On the Analysis of Raman Spectra by Curve Resolution

1977 ◽  
Vol 31 (5) ◽  
pp. 451-455 ◽  
Author(s):  
Peter Gans ◽  
J. Bernard Gill
Keyword(s):  
Raman Spectrum ◽  
Raman Spectra ◽  
Liquid Ammonia ◽  
Shape Function ◽  
Shape Functions ◽  
Large Uncertainty ◽  
Empirical Parameter ◽  
Curve Resolution ◽  
Lorentzian Shape

Raman spectra obtained during studies of solution equilibria are subjected to analysis using a combination of a small, manually controlled, digital minicomputer and a large digital computer. The shape-function of the bands is regarded as an empirical parameter, and the majority of bands are found to have Lorentzian shape. Simultaneous determination of shape-function and curved baseline is shown to be unsatisfactory. The possibility that components of a multiplet have different shape-functions is considered, and a probable example of such a case is given. Finally, it is shown that the ν3 region of the Raman spectrum of sodium nitrate in liquid ammonia probably contains three component bands, but uncertainty regarding shape-function introduces large uncertainty into the areas and positions of the bands.

scholarly journals The Effect of Noise in Raman Spectra on the Reconstruction of the Concentration of Amino Acids in the Mixture by Multivariate Curve Resolution (MCR) Analysis

2021 ◽  
Vol 7 (2) ◽  
pp. 020309
Author(s):  
Irina Matveeva ◽  
Lyudmila Bratchenko ◽  
Oleg Myakinin ◽  
Elena Tupikova ◽  
Valery Zakharov
Keyword(s):  
Amino Acids ◽  
Raman Spectrum ◽  
Amino Acid ◽  
Raman Spectra ◽  
Biological Tissues ◽  
Amino Acid Mixture ◽  
Multivariate Curve Resolution ◽  
Acid Mixture ◽  
Curve Resolution ◽  
Negative Effect

Changes in the concentration of free amino acids in biological tissues is a sign of impaired protein metabolism in patients with cancer. Recently, Raman spectroscopy has been used for early diagnostics of oncological diseases. The concentrations of individual components of biological tissue (for instance, the concentrations of amino acids) can be obtained by decomposing the tissue Raman spectrum. This study was designed to evaluate the effect of noise in the Raman spectra of individual amino acids on the result of the decomposition of the spectra of an amino acid mixture. As a decomposition method, we used Multivariate Curve Resolution-Alternating Least Squares (MCR–ALS) analysis and investigate experimental Raman spectra of amino acids and mathematically simulated Raman spectra of amino acid mixtures. Noise with different signal-to-noise ratios (SNR) was artificially added to both the experimental spectra of pure amino acids and the spectra of the mixtures. Concentration values for each amino acid obtained as a result of applying the MCR–ALS analysis have been compared with the corresponding true values and the correlation coefficients have been calculated. The results show a less pronounced negative effect of noise in the case when the spectra of pure amino acids (which were used as a basis for the MCR–ALS analysis) are noisy, and a more pronounced negative effect when the spectrum of the mixture is noisy. The accuracy of reconstruction of an amino acid is also negatively affected by strong background fluorescence in the amino acid spectrum. Moreover, the results indicate that using the basis spectra with a high SNR (SNR = 5) makes it possible to successfully estimate the amino acid concentrations in a mixture even when the Raman spectrum of the mixture is noisy and has a low SNR (SNR < 5).

scholarly journals The normal vibrations of carbonate and nitrate ions

1931 ◽  
Vol 134 (823) ◽  
pp. 265-277 ◽  
Keyword(s):  
Raman Spectrum ◽  
Raman Spectra ◽  
Raman Effect ◽  
Normal Modes ◽  
Potassium Nitrate ◽  
Nitrate Ions ◽  
Carbonate Ion ◽  
Infra Red ◽  
Modes Of Vibration

When the Raman effect was first discovered, it was believed that every line in the Raman spectrum referred to some characteristic vibration of the scatter­ing molecule. Later the tendency was to regard the lines as due to transitions between states of vibration of the molecule, so that the energies corresponded not to energies of vibration directly, but to differences in the energy of vibra­tion of two different modes. It is now realised that the infra-red spectrum of a substance and the Raman spectrum which it scatters give complementary information. Certain modes of vibration are represented solely in the infra­red spectrum, others are found only in the Raman spectrum, while others may appear in both spectra. Quite early a rough criterion on the basis of symmetry was put forward by Schaefer, for the determination of whether or not a particular vibration was to be expected in the Raman effect. Recently a selection rule has been formulated by Placzek; no vibration will appear as a fundamental in the Raman effect if it is such that any symmetrical operation upon it can change the signs of the displacements of the normal co-ordinates, without altering the energy. It is clear that a knowledge of the normal modes of vibration of the molecule under discussion must precede the application of any such rule, and it is the purpose of the present communication to discuss the normal modes of vibration of the carbonate and nitrate ions. In 1929 the writer showed that it was possible to obtain Raman spectra from powdered crystals, and the discovery was made when using powdered crystals of potassium nitrate. The method was applied first to carbonates and nitrates, so it became of interest to attempt to fix the structure of the anions of these salts by means of the Raman spectra combined with the infra-red data. In what follows the carbonate ion will first be dealt with in some detail, and then the nitrate ion can be treated summarily owing to the similarity of structure of the two ions.

Determination of the Resolution of a Multichannel Raman Spectrometer Using Fourier Transform Raman Spectra

2003 ◽  
Vol 57 (2) ◽  
pp. 190-196 ◽  
Author(s):  
Bryan T. Bowie ◽  
Peter R. Griffiths
Keyword(s):  
Raman Spectroscopy ◽  
Fourier Transform ◽  
Raman Spectra ◽  
Shape Function ◽  
Raman Spectrometer ◽  
Fourier Transform Raman ◽  
Nominal Resolution ◽  
Line Shape Function ◽  
Ft Raman

The resolution of a grating polychromator for Raman spectroscopy has been simulated by measuring spectra on a Fourier transform (FT) Raman spectrometer and selecting the FT of the apodization function so that the instrument line shape function mimics the triangular spectral slit function of the polychromator. To this end, FT-Raman spectra measured with a nominal resolution of 0.5 cm−1 were modified through the application of sinc2 apodization functions of various widths to simulate spectra measured on a polychromator at lower resolution. The success of this approach was validated using the 1085 cm−1 band of calcite. When the modified FT-Raman spectra were compared with spectra measured on a grating polychromator equipped with slits of widths 100 and 150 μm, the resolution of the polychromator was estimated to be 6.3 and 7.8 cm−1, respectively. This conclusion was verified experimentally by measuring the separation of two bands in the Raman spectrum of BaSO4 at ∼460 cm−1

scholarly journals Direct determination of shape functions for isoparametric elements with arbitrary node configuration

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Julian Hoth ◽  
Wojciech Kowalczyk
Keyword(s):  
Shape Function ◽  
Direct Determination ◽  
Correction Procedure ◽  
Shape Functions ◽  
Isoparametric Element ◽  
Lagrange Polynomial ◽  
Regular Node ◽  
Element Type ◽  
Single Formula

AbstractShape functions have been derived to describe different forms of elements, notably triangles and rectangles in 2-D, and tetrahedrons, cuboids, and triangular prisms in 3-D. There are generalised solutions for some regular node configurations, and hierarchical correction algorithms help with more difficult node distributions. But to this point there is no single formula or set of formulae that allows the direct determination of shape functions for any node configuration without restrictions. This paper shows how a general set of formulae can be derived which is applicable to any isoparametric element type with arbitrary node configuration. This formulation is in such a form that it is clear and concise. The approach is based on the Lagrange polynomial considering up to three Cartesian and four volume coordinates. Additionally, the correction procedure that is inherent in the formulation to guarantee an appropriate evaluation of the generalised shape functions and to fulfil all four isoparametric shape function criteria is discussed. The proof of validity illustrates the correctness of the method.

scholarly journals Learned Peak Shape Functions for Powder Diffraction Data

1988 ◽  
Vol 41 (2) ◽  
pp. 229 ◽  
Author(s):  
A Hepp ◽  
Ch Baerlocher
Keyword(s):  
Crystal Structure ◽  
Powder Diffraction ◽  
Shape Function ◽  
Linear Interpolation ◽  
Peak Shape ◽  
Powder Diffraction Data ◽  
Shape Functions ◽  
Inflection Points ◽  
Asymmetry Function

An algorithm is described for the determination of an experimental (learned) peak shape function, which has been used succesfully in crystal structure refinements from powder data. The function gives an optimal fit to almost any peak shape since it is not based on an analytical expression. It is determined from a single peak in a pattern by first fitting this peak with the proposed algorithm which ensures that the function is smooth and has only one maximum and two inflection points. The learned function is then normalised and decomposed into a symmetric and an asymmetric part. These are stored in tabulated form, permitting linear interpolation. As with an analytical function, a FWHM and asymmetry function describing the 26 dependence of the peak shape can be applied.

scholarly journals Possibility of Human Gender Recognition Using Raman Spectra of Teeth

Molecules ◽  
2021 ◽  
Vol 26 (13) ◽  
pp. 3983
Author(s):  
Ozren Gamulin ◽  
Marko Škrabić ◽  
Kristina Serec ◽  
Matej Par ◽  
Marija Baković ◽  
...  
Keyword(s):  
Raman Spectra ◽  
Principal Component ◽  
Support Vector ◽  
Gender Recognition ◽  
Proof Of Concept ◽  
Male And Female ◽  
Tooth Type ◽  
Tooth Apex ◽  
The Difference

Gender determination of the human remains can be very challenging, especially in the case of incomplete ones. Herein, we report a proof-of-concept experiment where the possibility of gender recognition using Raman spectroscopy of teeth is investigated. Raman spectra were recorded from male and female molars and premolars on two distinct sites, tooth apex and anatomical neck. Recorded spectra were sorted into suitable datasets and initially analyzed with principal component analysis, which showed a distinction between spectra of male and female teeth. Then, reduced datasets with scores of the first 20 principal components were formed and two classification algorithms, support vector machine and artificial neural networks, were applied to form classification models for gender recognition. The obtained results showed that gender recognition with Raman spectra of teeth is possible but strongly depends both on the tooth type and spectrum recording site. The difference in classification accuracy between different tooth types and recording sites are discussed in terms of the molecular structure difference caused by the influence of masticatory loading or gender-dependent life events.

The resonance Raman spectra and excitation profiles of some 4-sulfamylazobenzenes

1977 ◽  
Vol 55 (9) ◽  
pp. 1444-1453 ◽  
Author(s):  
Kamal Kumar ◽  
P. R. Carey
Keyword(s):  
Raman Spectrum ◽  
Raman Spectra ◽  
Resonance Raman ◽  
Valence Bond ◽  
Wavelength Dependence ◽  
Accurate Estimation ◽  
Intensity Changes ◽  
Stretching Vibration ◽  
Resonance Raman Spectra ◽  
Frequency Changes

The resonance Raman spectra of three pharmacologically important sulfonamides, 4-sulfamyl-4′-dimethylaminoazobenzene (1), 4-sulfamyl-4′-hydroxyazobenzene (2), and 4-sulfamyl-4′-aminoazobenzene (3), are compared with those of analogues lacking the sulfonamide group. The —SO2NH2 moiety does not directly contribute intense or moderately intense bands to the resonance Raman spectra of 1, 2, and 3. However, —SO2NH2 ionization is reflected by frequency changes in a band near 1140 cm−1 and intensity changes in the 1420 cm−1 region. The normal Raman spectrum of 2 confirms that the intensity changes reflect —SO2NH2 ionization rather than unrelated changes in vibronic coupling. The effect of —OH ionization on the resonance Raman spectrum of 2 emphasizes that caution must be exercised when relating spectral perturbations to changes in contributions from valence bond type structures. Resonance Raman excitation profiles for the 1138, 1387, and 1416 cm−1 bands of 2 show that these bands gain intensity by coupling with the electronic transitions in the 240 to 450 nm region and that, more than 1000 cm−1 to the red of λmax, the wavelength dependence can be closely reproduced by the FB type terms of Albrecht and Hutley. The excitation profile for each band shows evidence for structure in the 470 nm region, although lack of sufficient excitation wavelengths prevents accurate estimation of the spacing. Under conditions of rigorous resonance the intense Raman lines all occur in the 1400 cm−1 region, i.e. they are 'bunched' in the region known to contain the —N=N— stretching vibration.

Wormhole solutions in modified f(R,φ,X) gravity

2021 ◽  
Vol 36 (04) ◽  
pp. 2150021
Author(s):  
M. Farasat Shamir ◽  
Adnan Malik ◽  
G. Mustafa
Keyword(s):  
Shape Function ◽  
Scalar Potential ◽  
Three Dimensional ◽  
State Parameter ◽  
Energy Conditions ◽  
Kinetic Term ◽  
Anisotropic Fluid ◽  
Shape Functions ◽  
Current Analysis ◽  
Static Space

This work aims to investigate the wormhole solutions in the background of [Formula: see text] theory of gravity, where [Formula: see text] is Ricci scalar, [Formula: see text] is scalar potential, and [Formula: see text] is the kinetic term. We consider spherically symmetric static space–time for exploring the wormhole geometry with anisotropic fluid. For our current analysis, we consider a particular equation of state parameter to study the behavior of traceless fluid and examine the physical behavior of energy density and pressure components. Furthermore, we also choose a particular shape function and explore the energy conditions. It can be noticed that energy conditions are violated for both shape functions. The violation of energy conditions indicates the existence of exotic matter and wormhole. Therefore, it can be concluded that our results are stable and realistic. The interesting feature of this work is to show two- and three-dimensional plotting for the analysis of wormhole geometry.

Studies of the Jahn - Teller effect IV. The vibrational spectra of spin-degenerate molecules

1962 ◽  
Vol 255 (1050) ◽  
pp. 31-53 ◽  
Keyword(s):  
Raman Spectrum ◽  
Raman Spectra ◽  
Vibrational Spectra ◽  
Physical Theory ◽  
Vibronic Coupling ◽  
Infra Red ◽  
Jahn Teller ◽  
Jahn Teller Effect ◽  
Active Vibration ◽  
Degenerate States

The physical theory necessary for interpreting the vibrational spectra of spin-degenerate molecules is developed in this paper. Particular attention is paid to those molecules whose behaviour is expected to be markedly different from that of both orbitally non-degenerate molecules and those with purely spatial degeneracy. These include certain Kramers degenerate molecules, whose Raman spectra are expected to contain reverse-polarized contributions, and also tetrahedral and octahedral molecules in fourfold degenerate states. The case of a fourfold degenerate octahedral molecule is investigated in the limits of strong vibronic coupling by one of the Jahn—Teller active vibrations (e g and t 2g ). It turns out that the forbidden t 2u vibration may be infra-red active, that the Raman spectrum may contain reverse-polarized contributions and that both infra-red and Raman spectra may contain strong progressions of bands involving multiple excitations of the vibronically active vibration.

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