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The vibrational energy levels of a diatomic molecule like HCl can be described using the anharmonic oscillator model, which corrects the harmonic oscillator approximation by accounting for bond anharmonicity. The energy levels are given by [ E_v = h\nu_e \left(v + \frac{1}{2}\right) - h\nu_e x_e \left(v + \frac{1}{2}\right)^2 ] where (v = 0, 1, 2, \dots) is the vibrational quantum number, (\nu_e) is __________ __________ ________ _____ ___ _______ ___ ____ ______.
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