Second Derivative Method Research Articles

Analytic second derivatives in high-order many-body perturbation and coupled-cluster theories: Computational considerations and applications

The history of analytic first- and second-derivative methods in quantum chemistry is discussed, with special emphasis given to approaches that are associated with electron correlation treatments based on many-body perturbation theory (MBPT) and the coupled-cluster (CC) approximation. The computational requirements of recently developed analytical second derivative methods for high-order MBPT and CC methods are discussed in detail and compared with those associated with finite-difference procedures. Applications of these techniques to the calculation of anharmonic force fields used to deduce equilibrium geometries and fundamental vibrational frequencies for polyatomic molecules are reviewed.

Simultaneous determination of compounds in Septalen® pellets by derivative spectrophotometry

In this paper, a second-derivative spectrophotometric method of assaying Septalen ? pellets (Krka, Novo Mesto, Slovenia), which contain lidocaine 1 mg, and cetrimoniumbromide 2mg, is described. Lidocaine, 2-(diethylamino)-N-(2,6-dimethyl- phenyl)-acetamide, is a local anesthetic with pronounced antiarhythmic and anticonvulsant properties. Cetrimoniumbromide, N,N,N-trimethyl-l-hexadecanaminium bromide, is a topical antiseptic and cleansing agent. Lidocaine was determined at 250 nm using the "zero crossing" technique because the signals of centrimonium bromide and the colour ingredient are zero at this wavelength. Cetrimonium bromide was determined by correction of the peak amplitude at 215 nm according to lidocaine. In choosing the optimal magnitudes for the simultaneous determination of both drugs, the following criteria were considered: (1) the linearity of the calibration graphs as given by the correlation coefficients, (2) the intercept, (3) the sensitivity as given by the regression coefficient, (4) the degree of interference in the derivative measurement by the presence of the other compound, as given by the relative percent error and by the relative recovery, and (5) the reproducibility, as given by the coefficient of variation, calculated by recording the second-derivative spectra.

Determination of the partition coefficient of triflupromazine between phosphatidylcholine vesicles and water by 19F nuclear magnetic resonance spin-lattice relaxation time measurement

The 19F nuclear magnetic resonance (NMR) spin-lattice relaxation time ( T 1) of the trifluoromethyl signal of triflupromazine (TFZ) was measured in aqueous suspensions of phosphatidylcholine (lecithin) small unilamellar vesicles (SUV). The observed T 1 value depended on the concentration of SUV. Based on a simple two-site rapid exchange model, the partition coefficient ( K p) of TFZ between lecithin SUV and water was calculated from the relationship between the T 1 value and the lecithin concentration by using a nonlinear least-squares method. The obtained K p value (2.1±0.2×10 5) agreed well with that measured by a second-derivative spectrophotometric method. The 19F NMR T 1 method will be useful for the determination of partition coefficients of drugs having fluorine atom(s), especially for the drugs which do not have absorption in the ultraviolet or visible region, or for those having absorption but do not show any changes according to their incorporation into the lecithin bilayers. The method does not require any separation procedure that may disturb the equilibrium conditions.

Using contrasts as data pretreatment method in pattern recognition of multivariate data

A contrast method originally proposed by Spiegelman [C.H. Spiegelman, Calibration: a look at the mix of theory, methods and experimental data, presented at Compana '95, Wuerzburg, Germany.] is modified to pretreat multivariate data for classification. Three NIR data sets and one pollution data set are used as examples. Our results show that the contrast method greatly improves the ratios of between- to within-class variance. It is more powerful than offset correction, SNV, first- and second-derivative methods in the cases studied. This conclusion does not depend on the type of classifier used. Regularised discriminant analysis (RDA) and partial least squares (PLS2) with univariate feature selection based on Fisher's ratio were applied here. There is a risk that chance correlations occur after the contrast pretreatment. The chance correlation decreases after first eliminating un-informative variables using the modified Uninformative Variable Elimination (UVE)-PLS method.

19] Direct and simultaneous ultraviolet second-derivative spectrophotometric determination of nitrite and nitrate in preparations of peroxynitrite

We have determined the initial concentrations of nitrite and nitrate for three different methods of synthesizing peroxynitrite using an ultraviolet second-derivative spectroscopy method (Fig. 3). As expected, the net nitrogen balance in these preparations (Fig. 4) and the yields of nitrite and nitrate (Table II) indicate that, at pH 6.0, peroxynitrite decomposes to give essentially NO3-. Stock solutions of peroxynitrite prepared using method I (ozonation of azide) consistently contain more NO2- and NO3- than method II (isoamyl nitrite with hydrogen peroxide) and method III (hydrogen peroxide with nitrous acid). Method II gives the least amount of NO2- contaminants, and NO3- impurities are the lowest in method III (Table I).

PH-dependent secondary conformation of the peptide hormone leptin in different buffer solutions.

The secondary structure of leptin in each different pH buffer solution (pH 5.35, 6.75, 7.58 and 8.45) was first determined by attenuated total reflection (ATR)/Fourier transform infrared (FT-IR) spectrometer with second-derivative, Fourier self-deconvolution and band curve-fitting methods to quantitatively estimate the secondary structure of leptin. The results indicate that pH induced more stretching vibration of CH2 and bending vibration of C-H and/or symmetric stretching of carboxylate of leptin structure in higher pH buffer solution than in lower pH buffer solution. Moreover, the band area of amide I for leptin in the higher pH buffer solution markedly enlarged, suggesting the amide I contour of leptin was very sensitive to pH to alter the secondary conformation of leptin structure. The structural component and composition of amide I band for leptin in both pH 6.75 and pH 7.58 buffer solutions were similar and had 50-52% helical structure including alpha-helix at 1654 cm-1 and 3(10)-helical structure at 1659-1667 cm-1 and 1640 cm-1. Although the secondary structure of leptin in pH 5.35 and 8.45 buffer solutions were also similar, a different structural information was obtained.

Multivariate Sensitivity for the Interpretation of the Effect of Spectral Pretreatment Methods on Near-Infrared Calibration Model Predictions

Predictions obtained from a multivariate calibration model are sensitive to variations in the spectra such as baseline shifts, multiplicative effects, etc. Many spectral pretreatment methods have been developed to reduce these distortions, and the best method is usually the one that minimizes the prediction error for an independent test set. This paper shows how multivariate sensitivity can be used to interpret spectral pretreatment results. Understanding why a particular pretreatment method gives good or bad results is important for ruling out chance effects in the conventional process of "trial and error", thus obtaining more confidence in the finally selected model. The principles are exemplified using the transmission near-infrared spectroscopic prediction of oxygenates in ampules of the standard reference material gasoline. The pretreatment methods compared are the multiplicative signal correction, first-derivative method, and second-derivative method. It is shown that for this application the first- and second-derivative methods are successful in removing the background. However, differentiating the spectra substantially reduces multivariate net analyte signal (in the worst case by a factor of 21). Consequently, a significantly smaller multivariate sensitivity is obtained which leads to increased spectral error propagation resulting in a larger uncertainty in the regression vector estimate and larger prediction errors. Differentiating spectra also increases the spectral noise (each time by a factor 2(1/2)) but this effect, which is well-known, is of minor importance for the current application.

Analytical energy gradients in second-order Mo/ller–Plesset perturbation theory for extended systems

The spin-restricted formulas for the analytical gradients of the second-order Mo/ller–Plesset perturbation (MP2) energy are presented within the framework of ab initio crystal orbital theory of infinite one-dimensional lattices (polymers). The coupled perturbed Hartree–Fock equation for polymers is solved iteratively using the atomic-orbital-based algorithms. The MP2 energy and its gradient contributions are evaluated by the disk-based algorithms with the aid of the two-particle density matrix. The analytical-gradient method at the MP2 level, as well as the analytical first- and second-derivative methods at the Hartree–Fock (HF) level, is applied to calculate the equilibrium structures and harmonic vibrational frequencies of all-trans polyacetylene. The deviations of the calculated frequencies from the observed ones for the in-phase C=C stretching modes are reduced by about 70% on going from HF/6-31G to MP2/6-31G theory.

Non-destructive analysis of the conformational changes in human lens lipid and protein structures of the immature cataracts associated with glaucoma

Previous study has supposed a possible mechanism of exacerbating cataract formation in cataractous human lens capsules induced by hypertension or glaucoma. To clarify the glaucoma-induced cataract formation of the eyes lens, changes in the human lens lipid and protein structures of immature cataractous patients with or without glaucoma were investigated. Two normal lenses, ten immature cataractous lenses without any complication and four immature cataractous lenses with glaucoma were used after surgical operation. Each de-capsulated human lens sample was sliced with a number 15 surgical blade. The intact nuclear lens regions were used for non-destructive analysis. The lens lipid and protein structures, as well as compositions of these lens samples, were determined using a Fourier transform infrared (FTIR) microspectroscopy with second-derivative, de-convolution and curve-fitting methods. The results indicate that the IR spectrum of glaucomatous lenses appeared as a shoulder only at 2853 cm −1, thus the composition of the symmetric CH 2 stretching band at 2853 (2852) cm −1 decreased more significantly in glaucomatous lens to only one half of that in normal and immature cataractous lenses. The composition of the asymmetric CH 3 stretching band at 2965 cm −1 for normal lens decreases markedly from 32 to 20% for immature cataractous lenses with or without glaucoma. The compositional ratio of component at 2965 cm −1 to component at 2928 (2930) cm −1 for normal lenses was about 0.702, and that ratio for cataractous lenses without glaucoma was 0.382 but for glaucomatous lenses was 0.377. The maximum peak position of amide I band for IR spectra of the normal lens, immature cataractous lenses without complications or glaucomatous lenses appeared respectively at 1632, 1630 or 1622 cm −1, assigned to β sheet structure. A marked difference in peak intensity of amide I band for the normal lenses and immature cataractous human lenses with or without glaucoma was observed. The peak intensity ratio of amide I /amide II (1632/1545 cm −1) for normal lenses was in the range of 2.20–2.33, whereas in the spectra of immature cataractous lenses without glaucoma this ratio (1630/1545 cm −1) was 1.28–1.41 but was 1.04–1.13 for glaucomatous lens in the intensity ratio of 1622/1545 cm −1. The intensity of the glycogen bands in the wavenumber region 1135–1076 and 1069–1032 cm −1 was found to increase for the immature cataractous lenses with or without glaucoma, as compared with the normal ones. The peaks ranging from 1633 to 1610 cm −1 assigned to β-sheet structure also exhibited a pronounced compositional difference, particularly in glaucomatous lenses. The human lens lipid and protein secondary structures were more affected by glaucoma. Higher protein side chains and reduced lipid content contributed predominantly to the CH stretching vibrations of normal lens structure, whereas high lipid content and less protein side chains dominated the CH stretching vibrations of cataractous lenses with or without glaucoma. Decrease α-helix and random coil structures but enhanced β-sheet structure in the immature cataractous human lens induced by glaucoma might result from the formation of intermolecular hydrogen-bonding insoluble protein aggregates that modify the secondary structure of protein in lenses.

An Experiment in Electronic Spectroscopy: Information Enhancement Using Second Derivative Analysis

Second derivative (SD) analysis is extremely effective in enhancing and extracting information from experimental data where the information sought lies hidden. This paper describes an interesting experiment in molecular electronic spectroscopy in which information about the excited state vibrational levels of a molecule, contained in the absorption spectrum in latent form, is extracted by the SD analysis. The efficacy of the SD method is first demonstrated using synthetic data where the positions of hardly-noticeable gaussian features, buried obscurely in a strong, rising background, are recovered quantitatively. The method is then applied to the absorption spectrum of trimethylamine (TMA), which contains two absorption bands (arising from the nN --> 3sN and nN —> 3pN transitions) that show subtle undulations due to the presence of underlying vibronic features corresponding to the out-of-plane bending motion of the molecule. The positions of more than 30 vibrational features are determined using the SD analysis. The constancy of the spacing between adjacent features in each absorption band in the spectrum suggests that the excited state out-of-plane bending potential of TMA is considerably harmonic.

Simultaneous determination of medazepam and hyoscine butylbromide in tablets by second-derivative ultraviolet spectrometry

A second-derivative UV spectrophotometric method for the simultaneous determination of medazepam and hyoscine butylbromide in sugar-coated tablets without prior separation is described. In the derivative spectrophotometric determination of these drugs, calibration graphs were obtained by plotting peak-trough amplitudes at 252.6 and 264.8 run versus concentration of medazepam and zero-crossing amplitude at 212.5 nm versus concentration of hyoscine butylbromide. The relative standard deviation of the method was found to be ±0.56% for medazepam and ±0.08% for hyoscine butylbromide. This method has been successfully applied to tablets containing medazepam and hyoscine butylbromide.

Fourier transform infrared spectral evidences for protein conformational changes in immature cataractous human lens capsules accelerated by myopia and/or systemic hypertension

The possible changes in protein structures of the cataractous human lens capsules of the immature patients with myopia and/or systemic hypertension have been investigated using Fourier transform infrared (FT-IR) microspectroscopy. Second-derivative and deconvolution methods have been applied to obtain the position of the overlapping components of the amide I band and assign them to different secondary structures. Changes in the protein secondary structure and composition of amide I band were estimated quantitatively from Fourier self-deconvolution and curve fitting algorithms. The results indicate that myopia and/or systemic hypertension were found to significantly modify the protein secondary structure of the cataractous human lens capsules to increase the β-type structure and random coil and decrease the α-helix structure. Myopia-induced conformational change in triple helix structure was more pronounced. In conclusion, myopia and/or systemic hypertension seem to modify the conformation of the protein structures in cataractous human lens capsule to change ionic permeation through lens capsule to accelerate the cataract formation of senile patients.

Possible mechanism of exacerbating cataract formation in cataractous human lens capsules induced by systemic hypertension or glaucoma.

To clarify the role of the lens capsule in cataract formation, changes in the protein conformational structure of immature cataractous lens capsules from patients with systemic hypertension or glaucoma have been investigated, as compared to normal lens capsules. The protein secondary structure and composition of these capsular samples were determined using Fourier transform infrared microspectroscopy with second-derivative, deconvolution and curve-fitting methods. We found that the composition of both random coil and beta-type (beta-sheet and beta-turn) structures in the immature cataractous human lens capsules was increasingly induced by systemic hypertension or glaucoma, but alpha-helix content clearly decreased, leading to the alteration of protein conformational structures in lens capsules. A possible pathway of cataract formation exacerbated by systemic hypertension or glaucoma is discussed. According to the results, we propose that systemic hypertension or glaucoma induce changes in the protein conformational structures of the lens capsule, then cause alteration of membrane transport and permeability for ions, and finally increase intraocular pressure, resulting in the exacerbation of cataract formation. The effect on the conformational structure of cataractous human lens capsules is more pronounced for systemic hypertension than for glaucoma. The present study implies that systemic hypertension or glaucoma can exacerbate cataract formation in senile patients by modifying the protein secondary structures in the lens capsule.

Simultaneous determination of aluminium and iron in glasses,phosphate rocks and cement using first- and second-derivative spectrophotometry.

First- and second-derivative spectrophoto-metric methods for the simultaneous determination of aluminium and iron in their mixtures are described. The methods are based on the colored complexes formed by aluminium and iron with hematoxylin in the presence of cetyltrimethylammonium bromide as a surfactant. The zero-crossing method has been utilized to measure the first- and second-derivative value of the derivative spectrum. Aluminium (0.05-1 microg ml(-1)) could be determined in the presence of iron (0.09-1.6 microg ml(-1)) and vice versa. The detection limits of aluminium and iron are 0.01 and 0.09 microg ml(-1), respectively in the first-derivative mode and 0.014 and 0.1 microg ml(-1) in the second-derivative mode. The proposed method has been applied to the simultaneous determination of aluminium and iron in glasses, phosphate rocks, cement and magnesite alloy.

Second-Derivative UV Spectrometric Microdetermination of Dithiocarbamate Residues as Methyl Xanthate

Abstract The microdetermination of dithiocarbamate fungicide residues as methyl xanthate using second-derivative UV spectrometry is described. The residue analysis is based on a hot-acid decomposition, scrubbing the evolved CS2 with lead acetate and concentrated H2SO4, and absorbing the CS2 in methanolic KOH. The absorbance of the xanthate system (conventional method) and the height of the negative peak at 302 nm (second-derivative method) are used to quantitate the CS2. The molar absorptivity of the xanthate system within the range of 0.3–2.4 μg CS2/mL where Beer’s law is obeyed, was 1.70 × 104 L mol-1 cm-1. The derivative procedure was more selective and sensitive to CS2 than the classical method. The calibration graph of the derivative procedure was rectilinear from 0.1–1.1 μg/mL of CS2. The coefficient of variation for the determination (n = 10) of a 0.28 (μg/mL standard of CS2 was 2.6%. The detection limit for CS2 was 0.08 μg/mL. The second-derivative procedure was applied to the residue analysis of thiram on tomatoes.

Estimation of the Tolerance Level of Interfering Substances in Instrumental Analytical Methods

Abstract A model to estimate the tolerance level of interfering substances for analytical procedures, applying the linear simple regression, is proposed. The confidence interval on the analytical signal for the selected concentration value to check the interference, is calculated using the calibration data set. The tolerance levels of molybdenum, aluminium and iron in the spectro fluorimetric determination of boron with Alizarin Red S by means of direct, synchronous and first- and second-derivative methods, are estimated. The adequate selection of an analyte concentration for the interferent test is discussed.

Determination of sulphanilamide in milk by first-derivative and second-derivative spectrofluorimetry.

First-derivative and second-derivative spectrofluorimetric methods have been developed for the analysis of sulphanilamide (SAN) in milk, using an ethanol-water (60:40, v/v) medium. Linear calibration plots were obtained over a concentration range of 30-120 ppb, with correlation coefficients greater than 0.997. Relative standard deviations were within the range 1.6-3.6%. Limits of detection were 0.7-2.7 ppb. Recoveries of 90-102% were obtained. The derivative fluorescence methods are simple, rapid and sensitive and there is no interference from fluorescent impurities in the determination of low levels of SAN in milk.

Radiation-induced inactivation of angiotensin-converting enzyme in aqueous solutions

Radiation-induced inactivation of angiotensin-converting enzyme (ACE) was studied. The relationship of this process to damage to aromatic amino acid residues (tyrosine and tryptophan) was demonstrated by the method of second derivatives of UV spectra. In some cases, the dependence of inactivation on dose had an induction period. The comparison of the radiation-induced inactivation parameters of ACE, serine proteinases, and horseradish peroxidase points to a significant stabilizing effect of carbohydrate residues in glycoproteins (“autoprotective mechanism”). At pH 7.5, conformational changes occur in ACE. Low accessibility of the active center of this enzyme was suggested.

Second-derivative spectrophotometric determination of naproxen in the presence of its metabolite in human plasma.

A second-derivative spectrophotometric method for the determination of naproxen in the absence or presence of its 6-desmethyl metabolite in human plasma is described. The method consists of direct extraction of the non-ionized form of the drug with pure diethyl ether and determination of the naproxen by measuring the peak amplitude (mm) in the second-order derivative spectrum at a wavelength of 328.2 nm. The efficiency of the extraction procedure expressed by the absolute recovery was 94.6 +/- 0.7% (mean +/- s) for the concentration range tested, and the limit of quantification attained according to the IUPAC definition was 2.42 mg l-1. The linear dynamic range for naproxen was 5.0-100.0 mg l-1, the correlation coefficient for the calibration graphs was excellent, r = 0.99993 (n = 6), the precision (Sr) was better than 4.58% and the accuracy was satisfactory (Er < 2.32%). The results obtained by the proposed method were in good agreement with those found by an HPLC method.

Subμm registration of fiducial marks using machine vision

Sub/spl mu/m registration between circularly symmetric fiducial marks can be achieved simply by finding their centroids by fitting circles to distributed edge positions determined by the second-derivative zero-crossing method. However, because of diffraction fringes, substantial errors originating in the tilt of the microscope optical axis must be minimized. This method is used for laser-fibre alignment tolerance studies. >