Correction terms are used in order to make the approximation more accurate (makes a better approximation).
Expanding on the Rigid-Rotor approximation:
Expanding on the Harmonic Oscillator approximation:
The anharmonic correction brings the harmonic curve (pictured to the left) closer to the morse curve, which is why the accuracy increases.
The alpha, beta, and gamma correction terms further inceases the accuracy of the whole energy calculation.
Experimentalists find molecular constants through spectroscopy.