found in real molecules. However, this equation fails above some value of where is calculated to be zero or negative. Specifically,

: (integer part only).

This failure is due to the finite number of bound levels in the Morse potential, and some maximum that remains bound. For energies above all the possible energy levels are allowed and the equation for is no longer valid.

Below is a good approximation for the true vibrational structure in non-rotating diatomic molecules. In fact, the real molecular spectra are

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