Kubo Lineshape and its Fitted q-Gaussian Tsallis Function

Kubo Lineshape and its Fitted q-Gaussian Tsallis Function

Loading document ...
Loading page ...


Author(s): Amelia Carolina Sparavigna

Download Full PDF Read Complete Article

DOI: 10.18483/ijSci.2742 7 10 1-9 Volume 13 - Jan 2024


Here we consider the Kubo lineshape, that is the Fourier transform of Kubo stochastic time-correlation function, and its fitted q-Gaussian function. In particular we investigate how q-Tsallis Gaussian functions can be used as a substitute of a Kubo lineshape. In fact, the q-Gaussian has a simple analytic expression, whereas the Kubo lineshape requires a numerical calculation of Fourier transform. The aim of this investigation is to further generalize the application of q-Gaussian Tsallis functions in Raman spectroscopy.


Raman spectroscopy, q-Gaussian Tsallis lines, Time correlation functions, WolframAlpha by Wolfram Research


  1. Dutta, R., Bagchi, K., & Bagchi, B. (2017). Role of quantum coherence in shaping the line shape of an exciton interacting with a spatially and temporally correlated bath. The Journal of Chemical Physics, 146(19).
  2. Egelstaff, P. A., & Schofield, P. (1962). On the evaluation of the thermal neutron scattering law. Nuclear Science and Engineering, 12(2), 260-270
  3. Feng, Q., & Wilde, R. E. (1988). Vibrational dephasing in aqueous KSCN solution. A memory function and stretched exponential study. Chemical physics letters, 150(6), 424-428.
  4. Hanel, R., Thurner, S., & Tsallis, C. (2009). Limit distributions of scale-invariant probabilistic models of correlated random variables with the q-Gaussian as an explicit example. The European Physical Journal B, 72(2), 263.
  5. Kirillov, S. A. (1993). Markovian frequency modulation in liquids. Analytical description and comparison with the stretched exponential approach. Chemical physics letters, 202(6), 459-463.
  6. Kirillov, S. A. (1999). Time-correlation functions from band-shape fits without Fourier transform. Chemical physics letters, 303(1-2), 37-42.
  7. Kirillov, S. A. (2004). Novel approaches in spectroscopy of interparticle interactions. Raman line profiles and dynamics in liquids and glasses. Journal of molecular liquids, 110(1-3), 99-103.
  8. Kirillov, S. (2004). Novel approaches in spectroscopy of interparticle interactions. Vibrational line profiles and anomalous non-coincidence effects. In Novel Approaches to the Structure and Dynamics of Liquids: Experiments, Theories and Simulations; Springer: Berlin/Heidelberg, Germany, 2004; pp. 193–227
  9. Kubo, R. (1969). A stochastic theory of line shape. Advances in chemical physics, 15, 101-127.
  10. Meier, R. J. (2005). On art and science in curve-fitting vibrational spectra. Vibrational spectroscopy, 2(39), 266-269.
  11. Naudts, J. (2009). The q-exponential family in statistical physics. Central European Journal of Physics, 7, 405-413.
  12. Rothschild, W. G., Perrot, M., & Guillaume, F. (1987). On the vibrational T 2 processes in partially ordered systems. The Journal of chemical physics, 87(12), 7293-7299.
  13. Sparavigna, A. C. (2023). The Q(5) Raman Line of Carbon Monoxide and its q-Gaussian Function. Zenodo. https://doi.org/10.5281/zenodo.10396109
  14. Sparavigna, A. C. (2022). Entropies and Logarithms. Zenodo. DOI 10.5281/zenodo.7007520
  15. Sparavigna, A. C. (2023). q-Gaussian Tsallis Line Shapes and Raman Spectral Bands. International Journal of Sciences, 12(03), 27-40. http://dx.doi.org/10.18483/ijSci.2671
  16. Sparavigna, A. C. (2023). q-Gaussian Tsallis Functions and Egelstaff-Schofield Spectral Line Shapes. International Journal of Sciences, 12(03), 47-50. http://dx.doi.org/10.18483/ijSci.2673
  17. Sparavigna, A. C. (2023). q-Gaussian Tsallis Line Shapes for Raman Spectroscopy (June 7, 2023). SSRN Electronic Journal. http://dx.doi.org/10.2139/ssrn.4445044
  18. Sparavigna, A. C. (2023). Formamide Raman Spectrum and q-Gaussian Tsallis Lines (June 12, 2023). SSRN Electronic Journal. http://dx.doi.org/10.2139/ssrn.4451881
  19. Sparavigna, A. C. (2023). Tsallis and Kaniadakis Gaussian functions, applied to the analysis of Diamond Raman spectrum, and compared with Pseudo-Voigt functions. Zenodo. https://doi.org/10.5281/zenodo.8087464
  20. Sparavigna A. C. (2023). Tsallis q-Gaussian function as fitting lineshape for Graphite Raman bands. ChemRxiv. Cambridge: Cambridge Open Engage; 2023.
  21. Sparavigna A. C. (2003). Fitting q-Gaussians onto Anatase TiO2 Raman Bands. ChemRxiv. Cambridge: Cambridge Open Engage; 2023.
  22. Sparavigna, A. C. (2023). SERS Spectral Bands of L-Cysteine, Cysteamine and Homocysteine Fitted by Tsallis q-Gaussian Functions. International Journal of Sciences, 12(09), 14–24. https://doi.org/10.18483/ijsci.2721
  23. Sparavigna, A. C. (2023). Asymmetric q-Gaussian functions to fit the Raman LO mode band in Silicon Carbide. ChemRxiv. Cambridge Open Engage; 2023.
  24. Sparavigna, A. C. (2023). Generalizing asymmetric and pseudo-Voigt functions by means of q-Gaussian Tsallis functions to analyze the wings of Raman spectral bands. ChemRxiv, Cambridge Open Engage, 2023.
  25. Sparavigna, A. C. (2023). Convolution and Fourier Transform: from Gaussian and Lorentzian Functions to q-Gaussian Tsallis Functions. International Journal of Sciences, 12(11), 7-11.
  26. Tagliaferro, A., Rovere, M., Padovano, E., Bartoli, M., & Giorcelli, M. (2020). Introducing the novel mixed gaussian-lorentzian lineshape in the analysis of the raman signal of biochar. Nanomaterials, 10(9), 1748.
  27. Tokmakoff, A. (2009). MIT Dept. of Chemistry, Lecture Notes, Archive
  28. Townsend, R. (2008). Astronomy 310, Stellar Astrophysics, Fall Semester 2008, Lecture Notes, Archive
  29. Tsallis, C. (1988). Possible generalization of Boltzmann-Gibbs statistics. Journal of statistical physics, 52, 479-487.
  30. Tsallis, C. (1995). Some comments on Boltzmann-Gibbs statistical mechanics. Chaos, Solitons & Fractals, 6, 539-559.
  31. Tsallis, C. (2023). Senses along Which the Entropy Sq Is Unique. Entropy, 25(5), 743.
  32. Umarov, S., Tsallis, C., Steinberg, S. (2008). On a q-Central Limit Theorem Consistent with Nonextensive Statistical Mechanics. Milan J. Math. Birkhauser Verlag. 76: 307–328. doi:10.1007/s00032-008-0087-y. S2CID 55967725.

Cite this Article:

International Journal of Sciences is Open Access Journal.
This article is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) License.
Author(s) retain the copyrights of this article, though, publication rights are with Alkhaer Publications.

Search Articles

Issue June 2023

Volume 12, June 2023

Table of Contents

World-wide Delivery is FREE

Share this Issue with Friends:

Submit your Paper