In existing literatures , there have been Morse parameters sets fitted for these H-X bonds based on diatomic results, although we note that the bond strengths, bond lengths, and vibrational frequencies can vary with chemical environments and so do these parameters sets. We notice that in the existing Morse potential parameters sets, different H-X diatomic molecules tend to have similar χ e and x e values, but their ω e can vary more. Therefore, we fix the value of χ e to be 0.023 and the value of x e to be 1.0Å, and only scan the value of ω e in the range from 2000 cm -1 to 4000 cm -1 to model the H-X vibrations in different chemical environments. The reduced mass is approximated to be the mass of a hydrogen atom. We limit our discussions to 0 → 1, 1 → 2, and 2 → 3 transitions since the lowest few states are more important. Therefore, we construct the ground, the first excited, and the second excited CMESs using the Eq. 3 and Eq. 9. Since we are focusing on the zerotemperature limit, we numerically obtain the second-order derivatives around the minima of each CMES to approximate the vibrational frequencies with harmonic approximation.