Harmonic-oscillator function, hydrogen bonds bond vibrations

Tbus the anharmonicity in the vibration is captured by the coefficient x, which adopts values typically less than 1 % of ft>e for bond stretches, but may be up to 5% for those involving hydrogen. It can be shown that any function capable of representing the variation of potential energy with displacement will lead to energy levels given by a power series in (v + 1/2), so the simple harmonic and Morse oscillators are particular cases of this general anharmonic oscillator, with the power series truncated after the first and second terms, respectively. 

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