Figure shows the ground state, first excited state, and second excited state CMESs for ω e = 3500cm -1 . In addition to the relative energy difference, we also note that their energy minima correspond to different nuclear positions, which essentially indicates that the bond length will grow as the system is excited. Furthermore, these energy curves do not differ by a universal shift any more and thus will give different vibrational frequencies. Figure shows the CMES results for estimating 0 → 1, 1 → 2, and 2 → 3 transition frequencies. For the 0 → 1 fundamental frequencies (panel a), CMES harmonic approximation results excellently agree with the quantum reference results, with a percentage error of about 1%, whereas using the PES, the error is about 5%. These results are consistent with results from the previous paper by two of us, where we found CMES-MD can significantly outperform conventional MD in predicting fundamental frequencies. For 1 → 2 transitions (panel b), the excited state CMES gives lower vibrational frequencies than those obtained from the ground state CMES. This trend is in great agreement with the quantum reference results, where 1 → 2 energy gap is smaller than the 0 → 1 energy gap due to anharmonicity.