Functions for Spectral Bands

A symmetrical spectral band is described by three parameters position (wavelength or frequency corresponding to the absorption maximum), intensity (absorbance or molar absorptivity at the band maximum) and width (usually the bandwidth at half-height). The band shape functions most commonly used for deconvolution are the Gaussian function and the Lorentzian function. Both are symmetrical functions. UV-visible spectra generally have a Gaussian band shape. The Lorentzian function is useful for the simulation of NMR spectra. The 

Pelikan, M. C pan and M. Liska, Applications of Numerical Methods in Molecular Spectroscopy, CRC Press, Boca Raton FL, 1993. 

Many spectral bands can be closely approximated by a Gaussian line shape when the independent variable v is in energy units, e.g., cm . The absorbance A at a wavenumber v is given by equation 21-1, where Amax is the band maximum, Vmax is the wavenumber of the band maximum and Av is the half-width. 

The corresponding equation for a Lorentzian line shape is given by equation 

For unsymmetrical bands, the equation for the log-normal line shape is 

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