No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
DFT studies of long-chain FAMEs: Theoretical justification for determining chain length and unsaturation from experimental Raman spectra
Abstract
Density functional calculations, using B3LPY/6-31G(d) methods, have been used to investigate the conformations and vibrational (Raman) spectra of a series of long-chain, saturated fatty acid methyl esters (FAMEs) with the formula CnH2nO2 (n=5–21) and two series of unsaturated FAMEs. The calculations showed that the lowest energy conformer within the saturated FAMEs is the simple (all-trans) structure and, in general, it was possible to reproduce experimental data using calculations on only the all-trans conformer. The only exception was C6H12O2, where a second low-lying conformer had to be included in order to correctly simulate the experimental Raman spectrum.The objective of the work was to provide theoretical justification for the methods that are commonly used to determine the properties of the fats and oils, such as chain length and degree of unsaturation, from experimental Raman data. Here it is shown that the calculations reproduce the trends and calibration curves that are found experimentally and also allow the reasons for the failure of what would appear to be rational measurements to be understood. This work shows that although the assumption that each FAME can simply be treated as a collection of functional groups can be justified in some cases, many of the vibrational modes are complex motions of large sections of the molecules and thus would not be expected to show simple linear trends with changes in structure, such as increasing chain length and/or unsaturation. Simple linear trends obtained from experimental data may thus arise from cancellation of opposing effects, rather than reflecting an underlying simplicity.
... Theoretical studies of lipids compounds has been performed in order to establish the general rules which govern the relative energies of the conformers in short-chain FAME [26]. Density functional calculations have been used to investigate the conformations and Raman spectra of long-chain FAME [27]. ...
... Fig. 2 shows the Raman spectra for the main esters present in soybean biodiesel, as listed in Table 1, plus the (12:0) and (14:0), which are references for the analysis of unsaturated esters in the liquid phase. Differences are observed in the Raman intensities and frequencies of some bands due to several factors, including: liquid vs. solid phases [16,25], number of carbon atoms in the chains [16,26,27] and number of insaturations [16]. The line shape of a biodiesel Raman spectrum is determined by the relative amount of these esters. ...
This work provides a systematic and comprehensible lineshape analysis of the Raman spectra from (i) the main esters that compose the soybean biodiesel, namely Palmitate, Stearate, Oleate, Linoleate and Linol- enate, (ii) mixtures of these esters, (iii) a soybean biodiesel reference material. Using theoretical spectral simulation as a guide, the experimental spectra are fit considering all the 3N-6 vibrational modes, where N is the number of atoms in the molecule. We demonstrate that while intensity analysis may lead to uncertainty in the definition of the relative ester contents in a mixture, a complete spectral analysis involving all parameters, including peak frequencies, allows spectral determination of esters composi- tion. Finally we define a protocol that can be used for defining the specific composition of unknown, including adulterated biodiesels, important for quality control.
... 2, full panel, or ref. [17]), the position of which turns out to depend on the length of the fatty acid (FA) chains. In fact, it has been proved that the intensity of this 1,440 cm -1 band turns out to depend on the number of carbons within the FA chain [20, 44], which, on the other hand, is not constant in TGs chains forming WAT. In alternative, in the case of adipose tissue, the peak at 1,745 cm -1 seem to provides a much more reliable standard for evaluating the UI of WAT, being specifically related to number of carbonyl groups in TGs, i.e. the paramount component of WAT, as revealed by the NMR measurements, which also were not able to detect any The band regions are defined inFig. 2 [25] Lipids (2011) 46:659–667 663 appreciable component of free fatty acids in it [31]. ...
... In alternative, in the case of adipose tissue, the peak at 1,745 cm -1 seem to provides a much more reliable standard for evaluating the UI of WAT, being specifically related to number of carbonyl groups in TGs, i.e. the paramount component of WAT, as revealed by the NMR measurements, which also were not able to detect any The band regions are defined inFig. 2 [25] Lipids (2011) 46:659–667 663 appreciable component of free fatty acids in it [31]. By the way, it is worth to mention that the intensity of the peak at 1,745 cm -1 is is taken as the reference to evaluate the molar parameters of fatty acids methyl esthers (FAME) by some authors [20,434445. On the other hand, the intensity of this peaks cannot be properly adopted as the reference for the assessment of the UI of free fatty acids, for which the situation is much more complex due to the spectral intermixing of C=C and C=O stretching modes. ...
In the last 20 years increasing interest has been devoted to the investigation of white adipose tissue (WAT) because hypo- or hyperfunction of WAT is involved in the pathogenesis of obesity and other pathologies. The investigation and discrimination of different characteristics in adipose tissues by means of spectroscopic techniques appears as a topic of current interest, also in view of possible medical-technological applications. The aim of this work was to establish micro-Raman spectroscopy as a tool for the characterization of mammals fat tissue. After preliminary tests aimed at defining a suitable sample preparation protocol, Raman spectra of WAT specimens excised from mice of different ages were recorded in the energy range 750-3,350 cm⁻¹. Quantitative values of the unsaturation index were obtained through the calibration with HR-NMR spectra of lipid extracts. Raman spectroscopy detected a sharp increase in the unsaturation index between 22 and 30 days of age in close correspondence with the weaning of mice (21 days). The present results show that Raman spectroscopy is an inexpensive, fast and robust technique to analyze the unsaturation index of mammals fat tissues that could be routinely used in bioptic samples.
... Their peaks form well behaved trends and are relatively well separated and comprehensively understood as described by a body of published work on using Raman spectra for the analysis of fatty acids. [9][10][11][12][13][14] A code version of calculating PCA is presented which has been developed for understanding rather than computation speed and is freely available to support the reader in undertaking their own explorations. ...
Spectroscopy rapidly captures a large amount of data that is not directly interpretable. Principal Components Analysis (PCA) is widely used to simplify complex spectral datasets into comprehensible information by identifying recurring patterns in the data with minimal loss of information. The linear algebra underpinning PCA is not well understood by many applied analytical scientists and spectroscopists who use PCA. The meaning of features identified through PCA are often unclear.
This manuscript traces the journey of the spectra themselves through the operations behind PCA, with each step illustrated by simulated spectra. PCA relies solely on the information within the spectra, consequently the mathematical model is dependent on the nature of the data itself. The direct links between model and spectra allow concrete spectroscopic explanation of PCA, such the scores representing âconcentrationâ or âweightsâ. The principal components (loadings) are by definition hidden, repeated and uncorrelated spectral shapes that linearly combine to generate the observed spectra. They can be visualized as subtraction spectra between extreme differences within the dataset. Each PC is shown to be a successive refinement of the estimated spectra, improving the fit between PC reconstructed data and the original data. Understanding the data-led development of a PCA model shows how to interpret application specific chemical meaning of the PCA loadings and how to analyze scores.
A critical benefit of PCA is its simplicity and the succinctness of its description of a dataset, making it powerful and flexible.
... Thus, polymer chains are simulated by short segments capable of reproducing the chemical environment in terms of interaction sites and steric hindrance around them. Furthermore, molecular models containing aliphatic chains and multiple conformational degrees of freedom, such as aliphatic esters or amides, are known to exhibit shallow Potential Energy Surfaces (PES) [275,276]. A preliminary PES exploration to identify relevant stationary state(s) is a fundamental step in the structure-optimization strategy because any ab-initio method will invariably localize the minimum that is closer to the initial input geometry. ...
Understanding and predicting sorption thermodynamics of low molecular weight compounds in rubbery and glassy polymers is of great relevance to elucidate important phenomena in areas at the interface of various scientific branches, such as the colloid and interface science, membrane science, polymer foaming, tissue engineering, scaffolding, microcellular materials, aerogels, and for the implementation of technological applications. The development of thermodynamic models for polymer-based mixtures, applicable over a wide range of conditions, remains an active and fascinating research area. Recent advances in statistical thermodynamics and a better understanding of intra- and inter-molecular interactions, thanks to accurate experimental measurements and molecular simulations using realistic force fields, have contributed significantly to this end. In fact, sorption thermodynamics in polymers plays a relevant role in describing phase equilibria of polymer mixtures, (hydro)gel swelling, intramolecular association, hydrogen-bonding cooperativity and polymer degradation and stability, in assessing durability of polymers exposed to aggressive environments, in predicting penetrant induced crystallization and plasticization phenomena in polymers, in designing polymer-based separation processes, in tailoring polymer foaming processes, in improving gas and vapor barrier properties of polymer packaging, in modelling devolatilization of polymer solutions and migration phenomena of additives, in designing drug delivery systems, to mention a few.
In the last decades, models have been introduced rooted on Equation of State theories, some of them based on compressible lattice frameworks. Notably, these models have been structured to specifically account for non-random distribution of molecular species and for dealing with several kinds of self-interactions that establish between polymer molecules and between penetrant molecules as well as cross-interactions that establish between moieties present on polymer backbone and penetrants. These models have been built to describe the behaviour of both rubbery polymers and out-of-equilibrium glassy polymers. Towards the further development of these approaches to gain an increased predictive capability of this thermodynamic description, recently have been also introduced approaches aimed at the estimation of relevant parameters based on molecular descriptors for calculations of properties of pure-components bulk phases and solutions.
Such a quantitative description of the sorption process by use of advanced thermodynamic theories invariably relies on a molecular-level characterization of the system under scrutiny to validate and support the theoretical framework. Information is required on the molecular aggregates formed in the system, their structure, stoichiometry and, whenever possible, their population. In this respect, vibrational spectroscopy (FTIR, Raman) has demonstrated to be among the most powerful techniques, due to its sensitivity towards H-bonding detection and to its sampling flexibility, which allows the development of in-situ, time-resolved measurements. In the last ten years, significant advancements have occurred in terms of both experimental approaches and data analysis techniques, which considerably contributed to deepening the interpretation of the molecular interactions scenario. In particular, Two-dimensional correlation spectroscopy (2D-COS), Difference spectroscopy (DS) and first-principles quantum chemistry calculations have made a strong impact on the amount and quality of the acquired information.
In view of the progress in this rapidly advancing and technologically relevant subject, this review article summarizes the state of the art on sorption thermodynamics modelling and on synergic combination with the wealth of information recently made available thanks to advanced vibrational spectroscopy techniques.
... Raman spectroscopy is also a type of vibrational spectroscopy that measures the fundamental vibrational modes of chemical bonds and gives structural information about the sample, while requiring minimal or no sample preparation (Afseth, Wold, & Segtnan, 2006). There are various studies reporting the use of Raman spectroscopy for characterization (Oakes, Beattie, Moss, & Bell, 2003), quality assessment (Guzman, Baeten, Pierna, & Garcia-Mesa, 2011) and detection of adulteration of fats based on their fatty acid composition (Uysal, Boyaci, Genis, & Tamer, 2013). However, to the best of our knowledge, there has been no research conducted on determination of erucic acid using Raman spectroscopy so far. ...
This study presents a novel method to determine erucic acid in canola oil samples by using Raman spectroscopy and chemometric analysis. The oil mixtures were prepared at various concentrations of erucic acid ranging from 0% to 33.56% (w/w) through binary combinations of different oils. In order to predict erucic acid content, Raman spectroscopy and GC results were correlated by means of partial least squares analysis. High coefficient of determination values was obtained for both calibration and validation data sets, which are 0.990 and 0.982, respectively. The results of the present study reveal the potential of Raman spectroscopy for rapid determination (45 s) of erucic acid in canola oil. Further research would be useful to improve the method to put it forward as an alternative to GC in the erucic acid analysis.
... Previous DFT studies involving clays and/or fatty acids have looked at the structure of clays [75], the catalytic activity of anionic clays [76], the vibrational and conformational properties of fatty acid methyl esters (FAMEs) using the B3LYP density functional [77], the attachment of the COOH group of fatty acids on metallic monolayers [78] or, using a Gaussian 3 variation, the combustion pathway of methyl butanoate to find a CO 2 production pathway [79]. At the time of writing, the most recent DFT study of clays [80] investigating the adsorption of volatile molecules on clays, acknowledges the current deficit of quantum-chemical, periodic ...
... Previous DFT studies involving clays and/or fatty acids have looked at the structure of clays, 17 the catalytic activity of anionic clays, 18 the vibrational and conformational properties of fatty acid methyl esters (FAMEs) using the B3LYP density functional, 19 the attachment of the COOH group of fatty acids on metallic monolayers, 20 or, using a Gaussian 3 variation, the combustion pathway of methyl butanoate to find a CO 2 production pathway. 21 The most recent DFT study of clays 22 investigating the adsorption of volatile molecules on clays acknowledges the current deficit of quantum-chemical, periodic cell studies of clays and molecules in general, other than those involving cluster models, 1 peptides, 23,24 or amino acids. ...
Mineral-catalyzed decarboxylation reactions are important in both crude oil formation and, increasingly, biofuel production. In this study we examined decarboxylation reactions of a model fatty acid, propionic acid, C(2)H(5)COOH, to an alkane, C(2)H(6), in a model of pyrophillite with an isomorphic substitution of aluminum in the tetrahedral layer. We model a postulated reaction mechanism (Almon, W. R.; Johns, W. D. 7th International Meeting on Organic Geochemistry 1975, Vol. 7) to ascertain the role of Al substitution and a counterion in decarboxylation reactions. We employ a periodic cell, planewave, ab initio DFT computation to examine the total energies and the frontier orbitals of different model sets, including the effects of charge on the reaction, the effect of Al substitution, and the role of Na counterions. The results show that an uncharged system with a sodium counterion is most feasible for catalyzing the decarboxylation reaction in an Al-substituted pyrophillite and, also, that analysis of the orbitals is a better indicator of a reaction than charge alone.
Surface-enhanced Raman scattering (SERS) spectra contain information on the chemical structure on nanoparticle surfaces through the position and alignment of molecules with the electromagnetic near field. Time-dependent density functional theory (TDDFT) can provide the Raman tensors needed for a detailed interpretation of SERS spectra. Here, the impact of molecular conformations on SERS spectra is considered. TDDFT calculations of the surfactant cetyltrimethylammonium bromide with five conformers produced more accurate unenhanced Raman spectra than a simple all-trans structure. The calculations and measurements also demonstrated a loss of structural information in the CH2/CH3 scissor vibration band at 1450 cm-1 in the SERS spectra. To study lipid bilayers, TDDFT calculations on conformers of methyl phosphorylcholine and cis-5-decene served as models for the symmetric choline stretch in the lipid headgroup and the C═C stretch in the acyl chains of 1,2-oleoyl-glycero-3-phosphocholine. Conformer considerations enabled a measurement of the distribution of double-bond orientations with an order parameter of SC═C = 0.53.
In the present study, a Raman line-imaging setup was employed to monitor in situ the CO2 sorption at elevated pressures (from 0.62 to 7.10 MPa) in molten PCL. The method allowed the quantitative measurement of gas concentration in both the time-resolved and the space-resolved modes. The combined experimental and theoretical approach allowed a molecular level characterization of the system. The dissolved CO2 was found to occupy a volume essentially coincident with its van der Waals volume and the estimated partial molar volume of the probe did not change with pressure. Lewis acid-Lewis base interactions with the PCL carbonyls was confirmed to be the main interaction mechanism. The geometry of the supramolecular complex and the preferential interaction site were controlled more by steric than electronic effects. On the basis of the indications emerging from Raman spectroscopy, an equation of state thermodynamic model for the PCL-CO2 system, based upon a compressible lattice fluid theory endowed with specific interactions, has been tailored to account for the interaction types detected spectroscopically. The predictions of the thermodynamic model in terms of molar volume of solution have been compared with available volumetric measurements while predictions for CO2 partial molar volume have been compared with the values estimated on the basis of Raman spectroscopy.
Sorption of water in PCL, with specific focus on the hydrogen bonding interactions, has been analysed by combining ab-initio calculations, macroscopic thermodynamics modelling and relevant features emerging from spectroscopic and gravimetric measurements. FTIR data, analyzed by Difference spectroscopy, Two-dimensional correlation spectroscopy and least-squared curve fitting analysis, associated with gravimetric determination of water sorption isotherm, provided information on the system's behaviour and on the molecular interactions established between the polymer and the penetrant. A consistent physical picture emerged pointing to the presence of two spectroscopically discernible water species (first-shell and second-shell layers), that have been quantified. Water molecules are present in the form of dimers within the polymer equilibrated with water vapour, up to a relative humidity of 0.65. At higher humidities clustering of water sorbed molecules starts to take place. The multi-component (OH) band representative of absorbed water has been interpreted with the aid of ab-initio calculations performed on suitably chosen model systems. The outcomes of spectroscopic analyses were interpreted at a macroscopic level by modeling the thermodynamics of water sorption in PCL based on a non-random compressible lattice theory accounting for Hydrogen Bonding (HB) interactions. Starting from the fitting of the gravimetric sorption isotherm, the model provided quantitative estimates for the amount of self- and cross-HBs' which compare favorably with the FTIR results.
We have recently demonstrated that the second hyperpolarizability γ of a selected vibrational mode of a molecule can be determined by using the computational Raman activity against an internal standard with a known Raman γ value. This approach provides a convenient way for prediction of the γ magnitude of DOVE four wave mixing spectroscopy, an optical analogue to two-dimensional (2D) NMR. Here, by using the Hartree-Fock (HF) method, the density functional theory (DFT) method, and the second-order Møller-Plesset perturbation theory (MP2) method, we extend our early work from the less anharmonic region <2000 cm(-1) into the more anharmonic region >2000 cm(-1) covering C-H, C-D, and C≡N stretching modes of benzene, deuterated benzene, acetonitrile, deuterated acetonitrile, and tetrahydrofuran. The computed Raman γ values of these vibrational modes have been determined by using either the 992 cm(-1) Raman band of benzene or the compound's own Raman band (C-C stretch) around 800-1000 cm(-1) as an internal standard. In this more anharmonic region, the HF method with a larger basis set provides the best outputs and the predicted Raman γ values agree well with experimental values for most of the vibrational modes studied. By choosing a suitable method and basis set, this facile approach could be applied to a broader spectral range for Raman γ estimation of various materials.
Large-scale two-dimensional (2D) arrays of metallic nanostructures formed by thin-film evaporation over hexagonally close-packed polystyrene spheres are established substrates for surface-enhanced Raman spectroscopy (SERS). By using these substrates with an integrated atomic force microscopy (AFM) and inverted Raman spectroscopy system, simultaneous topographical imaging and high-sensitivity chemical mapping can be performed. In this paper, we have used this technique to investigate supported bilayers of long-chain fatty acids and phospholipids deposited by the Langmuir-Blodgett (LB) and spin-coating techniques. Nanosphere lithography (NSL) substrates created from 384 and 1002 nm polystyrene spheres and silver (Ag) deposition on glass and sapphire substrates were characterized for SERS in terms of their structure, distribution, and level of enhancement. SERS mappings of rhodamine 6G (R6G) and p-aminothiophenol (p-ATP) monolayers on the 384 nm substrates demonstrate high and uniform enhancement at a micrometer scale. The enhancement was sufficiently high to enable measurement of SERS spectra for arachidic acid (AA) and dipalmitoylphosphatidylcholine (DPPC) layers on sapphire/Ag substrates. The roughness of these substrates (<2 nm) was lower than for glass/Ag (∼5 nm); therefore, simultaneous to SERS it was possible to measure the topography of the samples by AFM and determine the number of layers of AA and DPPC. This study shows the potential of the combined AFM/SERS technique for spectral and topographical characterization of phospholipid bilayers. This may prove to be an interesting approach for further studies with more complex heterogeneous lipid mixtures aiming to measure spatially resolved features such as microdomains.
Doubly vibrationally enhanced (DOVE) four-wave mixing spectroscopy, an optical analogue to 2D NMR, involves two infrared transitions and a Raman transition. The magnitude of the DOVE second hyperpolarizability γ (or third-order susceptibility χ((3))) can be theoretically estimated if the values of the dipolar moments of the two infrared transitions and the γ of the Raman transition are known. The Raman γ can be measured by using the four-wave mixing interferometric method or conventional Raman spectroscopy in the presence of an internal standard. In this work, we examine if one can use the Raman activity computed from density functional theory calculation to determine the Raman γ of selected vibrational modes of several samples including deuterated benzene, acetonitrile, tetrahydrofuran, and sodium benzoate aqueous solution. The 992 cm(-1) Raman band of benzene serves as an internal standard for organic solvents, and the 880 cm(-1) Raman band of hydrogen peroxide is for the aqueous solution sample with known γ values. We have found that the predicted Raman γ values from the computational Raman activities match experimental data reasonably well, suggesting a facile approach to predict the Raman γ of interested systems.
The resonance Raman spectra of ground and excited triplet states of the free base meso-tetraphenylporphyrin (H2TPP) were investigated. The density functional theory (DFT) calculations were carried out on both the states of the H2TPP and its isotopomers. The calculations provided predictions vibrational frequency shifts on excitation, which are more accurate than the absolute band positions because of cancellation of errors. The predicted shifts on excitation were typically small in the H2TPP molecules as the excitation was delocalized over the entire porphyrin ring system. It was observed that the interpretation of the resonance Raman spectra of the excited states of other tetrapyrroles using DFT calculation was viable.
A series of copolymers of N-isopropylacrylamide (NIPAM) and the more hydrophobic comonomer N-tert-butylacrylamide (NTBAM), with increasing NTBAM content (i.e., increasing hydrophobicity) were prepared. The adhesion of human epithelial cells on polymer films prepared from copolymers of NIPAM:NTBAM was observed to increase with increasing polymer hydrophobicity. However, in the absence of serum, cell adhesion to the different surfaces was statistically indistinguishable. Thus, it appears that the copolymer films differentially support cell adhesion due to selective adsorption of proteins from the physiological environment (the serum). Using contact angle measurements, molecular simulations, and Raman spectroscopy to characterize the different surfaces, we show evidence that the different behavior of cells on the films of increasing hydrophobicity is actually due to the different chemical properties of the surfaces with increasing content of NTBAM in the copolymers. As the NTBAM content is increased, the number of NH residues at the surface decreases, due to the additional steric hindrance of the bulkier NTBAM group, which results in decreased hydrogen bonding and thus decreased adsorption of proteins such as albumin. However, in some cases, the adsorption is driven by hydrophobic interactions, and proteins such as fibronectin were found to adsorb more to the films with a higher content of NTBAM. There appears, thus, to be a direct correlation between surface composition, i.e., the functional groups exposed at the surface, and protein binding and subsequent cell adhesion.
The accuracy of various computational methods (Hartree–Fock, MP2, CCSD, CAS-SCF, and several types of DFT) for predicting
relative intensities in Raman spectra for C6H6, C6D6, and C6F6 was compared. The predicted relative intensities for ν1 and ν2 were compared with relative intensities measured by an FT-Raman spectrometer. While none of these methods excelled at this
prediction, Hartree–Fock with a large basis set was most successful for C6H6 and C6D6, while PW91PW91 was the most successful for C6F6.
Reduced–size polarized (ZmPolX) basis sets are developed for the second–row atoms X = Si, P, S, and Cl. The generation of these basis sets follows from a simple physical model of the polarization effect of the external electric field which leads to highly compact polarization functions to be added to the chosen initial basis set. The performance of the ZmPolX sets has been investigated in calculations of molecular dipole moments and polarizabilities. Only a small deterioration of the quality of the calculated molecular electric properties has been found. Simultaneously the size of the present reduced–size ZmPolX basis sets is about one-third smaller than that of the usual polarized (PolX) sets. This reduction considerably widens the range of applications of the ZmPolX sets in calculations of molecular dipole moments, dipole polarizabilities, and related properties.
The work presented here is aimed at determining the potential and limitations of Raman spectroscopy for fat analysis by carrying out a systematic investigation of C4−C24 FAME. These provide a simple, well-characterized set of compounds in which the effect of making incremental changes can be studied over a wide range of chain lengths and degrees of unsaturation. The effect of temperature on the spectra was investigated over much larger ranges than would normally be encountered in real analytical measurements. It was found that for liquid FAME the best internal standard band was the carbonyl stretching vibration ρ(C=O), whose position is affected by changes in sample chain length and physical state; in the samples studied here, it was found to lie between 1729 and 1748 cm−1. Further, molar unsaturation could be correlated with the ratio of the ρ(C=O) to either ρ(C=C) or δ(H−C=) with R
2>0.995. Chain length was correlated with the δ(CH2)tw/ρ(C=O) ratio, (where “tw” indicates twisting) but separate plots for odd- and even-numbered carbon chains were necessary to obtain R
2>0.99 for liquid samples. Combining the odd- and even-numbered carbon chain data in a single plot reduced the correlation to R
2=0.94–0.96, depending on the band ratios used. For molal unsaturation the band ratio that correlated linearly with unsaturation (R
2>0.99) was ρ(C=C)/δ(CH2)sc (where “sc” indicates scissoring). Other band ratios show much more complex behavior with changes in chemical and physical structure. This complex behavior results from the fact that the bands do not arise from simple vibrations of small, discrete regions of the molecules but are due to complex motions of large sections of the FAME so that making incremental changes in structure does not necessarily lead to simple incremental changes in spectra.
The accuracies of the calculated vibrational frequencies and Raman intensities given by two new, highly compact Pol-type basis sets, Z2PolX and Z3PolX, have been determined and compared to the 6-31G(d), PolX, and aug-cc-pVTZ basis sets. Calculation of accurate Raman intensities has previously required large basis sets, but the ZmPolX basis sets are smaller even than PolX, which are the most compact basis sets able to calculate accurate Raman intensities. For the largest compound studied, C5H10O2, Z3PolX required more than an order of magnitude less CPU time than PolX, which has been shown to be 10 times faster than aug-cc-pVTZ. Two sets of test molecules were studied: one was a series of small molecules for which experimental values for absolute Raman activities were available; the second was a series of medium-sized molecules (mainly common organic solvents) where only relative Raman band intensities were available. The accuracies of the Raman intensities given by both of the ZmPolX basis sets were good compared to those of the PolX and aug-cc-pVTZ sets, and much better than the 6-31G(d) values. The errors in even unscaled frequency values <2000 cm(-1) were also acceptable and were slightly lower for Z3PolX than Z2PolX (30 cm(-1) vs. 48 cm(-1)). The combination of good intensity and frequency data meant that for the medium-sized organic molecules there was a close correspondence between the simulated Raman spectra and experimental data, and that the observed bands could easily be assigned on the basis of these calculations. Achieving this level of accuracy in the simulations at modest computational cost should now allow computational methods to be combined with experimental Raman studies much more widely than is currently the case.
Following the recent studies of basis sets explicitly dependent on oscillatory external electric field we have investigated the possibility of some further truncation of the so-called polarized basis sets without any major deterioration of the computed data for molecular dipole moments, dipole polarizabilities, and related electric properties of molecules. It has been found that basis sets of contracted Gaussian functions of the form [3s1p] for H and [4s3p1d] for the first-row atoms can satisfy this requirement with particular choice of contractions in their polarization part. With m denoting the number of primitive GTOs in the contracted polarization function, the basis sets devised in this article will be referred to as the ZmPol sets. In comparison with earlier, medium-size polarized basis sets (PolX), these new ZmPol basis sets are reduced by 2/3 in their size and lead to the order of magnitude computing time savings for large molecules. Simultaneously, the dipole moment and polarizability data remain at almost the same level of accuracy as in the case of the PolX sets. Among a variety of possible applications in computational chemistry, the ZmPolX are also to be used for calculations of frequencies and intensities in the Raman spectra of large organic molecules (see Part II, this issue).
Raman spectroscopy has been used to predict the abundance of the FA in clarified butterfat that was obtained from dairy cows fed a range of levels of rapeseed oil in their diet. Partial least squares regression of the Raman spectra against FA compositions obtained by GC showed that good prediction of the five major (abundance >5%) FA gave R
2=0.74–0.92 with a SE of prediction (RMSEP) that was 5–7% of the mean. In general, the prediction accuracy fell with decreasing abundance in the sample, but the RMSEP was <10% for all but one of the 10 FA present at levels >1.25%. The Raman method has the best prediction ability for unsaturated FA (R
2=0.85–0.92), and in particular trans unsaturated FA (best-predicted FA was 18∶1tΔ9). This enhancement was attributed to the isolation of the unsaturated modes from the saturated modes and the significantly higher spectral response of unsaturated bonds compared with saturated bonds. Raman spectra of the melted butter samples could also be used to predict bulk parameters calculated from standard analyzes, such as iodine value (R
2=0.80) and solid fat content at low temperature (R
2=0.87). For solid fat contents determined at higher temperatures, the prediction ability was significantly reduced (R
2=0.42), and this decrease in performance was attributed to the smaller range of values in solid fat content at the higher temperatures. Finally, although the prediction errors for the abundances of each of the FA in a given sample are much larger with Raman than with full GC analysis, the accuracy is acceptably high for quality control applications. This, combined with the fact that Raman spectra can be obtained with no sample preparation and with 60-s data collection times, means that high-throughput, on-line Raman analysis of butter samples should be possible.
Raman spectroscopy has been used for the first time to predict the FA composition of unextracted adipose tissue of pork, beef, lamb, and chicken. It was found that the bulk unsaturation parameters could be predicted successfully [R
2=0.97, root mean square error of prediction (RMSEP)=4.6% of 4 δ], with cis unsaturation, which accounted for the majority of the unsaturation, giving similar correlations. The combined abundance of all measured PUFA (≥2 double bonds per chain) was also well predicted with R
2=0.97 and RMSEP=4.0% of 4 δ. Trans unsaturation was not as well modeled (R
2=0.52, RMSEP=18% of 4 δ); this reduced prediction ability can be attributed to the low levels of trans FA found in adipose tissue (0.035 times the cis unsaturation level). For the individual FA, the average partial least squares (PLS) regression coefficient of the 18 most abundant FA (relative abundances ranging from 0.1 to 38.6% of the total FA content) was R
2=0.73; the average RMSEP=11.9% of 4 δ. Regression coefficients and prediction errors for the five most abundant FA were all better than the average value (in some cases as low as RMSEP=4.7% of 4 δ). Cross-correlation between the abundances of the minor FA and more abundant acids could be determined by principal component analysis methods, and the resulting groups of correlated compounds were also well predicted using PLS. The accuracy of the prediction of individual FA was at least as good as other spectroscopic methods, and the extremely straightforward sampling method meant that very rapid analysis of samples at ambient temperature was easily achieved. This work shows that Raman profiling of hundreds of samples per day is easily achievable with an automated sampling system.
In this study multivariate analysis of Raman spectra has been used to classify adipose tissue from four different species (chicken, beef, lamb and pork). The adipose samples were dissected from the carcass and their spectra recorded without further preparation. 102 samples were used to create and compare a range of statistical models, which were then tested on 153 independent samples. Of the classical multivariate methods employed, Partial Least Squares Discriminant Analysis (PLSDA) performed best with 99.6% correct classification of species in the test set compared with 96.7% for Principal Component Linear Discrimination Analysis (PCLDA). Kohenen and Feed-forward artificial neural networks compared well with the PLSDA, giving 98.4 and 99.2% correct classification, respectively.
New scaling factors have been determined for obtaining fundamental vibrational frequencies and zero‐point vibrational energies from harmonic frequencies calculated at the HF/6–31G* and MP2/6–31G* levels. The scaling factors for the fundamental frequencies have been derived from a comparison of a total of 1066 calculated frequencies for 122 molecules with corresponding experimental values, while the zero‐point energy scaling factors were determined from a comparison of the computed values with the experimental zero‐point energies for a set of 24 molecules. The scaling factors recommended are, respectively, 0.8929 and 0.9427 for HF/6–31G* and MP2/6–31G* fundamental frequencies, and 0.9135 and 0.9646 for HF/6–31G* and MP2/6–31G* zero‐point energies. RMS errors were determined to be around 50 cm−1 for the HF and MP2 fundamental frequencies, and around 0.4 kJ mol−1 for the HF and MP2 zero‐point energies.
Raman spectra of low (13°C) and high (16°C) m.p. crystals of oleic acid were recorded and the spectral differences were ascribed to different conformations around a pair of sp2, CC axes, i.e. (skew, skew′) and (skew, skew). Crystalline modifications (m.p. 29°C and 29.5°C) of petroselinic acid were found for the first time; after spectral comparison with oleic acid conformations in those crystals were predicted to be (skew, skew′) and (skew, skew). Raman spectra of dioleoyl- and dipetroselinoyl-l-α-phosphatidylcholines were measured for different crystalline phases and the conformation was examined.The skeletal vibration bands of the polymethylene chains of cis- and trans-unsaturated fatty-acids were analysed by using the frequency-phase difference relationships of saturated fatty-acids. The ν4 (stretching) vibrations were localised within each polymethylene chain and the bands of an acid CH3(CH2)m−2CHCH(CH2)n−2COOH were explained in terms of the set of phase differences δ = kπ/m and kπ/n (k = 1, 2,..). A unique ν4 vibration with δ = π/2m was also found. The ν5 (bending) vibrations sometimes couple strongly with each other to form overall vibrations characterised by δ = kπ/(m + n).Implications of the cis-olefin group for the physical properties of phospholipid bilayers and the applicability of Raman spectroscopy in probing chain conformations were discussed.
Geometries and harmonic frequencies of CH4, NH3, H2O, HF, C2H2, C2H4, C2H6, HCN, CO, H2CO and CH3F are calculated via density functional theory (DFT) using the “hybrid” density functionals “Becke3-Lee-Yang-Parr” and “Becke3-Perdew86” at the 6-31G∗ and TZ2P basis set levels. At both basis set levels, the results are in better agreement with experiment than those obtained via DFT using the LSDA and BLYP functionals and via the SCF and MP2 methodologies. At the TZ2P basis set level, the mean absolute deviation of predicted and experimental bond lengths is 0.005 Å for both hybrid functionals; at 6-31G∗ it is 0.006 Å. The mean absolute percentage deviation of predicted and experimental harmonic vibrational frequencies is 1.2% at TZ2P and 1.9–2.0% at 6-31G∗.
The rapid analysis of fats and oils is of great importance in the food industry. It is shown that Fourier transform Raman spectroscopy may be used for this purpose. Good quality spectra, free of fluorescence, may be obtained and the spectra may be interpreted in terms of changes in total unsaturation, cis/trans isomer ratios and the number of double bonds in the hydrocarbon chains. Quantitative analysis of total unsaturation and cis/trans is possible and offers considerable improvements in speed when compared with conventional methods.
The Raman spectra of fatty acids, fatty acid methyl esters and several membrane lipids are analyzed in the 1300 cm−1 region. The ratio of peak intensities at 1303/1267 cm−1 varies linearly with the ratio of methylene to vinyl groups in the hydrocarbon chain. This parameter should be useful for estimating the degree of unsaturation in isolated lipids and lipids in membranes.
The quadratic configuration interaction calculation in the Gaussian‐2 second‐order Møller–Plesset perturbation theory approach, G2(MP2), is replaced by a coupled‐cluster (CC) singles and doubles calculation including a perturbational estimate of the triples excitations. In addition, the self‐consistent‐field (SCF) and MP2 geometry optimizations and SCF frequency calculation in the G2(MP2) approach are replaced by a density functional theory geometry optimization and frequency calculation [using the Becke three parameter hybrid functional with the Lee–Yang–Parr non‐local correlation functional (B3LYP)] in the proposed G2(B3LYP/MP2/CC) approach. This simplification does not affect the average absolute deviation from experiment, but decreases the maximum error compared with the G2(MP2) approach. The G2(B3LYP/MP2/CC) atomization energies are compared with those obtained using the B3LYP approach, and the G2(B3LYP/MP2/CC) model is found to be more reliable, even if the B3LYP calculations are performed using a large basis set.
One hundred and thirty-eight edible oil and fat samples from 21 different sources, either vegetable (Brazil nut, coconut, corn, high oleic sunflower, olive oil, peanut, palm, palm kernel, rapeseed, soybean, sunflower, etc.) or animal (butter, hydrogenated fish, and tallow) have been analyzed. The spectral features of the most noteworthy bands are studied, and their correlations with the amount of fatty acids quantified by gas chromatography are presented. Principal component analysis is applied to classify the set of samples by their level of unsaturation [saturated (SFA), monounsaturated (MUFA), and polyunsaturated fatty acids (PUFA)]. The most remarkable MUFA and PUFA oil sources are independently classified by applying stepwise linear discriminant analysis to the Raman shifts selected by their correlation with fatty acids or structural assignments. The results show that FT-Raman spectra not only have information of the degree of unsaturation but also of the balance among the amounts of SFA, MUFA, and PUFA. The scattering intensities near different Raman shifts (3013, 1663, and 1264 cm-1) show high correlations with the fatty acid profile determined by gas chromatography. Keywords: Oils and fats; FT-Raman spectroscopy; chemometrics
Harmonic force fields were calculated using fourth-order Møller-Plesset (MP4) theory for CH4, NH3, H2O, HF, SiH4, PH3, H2S, HCl, acetylene, HCN, ethylene, formaldehyde, chloromethane, and fluoromethane. These were compared with the experimental force fields. Most of the diagonal force constants for these molecules are computed reliably (1-2% error) at the MP4/6-311+g(2d,2p) level. Exceptions are force constants for out-of-plane bending in the π-bonded molecules and for stretching of the multiple bonds. For computations using second-order Møller-Plesset (MP2) theory, the 6-31g* basis is inferior to basis sets having polarization functions on all atoms such as 6-311+g** and 6-311+g(2d,2p). The force fields computed with MP2 theory are as accurate as those computed at the MP4 level except that HX stretching force constants are consistently overestimated by ca. 3% with MP2 theory. Reduced isotopic partition function ratios, (s2/s1)f, and fractionation factors (FFs) for hydrogen/deuterium substitution were computed for the same set of molecules. The (s2/s1)f values were compared with values computed from experimental harmonic frequencies. The (s2/s1)f values are overestimated by RHF and MP2 theory, but the error is removed when frequencies for the isotopomers are scaled uniformly. The resulting values agree with experiment to within ±2.5% at the MP2 level and ±3.3% at the RHF level.
Predicted vibrational frequencies are reported for 15 small cationic species from Hartree-Fock calculations using the 4-21G and 6-31G* basis sets. Force constants from these calculations were corrected using empirical scale factors taken from a collection of similar neutral molecules. These scale factors reproduce 184 experimental frequencies for the neutral molecules with percent errors of 3.1% and 2.5% for the 4-21G and 6-31G* basis sets, respectively. When these scale factors are applied to the cations, 22 known experimental frequencies are predicted with percent errors of 4.5% and 2.0%, respectively.
Density functional theory (DFT) using the 6-31G* basis set and two nonlocal exchange-correlation functionals (Becke-Lee-Yane-Parr [B-LYP] and the three-parameter compound function of Becke [B3-LYP]) has been used for the calculation of vibrational force fields of a set of 31 organic molecules including a wide range of functional groups. The calculated force constants have been scaled to experimental vibrational frequencies by using (a) an overall scaling constant and (b) a set of 11 factors paying respect to the different kinds of internal coordinates. The comparison of the scaled fundamental frequencies with experiment shows that density functional theory is a reliable tool for the interpretation of IR spectra. The uncorrected DFT frequencies and force constants approximate the experimental ones in a much more uniform fashion than does Hartree-Fock theory. Nevertheless, the use of multiple scale factors leads to further significant improvement. The scaled B3-LYP results are superior to the B-LYP ones, even though the unsealed B-LYP frequencies are, through error cancellation, slightly better than the B3-LYP ones. The reliability of scaled force fields is demonstrated by comparing the calculated and experimental vibrational spectra of aniline.
Deuteration studies, hydration studies, melting studies and model compound studies are utilized to assign and interpret the 800–900 cm−1 region of the Raman spectra of the phospholipids dipalmitoyl phosphatidylcholine and dipalmitoyl phosphatidylethanolamine. Head group Raman bands in this region are shown to be sensitive to hydration and melting. The acyl carbon-carbon stretches, assigned to Raman bands appearing at 860–890 cm−1, are shown to be sensitive probes of molecular packing order, specifically in the acyl interface region.
The performance of semiempirical, ab initio, and density functional methods in calculating and describing the vibrational frequencies of benzene was determined. Different levels were used. The modes were characterized by the magnitude and direction of the displacement vector. The error in the calculated frequencies was reduced using two procedures to obtain the scaled frequencies. Scaling equations were determined for each theoretical method. Specific scale factors were calculated to reduce the error in the ring modes of benzene derivatives. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 661–684, 2000
Density functional calculations, using B3LPY/6-31G(d) methods, have been used to investigate the conformations and vibrational (Raman) spectra of three short-chain fatty acid methyl esters (FAMEs) with the formula CnH2nO2 (n=3–5). In all three FAMEs, the lowest energy conformer has a simple ‘all-trans’ structure but there are other conformers, with different torsions about the backbone, which lie reasonably close in energy to the global minimum. One result of this is that the solid samples we studied do not appear to consist entirely of the lowest energy conformer. Indeed, to account for the ‘extra’ bands that were observed in the Raman data but were not predicted for the all-trans conformer, it was necessary to add-in contributions from other conformers before a complete set of vibrational assignments could be made. Provided this was done, the agreement between experimental Raman frequencies and 6-31G(d) values (after scaling) was excellent, However, the agreement between predicted and observed intensities was much less satisfactory. To confirm the validity of the approach followed by the 6-31G(d) basis set, we used a larger basis set, Sadlej pVTZ, and found that these calculations gave accurate Raman intensities and simulated spectra (summed from two different conformers) that were in quantitative agreement with experiment. In addition, the unscaled Sadlej pVTZ, and the scaled 6-31G(d) calculations gave the same vibrational mode assignments for all bands in the experimental data.This work provides the foundation for calculations on longer-chain FAMEs (which are closer to those found as triglycerides in edible fats and oils) because it shows that scaled 6-31G(d) calculations give equally accurate frequency predictions, and the same vibrational mode assignments, as the much more CPU-expensive Sadlej pVTZ basis set calculations.
An improved Raman spectroscopic procedure for the determination of the total unsaturation in oils and fats using Fourier Transform
Raman (FT-Raman) spectroscopy is described. An important advantage of FT-Raman for these samples is that the spectra are fluorescence-free
unlike dispersive Raman which often uses visible excitation. Samples can be analyzed without any pre-treatment thus eliminating
the need for dissolution in toxic solvents. The short acquisition time of FT-Raman and the ease of application allowed for
a rapid sample turnover.
The effects of repeated food deprivation, prior to slaughter, on performance, feeding behaviour and meat quality of pigs was examined. Three experimental treatments were compared. In treatment 1 pigs had ad libitum access to feed up to the point of loading on the day of slaughter. Treatment 2 involved a 12-h fast prior to slaughter and treatment 3 involved a 20-h fast prior to slaughter. Pigs were slaughtered on a weight basis therefore each pen was emptied over a period of weeks. This meant some pigs experienced repeated food deprivation. The feeding pattern of pigs which were deprived of food for 12 h was very similar to that observed before feed restriction. Pigs which were deprived of food for 20 h spent significantly more time at the feeder post fasting. This was particularly marked during the first 2-3 h when access to feed was restored. Feed deprivation for 12 h prior to slaughter did not adversely affect performance, carcass weight, meat quality or welfare in the present study. Fasting for 20 h reduced carcass weight by 1 kg, which was not statistically significant but could result in financial losses related to carcass weight. The negative effects on meat quality, of repeated feed deprivation, resulted from slower growth rates rather than feed deprivation per se.
Raman spectra of dihexadecylphosphatidic acid and of dimyristoylphosphatidylcholine and its longer chain homologs were obtained as a function of temp. to study the conformational order of the hydrocarbon chains in lipid bilayers. The frequency of the longitudinal acoustical vibration band is evaluated in terms of the length of all-trans chain segments. In the ordered phase, the chains are found to be overwhelmingly in the all-trans conformation. In the fluid phase, definite all-trans segments occur predominantly, the length of which coincides with the extension of the order parameter plateau known from 2H NMR. The frequency of the skeletal optical trans vibration band leads to the same result, if evaluated under the assumption of vibrational decoupling by gauche bands in the fluid phase, thus lending support to this assumption. The intensity of this band detd. from the band area increases linearly with chain length in the ordered phase and is independent of chain length in the fluid phase. Evaluating the intensity for the length of all-trans segments, the same result for the chain conformation is obtained as derived from the frequencies, with the addnl. information that the length of the all-trans segments in the fluid phase does not vary with chain length. [on SciFinder (R)]
This study examined the effects of polymeric components on the physical state of chlorhexidine within bioadhesive, semisolid formulations using Raman spectroscopy. Semisolid formulations were prepared in which chlorhexidine base (CHX, 5%w/w, particle size <63 microm) was dispersed in aqueous (phosphate-buffered saline, pH 6.8) polymer matrices consisting of one or more polymeric components, namely HEC (3%w/w), PVP (3%), and PC (PC, 3%). Raman spectra were recorded using 785-nm excitation and were typically accumulated for 360 s. The Raman spectra were dominated by the presence of CHX. The spectra of CHX in HEC and in HEC/PVP gels were indistinguishable from that for solid CHX as a result of the insolubility of CHX in these formulations. However, in systems containing PC and CHX, there was a shift in the strongest band from 1564 cm(-1) to 1608 cm(-1), which may be accredited to protonation of the basic CHX by the numerous carboxylic acidic groups on PC. Identical shifts in the band positions were observed when this protonation was modeled using ethanoic acid, supporting the view that there was a simple acid base reaction between PC and CHX. However, there were notable differences in the relative intensities of the peaks from these samples, with the spectrum of CHX in the PC matrix displaying properties intermediate between those of CHX dissolved in ethanoic acid and solid CHX diacetate. This may be accredited to the limited solubility of the CHX-PC ion pair. In matrices containing HEC and PC, no peak was observed at 1564 cm(-1), whereas the intensity of the peak at 1608 cm(-1) was increased. Therefore, in these formulations CHX was completely converted to the di-cation as a result of the synergistic effects of PC (which protonated CHX) and HEC (which solubilized the di-cation). In the absence of either HEC or PC, complete protonation was not achieved. It is suggested that this enhancement of solubility of H(2)CHX(2+) may be due to hydrogen bonding, given the hydroxylated nature of HEC. In conclusion, this study has shown the applicability of Raman spectroscopy for both the analysis of opaque, semisolid formulations and, additionally, for the examination of the state of therapeutic agents within such matrices. In particular, using Raman spectroscopy, it was uniquely possible to identify the roles of various polymeric components on both the ionization and solubilization of CHX within aqueous semisolid systems.
Recent spectroscopic advances have led to the first determinations of infrared vibration-rotation bands of polyatomic molecular ions. These initial detections were guided by ab initio predictions of the vibrational frequencies. The calculations reported here predict the vibrational frequencies of additional ions which are candidates for laboratory analysis. Vibrational frequencies of neutral molecules computed at three levels of theory, HF/3-21G, HF/6-31G*, and MP2/6-31G*, were compared with experiment and the effect of scaling was investigated to determine how accurately vibrational frequencies could be predicted. For 92% of the frequencies examined, uniformly scaled HF/6-31G* vibrational frequencies were within 100 cm-1 of experiment with a mean absolute error of 49 cm-1. This relatively simple theory thus seems suitable for predicting vibrational frequencies to guide laboratory spectroscopic searches for ions in the infrared. Hence, the frequencies of 30 molecular ions, many with astrochemical significance,were computed. They are CH2+, CH3+, CH5+, NH2+, NH4+, H3O+, H2F+, SiH2+, PH4+, H3S+, H2Cl+, C2H+, classical C2H3+, nonclassical C2H3+, nonclassical C2H5+, HCNH+, H2CNH2+, H3CNH3+, HCO+, HOC+, H2CO+, H2COH+, H3COH2+, H3CFH+, HN2+, HO2+, C3H+, HOCO+, HCS+, and HSiO+.
- R E Oakes
- J R Beattie
- B W Moss
- S E J Bell
R.E. Oakes, J.R. Beattie, B.W. Moss, S.E.J. Bell, J. Mol.
Struct. THEOCHEM 586 (2002) 91.
- Y Koyama
- K Ikeda
Y. Koyama, K. Ikeda, Chem. Phys. Lipids 26 (1980) 149.
- V Baeten
- P Hourant
- M T Morales
- R Aparicio
V. Baeten, P. Hourant, M.T. Morales, R. Aparicio, J. Agric.
Food Chem. 46 (1998) 2638.
- C W Bauschlicher
- H Partridge
C.W. Bauschlicher, H. Partridge, J. Chem. Phys. 103 (1995)
1788.
- J A Pople
- A P Scott
- M W Wong
- L Radom
J.A. Pople, A.P. Scott, M.W. Wong, L. Radom, Isr. J. Chem.
33 (1993) 345.
- G Rauhut
- P Pulay
G. Rauhut, P. Pulay, J. Phys. Chem. 99 (1995) 3093.
- J A Pople
- H B Schlegel
- R Krishnan
- D J Defrees
- J S Binkley
- M J Frish
- R A Whiteside
- R F Hout
- W J Hehre
J.A. Pople, H.B. Schlegel, R. Krishnan, D.J. DeFrees, J.S.
Binkley, M.J. Frish, R.A. Whiteside, R.F. Hout, W.J. Hehre,
Int. J. Quantum Chem. 15 (1981) 269.
- H Vogel
- F Jahnig
H. Vogel, F. Jahnig, Chem. Phys. Lipids 29 (1981) 83.
- M Butler
- N Salem
- W Hoss
- J Spoonhower
M. Butler, N. Salem, W. Hoss, J. Spoonhower, Chem. Phys.
Lipids 29 (1979) 99.
- E Bicknell-Brown
- K G Brown
- W B Person
E. Bicknell-Brown, K.G. Brown, W.B. Person, J. Raman
Spectrosc. 11 (1981) 356.
- D S Jones
- A F Brown
- A D Woolfson
- A C Dennis
- L J Matchett
- S E J Bell
D.S. Jones, A.F. Brown, A.D. Woolfson, A.C. Dennis, L.J.
Matchett, S.E.J. Bell, J. Pharm. Sci. 89 (2000) 563.
- R F Hout
- B A Levi
- W J Hehre
R.F. Hout, B.A. Levi, W.J. Hehre, J. Comput. Chem. 3 (1982)
234.
[10] M.A. Palafox, Int. J. Quantum Chem. 77 (2000) 661.
[11] P.E. Peterson, M. Abuomar, T.W. Johnson, R. Parham, D.
Goldin, C. Henry, A. Cook, K.M. Dunn, J. Phys. Chem. 99
(1995) 5927.