954 (2002) 59–76 Journal of Chromatography A, www.elsevier.com / locate / chroma Parabolic-Lorentzian modified Gaussian model for describing and deconvolving chromatographic peaks * ´ R.D. Caballero, M.C. Garcıa-Alvarez-Coque, J.J. Baeza-Baeza ´ ´ ´ ` ` Departamento de Quımica Analıtica, Facultad de Quımica, Universitat de Valencia, 46100 Burjassot, Valencia, Spain Received 22 November 2001; received in revised form 15 February 2002; accepted 20 February 2002 Abstract A new mathematical model for characterising skewed chromatographic peaks, which improves the previously reported polynomially modified Gaussian (PMG) model, is proposed. The model is a Gaussian based equation whose variance is a combined parabolic-Lorentzian function. The parabola accounts for the non-Gaussian shaped peak, whereas the Lorentzian function cancels the variance growth out of the elution region, which gives rise to a problematic baseline increase in the PMG model. The proposed parabolic-Lorentzian modified Gaussian (PLMG) model makes a correct description of peaks showing a wide range of asymmetry with positive and / or negative skewness. The new model is shown to give better fittings ´ than other models as the Li, log-normal or Pap–Papai models, which have a different mathematical basis. The model parameters are also related to peak properties as the skewness and kurtosis. The PLMG model is applied to the deconvolution of peaks in binary mixtures of structurally related compounds that are highly overlapped (retention times in min): oxytetracycline (9.00)—tetracycline (10.20), sulfathiazole (3.67)—sulfachloropyridazine (3.93), and sulfisoxazole (5.14)—sulfapyridine (5.24). The use of non-linear least-squares calibration in combination with the PLMG model gave superior results than the classical multiple linear least-squares and partial least-squares regressions. The proposed method takes into account run to run changes in retention time that occur along the injection of standards and samples, and the possible interactions that exist between the coeluting compounds. This decreases significantly the quantitation errors.  2002 Elsevier Science B.V. All rights reserved. Keywords: Skewed peaks; Modified Gaussian model; Peak modelling; Deconvolution 1. Introduction ing at least two overlapped peaks when complex samples are processed. In this case, a deconvolution Although chromatography is a powerful separation technique must be applied to quantitate appropriately technique, full resolution of all components in a each analyte. However, the stability of the baseline, sample may not be feasible by optimising the and the changes in retention time and peak shape experimental conditions, such as the column type or among standards and samples, as well as the possible nature of the modifiers, and the mobile phase com- interactions between the solutes that elute at close position. Actually, a high probability exists of find- times, limits the accuracy and precision of the deconvolution. These problems can be overcome by using a model, flexible enough to cope with the *Corresponding author. E-mail address: juan.baeza@uv.es (J.J. Baeza-Baeza). changes that affect the chromatographic peaks. 0021-9673 / 02 / $ – see front matter  2002 Elsevier Science B.V. All rights reserved. PII: S0021-9673(02)00194-2