω² and multiplying by the reduced Planck constant ħ, and the displacements are obtained from the eigenvectors W using eqn (3) with a unit amplitude Q = 1.