# When simulating spectral line broadening, which convolution is preferred?

Many computational chemistry packages permit the calculation of vibrational and electronic spectra. These spectra are obtained as a set of discrete eigenvalues however they are often convolved with some distribution to give a continuous spectrum that is realistic for a finite temperature, rather than a sequence of impulse functions.

The ADF package allows the user to convolve the spectrum with either a Gaussian or Cauchy (Lorentzian) function. My understanding is that the latter affords a more realistic line broadening, however the Gaussian must be there for a reason.

Which spectral broadening scheme is preferred? Why the choice?

• As I recall, it depends on the conditions the gas is under, if collisions are causing changes in the spectra or not. I can't remember which was which though. – Canageek May 10 '12 at 4:41
• What are the 'raw' signals the vibrational and electronic spectra are calculated from? Do you first have some time-domain signals that are then transformed as frequency-domain signals? – mmh May 27 '15 at 15:21

I'm not familiar with the computational packages -- I'm an experimentalist, not a theoretician.

As an example for why both might be present, we can turn to gaseous infrared spectroscopy: one will quickly find that the line-widths in vibration-rotation spectra depend on pressure. At lower pressures, say less than a torr, Doppler-broadening is the main mechanism. This is Gaussian in nature. While at higher pressures the broadening is instead due to collisions, which are Lorentzian. You'll find combinations of the two and so forth depending on the specifics of your case.

• Aha! That makes great sense. Are liquid and solid-state spectral broadenings also Lorentzian? – Richard Terrett May 10 '12 at 4:45
• There are also useful model lineshapes for intermediate cases, such as the Voigt function: scienceworld.wolfram.com/physics/VoigtLineshape.html – Jiahao Chen May 10 '12 at 23:35
• Liquid are sometimes modeled using the sum of Lorentzian and Gaussian. There are very few deep studies on these bands in solids, but as a general rule the solid bands are typically more narrow than their solution counterparts. The sum would probably be fine for most purposes too. – Chris May 12 '12 at 6:01