q-Gaussians and the shapes of Raman spectral lines

Abstract

q-Gaussians are probability distributions having their origin in the framework of Tsallis statistics. A continuous real parameter q is characterizing them so that, in the range 1 < q < 3, the q-functions pass from the usual Gaussian form, for q close to 1, to that of a heavy tailed distribution, at q close to 3. The value q=2 corresponds to the Cauchy-Lorentzian distribution. This behavior of q-Gaussian functions could be interesting for a specific application, that regarding the analysis of Raman spectra, where Lorentzian and Gaussian profiles are the most commonly used line shapes to fit the spectral bands. Therefore, we will discuss q-Gaussians with the aim of comparing the resulting fit analysis with data available in literature. In particular, we will discuss results given in a recently proposed analysis of carbon-based materials, obtained by means of mixed Gaussian and Lorentzian line shapes, defined as GauLors (Tagliaferro et al., 2021).

Some SERS Fingerprints of Metabolites from the Database Provided by Sherman et al., 2020

“…The metabolites were L-Cysteine, Cysteamine and Homocysteine, and the SERS peaks were fitted by means of the Tsallis q-Gaussian functions. These functions are considered by the author (AC Sparavigna) as fundamental for any deconvolution of Raman spectra, as shown by several cases (see for instance, [3]- [8]). Here we consider again some of the SERS spectra of metabolites given in [2], to show the importance of gaining information from their fingerprints.The first use of the term "fingerprint" in relation with the Raman spectroscopy, to the best of my knowledge, is in an article published in 1947, about the Raman spectra of hydrocarbons [9].…”

“…From that time on, the points of identification, such as positions of peaks, shoulders and valleys are creating the characteristic spectral pattern which is defined as the "Raman fingerprint" of a given material. This pattern allows the material classification, "without any preliminary information about composition and structural origin of the individual features", as mentioned by D 'Ippolito, et al, 2015 [10].In [11], we proposed a method based on the first derivative behavior, that is on the "first derivative spectrum" [12], to determine the position of the peaks. Details of the method are provided in [11].…”

“…This pattern allows the material classification, "without any preliminary information about composition and structural origin of the individual features", as mentioned by D 'Ippolito, et al, 2015 [10].In [11], we proposed a method based on the first derivative behavior, that is on the "first derivative spectrum" [12], to determine the position of the peaks. Details of the method are provided in [11]. As previously told, here we apply it to determine some of the SERS fingerprints of the metabolites, the spectra of which have been kindly provided by Sherman et al, 2020.…”

“…In [11], we proposed a method based on the first derivative behavior, that is on the "first derivative spectrum" [12], to determine the position of the peaks. Details of the method are provided in [11].…”

“…In [11], we proposed a method based on the first derivative behavior, that is on the "first derivative spectrum" [12], to determine the position of the peaks. Details of the method are provided in [11]. As previously told, here we apply it to determine some of the SERS fingerprints of the metabolites, the spectra of which have been kindly provided by Sherman et al, 2020.…”