A fiber optic evanescent field absorption sensor for monitoring organic contaminants in water

Summary A fiber optic chemical sensor for determination of organic compounds in aqueous solution has been developed. Based on the evanescent field principle, a quartz glass fiber with a polysiloxane cladding is used as in-situ measuring probe. A compact sensor built from a 6-m coiled fiber has been connected to a commercially available fast scanning dispersive NIR spectrometer. The siloxane cladding fulfils two functions: on the one hand, it acts as protecting layer of the fragile silica fiber core, and on the other hand, it is selective with respect to non-polar organic compounds due to its organophilic properties. Hence, interactions of the evanescent field at the core/cladding interface with organic species penetrating into the cladding can be measured without interferences from broad water OH absorption bands. Aqueous solutions of chlorinated hydrocarbon solvents (CHS) have been used to test the sensor response. NIR evanescent field absorbance spectra of methylene chloride, chloroform and trichloroethylene diffused into the fiber cladding are shown in the 900–2100 nm spectral range. Different amounts of CHCl₃ dissolved in water have been determined in order to evaluate the quantitative sensor response. A linear absorbance/concentration relationship has been found for solutions between 80–6800 mg l^–1. Kinetic experiments performed with CHCl₃ solutions resulted in sensor response times of 5–10 min. The sensor seems to be promising for the remote monitoring of organic contaminants, e.g. CHS, in drainage waters of contaminated areas.     

Process analysis of electroless nickel deposition baths using optical spectroscopies

Summary The analytical techniques of Vis-spectrophotometry and FTIR spectroscopy have been applied to the quantitative determination of important plating bath constituents of an electroless nickel-phosphorus electrolyte under realistic bath operation conditions. In combination with multivariate calibration methods (partial-least squares (PLS)- and principal component (PCR) regression) Ni²⁺, the reducing agent H₂PO ₂ ^– and its oxidation product HPO ₃ ^– could be directly determined even in the presence of other bath constituents like malic, lactic and adipic acids. For Ni²⁺, absorbance spectra in the 500–900 nm wavelength range were used to develop a PLS calibration model that allows to compensate matrix influences on the Ni²⁺ spectrum. PLS regression was carried out in the concentration range 0.5–6 g l^–1 Ni²⁺ with independently varying bath parameters (concentration of other bath constituents, pH and temperature). Evaluation of the model by predicting the concentrations of test samples which had been drawn from real process solutions of a Ni plating bath yielded a root-mean-squared error of 0.06 g l^–1. The metal concentration of the nickel electrolyte in a compact electroplating unit was monitored in-line by measuring spectra by means of a Vis-spectrometer adapted to the process via quartz glass fiber optical cables of 50 m length. A comparison of the in-line data with potentiometric off-line reference analyses showed good agreement of both data sets with a root mean-squared error of 0.15 g l^–1. The potential of FTIR spectroscopy for process analysis of plating bath solutions could be demonstrated by measuring off-line the concentrations of H₂PO ₂ ^– and HPO ₃ ^– . For these two components calibration samples containing all other main bath constituents were used to set up a PCR calibration model with IR spectra measured in the range from 850 to 1800 cm^–1 with an ATR trough technique. The data showed — within the error of the method of about 10% — generally a good accordance with the stoichiometry of the Ni²⁺/H₂PO ₂ ^– reduction process. The correlation of both parameters which was confirmed in these experiments could allow effective bath control with minimum analytical instrumentation, e.g. only a Vis-spectrophotometer.Dedicated to Professor Dr. Wilhelm Fresenius on the occasion of his 80th birthday     

Development of a PLS based method for determination of the quality of beers by use of NIR: spectral ranges and sample-introduction considerations

Near infrared spectroscopy (NIR) has been used to determine important indicators of the quality of beers, for example original and real extract and alcohol content, using a partial least squares (PLS) calibration approach. A population of 43 samples, obtained commercially in Spain and including different types of beer, was used. Cluster hierarchical analysis was used to select calibration and validation data sets. Absorbance sample spectra, in transmission mode, were obtained in triplicate by using a 1-mm pathlength quartz flow cell and glass chromatography vials of 6.5 mm internal diameter. The two methods of sample introduction were compared critically, on the basis of spectral reproducibility for triplicate measurements and after careful selection of the best spectral pre-processing and the spectral range for building the PLS model, to obtain the best predictive capability. For each mode of sample introduction two calibration sets were assayed, one based on the use of 15 samples and a second extended based on use of 30 samples, thus leaving 28 and 13 samples, respectively, for validation. The best results were obtained for 1 mm flow cell measurements. For this method original zero-order spectra data in the ranges 2220–2221 and 2250–2350 nm were chosen. For the real extract, original extract, and alcohol d_x-y and s_x-y values of –0.04 and 0.07% w/w, –0.01 and 0.13% w/w, and –0.01 and 0.1% v/v, respectively, were obtained. The maximum errors in the prediction of any of these three indicators for a new sample were 2.2, 1.2, and 1.9%, respectively. This method compares favorably with the automatic reference method in terms of speed, reagent consumed, and waste generated.     

Multivariate calibration of glucose in blood by PLS using spectral and fourier-domain data

Infrared attenuated total reflection spectra of 133 whole EDTA blood samples, from patients of a general hospital population, in the range from 1500 to 750 cm^–1 were used for the calibration of glucose. Reference concentration values were provided by the enzymatic glucose dehydrogenase method. The partial-least squares (PLS) algorithm was used to solve the inverse regression problem. The prediction results from, calculations using spectral and Fourier-transformed data were compared, and in the latter case, the data reduction yielded no advantage. The spectral range optimization for calibration can be carried out more flexibly in the spectral domain which is more readily interpreted by the spectroscopist.     

Rapid determination of mono and dinitrophenols by DPP, in the presence of lead and cadmium and using concentrated CaCl2 electrolyte

The contamination of drinking water and industrial wastewaters is a critical environmental problem. The nitrophenol, dinitrophenol, cadmium, and lead contaminants are classified as hazardous compounds. Their rapid determination may be obtained using differential pulse polarography with concentrated electrolyte. CaCl₂, which is very soluble to levels exceeding 5 mol l^–1, allows separation of coalescent peaks at 0.1 mol l^–1. A systematic study undertaken from 0.1 to 5 mol l^–1 shows good separation of lead and cadmium from the organic compounds, and optimization of the electrolyte concentration according to the objective is described. Preconcentration of real samples is necessary because pollution levels are usually very low.     

Integrated optical NIR-evanescent wave absorbance sensorfor chemical analysis

A new, long-path integrated optical (IO) sensor for the detection of non-polar organic substances is described. The sensing layer deposited on a planar multimode IO structure is built by a suitable silicone polymer with lower refractive index (RI). It acts as a hydrophobic matrix for the reversible enrichment of non-polar organic contaminants from water or air. Light from the near-infrared (NIR) range is coupled into the planar structure and the evanescent wave part of the light field penetrating into the silicone layer interacts with the enriched organic species. As a result, light is absorbed at the characteristic frequencies of the corresponding C-H, N-H or O-H overtone and combination band vibrations of the analytes. To perform evanescent field absorbance (EFA) measurements, the arc-shaped strip waveguide structure of 172 mm interaction length was adapted to a tungsten-halogen lamp and an InGaAs diode array spectrograph over gradient index fibers. Dimethyl-co-methly(phenyl)polysiloxanes with varying degrees of phenylation were prepared and used as sensitive coating materials for the IO structure. Light attenuation in the arc-shaped waveguides is high and typical insertion losses in the range of 14–18 dB were obtained. When the coated sensors were brought in contact with aqueous samples, the light transmission decreases, which is due to the formation of H₂O micro-emulsions in the silicone superstrates. Nevertheless, after reaching constant light transmissions, absorbance spectra of aqueous trichloroethene samples were successfully collected. For gas measurements, where water cross sensitivity problems are absent, the sensitivity of the IO device for trichloroethene was tested as a function of the RI of the silicone superstrate. The slope of the TCE calibration function increases by a factor of 10 by using a poly(methylphenylsiloxane) layer with a RI of 1.449 instead of poly(dimethylsiloxane) (RI: 1.41). A comparison of the IO-EFA and an earlier developed fiber-optic EFA sensor for trichloroethene measurements in the gas phase showed an increase in sensitivity per unit length of the waveguide by a factor of up to 120.     

Fast spectrophotometric determination of fluoride in ground waters by flow injection using partial least-squares calibration

The presence of sulphate constitutes a serious interference in the usual zirconium lake-based spectrophotometric method for the determination of fluoride in water. In this report, full spectral data have been recorded for the zirconium lake of 2-(parasulfophenylazo)-1,8-dihydroxy-3,6-naphthalene-disulfonate (SPADNS) in the simultaneous presence of fluoride and sulphate, as obtained with a flow injection system with a diode-array detector. The information has been processed with partial least-squares (PLS) multivariate calibration. Adequate modeling using a sixteen-sample calibration set allows fluoride to be determined in ground waters by the automated flow injection method, even in the presence of sulphate in concentrations up to 1000 mg l⁻¹. In the calibration range 0-1.50 mg l⁻¹ for fluoride, the limit of detection is 0.1 mg l⁻¹. The fluoride contents in real samples, as determined with the present method, were satisfactorily compared with those provided by ion selective potentiometry.     

Simultaneous Spectrophotometric Determination of Rare-Earth and Transition Elements Using Partial Least-Squares (PLS) Multivariate Calibration

A spectrophotometric method for the simultaneous determination of rare-earth and transition elements in synthetic superconductors, [(La_{1 – x} Eu _x )_1.82Sr_0.18CuO₄], by the use of 2-(5-bromo-2-pyridylazo)-5-diethylaminophenol (5-Br-PADAP) as chelating agent was developed. The influence of chemical variables affecting the reaction was studied. A partial least-squares (PLS) multivariate calibration procedure was used to assess the data obtained from several calibration solutions measured over the wavelengths range 400–700 nm. The concentration range for Cu was (1–12) × 10^–6 mol/L, while the range for the rare-earth elements La and Eu was (2–8) × 10^–6 mol/L. The relative errors in the determinations were less than 5% in most cases.     

Rapid screening for ethyl carbamate in stone-fruit spirits using FTIR spectroscopy and chemometrics

Ethyl carbamate (EC, urethane, C₂H₅OCONH₂) is a known genotoxic carcinogen of widespread occurrence in fermented food and beverages with the highest concentrations being found in stone-fruit spirits. Time-consuming procedures requiring extraction and gas chromatographic–mass spectrometric determination are regarded as reference procedures for the analysis of EC in alcoholic beverages. In this study, the rapid method of Fourier transform infrared (FTIR) spectroscopy in combination with partial least-squares (PLS) regression using selected wavelength bands is applied for the first time to the screening analysis of EC in stone fruit spirits (analysis time only 2 min). Apart from the actual content of EC in the sample, additional information was available from the FTIR spectra. This included data concerning the EC precursor hydrocyanic acid (HCN) and the maximum EC concentration which could be formed during storage. The PLS procedure was validated using an independent set of samples (Q² = 0.71–0.76, SEP = 0.42–0.67). The method was found to lack the accuracy required for a quantitative determination; it could only be used semi-quantitatively in the context of a screening analysis. If a rejection level of 0.8 mg L^–1 is applied as cut-off, overall correct classification rates of 85–91% for the calibration set and 77–85% for the validation set were achieved. False negative results can be avoided by lowering the cut-off to 0.6 mg L^–1. Through use of FTIR screening, 60–70% of all samples can be classified as negative and removed, leaving only conspicuous analysis results exceeding cut-off to be confirmed by complex and labour-intensive reference analyses.     

Direct determination of polymerized triglycerides in deep-frying olive oil by attenuated total reflectance–Fourier transform infrared spectroscopy using partial least squares regression

A partial least squares (PLS) regression model based on attenuated total reflectance–Fourier transform infrared spectra of heated olive oil samples has been developed for the determination of polymerized triacylglycerides (PTGs) generated during thermal treatment of oil. Three different approaches for selection of the spectral regions used to build the PLS model were tested and compared: (1) variable selection based on expert knowledge, (2) uninformative variable elimination PLS, and (3) interval PLS. Each of the three variable selection methods provided PLS models from heated olive oil samples with excellent performance for the prediction of PTGs in fried olive oils with comparable model statistics. However, besides a high coefficient of determination (R ² of 0.991) and low calibration, validation, and prediction errors of 1.14%, 1.21%, and 1.40% w/w, respectively, variable selection based on expert knowledge gave additionally almost identical low calibration (−0.0017% w/w) and prediction (−0.0023% w/w) bias. Furthermore, it was verified that the determination of PTGs was not influenced by the type of foodstuff fried in the olive oil.     

Spectroscopic and voltammetric studies of Pefloxacin bound to calf thymus double-stranded DNA

Spectral and electrochemical studies have been carried out on the interaction of pefloxacin with calf thymus double-stranded dsDNA. The voltammetric behavior of pefloxacin was investigated at glassy carbon, carbon paste and dsDNA-modified carbon paste electrodes using cyclic voltammetry. Pefloxacin was oxidized, yielding one irreversible oxidation peak. The modification of the carbon paste surface with dsDNA allowed an accumulation process to take place for pefloxacin such that higher sensitivity was achieved compared with the bare surface. The response was characterized with respect to ionic strength, accumulation time, pefloxacin concentration, and other variables. The stripping differential pulse voltammetric response showed a linear calibration curve in the range 1.0×10^–7–1.0×10^–5 mol l^–1 with a detection limit of 5.0×10^–8 mol l^–1 at the dsDNA modified electrode. The method was applied to the direct determination of pefloxacin in diluted urine samples.     

Simultaneous fluorimetric determination of glyphosate and its metabolite, aminomethylphosphonic acid, in water, previous derivatization with NBD-Cl and by partial least squares calibration (PLS)

The reactions of 4-chloro-7-nitrobenzofurazan (NBD-Cl) with glyphosate (GLY) and with its main metabolite, aminomethylphosphonic acid (AMPA), have been studied. The resolution of binary mixtures of glyphosate and aminomethylphosphonic acid has been accomplished by partial least squares (PLS) multivariate calibration. The method of determination is based on the fluorescence emission of the derivatives formed in presence of NBD-Cl at 90 °C, in methanol and in basic medium. The dynamic ranges of the methods were comprised between 10 and 150 μg l⁻¹ for GLY and between 10 and 200 μg l⁻¹ for AMPA, being the detection limits 2 and 5.4 μg l⁻¹ for GLY and AMPA, respectively. The total luminiscence information of the derivatives has been used to optimize the spectral data set to perform the calibration, by analysis of the three-dimensional excitation-emission matrices. A comparison between the predictive ability of the multivariate calibration method, partial least squares type 1 (PLS-1), on two spectral data sets, emission and synchronous spectra, has been performed. The PLS-1 method, applied to the emission spectra, has been selected as optimum. The proposed method has been applied to the simultaneous determination of GLY and AMPA in river water. For concentrations ranging from 100 to 600 μg l⁻¹ of each compound in the samples, analytical recoveries range from 83 to 94% for GLY and from 104 to 120% for AMPA.     

Prediction of wood property in Chinese Fir based on visible/near-infrared spectroscopy and least square-support vector machine

A method for the quantification of density of Chinese Fir samples based on visible/near-infrared (vis–NIR) spectrometry and least squares-support vector machine (LS-SVM) was proposed. Sample set partitioning based on joint x–y distances (SPXY) algorithm was used for dividing calibration and prediction samples, it is of value for prediction of property involving complex matrices. A stepwise procedure is employed to select samples according to their differences in both x (instrumental responses) and y (predicted parameter) spaces. For comparison, the models were also constructed by Kennard–Stone method, as well as by using the duplex and random sampling methods for subset partitioning. The results revealed that the SPXY algorithm may be an advantageous alternative to the other three strategies. To validate the reliability of LS-SVM, comparisons were made among other modeling methods such as support vector machine (SVM) and partial least squares (PLS) regression. Satisfactory models were built using LS-SVM, with lower prediction errors and superior performance in relation to SVM and PLS. These results showed possibility of building robust models to quantify the density of Chinese Fir using near-infrared spectroscopy and LS-SVM combined SPXY algorithm as a nonlinear multivariate calibration procedure.     

Measurement of lactate in whole human blood with near-infrared transmission spectroscopy

We have evaluated the potential of near-infrared spectroscopy (NIRS) as a technique for rapid analysis of lactate in whole blood. To test the NIRS technique, a comparison was made with a standard clinical method using whole blood samples taken from five exercising human subjects at three different stage of exercise. To expand lactate concentration within the physiological range, standard additions method was used to generate 45 unique data points. Spectra were collected over the 2050-2400 nm spectral range with a 1 mm optical path length quartz cell. Reference lactate concentrations in the samples were determined by enzymatic measurements. Estimates and calibration of the lactate concentration with NIRS was made using partial least squares (PLS) regression analysis and leave-N-out cross validation on second derivative spectra. Separate calibrations were determined from each of the subject samples and cumulative PRESS was used to determine the number of PLS factors in the final model. The results from the PLS model presented are generated from the five individual calibration coefficient vectors and provided a correlation coefficient of 0.978 and a standard error of cross validation of 0.65 mmol l⁻¹ between the enzymatic assay and the NIRS technique. To study the parameters that impact the spectra baseline and the correlation between the calculated model and the data, referenced measurements of lactate against baseline spectrum were made for each individual. A correlation coefficient of 0.992 and a standard error of cross validation of 0.21 mmol l⁻¹ were found. The results suggest that NIRS may provide a valuable tool to assess physiological status for both research and clinical needs.     

Ultraviolet Spectroscopic Detection of Nitrate and Nitrite in Seawater Simultaneously Based on Partial Least Squares

A direct, reagent-free, ultraviolet spectroscopic method for the simultaneous determination of nitrate (NO₃⁻), nitrite (NO₂⁻), and salinity in seawater is presented. The method is based on measuring the absorption spectra of the raw seawater range of 200–300 nm, combined with partial least squares (PLS) regression for resolving the spectral overlapping of NO₃⁻, NO₂⁻, and sea salt (or salinity). The interference from chromophoric dissolved organic matter (CDOM) UV absorbance was reduced according to its exponential relationship between 275 and 295 nm. The results of the cross-validation of calibration and the prediction sets were used to select the number of factors (4 for NO₃⁻, NO₂⁻, and salinity) and to optimize the wavelength range (215–240 nm) with a 1 nm wavelength interval. The linear relationship between the predicted and the actual values of NO₃⁻, NO₂⁻, salinity, and the recovery of spiked water samples suggest that the proposed PLS model can be a valuable alternative method to the wet chemical methods. Due to its simplicity and fast response, the proposed PLS model can be used as an algorithm for building nitrate and nitrite sensors. The comparison study of PLS and a classic least squares (CLS) model shows both PLS and CLS can give satisfactory results for predicting NO₃⁻ and salinity. However, for NO₂⁻ in some samples, PLS is superior to CLS, which may be due to the interference from unknown substances not included in the CLS algorithm. The proposed method was applied to the analysis of NO₃⁻, NO₂⁻, and salinity in the Changjiang (Yangtze River) estuary water samples and the results are comparable with that determined by the colorimetric Griess assay.     

Rapid determination of telmisartan in pharmaceuticals and serum by the parallel catalytic hydrogen wave method

The polarographic characteristics of telmisartan have been investigated in 0.8 mol L^–1 NH₃.H₂O–NH₄Cl (pH 8.9)–0.01 mol L^–1 H₂O₂ as supporting electrolyte. The results demonstrate that the polarographic reduction wave at ca. –1.30 V in the absence of H₂O₂ is a catalytic hydrogen wave, and the reduction wave enhanced by H₂O₂ is a so-called parallel catalytic hydrogen wave. The analytical sensitivity of the parallel catalytic hydrogen wave is ca. 60 times higher than that of the corresponding catalytic hydrogen wave. Based on the parallel catalytic hydrogen wave a novel method has been developed for determination of telmisartan by linear sweep polarography. The calibration curve is linear in the range 2.0×10^–8–2.0×10^–6 mol L^–1 and the detection limit is 1.0×10^–8 mol L^–1. The precision is excellent with relative standard deviations of 2.6% at a concentration of 1.0×10^–7 mol L^–1 telmisartan. The proposed method has been applied to the direct determination of the telmisartan in capsule forms and biological samples. The proposed method has been proved to be advantageous over existing CZE and MEKC methods in simplicity, rapidity, and reproducibility.     

Indirect determination of chloride and sulfate ions in alcohol fuel by capillary electrophoresis

A capillary zone electrophoresis method using indirect UV detection for the analysis of chloride and sulfate in alcohol fuel samples was developed. The anions were analyzed in less than 3 min using an electrolyte containing 10 mmol l^–1 chromate and 0.75 mmol l^–1 hexamethonium bromide (HMB) as electroosmotic flow modifier. Coefficients of variation were better than 0.6% for migration time (n=10) and between 2.05 and 2.82% for peak area repeatabilities. Analytical curves of peak area versus concentration in the range of 0.065–0.65 mg kg^–1 for chloride and 0.25–4.0 mg kg^–1 for sulfate were linear with coefficients of correlation higher than 0.9996. The limits of detection for sulfate and chloride were 0.033 and 0.041 mg kg^–1, respectively. Recovery values ranged from 85 to 103%. The method was successfully applied for the quantification of sulfate and chloride in five alcohol fuel samples. The concentration of sulfate varied from 0.45 to 3.12 mg kg^–1. Chloride concentrations were below the methods LOD.     

Quantitative determination of acyclovir in plasma by near infrared spectroscopy

The aim of this study was to assess the feasibility of near infrared spectroscopy (NIRS) for analysis of acyclovir in plasma. This methodology was based on the direct measurement of the transmission spectra of liquid samples and a multivariate calibration model (partial least squares, PLS) to determine the acyclovir concentration in plasma sample. The PLS calibration set was built on using the spiked samples by mixing different amounts of acyclovir. Concentration of acyclovir in the plasma samples was calculated employing a 6-factors PLS calibration using the spectral information in the range of 6102-5450 cm^− 1. The root mean square errors of prediction (RMSEP) found was 1.21 for acyclovir. The developed PLS-NIRS procedure allows the determination of 120 samples/h does not require any sample pretreatment and avoids waste generation.     

Use of near-infrared reflectance spectroscopy in predicting nitrogen,phosphorus and calcium contents in heterogeneous woody plant species

Near-infrared reflectance spectroscopy was applied to determine nitrogen (N), phosphorus (P) and calcium (Ca) content in leaf samples of 18 woody species. A total of 183 samples from mountain, riparian and dry areas from the Central–Western Iberian Peninsula were collected for this purpose. The wide intervals of variation observed in nutrient concentrations (6.6–45.0 g kg^–1 for N, 0.24–2.97 g kg^–1 for P, and 1.00–20.06 g kg^–1 for Ca) were due to the great heterogeneity of the samples. To develop calibration equations, multiple linear regression, and partial least-squares regression (PLSR) were used. In both cases, three mathematical transformations of the data were applied: log1/R and first and second derivatives. The best calibration statistics were obtained using PLSR and derivative transformations (second derivative for N and first derivative for P and Ca). The following coefficients of multiple determination (R²) and standard errors of cross validation were obtained: 0.99 and 0.93 for N, 0.94 and 0.15 for P, and 0.95 and 0.88 for Ca. In the external validation the standard errors of prediction obtained were 0.76 (N), 0.11 (P) and 0.60 (Ca).     

First order pair functions for the beryllium isoelectronic sequence

The first order pair equations have been solved for the four electron sequence Li^– to Ne⁶⁺. A variational perturbation procedure is blended with numerical methods to generate a method for computing pair functions which is both accurate and efficient with respect to time of computation.The variation in the pair correlation energies as a function of atomic number is discussed and the asymptotic behaviour ofE ²(l) asl ^–4 andl ^–6 for singlet and triplet states respectively is corroborated. An estimate is made for the electron affinity of lithium.

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Zusammenfassung Die Paargleichungen 1. Ordnung wurden für die Reihe der Ionen mit 4 Elektronen von Li^– bis Ne⁶⁺ gelöst. Ein Variations-Störungsverfahren wird mit numerischen Methoden verknüpft, um eine Methode zur Berechnung von Paarfunktionen zu erhalten, die genau ist und möglichst geringe Rechenzeiten benötigt. Die Variation der Paarkorrelationsenergien als Funktion der Atomnummer wird diskutiert und das asymptotische Verhalten vonE ²(l) wiel ^–4 undl ^–6 für Singulet- und Tripletzustände wird bestätigt. Für Lithium wird die Elektronenaffinität abgeschätzt.

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Résumé Résolution des équations de paires au premier ordre pour la série à 4 électrons: Li^– à Ne⁶⁺. Un procédé de perturbation variationnel est lié à des méthodes numériques pour engendrer une méthode de calcul des fonctions de paires simultanément précise et économique. La variation des énergies de corrélation de paires en fonction du nombre atomique est discutée ainsi que le comportement asymptotique deE ²(l) par rapport àl ^–4 etl ^–6 pour les états singlet et triplet respectivement.