To go beyond the simple harmonic oscillator model, here we test our proposed method on a series of anharmonic model systems. Note that conventional MD has only one PES and cannot construct vibrational excited state surface. Therefore, we can only obtain the same frequency for both 0 → 1 fundamental transition and other n → n + 1 excited states transitions. In contrast, in the CMES-MD framework, we can use MD on the ground state CMES to obtain 0 → 1 transition frequencies, use MD on the first excited CMES to obtain 1 → 2 transitions, and so forth. We note that although MD results depend on the simulation temperature, this temperature effect is relatively small in the temperature range that most chemists care about. Therefore, in this paper, we will simply focus on the zero-temperature limit and only use their second-order derivative information to approximate the vibrational transition energies. We will provide results for the Morse potential, the quartic potential, and the double-well potential, all of which are important model systems for modeling practical chemical problems. The quantum results are used as reference, which are obtained either analytically or numerically with a dense grid.