Discrimination between linear and non-linear models describing retention data of alkylbenzenes in gas-chromatography

Quantitative structure-(chromatographic) retention relationships

Since the pioneering works of Kaliszan (R. Kaliszan, Quantitative Structure-Chromatographic Retention Relationships, Wiley, New York, 1987; and R. Kaliszan, Structure and Retention in Chromatography. A Chemometric Approach, Harwood Academic, Amsterdam, 1997) no comprehensive summary is available in the field. Present review covers the period of 1996-August 2006. The sources are grouped according to the special properties of kinds of chromatography: Quantitative structure-retention relationship in gas chromatography, in planar chromatography, in column liquid chromatography, in micellar liquid chromatography, affinity chromatography and quantitative structure enantioselective retention relationships. General tendencies, misleading practice and conclusions, validation of the models, suggestions for future works are summarized for each sub-field. Some straightforward applications are emphasized but standard ones. The sources and the model compounds, descriptors, predicted retention data, modeling methods and indicators of their performance, validation of models, and stationary phases are collected in the tables. Some important conclusions are: Not all physicochemical descriptors correlate with the retention data strongly; the heat of formation is not related to the chromatographic retention. It is not appropriate to give the errors of Kovats indices in percentages. The apparently low values (1-3%) can disorient the reviewers and readers. Contemporary mean interlaboratory reproducibility of Kovats indices are about 5-10 i.u. for standard non polar phases and 10-25 i.u. for standard polar phases. The predictive performance of QSRR models deteriorates as the polarity of GC stationary phase increases. The correlation coefficient alone is not a particularly good indicator for the model performance. Residuals are more useful than plots of measured and calculated values. There is no need to give the retention data in a form of an equation if the numbers of compounds are small. The domain of model applicability of models should be given in all cases.

Comparison of Ridge Regression, Partial Least-Squares, Pairwise Correlation, Forward- and Best Subset Selection Methods for Prediction of Retention Indices for Aliphatic Alcohols

A quantitative structure-retention relationship (QSRR) study based on multiple linear regression (MLR) was performed for the description and prediction of Kováts retention indices (RI) of alcohol compounds. Alcohols were of saturated, linear or branched types and contained a hydroxyl group on the primary, secondary or tertiary carbon atoms. Constitutive and weighted holistic invariant molecular (WHIM) descriptors were used to represent the structure of alcohols in the MLR models. Before the model building, five variable selection methods were applied to select the most relevant variables from a large set of descriptors, respectively. The selected molecular properties were included into the MLR models. The efficiency of the variable selection methods was also compared. The selection methods were as follows: ridge regression (RR), partial least-squares method (PLS), pair-correlation method (PCM), forward selection (FS) and best subset selection (BSS). The stability and the validity of the MLR models were tested by a cross-validation technique using a leave-n-out technique. Neither RR nor PLS selected variables were able to describe the Kováts retention index properly, and PCM gave reliable results in the description but not for prediction. We built models with good predicting ability using FS and BSS as a selection method. The most relevant variables in the description and prediction of RIs were the mean electrotopological state index, the molecular mass, and WHIM indices characterizing size and shape.

Artificial neural network prediction of quantitative structure: Retention relationships of polycyclic aromatic hydocarbons in gas chromatography

A feed-forward artificial neural network (ANN) model was used to link molecular structures (boiling points, connectivity indices and molecular weights) and retention indices of polycyclic aromatic hydrocarbons (PAHs) in linear temperature- programmed gas chromatography. A randomly taken subset of PAH retention data reported by Lee et al. [Anal. Chem. 51 (1979) 768], containing retention index data for 30 PAHs, was used to make the ANN model. The prediction ability of the trained ANN was tested on unseen data for 18 PAHs from the same article, as well as on the retention data for 7 PAHs experimentally obtained in this work. In addition, two different data sets with known retention indices taken from the literature were analyzed by the same ANN model. It has been shown that the relative accuracy as the degree of agreement between the measured and the predicted retention indices in all testing sets, for most of the studied PAHs, were within the experimental error margins (+-3 %).

Prediction of gas chromatographic retention indices of a diverse set of toxicologically relevant compounds

For a set of 846 organic compounds, relevant in forensic analytical chemistry, with highly diverse chemical structures, the gas chromatographic Kovats retention indices have been quantitatively modeled by using a large set of molecular descriptors generated by software Dragon. Best and very similar performances for prediction have been obtained by a partial least squares regression (PLS) model using all considered 529 descriptors, and a multiple linear regression (MLR) model using only 15 descriptors obtained by a stepwise feature selection. The standard deviations of the prediction errors (SEP), were estimated in four experiments with differently distributed training and prediction sets. For the best models SEP is about 80 retention index units, corresponding to 2.1-7.2% of the covered retention index interval of 1110-3870. The molecular properties known to be relevant for GC retention data, such as molecular size, branching and polar functional groups are well covered by the selected 15 descriptors. The developed models support the identification of substances in forensic analytical work by GC-MS in cases the retention data for candidate structures are not available.

Temperature dependence of Henry's law constant in an extended temperature range

The Henry's law constants H for chloroform, 1,1-dichloroethane, 1,2-dichloropropane, trichloroethene, chlorobenzene, benzene and toluene were determined by the EPICS-SPME technique (equilibrium partitioning in closed systems--solid phase microextraction) in the temperature range 275-343 K. The curvature observed in the ln H vs. 1/T plot was due to the temperature dependence of the change in enthalpy delta H0 during the transfer of 1 mol solute from the aqueous solution to the gas phase. The nonlinearity of the plot was explained by means of a thermodynamic model which involves the temperature dependence of delta H0 of the compounds and the thermal expansion of water in the three-parameter equation ln (H rho TT) = A2/T + BTB + C2, where rho T is the density of water at temperature T, TB = ln(T/298) + (298-T)/T, A2 = -delta H298(0)/R, delta H298(0) is the delta H0 value at 298 K, B = delta Cp0/R, and C2 is a constant. delta Cp0 is the molar heat capacity change in volatilization from the aqueous solution. A statistical comparison of the two models demonstrates the superiority of the three-parameter equation over the two-parameter one ln H vs. 1/T). The new, three-parameter equation allows a more accurate description of the temperature dependence of H, and of the solubility of volatile organic compounds in water at higher temperatures.