Evaluation of chemical equilibria with the use of artificial neural networks

Multivariate calibration with experimental design (ED) and artificial neural networks (ANN) modeling can be used to estimate equilibria constants from any kind of protonation or metal–ligand equilibrium data like potentiometry, polarography, spectrophotometry, extraction, etc. The method was tested on evenly or randomly distributed experimental error-free data and data with random noise and the results show that even rather higher experimental errors do not influence significantly the prediction power and correctness of ANN prediction. ANN with appropriate ED can provide accurate prediction of stability constants with the relative errors in the range of ±4% or smaller while the approach is very robust. Comparison with a hard model evaluation based on non-linear regression techniques shows excellent agreement. Proposed ANN method is of a general nature and, in principal, can be adopted to any analytical technique used in equilibria studies.     

Non‐linear least‐squares and chemical kinetics. An improved method to analyse monomer‐excimer decay data

The least squares fitting of experimental results with a non‐linear model can result in a serious loss of accuracy in the model parameters estimation if the statistical nature of the method is not correctly considered. This occurs when the experimental data is fitted to a set of functional parameters that depend in the model parameters to be estimated in the end. A realistic example can be found in the two state model of monomer‐excimer kinetics. The decay curves of the monomer and excimer are a sum and a difference of two exponentials, respectively. It is usual to fit the experimental decays in order to obtain the pre‐exponential factors and decay constants, thus using a reparametrization that is non‐linear with respect to the model parameters. This procedure is thoroughly discussed and a new method to analyse the decay curves that circumvents the problem of reparametrization is presented. The proposed method yields improved results with less than 7% bias in the recovered rate constants. Monte Carlo simulations have been performed in order to obtain confidence intervals for the fitting and model parameters. This revised version was published online in July 2006 with corrections to the Cover Date.     

Determination of apparent association constants of steroid-cyclodextrin inclusion complexes using a modification of the Hummel-Dreyer method

A modified Hummel-Dreyer method was used to calculate the apparent association constants of steroid-cyclodextrin inclusion complexes. An external calibration technique was employed, using the y-intercept from a plot of peak area versus concentration to correct for sample solvent effects. Mobile phase temperature and sample diluent organic content were found to be critical factors affecting the accuracy and reproducibility of the results. For four of six sets of data, the modified Hummel-Dreyer method yielded statistically equivalent results to another HPLC method for determining apparent association constants. Limitations of the modified Hummel-Dreyer method are discussed. In particular, the accuracy of the method is poor when measuring small apparent association constants.     

Two-dimensional and three-dimensional fitting of enzyme kinetic data with the kalman filter

The availability of instrumentation which is capable of collecting multidimensional data has put increased demands on the data-processing methods utilized to obtain information about reaction kinetics. An enzyme-catalyzed reaction, the hydrolysis of p-nitrophenyl phosphate to p-nitrophenol, is examined so that various data-processing methods and data-collection formats can be examined and compared. The extended Kalman filter is used to obtain rate constants and values for the initial substrate concentration for three-dimensional data, and for two-dimensional kinetically perturbed data. In addition, non-linear least-squares regression with the simplex algorithm, and linear least-squares regression methods are used to analyze absorbance/time curves for this reaction. These results are compared to the results from a two-point kinetic method, and the accuracy and precision of each of the methods is evaluated. It is found that the methods based on the Kalman filter yielded results which were equivalent to or better than the results obtained from the other approaches.     

Optimized sample-weighted partial least squares

In ordinary multivariate calibration methods, when the calibration set is determined to build the model describing the relationship between the dependent variables and the predictor variables, each sample in the calibration set makes the same contribution to the model, where the difference of representativeness between the samples is ignored. In this paper, by introducing the concept of weighted sampling into partial least squares (PLS), a new multivariate regression method, optimized sample-weighted PLS (OSWPLS) is proposed. OSWPLS differs from PLS in that it builds a new calibration set, where each sample in the original calibration set is weighted differently to account for its representativeness to improve the prediction ability of the algorithm. A recently suggested global optimization algorithm, particle swarm optimization (PSO) algorithm is used to search for the best sample weights to optimize the calibration of the original training set and the prediction of an independent validation set. The proposed method is applied to two real data sets and compared with the results of PLS, the most significant improvement is obtained for the meat data, where the root mean squared error of prediction (RMSEP) is reduced from 3.03 to 2.35. For the fuel data, OSWPLS can also perform slightly better or no worse than PLS for the prediction of the four analytes. The stability and efficiency of OSWPLS is also studied, the results demonstrate that the proposed method can obtain desirable results within moderate PSO cycles.     

Maintaining the predictive abilities of multivariate calibration models by spectral space transformation

In quantitative on-line/in-line monitoring of chemical and bio-chemical processes using spectroscopic instruments, multivariate calibration models are indispensable for the extraction of chemical information from complex spectroscopic measurements. The development of reliable multivariate calibration models is generally time-consuming and costly. Therefore, once a reliable multivariate calibration model is established, it is expected to be used for an extended period. However, any change in the instrumental response or variations in the measurement conditions can render a multivariate calibration model invalid. In this contribution, a new method, spectral space transformation (SST), has been developed to maintain the predictive abilities of multivariate calibration models when the spectrometer or measurement conditions are altered. SST tries to eliminate the spectral differences induced by the changes in instruments or measurement conditions through the transformation between two spectral spaces spanned by the corresponding spectra of a subset of standardization samples measured on two instruments or under two sets of experimental conditions. The performance of the method has been tested on two data sets comprising NIR and MIR spectra. The experimental results show that SST can achieve satisfactory analyte predictions from spectroscopic measurements subject to spectrometer/probe alteration, when only a few standardization samples are used. Compared with the existing popular methods designed for the same purpose, i.e. global PLS, univariate slope and bias correction (SBC) and piecewise direct standardization (PDS), SST has the advantages of implementation simplicity, wider applicability and better performance in terms of predictive accuracy.     

Evaluation of the rate constants in chemical reactions

This article is concerned with the application of a new method to recover the rate constants in chemical reactions. The method is based on treating the unknown parameters as time dependent. With appropriate experimental data the unknown rate constants are guided from an arbitrary initial condition to their true value at a final time. An explicit equation describing the time evolution of the parameters is obtained by minimizing the error along the trajectory. The method leads to an iterative algorithm which is described in detail. Numerical results with the method indicate that accurate estimates of the rate constants can be obtained directly from experimental data. © 1998 John Wiley & Sons, Inc. Int J Chem Kinet 30: 151–159, 1998.     

Canonical variational transition-state theory study of the CF3CH2CH3 + OH reaction

Variational transition-state theory rate constants with multidimensional tunneling contributions using the small curvature method have been calculated for the CF3CH2CH3 (HFC-263fb) + OH reaction over a temperature range from 200 to 373 K. The mPW1B95-41.0 hybrid functional, parametrized by Albu and Swaminathan to generate theoretical rate constants nearly identical to the experimental values for the CH3F + OH reaction, has been used in conjunction with the 6-31+G** basis set to explore the potential energy surface of the title reaction. The good agreement found between theoretical predictions and the experimental data available suggests that the present approach is an excellent option to obtain high-quality results at low computational cost for direct dynamics studies of hydrogen abstraction reactions from complex hydrofluorocarbons. The reliability of the structure activity relationship used to estimate rate constant values for OH reactions with hydrofluorocarbons is also discussed in detail.     

Petroleum resins adsorption onto quartz sand: near infrared (NIR) spectroscopy study

In this paper we have tried to evaluate adsorption parameters of petroleum resins. Near infrared (NIR) spectroscopy is applied for resins bulk concentration evaluation during adsorption process. NIR experimental scheme and parameters are provided. NIR spectra range of 9000-13,000 cm(-1) is chosen. Quartz sand (0.2-0.8 mm fraction) is used as adsorbent; benzene is used as solvent. Different approaches of "NIR spectra-resins concentration" calibration model building are discussed. Partial least squares (PLS) regression method is used. Langmuir model is chosen for experimental data fitting. Combined usage of kinetic and isothermic data gives us ability to evaluate the maximal adsorbed mass density, the equilibrium constant of adsorption, and the rate constants of adsorption (and desorption). The rate constants of resins adsorption and desorption are found to be concentration independent.     

Third-order rate constants of atmospheric importance

Input data and results are presented for the calculation of a number of third-order rate constants of atmospheric interest using Troe′s approximate method. A comparison with experimental data indicates that this approach provides a reliable method for predicting unknown rate constants and estimating temperature dependences. These calculations form the basis of the recommendations of the NASA review panel for third-order rate constants to be used in atmospheric modeling.     

Prediction of electrophoretic behaviour of a series of quinolones in aqueous methanol.

Quinolones are a family of antibacterial agents used in human and veterinary clinics. The examination of protonation equilibria is essential because their antibacterial activity is pH-dependent. In this work, dissociation constants of quinolones in MeOH-water mixtures were obtained using capillary electrophoresis. The method is based on a model that relates electrophoretic mobility of the solute with pH. The effect of pH, pKa and activity coefficient on electrophoretic behaviour was considered. Standard pH values for buffer solutions were previously determined in MeOH-water mixtures, and the pH can thus be measured in these media as in water. This model is also used to obtain the optimum conditions for the separation of a series of substances because it allows one to predict the resolution between adjacent peaks from a few experimental data.     

Modeling unimolecular reactions in photoelectron photoion coincidence experiments

A computer program has been developed to model and analyze the data from photoelectron photoion coincidence (PEPICO) spectroscopy experiments. This code has been used during the past 12 years to extract thermochemical and kinetics information for almost a hundred systems, and the results have been published in over forty papers. It models the dissociative photoionization process in the threshold PEPICO experiment by calculating the thermal energy distribution of the neutral molecule, the energy distribution of the molecular ion as a function of the photon energy, and the resolution of the experiment. Parallel or consecutive dissociation paths of the molecular ion and also of the resulting fragment ions are modeled to reproduce the experimental breakdown curves and time‐of‐flight distributions. The latter are used to extract the experimental dissociation rates. For slow dissociations, either the quasi‐exponential fragment peak shapes or, when the mass resolution is insufficient to model the peak shapes explicitly, the center of mass of the peaks can be used to obtain the rate constants. The internal energy distribution of the fragment ions is calculated from the densities of states using the microcanonical formalism to describe consecutive dissociations. Dissociation rates can be calculated by the RRKM, SSACM or VTST rate theories, and can include tunneling effects, as well. Isomerization of the dissociating ions can also be considered using analytical formulae for the dissociation rates either from the original or the isomer ions. The program can optimize the various input parameters to find a good fit to the experimental data, using the downhill simplex algorithm. Copyright © 2010 John Wiley & Sons, Ltd.     

General equation for determining the dissociation constants of polyprotic acids and bases from additive properties. Part I. Theory

Measured additive properties of polyprotic acids and bases as functions of the pH of the solution can be used for the determination of the dissociation constants. A rigorous general equation is derived in this paper for this purpose. The equation relates the additive property of the acid or base to the dissociation constants, the limiting values and activity coefficients of the solute species, and to the pH of the solution. The equation is used to obtain the dissociation constants by fitting it to the experimental data in a nonlinear least-square fitting procedure. Overlapping dissociation constants pose no problem in this method. Applications to spectrophotometry and reversed-phase high performance liquid chromatography are presented in a following paper (Part II of this series).     

Comprehensive experimental and theoretical study of chemical equilibria in the reacting system of the tert-amyl methyl ether synthesis

The chemical equilibrium of the reactive system (methanol+isoamylenes<-->methyl tert-amyl ether) was studied in the temperature range 298-393 K in the liquid phase using the method of sealed ampoules as well as in the gaseous phase using a tubular flow reactor in the temperature range 355-378 K. In both cases, a cation exchanger Amberlist-15 was used as a heterogeneous catalyst. The reactive system of the methyl tert-amyl ether synthesis exhibits a strong nonideal behavior of the mixture compounds in the liquid phase. The knowledge of the activity coefficients is required in order to obtain the thermodynamic equilibrium constants Ka. Two well-established procedures, UNIFAC and COSMO-RS, have been used to assess activity coefficients of the reaction participants in the liquid phase. Thermodynamic equilibrium constants KP measured in the gaseous phase together with the vapor pressures of the pure compounds have been used to obtain Ka in the liquid phase on a consistent experimental basis in order to check the results obtained from the UNIFAC and COSMO-RS methods. Enthalpies of reactions DeltarH degrees of the methyl tert-amyl ether synthesis reaction in the gaseous and in the liquid phase were obtained from temperature dependences of the corresponding thermodynamic equilibrium constants. Consistency of the experimental data of DeltarH degrees was verified with help of enthalpies of formation and enthalpies of vaporization of methyl tert-amyl ether, methanol, and methyl-butenes, available from the literature. For the sake of comparison, high-level ab initio calculations of the reaction participants have been performed using the Gaussian-03 program package. Absolute electronic energy values, normal frequencies (harmonic approximation), and moments of inertia of the molecules have been obtained using G2(MP2), G3(MP2), and G3 levels. Using these results, calculated equilibrium constants and the enthalpy of reaction of the methyl tert-amyl ether synthesis in the gaseous phase based on the principles of statistical thermodynamics are found to be in acceptable agreement with the data obtained from the thermochemical measurements.     

Systematic prediction error correction: a novel strategy for maintaining the predictive abilities of multivariate calibration models

The development of reliable multivariate calibration models for spectroscopic instruments in on-line/in-line monitoring of chemical and bio-chemical processes is generally difficult, time-consuming and costly. Therefore, it is preferable if calibration models can be used for an extended period, without the need to replace them. However, in many process applications, changes in the instrumental response (e.g. owing to a change of spectrometer) or variations in the measurement conditions (e.g. a change in temperature) can cause a multivariate calibration model to become invalid. In this contribution, a new method, systematic prediction error correction (SPEC), has been developed to maintain the predictive abilities of multivariate calibration models when e.g. the spectrometer or measurement conditions are altered. The performance of the method has been tested on two NIR data sets (one with changes in instrumental responses, the other with variations in experimental conditions) and the outcomes compared with those of some popular methods, i.e. global PLS, univariate slope and bias correction (SBC) and piecewise direct standardization (PDS). The results show that SPEC achieves satisfactory analyte predictions with significantly lower RMSEP values than global PLS and SBC for both data sets, even when only a few standardization samples are used. Furthermore, SPEC is simple to implement and requires less information than PDS, which offers advantages for applications with limited data.     

Determination of enzyme/substrate specificity constants using a multiple substrate ESI-MS assay

The traditional method used to investigate the reaction specificity of an enzyme with different substrates is to perform individual kinetic measurements. In this case, a series of varied concentrations are required to study each substrate and a non-regression analysis program is used several times to obtain all the specificity constants for comparison. To avoid the large amount of experimental materials, long analysis time, and redundant data processing procedures involved in the traditional method, we have developed a novel strategy for rapid determination of enzyme substrate specificity using one reaction system containing multiple competing substrates. In this multiplex assay method, the electrospray ionization mass spectrometry (ESI-MS) technique was used for simultaneous quantification of multiple products and a steady-state kinetics model was established for efficient specificity constant calculation. The system investigated was the bacterial sulfotransferase NodH (NodST), which is a host specific nod gene product that catalyzes the sulfate group transfer from 3'-phosphoadenosine 5'-phosphosulfate (PAPS) to natural Nod factors or synthetic chitooligosaccharides. Herein, the reaction specificity of NodST for four chitooligosaccharide acceptor substrates of different chain length (chitobiose, chitotriose, chitotetraose, and chitopentaose) was determined by both individual kinetic measurements and the new multiplex ESI-MS assay. The results obtained from the two methods were compared and found to be consistent. The multiplex ESI-MS assay is an accurate and valid method for substrate specificity evaluation, in which multiple substrates can be evaluated in one assay.     

Solvent extraction studies using tetracycline as a complexing agent

Stability constants for uranium-tetracycline complexes were determined by the method of average number of ligands, the method of limiting values, the method of two parameters and the method of weighted least squares. Solvent extraction technique was used to obtain experimental data.