Using the Tsallis distribution and the fractional differentiation to resolve the overlapping bands

Using the Tsallis distribution, which facilitates the generalization of well-known distributions such as Gaussian and Lorentzian by varying a non-extensivity parameter q as a model of the individual band to correctly assign overlapping bands and the fractional differentiation as mathematical tool to help to determine the spectral parameters of the individual band, a new resolution method for the overlapping bands is presented. According to variation of the maximum and the zero-crossing of the Tsallis distribution at different differential order, two types of parameter estimators are obtained, which are utilized to calculate the parameters of position, height, and width of Tsallis distribution. To verify the suggested method, separation of several kinds of overlapping bands simulated by computer and the experimental infrared spectrum of 1,2-bromofluoroethane have been performed and discussed. Figure α-Order differentiation of the overlapping band     

Spectral quality enhancement as an aid to polymer characterisation

The limit to the information on the microstructure of polymers that may be obtained from their vibrational spectra is often set by overlapping bands, markedly broader than the spectrometer resolution. Following the initial pioneering work of Pohl and Hummel, using a simple curve fitting technique, mathematical methods of spectral quality enhancement have progressed very considerably. These methods are reviewed critically and new results are presented. The desirability of imposing some parameter constraints in curve fitting is demonstrated, and this has led to the development of methods for peak narrowing, as an aid to peak finding. The two important approaches, derivative spectroscopy and Fourier selfdeconvolution (FSD), are discussed in terms of their application to the complex of overlapping bands in the v(C-Cl) region of the infrared spectrum of poly(vinyl chloride). A development of the FSD method termed Fourier band isolation, is described and preliminary results indicate that it has considerable promise. The maximum entropy method is discussed briefly.     

Quantitative Conformational Studies on Poly(vinyl Chloride)

Although curve fitting provides a method for obtaining intensity data for the individual components of overlapping band systems, the number of configurational and conformational bands in the C-Cl stretching region of the vibrational spectrum of poly(vinyl chloride) is such that many parameters have to be optimized. It is therefore desirable to impose constraints in the calculations, and prior knowledge of the number of component bands would be valuable. The potential of derivative spectroscopy for obtaining this information has been examined. It is shown that the superior resolution of second and fourth derivative spectra is partially offset by their inferior signal-to-noise ratio, a discriminatory effect against broader bands, and interference by subsidiary derivative peaks. The method has been used to examine the CH₂ deformation and C-Cl stretching modes of three PVC samples of different tacticity. With the former the overlapping system proves to be more complex than hitherto realized; hence, tacticity determinations based on the intensity ratio of two peaks only at 1428 and 1434 cm^?1 must be suspect. With the C-Cl stretching bands second derivatives are more useful than fourth derivatives, and the number and positions of the located bands are in broad agreement with the results from curve fitting, so providing confirmatory evidence for the correctness of the latter.     

Some aspects of the scope and limitations of derivative spectroscopy

Synthesised spectra are used to illustrate discussion of some relationships between recorded absorption profiles and their second and fourth derivative spectra. Limitations arising from the fortuitous overlap of a derivative peak with a neighbouring wing, and the possibilities of resolving spectra into their overlapping bands are also considered. The combined use of second and fourth derivative spectra to ascertain the correct number of bands within an observed profile is described. It is suggested that the practice of computing a least-squares fit of overlapping bands to a spectral profile be changed, because the minimisation achieved often produces a result involving excessive or negative absorbances: the spectral profile should be regarded as a boundary limit and any unaccounted (positive) absorbance then assessed as possible evidence for an additional band. An example is given, concerning the resolution of the spectrum of a thin, single crystal of uranium(IV) oxide at 77 K superimposed on an absorption edge. A comparison of the difference between the observed spectrum and the sum of its resolution into twelve overlapping bands, plus a similar comparison of their fourth derivative spectra, reveals a thirteenth band.     

Protein dynamics from NMR: the slowly relaxing local structure analysis compared with model-free analysis

(15)N-(1)H spin relaxation is a powerful method for deriving information on protein dynamics. The traditional method of data analysis is model-free (MF), where the global and local N-H motions are independent and the local geometry is simplified. The common MF analysis consists of fitting single-field data. The results are typically field-dependent, and multifield data cannot be fit with standard fitting schemes. Cases where known functional dynamics has not been detected by MF were identified by us and others. Recently we applied to spin relaxation in proteins the slowly relaxing local structure (SRLS) approach, which accounts rigorously for mode mixing and general features of local geometry. SRLS was shown to yield MF in appropriate asymptotic limits. We found that the experimental spectral density corresponds quite well to the SRLS spectral density. The MF formulas are often used outside of their validity ranges, allowing small data sets to be force-fitted with good statistics but inaccurate best-fit parameters. This paper focuses on the mechanism of force-fitting and its implications. It is shown that MF analysis force-fits the experimental data because mode mixing, the rhombic symmetry of the local ordering and general features of local geometry are not accounted for. Combined multifield multitemperature data analyzed with the MF approach may lead to the detection of incorrect phenomena, and conformational entropy derived from MF order parameters may be highly inaccurate. On the other hand, fitting to more appropriate models can yield consistent physically insightful information. This requires that the complexity of the theoretical spectral densities matches the integrity of the experimental data. As shown herein, the SRLS spectral densities comply with this requirement.     

Comparative spectral analysis of veterinary powder product by continuous wavelet and derivative transforms

Comparative simultaneous determination of chlortetracycline and benzocaine in the commercial veterinary powder product was carried out by continuous wavelet transform (CWT) and classical derivative transform (or classical derivative spectrophotometry). In this quantitative spectral analysis, two proposed analytical methods do not require any chemical separation process. In the first step, several wavelet families were tested to find an optimal CWT for the overlapping signal processing of the analyzed compounds. Subsequently, we observed that the coiflets (COIF-CWT) method with dilation parameter, a=400, gives suitable results for this analytical application. For a comparison, the classical derivative spectrophotometry (CDS) approach was also applied to the simultaneous quantitative resolution of the same analytical problem. Calibration functions were obtained by measuring the transform amplitudes corresponding to zero-crossing points for both CWT and CDS methods. The utility of these two analytical approaches were verified by analyzing various synthetic mixtures consisting of chlortetracycline and benzocaine and they were applied to the real samples consisting of veterinary powder formulation. The experimental results obtained from the COIF-CWT approach were statistically compared with those obtained by classical derivative spectrophotometry and successful results were reported.     

分解色谱重叠峰的参数契合法

本文研究了色谱重叠峰一阶导数曲线中各极值点的相对位置与重叠子峰面积比之间的关系，提出了一种模式参数契合的色谱重叠峰分解方法，它在准确性方面优于传统的垂线法，在速度方面优于模型拟合法，可用于实时快速处理。     

Band shape determination with robust estimator based on continuous wavelet transform

The paper focuses on an alternative approach that allows one to identify overlapping band shapes with the help of the continuous wavelet transform (CWT). We show that less number of special points for determining a band shape is required unlike the fractional derivative spectrometry method [S.S. Kharintsev, M.Kh. Salakhov, Spectrochim. Acta Part A, 60 (2004) 2125]. Besides, the CWT-based derivative spectrometry can be successfully utilized in a case of complex spectra corrupted with a white and/or high-frequency noise. The power of this method is illustrated on model examples and experimental spectra of 1,2-diphenylethane in crystalline and melted phase.     

A new approach to data reduction and evaluation in high-resolution time-of-flight mass spectrometry using a time-to-digital convertor data-recording system

A new effective and robust approach to the detection of incompletely resolved peaks, and evaluation of their parameters in high-resolution time-of-flight mass spectra for time-to-digital convertor (TDC) data acquisition mode, is described. The method is based on fast construction of a smoothed continuous curve that approximates the initial data (transformed to a constant relative width of time intervals for ion counting) with respect to precision of measurements. The first derivative of this curve is used for correction of skewness of the peak shape as far as possible. A contribution of the second derivative is subtracted from the smoothed curve for better resolution of partially resolved peaks. The comparison of local maxima of this resulting final curve with those for the initial smoothed curve allows reliable detection of the peaks and to test whether or not they are spoiled by overlapping. Ion counting performed by TDC gives an opportunity to estimate standard deviations of peak locations and their intensities. These values proved to be close to theoretically minimal standard deviations for these parameters for single fully resolved peaks. Thus, estimates of the main parameters of mass peaks by the described method are close to statistically efficient estimators for these parameters.     

Impurity spectroscopy at its ultimate limit: relation between bulk spectrum, inhomogeneous broadening, and local disorder by spectroscopy of (nearly) all individual dopant molecules in solids

We present a technique for the measurement of the low-temperature fluorescence excitation spectra and imaging of a substantial fraction of all single chromophore molecules (hundreds of thousands and even more) embedded in solid bulk samples as nanometre-sized probes. An important feature of our experimental studies is that the full information about the lateral coordinates and spectral parameters of all individual molecules is stored for detailed analysis. This method enables us to study a bulk sample in a broad spectral region with ultimate sensitivity, combining excellent statistical accuracy and the capability of detecting rare events. From the raw data we determined the distributions of several parameters of the chromophore spectra and their variations across the inhomogeneous absorption band, including the frequencies of the electronic zero-phonon lines, their spectral linewidths, and fluorescence count rates. Relationships between these distributions and the disorder of the matrix were established for the examples of two polycrystalline solids with very different properties, n-hexadecane and o-dichlorobenzene, and the amorphous polymer polyisobutylene. We also found spatially inhomogeneous distributions of some parameters.     

Theoretical prediction of spectral and optical properties of bacteriochlorophylls in thermally disordered LH2 antenna complexes

A general approach for calculating spectral and optical properties of pigment-protein complexes of known atomic structure is presented. The method, that combines molecular dynamics simulations, quantum chemistry calculations, and statistical mechanical modeling, is demonstrated by calculating the absorption and circular dichroism spectra of the B800-B850 bacteriochlorophylls of the LH2 antenna complex from Rs. molischianum at room temperature. The calculated spectra are found to be in good agreement with the available experimental results. The calculations reveal that the broadening of the B800 band is mainly caused by the interactions with the polar protein environment, while the broadening of the B850 band is due to the excitonic interactions. Since it contains no fitting parameters, in principle, the proposed method can be used to predict optical spectra of arbitrary pigment-protein complexes of known structure.     

The direct inverse method: A novel approach to estimate adsorption isotherm parameters

A novel method to estimate adsorption isotherm parameters is presented and its applicability is studied through synthetic as well as experimental data. This approach assumes a linear dependency of the UV absorption intensity on the solute concentration in the fluid phase, at least in certain ranges of the UV spectra. It was demonstrated that by fitting the absorption profiles, i.e. the new direct inverse method, and by fitting the concentration profiles, i.e. the classical inverse method, very similar adsorption isotherm parameters can be obtained. The findings presented in this work have as important implication the elimination of the requirement of converting a measured absorption intensity into a concentration value, i.e. the elimination of the calibration of the UV signal.     

An SCF-CI method for determining the potential energy surface of a triatomic molecule

A self-consistent-field (SCF)-configuration interaction (CI) (SCF-CI) method for determining the potential energy surface of a triatomic molecule from the observed vibrational band origins has been suggested. By this method, the SCF-CI procedure in the internal coordinates is used to calculate the vibrational bond origins and their first derivatives with respect to parameters in the potential energy function using the exact vibrational Hamiltonian, and the optimizer LMF in the nonlinear-squares problem is employed to optimize parameters in the potential energy function. This approach is used to optimize the potential energy function of the water molecule. The standard deviation of this fitting to the 70 observed band origins is 1.154cm-1.     

A multidimensional approach to the analysis of chemical shift titration experiments in the frame of a multiple reaction scheme

We present a method for fitting curves acquired by chemical shift titration experiments, in the frame of a three‐step complexation mechanism. To that end, we have implemented a fitting procedure, based on a nonlinear least squares fitting method, that determines the best fitting curve using a “coarse grid search” approach and provides distributions for the different parameters of the complexation model that are compatible with the experimental precision. The resulting analysis protocol is first described and validated on a theoretical data set. We show its ability to converge to the true parameter values of the simulated reaction scheme and to evaluate complexation constants together with multidimensional uncertainties. Then, we apply this protocol to the study of the supramolecular interactions, in aqueous solution, between a lanthanide complex and three different model molecules, using NMR titration experiments. We show that within the uncertainty that can be evaluated from the parameter distributions generated during our analysis, the affinities between the lanthanide derivative and each model molecule can be discriminated, and we propose values for the corresponding thermodynamic constants. Copyright © 2013 John Wiley & Sons, Ltd.     

Quantum-chemical investigation of the electroabsorption spectra of directly meso-meso-linked porphyrin arrays: essential role of charge-transfer excited states accidentally overlapping with soret bands

The electroabsorption (EA) spectra of directly meso-meso-linked porphyrin arrays (Zn, n = 1-3) have been investigated by means of the sum-over-states (SOS) approach at the INDO/S-SCI level theory. The experimental EA spectra of Zn (n > or = 2) exhibit an unusual second-derivative line shape at the exciton split low-energy B(x) band in contrast to the first-derivative spectrum of Z1, which is readily ascribed to a quadratic Stark shift of the B (Soret) band. Although the second-derivative line shape is usually attributed to a difference in the permanent dipole moment (Deltamu) between the ground and excited states, it should be vanishing for Zn due to their essentially D(2)(d) or D(2)(h) symmetry. As pointed out in our previous studies, the interporphyrinic charge-transfer (CT) excited states are accidentally overlapping with the excitonic B bands and the present calculations reveal that the B(x) state is strongly coupled via a transition dipole moment with two such CT states. These situations give rise to a quadratic Stark effect on the B(x) band that is intermediate between Stark shift (first derivative) and Stark broadening (second derivative), and play a central role in establishing the anomalous second derivative nature of the EA spectrum. Moreover, based on the comparison between the theoretical and experimental spectra, there must be an additional factor that further enhances the second derivative nature of the EA spectrum of porphyrin arrays. Discussions on this issue including the preliminary investigations on the role of solvent (PMMA)-induced asymmetry are also presented.     

Synthesis,characterization, thermal behavior,and DFT calculation of solid 1,4-bis(3-carboxy-3-oxo-prop-1-enyl) benzene of some trivalent lanthanides

In this paper, the derivative thermogravimetry (DTG) curve displays an overlapping peak which consists of two subpeaks for the major oil-producing stage of Indonesian oil sand. This study was conducted to supplement the insufficiencies of the previous studies, which neglected or oversimplified the processing of the overlapping peak and did not determine the kinetic mechanism. First of all, we assume a two-component parallel reaction model to describe the mass-loss process of the major oil-producing stage (overall stage) to obtain the separated stages. Then, we present an asymmetric multi-peak fitting method, bi-Gauss, to separate the overlapping peak. Based on the results of the bi-Gauss method, the kinetic mechanism was obtained using the integral master plot method, followed by the determination of the activation energy by the integral iso-conversional non-linear (NL-INT) method. The results show that the bi-Gauss method can produce satisfactory fitting results. Moreover, the separated stages follow single mechanism; while the overall stage does not follow a single mechanism and the mechanisms of the front and back segments of the overall stage are in accordance with those of the separated stages, which prove the reliability of the two-component parallel reaction model.     

Resolution of Overlapping Chromatographic Peaks Using a Genetic Algorithm

ABSTRACT

A genetic algorithm for resolution of overlapping chromatographic peaks (GAROCP) using real-number coding, non-uniform mutation and arithmetical crossover methods is described in this paper. It was applied to resolution of highly overlapped multicomponent high-performance liquid chromatographic peaks by fitting experimental chromatogram to the exponentially modified Gaussian (EMG) model. The genetic algorithm was used to find the minimum of fitting error to optimize the parameters in the EMG functions which determine the shape and area of each peak. The applicability of the method was investigated with both simulated signals calculated by EMG functions and experimental multicomponent overlapping chromatograms.     

Semi-Quantitative MALDI Measurements of Blood-Based Samples for Molecular Diagnostics

Accurate and precise measurement of the relative protein content of blood-based samples using mass spectrometry is challenging due to the large number of circulating proteins and the dynamic range of their abundances. Traditional spectral processing methods often struggle with accurately detecting overlapping peaks that are observed in these samples. In this work, we develop a novel spectral processing algorithm that effectively detects over 1650 peaks with over 3.5 orders of magnitude in intensity in the 3 to 30 kD m/z range. The algorithm utilizes a convolution of the peak shape to enhance peak detection, and accurate peak fitting to provide highly reproducible relative abundance estimates for both isolated peaks and overlapping peaks. We demonstrate a substantial increase in the reproducibility of the measurements of relative protein abundance when comparing this processing method to a traditional processing method for sample sets run on multiple matrix-assisted laser desorption/ionization-time of flight (MALDI-TOF) instruments. By utilizing protein set enrichment analysis, we find a sizable increase in the number of features associated with biological processes compared to previously reported results. The new processing method could be very beneficial when developing high-performance molecular diagnostic tests in disease indications.