The percentage error is about 2% and slightly larger than that for the 0 → 1 fundamental transition. In contrast, the harmonic approximation based on the PES gives the same vibrational frequencies as the fundamental transitions and deviate more severely from the quantum reference. The story for 2 → 3 transitions (panel c) is highly similar: although the harmonic approximation based on CMES gives an larger percentage error (around 5%) than in the 0 → 1 and 1 → 2 cases, it captures the decreasing trend of the energy gap and significantly outperforms the harmonic approximation results based on the original PES.