Anharmonicity and overtones

As can be seen from the graphic representation, the energy levels in the anharmonic oscillator are not equal. The levels are slightly closer as the energy increases. This phenomenon can be seen in the equation 

Depending on structural or ambient conditions, the numerical value may range from 1785 to 1925 nm for this one example. However, it would generally appear at 3500/2 plus a relatively small shift to a longer wavelength. 

For example, a fundamental carbonyl stretching vibration at 1750 cm or 5714 nm would have a first overtone at approximately 3000 nm, a weaker second overtone at 2100 nm, and a third very weak overtone at 1650 nm. The fourth overtone, at about 1370 nm, would be so weak as to be analytically useless. (These values are based on a 5% anharmonicity constant.) 

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