Fig. 3. Potential energy as a function of amplitude E(Q) for the two stretch modes in CO₂ determined from eqn (2): (a) the symmetric stretch with ħω = 1315 cm⁻¹, and (b) the antisymmetric stretch with ħω = 2357 cm⁻¹. The E(Q) for both modes are shown over a range of Q = ±0.5, and the energies are given in units of ħω. On each plot, the black lines show the harmonic energy levels E_v determined from eqn (4). Note that as the energies are given in units of ħω, the implication is that modes with small ħω will, in general, have larger displacements |Q| for a given vibrational quantum state than will modes with large ħω.