Vibrational spectrum

A vibrational spectrum resolves transitions associated with molecular vibrations. In the harmonic approximation, a normal mode of angular frequency $\omega$ has levelsFor 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.