Method for the Estimation of the Mean Lorentzian Bandwidth in Spectra Composed of an Unknown Number of Highly Overlapped Bands

Abstract

We introduce a method for the estimation of the mean Lorentzian bandwidth of the component bands in a spectrum. The method is computationally simple, using only the module of the Fourier transform of the spectrum, and its first derivative. Moreover, the presented method does not require knowledge of the number of bands in the spectrum, their band positions, or their band areas. Furthermore, it works on spectra containing Lorentzian bands, as well as Gaussian and Voigtian bands. Therefore, the introduced method seems especially well suited for obtaining a representative Lorentzian width for highly overlapped bands, independent of their number and Lorentzian/Gaussian character. We describe how different experimental limitations (spectral truncation, offset error, presence of noise, etc.) may affect the performance of the method, and when required we propose effective alternatives to minimize their effects. Finally, we show the application of the method to an experimental spectrum: the amide I band of a dry film of the solubilized ADP/ATP carrier. The estimation of the mean Lorentzian width can allow, for instance, for a more objective selection of the deconvolution width in Fourier self-deconvolution, allowing for a more objective and reliable analysis of the amide I band of proteins. The mean Lorentzian width can also be useful to obtain an estimation of the homogenous broadening and vibrational relaxation of the amide I vibration of proteins, without requiring complex pump-probe experiments.