Three and four generalized Lorentzian approximations for the Voigt line shape

Abstract

Three and four generalized Lorentzians in two variables have been obtained to approximate the Voigt function by using the asymptotical Padé method. The accuracy has been greatly improved with respect to the one and two generalized Lorentzian approximations reported in a previous paper. Furthermore, the four Lorentzian function is always positive for all values of the normalized collision width and line separation. This approximation gives an accuracy for most of the values of better than 0.0001, and in the worst region the absolute error is ~0.001. In the limits of low and high pressure adequate limit functions are obtained. A four generalized Lorentzian gives a reliable and easily calculable approximation to the Voigt function for most of the experimental needs.

The interaction of novolak oligomers with hydrogen bond acceptors.

“…The IR spectra of novolak oligomers were reported by Cairns and Eglinton [S] as early as 1962 . We have now re-recorded the spectra on an Analect FTIR spectrometer and deconvoluted their component bands with the help of a computer program [9], in the hope of gaining more detailed information from the data [10]. The Key to a conformational analysis of the oligomers is the spectrum of the dimer shown in the upper part of The existence of an ionic structure in the mesomeric ensemble of the dimer implies ionization.…”

“…The spectral data were analyzed with a deconvolution program [9] ("Peak Fit" by Jandel Scientific, of San Francisco). It was found that Voigt functions [10] were best suited to describe the shape of the spectra, and they were therefore used for the deconvolutions as well. The accuracy of the procedure was tested by determining the equilibrium constant of the interaction of phenylsulfoxide with p-cresol by deconvoluting the absorption spectra of both components in the mixed solution, and calculating the interaction constants from both sets of data.…”

Inhomogeneously broadened EPR lineshape of axial powder

“…(4), we use the following exact representation for the Voigt integral Eq. (3b) in terms of the generalized Lorentzian function [24]:…”

“…If only four terms (n = 4) in the summation Eq. (5) are taken, the approximation for the Voigt lineshape is within an accuracy better than 0.001 for any value of r and v [24]. Substituting the value of H•(r,v(x)) defined by Eq.…”

Asymmetries of the Voigt line shape

“…The VLS has been accurately calculated using the asymptotical Pade  method (Puerta & Martin, 1981), as well as with continued fractions (Fried & Conte, 1961;McCabe, 1984). The VLS has been used successfully in X-ray diffraction studies, since speci®c information can been obtained about crystallite size and strain from experimental spectra (Keijser, Langford, Mittemeijer & Vogels, 1982;Keijser, Mittemeijer & Rozendaal, 1983), as well as in several types of spectroscopy, such as Mo È ssbauer spectroscopy to analyse spectra that present an anomalous broadening (Evans & Black, 1970;Rancourt, 1989), in electron paramagnetic resonance (EPR) to determine the relaxation times T 1 and T 2 (Zhidkov et al, 1967;Korb & Maruani, 1982), and in coherent anti-Stokes Raman spectroscopy, where a linear combination of a Voigt and a Gaussian function creates an effective slit function (Heneghan & Vangsness, 1991).…”