The intrinsic broadening of the spectral line in a molecule or a population of homogeneous molecules is determined by the dephasing rate and Uncertainty Principle. Perhaps the purest example is the broadening of NMR lines. For this reason we will develop the analogy between UV-vivisle spectroscopy and NMR. Homogeneous broadening is instrinsic to the molecule and therefore it is assumed to follow first order kinetics. The exponential decay with relaation time T2 leads to a Lorentzian line shape. The Fourier transform relationship is derived in the presentation. Gaussian line shapes are compared. The versatile Gaussian is introduced in the presentation and application to intertial broadening (homogeneous) and statistical site broadening (inhomogeneous) are both discussed in the presentation.
The NMR analogy
The fact that NMR lines are nearly perfect Lortentzians suggests that NMR is an excellent method to use as a model to understand homogeneous broadening. Inhomogeneous broadening arises due to poor shimming, but if the magnetic is well shimmed then homogeneous broadening dominates line shape. This quite different than the situtaion in solution or frozen glass where inhomogeneous broadening is typically at least an order of magnitude greater than homogeneous broadning. The NMR analogy is also important since NMR provides excellent ways to understand the contributions to T1, population relaxation and T2, dephasing, respectively. Once also clearly see the Fourier transform relationships in the NMR since the data are obtained as a Free Induction Decay (FID), which is a damped sinuisoid. We picture that such a damped sinusoid underlies optical absorption and resonance Raman spectra, but it is not easy to directly observe it. Thus, the NMR methods give us a unique perspective.
Holeburning
Holeburning refers to a low temperature experiment that involves irradiation with a narrow bandwidth laser to cause a depopulation of particular site energy. The results is a dip in the absorbance at the "burn frequency". From a fundamental perspective, the objective of the experiment is to measure the line width of the particular subpopulation that is affected. This is interpreted to be the homogeneous linewidth. At sufficiently low temperature the molecules cannot relax back and the "hole" is observed indefinitely. However, if the temperature is increased the hold fills in because molecules can once again sample all of the possible site energies in the inhomogeneous distribution due their thermal energy.
Doppler broadening
Doppler broadening is observed in gas phase spectra. It is observed because the molecular velocity results in a Doppler shift. This is surprising considering the fact that molecular velocities are a million times less than the speed of light. In fact, Doppler broadening is quite small compared to line broadening in condensed phases.
