Vibrational excitation

Vibrational excitation raises the energy associated with internal nuclear motion in a molecule. It can occur within one electronic state; changing vibrational energy does not necessarily promote an electron. For a diatomic molecule, the simplest coordinate is a change in the separation of its two atomic nuclei.

Near a stable equilibrium bond length, the quantum harmonic oscillator model haswith adjacent spacing $\hslash \omega$. The $v=0$ state already has zero-point energy; vibrational excitation refers to raising the level above that ground state.^[ref] Anharmonicity changes the spacing and becomes important away from the potential minimum.

For a chosen vibrational spacing $\tilde{\nu }=1000\mathrm{c}{\mathrm{m}}^{-1}$, $\Delta E=hc\tilde{\nu }\approx 0.124\mathrm{eV}$, corresponding to wavelength $10\mu \mathrm{m}$. In thermal equilibrium, the population ratio of adjacent nondegenerate harmonic levels isAt $300\mathrm{K}$ it is about $0.0083$. This stipulated example illustrates why a high-frequency mode can be mostly in its vibrational ground state even though the sample is not at zero temperature.

A motivating apparatus is the University of Florida HCl and DCl FTIR experiment: an infrared transmission spectrum is measured using Fourier transform spectroscopy and a matched background. The observed rotational-vibrational bands constrain stretching energies and isotope dependence.^[ref] Whether a vibrational transition absorbs infrared light also depends on vibrational infrared activity, not just its energy spacing.

A short excitation pulse can create a nonequilibrium vibrational population. Subsequent vibrational relaxation redistributes that energy through other modes or the surroundings. Measuring a population change, a transient spectrum and energy deposited as heat are related but distinct experimental observations.