= Vibrational spectrum
= Vibrational spectra
{synonym}
A <vibrational spectrum> resolves transitions associated with <molecular vibrations>. In the <harmonic approximation>, a <normal mode> of angular frequency $\omega$ has levels
$$
E_v=\hbar\omega\left(v+\frac12\right),\qquad v=0,1,2,\ldots.
$$
For a diatomic <molecule>, $\omega\simeq\sqrt{k/\mu}$, where $k$ is the effective bond stiffness and $\mu$ the <reduced mass>. Replacing an <atom> by a heavier <isotope> therefore usually lowers the associated vibrational frequency without changing the basic electronic bonding.
<Infrared spectroscopy> detects a vibration when it couples to the <electric dipole moment>; <Raman spectroscopy> instead involves changing <polarizability>. Their selection rules can make complementary modes visible. Anharmonicity shifts frequencies and permits weaker transitions absent from the ideal harmonic picture.
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