NIR Spectra Simulations by Anharmonic DFT-Saturated and

Subscriber access provided by University of Rochester | River Campus & Miner Libraries

B: Biophysics; Physical Chemistry of Biological Systems and Biomolecules

NIR Spectra Simulations by Anharmonic DFT Saturated and Unsaturated Long-Chain Fatty Acids Justyna Grabska, Krzysztof B. Bec, Mika Ishigaki, Christian W. Huck, and Yukihiro Ozaki J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b04862 • Publication Date (Web): 12 Jun 2018 Downloaded from http://pubs.acs.org on June 14, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

NIR Spectra Simulations by Anharmonic DFT Saturated and Unsaturated Long-Chain Fatty Acids Justyna Grabska†1,2, Krzysztof B. Beć†*1, Mika Ishigaki1, Christian W. Huck3 and Yukihiro Ozaki*1

1

Department of Chemistry, School of Science and Technology, Kwansei Gakuin

University, Sanda, Hyogo 669-1337, Japan 2

Faculty of Chemistry, University of Wroclaw, F. Joliot-Curie 14, 50-383 Wrocław,

Poland 3

Institute of Analytical Chemistry and Radiochemistry, Leopold-Franzens

University, Innrain 80-82, 6020 Innsbruck, Austria

† The first and second authors contributed equally to this work Corresponding Authors. Email: [email protected] Email: [email protected]

1 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 44

Abstract

Spectra simulation based on quantum mechanical calculations is often an ultimate tool bringing decisive answers on spectroscopic problems but in the case of NIR spectroscopy such studies still remain very rare, particularly those on rather complicated molecules. In the present work we have employed fully anharmonic spectra simulation for saturated and unsaturated long-chain fatty acids (arachidic acid, palmitic acid, stearic acid, linoleic acid, linolenic acid and oleic acid). The spectral features corresponding to the saturation of fatty acid was

accurately

reproduced

by

deperturbed

vibrational

second-order

perturbation theory (DVPT2) throughout a wide NIR region (8000-4000 cm-1) which contains mostly combination bands, and detailed band assignments have been provided. The effect of the saturation of the alkyl chain and the dependency of the number of C=C bonds were reflected in the simulated NIR spectra. This allowed for drawing reliable conclusions about how exactly the existence of C=C bonds and their number in a molecule are translated into the observed spectra. The baseline elevation in the NIR spectra due to the combination bands involving OH stretching and bending modes of the long-chain fatty acid cyclic dimers were confirmed to be similar to those of short- and medium-chain fatty acids. Additionally, for two examples (linoleic and palmitic acid) highly anharmonic OH stretching modes were studied in detail by probing the relevant vibrational potentials over dense grid for monomers and dimers. Subsequent solving of the time-independent Schrodinger equation by generalized matrix Numerov method allowed improving the inconsistency of prediction by DVPT2 route of 2νOH modes of the monomers. For the cyclic dimers, the symmetric (Ag) and antisymmetric (Bu) 2 ACS Paragon Plus Environment

Page 3 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


OH stretching potential curves have been investigated as well. These observations were discussed in relation to the previous investigations of shortand medium-chain fatty acids.



1. Introduction Near-infrared (NIR) spectroscopy has been gaining general importance over the last two decades or so both in basic sciences and applications.1,2,3,4 The applications include a wide range of fields, in which biological samples are focused on, i.e. qualitative and quantitative analysis of foods, pharmaceuticals, and biological and biomedical materials or hyperspectral imaging in biology, pharmaceuticals, and medicine. 5 , 6 In the field of basic sciences, NIR spectroscopy unveils advantageous features, such as the appearance of the forbidden bands, articulation of X-H modes, wide tolerance for the sample thickness and physical properties. Therefore, it offers unique potential for studying inter-intramolecular interactions, anharmonicity, hydrogen bondings, molecular structure, phase transition, solution chemistry, etc. 7 , 8 , 9 , 10 This approach provides

information about biological samples complementary to

that obtainable by classical microscopy and allows correlating the observed details of an image with background molecular features. Regarding this role in some cases NIR spectroscopy is more universal than IR spectroscopy11,12,13,14 due to less sensitivity to the absorption of water. However, NIR spectra are intrinsically complex and difficult for direct interpretation; even more so in the cases of complex samples, i.e. biosamples. An extensive number of overlapping contributions from combination bands and overtones creates a complex spectral outline in the cases of complex molecules, and unlike IR or Raman spectra, in NIR spectra uniform bands can seldom be observed.15 Therefore, our understanding of NIR spectra is still not sufficient. Although it is possible to estimate the wavenumber regions in which specific modes may appear, it is much more difficult to explain the reasons for observed spectral shifts or intensity alterations. Observed NIR spectral outline undergoes 4 ACS Paragon Plus Environment

Page 4 of 44

Page 5 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


strongly convoluted variations, as multiple contributing modes may not follow a consecutive pattern of changes in response to an external perturbation. The final spectral response in the NIR region is often very complex and rich in fine effects. This creates a significant limiting factor in elucidating information about molecular properties of the sample which stands behind studied spectral features.1-4 These factors are ruled by anharmonic effects, i.e. inter-mode anharmonicities, which are the essence of origin of NIR spectra. The simplistic model of harmonic oscillator used routinely for the simulation of IR spectra does not describe anharmonic effects and is not capable of predicting NIR bands. Anharmonic quantum mechanical calculations have been facing a strong limiting factor due to their extensive computational cost, however, recent advances in the theory have allowed the simulation of entire NIR spectra of even fairly large molecules.16,17 This has opened new possibilities for advancing NIR spectroscopy as a whole, in particular, in these fields which are focused on complex molecules, i.e. biomolecules. Anharmonic calculations also provide a noticeable increase in the quality of simulations of IR and Raman spectra.18,19,20,21,22,23,24 Anharmonic methods are being used mostly in basic studies of relatively simple molecules;25,26 the linkage with the field of applied spectroscopy, which is oriented towards more complex systems, presently remains underdeveloped. The two-fold benefits of anharmonic methods should be mentioned here from the point of view of applied spectroscopy; the description of single-mode and multimodal anharmonicity. The former yields more accurate wavenumbers and intensities of fundamental bands and prediction of overtone bands. The latter one describes mode-mode couplings which allows reproducing combination bands and vibrational resonances, which often substantially influence fundamental bands, and therefore anharmonic 5 ACS Paragon Plus Environment


Page 6 of 44

approaches are essential to both IR (and Raman) and NIR spectroscopy. This importance largely grows in examination of complex molecules, again highlighting an urgent need for establishing a robust link between the frontiers of advance of theoretical methods and spectroscopy.27 Long-chain fatty acids (LCFAs) feature protracted aliphatic chains and the most common of them have the chains with 16 to 22 carbons. They are the second energy source of the animal body and are also part of the chemical composition of several vegetable oils. 28 They have also a wide range of industrial applications, including the use in pharmaceutical products, 29 cosmetics30,31 as well as being utilized as food additives.32,33,34,35 Several experimental techniques such as the differential scanning calorimetry (DSC),

36 , 37

X-ray powder diffraction (XRPD),

38 , 39

Raman

spectroscopy,38,40,41,42,43,44,45 IR spectroscopy36,46,47,48 and NIR spectroscopy49,50 have been used for investigating the structure and functions of fatty acids. Physical chemistry of fatty acids has been deeply explored for multiple reasons; i.e. self-association mechanism 51,52 and dimerization, 53 phase-transition,48,54 behaviour in aqueous solutions,55 etc. As one of the major kinds of biological substances, fatty acids and their properties have received keen interest of investigations, where vibrational spectroscopy is frequently involved.56 Even basic carboxylic acids such as propionic acid or butyric acid are essential in physiological processes; 57 , 58 all kinds of fatty acids from short-chain to long-chain ones appear in metabolic pathways, and are of relevance to physiology, microbiology, biochemistry and medicine.59,60,61 Knowledge about simple fatty acids increases our understanding of complex biomolecules containing a carboxyl group such as lipids.62 One of the main focuses of state-of-the-art NIR spectroscopy is spectral imaging of 6 ACS Paragon Plus Environment

Page 7 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


biological samples.11,63,64 Fatty acids are substances found in most living beings in nature. Their omnipresence makes them one of the most important molecules which are observed in spectral images of biosamples. Recent reports on in-situ and non-invasive monitoring of fish embryo growth by NIR imaging have given new insights into the factors determining the hatching rate and allowed following the metabolism of an ovum.5,6 One of important aspects of such studies is the distribution of saturated and unsaturated fatty acids in an egg. A good understanding of spectroscopy of carboxylic acids is of importance also in these kinds of studies. A moderate change in the length of aliphatic chain in long-chain fatty acids does not induce significant difference in chemical and physical properties. This similarity is quite evident when comparing their vibrational spectra. In our previous study we have investigated short-65 and medium-66 chain fatty acids in NIR region. Quantum mechanical simulation of the NIR spectra of these molecules proved to be achievable with decent accuracy. These studies have provided detailed insights into the origins of the NIR bands, and band assignments, revealed the complexity of NIR spectra and suggested the reasons standing behind pronounced baseline elevation which can be observed in the experimental spectra of these compounds. Several structural features were evidenced to be reflected prominently in their NIR spectra as well and the role of conformational flexibility has been explained. These studies supplemented the wide front of research in the field of fatty acids.49-56,60 In the present work we aim at reproducing NIR spectra of long-chain fatty acids (LCFAs). As the object of this study a selection of saturated LCFAs: arachidic acid, palmitic acid, stearic acid; and unsaturated ones: oleic acid, linoleic acid and α-linolenic acid. Special attention will be paid on the influences 7 ACS Paragon Plus Environment


of the saturated vs. unsaturated alkyl chains on the respective experimental bands, in order to elucidate the correlations between molecular structure and NIR spectra. Comprehensive band assignments in the NIR region of these compounds will allow augmenting i.e. applied biochemical studies where knowledge about NIR features of biomolecules persistent in complicated samples is essential. The possibilities stemming from this knowledge will be directly discussed with the recent NIR imaging studies of a fish embryo during its development stages.5,6 Further focus will be put on the anharmonic potentials of the OH stretching modes, which reveal dependency on the saturation of the alkyl chain as well as the conformational flexibility of these molecules. This study demonstrates the feasibility of NIR spectra simulation of complex molecules, opening the new lane for applied NIR spectroscopy.

2. Materials and methods 2.1. Experimental The chemicals were purchased from WAKO Chemicals (palmitic acid, min. 95%, oleic acid, min. 99%, linoleic acid, min. 88% and carbon tetrachloride Infinity Pure, min. 99.9%) and Tokyo Chemical Industry (arachidic acid, min. 98%; stearic acid, min. 98%, α-linolenic acid, min. 70%) and used without further purification. NIR spectra of the fatty acids were measured in CCl4 solutions a in a wide range of concentrations (5·10-4 M - 0.05 M) and in neat liquid and polycrystalline solid states. Measurements of NIR spectra of all LCFAs in CCl4 were carried out on a Perkin Elmer Spectrum One NTS FT-NIR spectrometer operating in a transmittance mode. Rectangular quartz cells with an optical path of 10 or 100 mm were used. The spectra were collected in the 10,000 – 4000 cm-1 region, 8 ACS Paragon Plus Environment

Page 8 of 44

Page 9 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


with a 4 cm-1 spectral resolution and an interpolated data spacing of 1 cm-1; 64 scans were accumulated every time and each measurement was repeated 3 times, preceded with a background collection. As the background data the corresponding cell filled with solvent was used. All spectra were acquired at controlled temperature of 298 K. NIR measurements of neat samples were carried out on a Bruker Vector 22/N FT-NIR spectrometer working in a reflectance mode. Three samples of polycrystalline acids were prepared by milling. NIR reflectance of each sample was measured in the 10,000 – 4000 cm-1 region, with a spectral resolution of 4 cm-1, resulting with 2 cm-1 of interpolated data spacing. The number of scans accumulated was 128 and the measurements of each sample were repeated three times each. The collection of spectra was done at a room temperature of 298 K, with no sample temperature control. The spectra were converted to absorbance scale using the software operating the spectrometer.

2.2. Computational details 2.2.1 NIR spectra simulation To simulate NIR spectra of the long-chain fatty acids anharmonic fully quantum mechanical calculations of the wavenumbers and intensities of the first overtones and binary combinations of vibrational modes was carried out. The determination of electronic structure necessary for deriving all the subsequent molecular properties was performed with the use of density functional theory (DFT) calculations, which offer favorable balance of accuracy and computational affordability. The single-hybrid Becke, three parameter, Lee-Yang-Parr (B3LYP)67 exchange-correlation functional was chosen as it suits well the need of vibrational analysis of complex molecules with regard to the 9 ACS Paragon Plus Environment


Page 10 of 44

reliability and computational time. 68 True energy minima are required for solving vibrational problems, and thus the geometry optimization of all structures was carried out at B3LYP/N07D level for the monomers and B3LYP/6-31+G(d,p) level for the cyclic dimers. The anharmonic vibrational analysis by the means of deperturbed second-order vibrational perturbation (DVPT2) method has been subsequently carried out on the analogous levels of electronic theory. All quantum chemical calculations were carried out in Gaussian 09 Rev. E.01 software69. The obtained frequencies and intensities of first overtones and binary combinations have been used for modelling NIR bands of the investigated structures. For band broadening (spectral convolution) a four parameter Cauchy-Gauss product function (eq. 1) has been employed. A(ν ) =

a1 2 2

1+ a

(ν − a3 )2

(

× exp − a42 (ν − a3 )

2

)

(1)

The parameters a1 and a3 are, respectively, the calculated intensity and wavenumber; the following shape parameters, a2 and a4, chosen arbitrarily as 0.08 and 0.02, for the best agreement with the experimental band shape. The advantage of the chosen convolution method has been explained by us before.65 To reflect the spectral baseline increase due to the broadening of the specific bands of cyclic dimers the final modelled NIR spectra involved band fitting procedure for the relevant bands. The details of the procedure have been explained by us previously,

65

and as such only a brief description will be

provided here. Previous observations65,66,71 suggested the origin of the baseline elevation observed in the NIR spectra of carboxylic acids being an extensive broadening and increase of the integral intensity of specific combination bands, which involve stretching and bending mode of the hydrogen-bonded OH groups. 10 ACS Paragon Plus Environment

Page 11 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Since the band shape does not result from quantum mechanical calculations in the form used in our work, this prominent feature is not possible to be reproduced. However, to approximate the change in the bandwidth and integral intensity, we have performed a rudimentary band-fitting procedure for these selected combination bands, which increases the agreement with the experimental data and improves the readability of the presented spectra. The fitting procedure was based on least-squares method with Powell gradientless optimization algorithm; band shape function remained as explained above. The results of the fitting provide a rough estimation of the peak-shift and broadening.71 The final simulated NIR spectra presented in this work include the results of this procedure. The band assignment as well as the discussion of the spectral features has been based on the comparison of the experimental and simulated spectra. The comparison involved the entirety of the spectra; not only peak positions but also higher-order spectral parameters and relative values between the relevant bands. Due to the extensive complexity of NIR spectra66 such approach largely increases the reliability of the spectral analysis. 2.2.2 Detailed study of the anharmonicity of the OH stretching modes To evaluate accurately highly anharmonic OH stretching modes of monomers as well as cyclic dimers, solving time-independent Schrödinger equation (Eq. 1); డమ అሺொሻ డொమ

=ቄ

ଶఓ ℏమ

ሺܸሺܳሻ − ‫ܧ‬ሻቅ ߖሺܳሻ

(2)

by generalized Numerov matrix method with seven-point numerical differentiation was carried out.70 In Eq. 1 Q denotes the respective normal coordinate, Ψ the wave function, µ the reduced mass of the corresponding oscillator, V the potential energy, and E the energy eigenvalue. Two exemplary 11 ACS Paragon Plus Environment


fatty acids were studied this way; to represent saturated (palmitic) and unsaturated (linoleic) ones. The scan of the potential energy over the relevant normal coordinate was performed with 0.02 Å/step. The harmonic analysis to determine the normal coordinate was carried out at B3LYP/6-311G(d,p) level and included geometry optimization with very tight convergence criteria, 10-12 SCF convergence level, superfine integration and CPHF grids and CPCM solvent model of CCl4. The following grid-based energies were obtained at the same level of theory.

3. Results and discussion 3.1 The dimerization of LCFAs In our previous studies of the dimerization of acetic acid71, short-chain fatty acids,65 and medium-chain fatty acids,66 aided with the quantum chemical calculation of NIR spectra, we have suggested that the baseline increase in the NIR region of carboxylic acids is due to the combination modes of the hydrogen-bonded OH groups in a cyclic dimer.71 Two particular combination bands (a + b; a + c), which involve the following OH modes of the cyclic dimer, (a) antisymmetric Bu stretching, (b) OH bending mode and (c) symmetric Ag stretching, have been reported to have a pronounced influence on NIR spectra of carboxylic acids.65,66,71 The present study of LCFAs supports the earlier observations (Figure 1) and the same feature is observed in the present work. The combination bands a + b and a + c have remarkably high calculated intensities, yet they do not develop as isolated and well-resolved bands in the experimental spectra. Instead, as it has been suggested before, they may contribute to the NIR baseline elevation of LCFAs. A correlation of the level of the elevation with the sample concentration 12 ACS Paragon Plus Environment

Page 12 of 44

Page 13 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


is also conformed. It reaches a significant level in the case of neat samples. Accordingly, the experimental concentration-dependent spectral variability can be roughly reproduced by varying the assumed relative abundances of the monomers vs. the dimers.65,66 Analysis of the concentration-dependent spectra of palmitic acid (Figure 2) reveals a correlated change in the intensity of monomer bands, ascribed with an aid of the simulated spectra. The first overtone band of free OH stretching mode of monomer can be identified at 6908 cm-1; another clear monomer band is located at around 5290 cm−1, originating from the binary combination of OH and C=O stretching modes. As in the case of our previous studies on short-,65 and medium-chain66 fatty acids, these molecules tend to form the cyclic dimers even in very low concentration levels (the tendency is further strengthened in non-polar solvents).71 We do not see any consecutive role of the chain length in this case, as the differences are seemingly too small to impose noticeable impact on NIR line shapes (Figure 1).

Figure 1. Experimental (0.05 M in CCl4) NIR spectra of six kinds of LCFAs (oleic, 13 ACS Paragon Plus Environment


linolenic, linoleic, stearic, arachidic, palmitic).

Figure 2. Experimental NIR spectra of palmitic acid measured in neat liquid and CCl4 solutions with different concentrations (0.05 M, 0.01 M and 0.005 M).

3.2. In-depth analysis of the NIR features of saturated and unsaturated LCFAs based on quantum mechanical spectra simulation The agreement achieved between the calculated and experimental NIR spectra of long chain fatty acids is good (Figure 3a-f), taking into account of the complexity of these systems and the fact that conformational analysis is not feasible in this case. It is possible to provide reliable conclusions about the correlations between the structure and NIR spectra of these representative fatty acids. We will provide a detailed overview of their NIR spectra and elucidate the most relevant spectral features. 14 ACS Paragon Plus Environment

Page 14 of 44

Page 15 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3.2.1 NIR spectra NIR spectra of molecules as complex as those investigated in this work consist of a substantial number of contributing modes. The level of band overlapping is much higher than for the corresponding IR or Raman spectra. Multiple contributions from numerous combination modes18 mean that almost no peaks observed experimentally can be described as homogenous. NIR spectral features of LCFAs are more similar to each other, compared to what we could observe for smaller molecules. Nevertheless, the saturated and unsaturated LCFAs can be distinguished well by NIR spectra. It is noted that the two spectral sub regions (6000-5500 and 4500-4700 cm-1) are very specific to the type of the alkyl chain. Based on quantum mechanical simulation study it is possible to explain in detail the origins of this difference. The proposed band assignments in the NIR spectra of LCFAs are presented in Table 1-2 and Tables S1-S4 in Supporting Information.

The vicinity of 7000 cm-1 In the vicinity of 7000 cm-1 the spectra of all investigated fatty acids reveal a well-resolved band (Figure 1). It originates from the first overtone of non-bonded OH group. The LCFAs feature a large number of significant conformers, and thus, the broadening of the 2νOH band is apparent in their spectra; a similar effect has been studied in detail for shorter chained fatty acids65,66 as well as alcohol molecules.15,17 Consistently with previous studies it should be ascribed to monomeric species, although a contribution of terminal carboxyl groups in linear associates should not be neglected.51,52,54,56 The DVPT2 calculated 2νOH wavenumber varies among the studied molecules, unlike the 15 ACS Paragon Plus Environment


experimental peak position. This will be discussed in detail in Section 3.3.

The region of 6000-5500 cm-1 This region is rich in the first overtones and combinations involving CH3, CH2 and CH stretching modes. The spectra of saturated fatty acids are much more similar to each other than those of the unsaturated ones (Figure 1), highlighting consistency in the structure-spectra relationship and the influence of C=C bond. One can observe two broadened peaks in the spectra in this region of both groups. For the three saturated LCFAs the peak maxima remain exactly the same, 5785 and 5676 cm-1. Among the unsaturated compounds the position of the lower frequency peak is the same (the maximum difference of 1 cm-1; 5680-5679 cm-1; Figure 1). The wavenumber of the higher frequency peak is much less consistent and varies more; for oleic acid this peak appears at 5793 cm-1 and for linoleic acid at 5836 cm-1 while linolenic acid features an even further blueshift to 5841 cm-1 (the maximum difference of 48 cm-1; Figure 1). In all the cases these peaks are blue-shifted against the analogous peaks of saturated LCFAs. The same observation has been reported for short-chain fatty acids.65 With the increase of the number of C=C bonds, the position of the peak at around is blue-shifted; from 5793, through 5836 to 5841 cm-1 for the compounds with one, two or three C=C bonds, respectively. The NIR spectral differences between saturated and unsaturated fatty acids were already noticed many years ago.72 Yet, intrinsic complexity of the spectra of these molecules as well as difficulty in accurate description of the anharmonic effects standing behind this complexity have prevented any deeper studies of these features so far. 16 ACS Paragon Plus Environment

Page 16 of 44

Page 17 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Comparatively, the two bands of saturated fatty acids are narrower and sharper, resulting from less diffused contributions of the combinations involving methylene stretching modes. It seems that it is a feature of an unsaturated that the νCH2 combination modes are less grouped by their frequency, giving a broader and lower spectral outline in this region.

The region of 5000-4500 cm-1 The next NIR subregion where a distinction between the saturated and unsaturated LCFAs is most pronounced is the 5000 – 4500 cm-1 region. The principal reason for this is the specificity of combination bands of unsaturated acids being manifested in this region. The νC=C modes combined with νC-H modes, both highly localized, give rise to a fairly prominent band in the vicinity of 4672cm-1. The saturated fatty acids have only a weak, broadened feature of highly overlapped very weak bands in this case.

The region of 4500-4000 cm-1 The lower wavenumber region between 4500 and 4000 cm-1 is mostly populated by the combination bands involving CH3 and CH2 stretching and bending modes. This is the region of the most significant overlapping, as the number of contributing bands is the highest among all subregions as arbitrarily involved in the present discussion. Such conclusion is consistent with the previously reported feature of an NIR spectrum, not only for fatty acids but also for any kinds of molecules.15,17,77 However, in the present case this phenomenon is largely amplified due to the size of molecules resulting in a high number of modes involved. The extensive overlapping is likely a key factor responsible for large similarity of the NIR spectra of all subjects of the present 17 ACS Paragon Plus Environment


study (Figure 1). It is difficult to notice any clear difference between the saturated and unsaturated compounds in this region; in fact all the studied LCFAs bear strong similarity in the 4500-4000 cm-1 region. Consequently, this region is unsuitable for qualitative analysis of the LCFAs.

3.2.2 Relevance of the obtained results to NIR spectra of complicated biological system; in vivo NIR study of a fish egg The spectra simulation enables in-depth analysis of the NIR spectral features of long-chain fatty acids. The comparisons of the calculated spectra with those measured for pure fatty acids or their solution in CCl4 yield band assignments, strongly exceeding in detail those which are based on spectral analysis classical methods.73 The present work is the first reported attempt in computational reproduction of NIR spectra of such complex molecules. The possible further studies may include interactions of biomolecules in complex samples, aiding the advancing NIR spectroscopy and imaging of biological samples.5,6 NIR spectroscopy offers strong practical advantages in this field (low-complexity, fast and robust spectra collection, application to a variety of biosamples), but, on the other hand, still it suffers from the difficulties in the interpretation of the spectral features and still relatively underdeveloped knowledge about the spectra-structure correlations in NIR region. However, even at this stage it is possible to correlate the results obtained here with the conclusions stemming from experimental studies. In their recent investigation, Puangchit et al.74 used NIR imaging for exploring day-dependent variations in embryogenesis and energy metabolism of fish eggs. The primary source of information in this study originate from chemical components, mainly proteins and lipids. As the variations in lipids play major roles in the significant part of 18 ACS Paragon Plus Environment

Page 18 of 44

Page 19 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the egg, an ability to unambiguously discriminate the wavenumber regions for obtaining a valid and relevant NIR image is crucial. In their study, Puangchit et al.74 were able to discriminate between the saturated and unsaturated fatty acids, by following the linear NIR spectra analysis supported by the conclusions from earlier reports on spectra simulation of short- and medium-chain fatty acids.65,66 For example, it was found that yolk does not consist of unsaturated compounds.74 By selecting the specific wavenumber region they also observed clearly the biological structures, i.e. lipid bi-layer in the image of an egg.74 Due to complex nature of biosamples not always an entire NIR spectral region can be successfully used, i.e. due to overlapping strong bands originating from other constituents of a biological sample, i.e. water bands.1-4 Therefore, frequently these studies are limited to narrow wavenumber regions. In such cases, an ability to conclude independently from different narrow NIR sub-regions is helpful. Puangchit et al.74 found that the bands in the 5500-6200 cm-1 region and those around 4666 cm-1 selected for NIR image assembly lead to consistent conclusions. The present work confirms these earlier findings, as these regions clearly differ between the saturated and unsaturated long-chain fatty acids. Owing to the availability of the simulated NIR spectra, it is possible to link these differences with the differences in the vibrational properties of these two kinds of molecules (Figure 3). Despite the structural complexity, long-chain fatty acids still offer an advantage in establishing this kind of joint computational-experimental study, as these molecules do not interact strongly with the hydrophilic chemical environment common to biosamples. The future advance may be able to shed light on more interacting molecules, in which case the availability of the simulated spectra may provide significant advantages.



3.2.3. Mode contributions to NIR spectra of saturated and unsaturated long chain fatty acids The simulation allowed elucidation of a consistent trend featured in the NIR spectra of long-chain fatty acids, which would be otherwise very difficult to conclude on the basis of experimental data alone. In the region of 6200 – 5500 cm-1 the contribution of overtones are much smaller than those of combination modes for both saturated and unsaturated LCFAs (Table 3). Particularly, for the saturated ones the relative contributions from overtones are consistently lower. The intensities of analogous peaks are also of similar magnitudes. For the structures involving C=C bonds one can notice higher intensities of the first overtone bands in this region. Unlike the unsaturated ones, the NIR spectra of saturated LCFAs do not manifest any bands in the region of 6100-6000 cm−1. The above findings remain consistent with previous studies of short- and medium-chain fatty acids.65,66 The simulated spectra reveal prominent differences in the contribution levels between different kinds of NIR modes (first overtones, binary combinations) among the LCFAs. Quantifications of these differences may be estimated based on the relations between integral intensities of simulated bands. In the region of 10000-4000 cm-1 the contribution of combination bands are between 95 and 99% (98-99% for saturated ones, 95-98% for unsaturated chain). The relative balance between these contributions follows a pattern, depending on the saturation level of the alkyl chain. When analysing a narrower region of 6200-5400 cm-1 the significance of the first overtones is higher (Figure 4a-f, Table 3) for both kinds of chains. At the moment it is difficult to interpret the observed differences as calculated data for a larger number of similar molecules is needed to be collected to enable comparative 20 ACS Paragon Plus Environment

Page 20 of 44

Page 21 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


discussion and to verify the trend outlined in the present work. There are some discrepancies between the simulated and experimental NIR spectra in the region of 6200-5400 cm-1 (Figure 4). The reason lies likely in the high anharmonicity of C-H stretching vibrations whose first overtones and binary combination populate the region; lower accuracy of prediction by VPT2 calculations should be expected in this case. The resulting lower agreement is convergent with the previously simulated spectra of carboxylic acids65,66 and alcohol molecules15,17 in the vicinity of C-H stretching vibrations. Coincidently, VPT2 simulations have yielded better accuracy for acetic acid71 a much simpler carboxylic acid in which case the overlapping effect is not so strong in the region of NIR spectrum. For saturated compounds one can notice that the overtone contribution is below 6%, while in the case of unsaturated ones it is between 5% and 17%. However, there is no clear pattern between the number of C=C bonds and the percentage of overtone contribution. No relation between the number of carbon in the chain and overtone contribution could be evidences as well. Interestingly, the overtone contribution yielded for palmitic acid is very low; the reasons of this observation are not fully understood at present.



Figure 3. Experimental (0.05 M in CCl4) and simulated NIR spectra of: a) arachidic acid, b) palmitic acid, c) stearic acid, d) linoleic acid, e) α-linolenic acid, and f) oleic acid. The band numbers correspond to those in Table 1-2 and Tables S1-S4 in Supporting Information).


Page 22 of 44

Page 23 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4. Contributions of overtones modes into NIR spectra of: a) arachidic acid, b) palmitic acid, c) stearic acid, d) linoleic acid, e) α-linolenic acid, and f) oleic acid.



Table 1. Band assignments proposed for NIR Spectra of palmitic acid. Band

Wavenumber [cm-1]

number

Experimental

Calculated

1

6909

7006

2νOH (m1))

2

5905

5901

(νas’CH3, νasCH2) + νasCH3

3

5786

5842

νasCH3 + νasCH3

Band assignment

νsCH3 + νasCH3 (νas’CH3, νasCH2) + νasCH2 4

5677

5762

νasCH2 + νsCH2

5

5600-5400

5700-5500

δas’CH3 + νasCH3 δscissCH2 + νsCH2

6

5285

5396

νC=O + νOH (m)

7

4670

4703

δas’CH3 + νsCH2 (δOH, δscissCH2) + νsCH2

8

4334

4357

νsCH2 + (νsCH2, δOH) δwagCH2 + νsCH2

9

4261

4329

δ’CH3 + νsCH2 δscissCH2 + νsCH2 δwaggCH2 + νsCH2

10

4191

4223

δwaggCH2 + νasCH2 δwaggCH2 + νsCH2 (δC=O, δOH) + δrockCH2

11

4171

4176

δscissCH2 + δrockCH2

12

4071

4110

δwaggCH2 + νsCH2

1

m – bands originating from monomer


Page 24 of 44

Page 25 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2.Band assignments proposed for NIR Spectra of linoleic acid. Band

Wavenumber [cm-1] Band assignment

number

Experimental

Calculated

1

6908

7082

2νOH (m1))

2

6009

6004

2νCH νCH + νCH

3

5911

5949

νCH + νCH

4

5835

5874

2νCH νasCH2 + νsCH2 νasCH3 + νCH

5

5798

5858

2νCH νasCH3 + νas’CH3 νasCH2 + νasCH2

6

5680

5792

2νsCH2 νasCH3 + νasCH2 νasCH2 + νasCH2

7

5600-5400

5700-5500

νC=O + νasCH2 νsCH2 + νsCH2

8

5291

5367

νC=O + νOH (m)

9

4711

4701

(δOH, νC=O) + νCH νC=C + νCH

10

4663

4648

νC=C + νCH

11

4588

4606

δscissCH2 + νCH δscissCH2 + νasCH3



12

4337

4329

δscissCH2 + νasCH2 δscissCH2 + νsCH2 δscissCH2 + νsCH3

13

4263

4245

(δwagCH2, δOH) + νsCH2

14

4191

4160

δtwistCH2 + νsCH3 δtwistCH2 + νsCH2 δrockCH2 + νCH

15

4173

4115

δtwistCH2 + (δOH, νC=O)

16

4067

4065

δwagCH2 + νsCH2 δrockCH3 + νsCH2

1

m – bands originating from monomer


Page 26 of 44

Page 27 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 3. Percentage contributions of the first overtone and binary combinations to NIR spectra of long chain fatty acids

4000-10000 cm-1

5400-6200 cm-1

νa+νb = 99.96%

νa+νb = 99.84%

2ν = 0.04%

2ν = 0.16%

νa+νb = 98.44%

νa+νb = 93.91%

2ν = 1.56%

2ν = 6.09%

νa+νb = 98.62%

νa+νb = 94.75%

2ν = 1.38%

2ν = 5.25%

Oleic acid (C18)

νa+νb = 94.65%

νa+νb = 83.39%

1x(C=C)

2ν = 5.35%

2ν = 16.61%

Linoleic acid (C18)

νa+νb = 98.28%

νa+νb = 95.11%

2x(C=C)

2ν = 1.72%

2ν = 4.89%

α-Linolenic acid (C18)

νa+νb = 95.02%

νa+νb = 87.37%

3x(C=C)

2ν = 4.98%

2ν = 12.63%

Compounds

Palmitic acid (C16)

saturated

Stearic acid (C18)

Arachidic acid (C20)

unsaturated

The number of NIR modes increases very rapidly for larger molecules; this is particularly evident in the case of binary combinations. The number of the binary combination modes equals to f(f-1)/2, where f is the number of fundamental modes. This makes difficult an analysis of the levels of influence on the NIR spectrum arising from the modes of interest, i.e. OH or CH3 27 ACS Paragon Plus Environment


Figure 5. Generalized contributions into NIR spectra of the selected types of modes involved in the binary combinations as uncovered by quantum mechanical spectra simulation of linoleic and palmitic acid. 28 ACS Paragon Plus Environment

Page 28 of 44

Page 29 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


stretching modes, or C=C stretching modes. For this purpose it is useful to assemble density plots in the form of colormaps highlighting these contributions in a straightforward way (Figure 5). In the present case, the level of contribution is determined as the square rooted ratio between the summed intensity of the selected modes and the total calculated intensity at a given wavenumber of the simulated spectrum. A zero value indicates no contribution while a value of one indicates that no other mode apart of the selected one contributes into an NIR spectrum at a given wavenumber. Note that the square-rooting is applied to elucidate weak contributions; it is particularly useful in the case of very complex molecules with multitude of contributing modes; this is true for LCFAs in the present study. Figure 5 enables straightforward categorization and generalization of the influential modes in the NIR spectra of linoleic and palmitic acid, suiting as examples of unsaturated and saturated LCFAs, respectively. By highlighting the combinations of νOH mode one can see that linoleic acid features contributions over broader wavenumber regions, i.e. noticeable influence in the 6000-5900 and 4700-4500 cm-1 regions (Figure 5). The latter region is identified as meaningful in discriminating the two kinds of fatty acids, while the former one is rather indistinctive due to the low intensity of the bands therein. Subtle differences can be noticed in the contribution of δOH combination modes. Analysis of the combinations of νCH3 mode reveals that palmitic acid features a relatively wider region of influence in the vicinity of 5900-5700 cm-1 (Figure 5). An interesting picture results from the highlight of νC-H combinations specific to the unsaturated molecule. The contribution is considerable over the multiple wavenumber regions, as this mode couples strongly to a number of other modes. On the contrary, the νC=C mode couples to rather lower number of 29 ACS Paragon Plus Environment


other modes, and thus, the resulting combination bands appear in the rather narrow region of 4750-4500 cm-1 (Figure 5). The differences between linoleic and palmitic acid elucidated here remain coherent with previous discussion of the distinctness of unsaturated and saturated LCFAs. The presented approach provides information helpful i.e. in screening for the wavenumber regions meaningful from the point of view of NIR imaging of samples containing complex molecules. 3.3 Anharmonicity of OH stretching modes of long-chain fatty acids The methods based on VPT2 scheme are efficient and preferable for generic spectroscopic studies 75 in particular for NIR spectra simulation of complex molecules. It is known limitation of this approach that treatment of highly anharmonic modes may produce inaccurate results.76,77 In the present work this could be seen in the calculated 2νOH frequencies of the monomers. While the experimental wavenumbers are similar among all studied molecules, remaining within 2 cm-1 of difference (6909-6907 cm-1; Figure 1), the DVPT2 calculated ones differ much more significantly, being spread by 162 cm-1 (7082-6920 cm-1; Table 1-2 and Tables S1-S4 in Supporting Information). By solving the vibrational problem based on dense probing of the corresponding potential (as described in Section 2.2.2) it is possible to capture vastly higher amount of mode anharmonicity (Figure 6) compared to standard two-point differentiation in VPT2 route at the cost of largely increased computational time; however, focused development of theoretical methods is being aimed at improving the efficiency of the concept.78,79 By taking palmitic acid and linoleic acid as examples, the calculated relative 2νOH frequencies are consistent with the experimental ones (Table 4). Both calculated frequencies are embarked by a systematic error of ca. 1 %; this may be resulting from the chosen level of 30 ACS Paragon Plus Environment

Page 30 of 44

Page 31 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


theory for derivation of normal coordinate or the potential values as well as imperfect solvation model. Table 4. Comparison of 2νOH vibrational frequencies in [cm-1] of palmitic acid and linoleic acid determined with the use of DVPT2 approach and numerical solving of Schrödinger equation based on scanning of the potential energy along the 2νOH normal coordinate. calc. calc. exp.

(V(Q) probing// (DVPT2//B3LYP/N07D) B3LYP/6-311G(d,p))

palmitic acid

6909

7006

6975

Linoleic acid

6908

7082

6974

∆ν

1

76

1



Figure 6. The OH stretching vibrational potential and vibrational states of the monomer of palmitic acid. Additional insights on the anharmonicity of OH stretching modes in the case of cyclic dimers of fatty acids are provided by solving the corresponding vibrational problem. It has been shown that fatty acids form cyclic dimers easily, which is further enhanced by nonpolar solvent in which dimerization is strongly preferred.80,81 The vibrational potential curves of the two OH stretching modes of the cyclic dimer, symmetric and antisymmetric (for centrosymmetric C2h conformations: Ag and Bu modes, respectively), differ considerably between each other (Figure 7 and Figure 8a-b) but also seem to be affected by the conformational isomerism of the alkyl chain of the molecule (Figure 9). The potential curve along antisymmetric OH stretching coordinate is symmetric with large contribution of quartic anharmonicity (Figure 7 and Figure S2a-b in SI). The shape of the potential does not vary noticeably between these two fatty acids and the shape of vibrational wavefunctions also remains largely similar among these two different fatty acids (Figure S2 in SI). This mode is also rather insensitive to the conformation of the alkyl chain; this feature will be discussed in detail later on. The potential along symmetric OH stretching coordinate is more specific to a given molecule, and it differs considerably between palmitic acid and linoleic acid (Figure 8). It is noted that palmitic acid reveals the known shallow local minimum at the higher elongation of the covalent bond approaching double-well potential specific to the proton transfer state known from cyclic dimers of less complex carboxylic acids.82,83,84,85 A striking difference in the vibrational potential and energy eigenstates between the saturated and unsaturated fatty acids in the case of symmetric OH 32 ACS Paragon Plus Environment

Page 32 of 44

Page 33 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


stretching mode (Figure 7 and Figure S2 in SI) in contrast to very minor difference in the case of antisymmetric OH stretching (Figure 8 and Figure S3a-b in SI) should be highlighted. It remains to be verified, if the symmetric mode is generally such sensitive to the property of aliphatic chain and whether this feature is a general rule separating saturated fatty acids from unsaturated ones.

Figure 7. The antisymmetric OH stretching (Bu) vibrational potential and vibrational states of the cyclic dimer of linoleic acid.

Figure 8. The symmetric OH stretching (Ag) vibrational potential and 33 ACS Paragon Plus Environment


vibrational states of the cyclic dimer of (A) palmitic acid and (B) linoleic acid.

Figure 9. The influence of symmetry on the vibrational potential of symmetric OH stretching mode of different conformers of palmitic acid (refer to Fig. S1 and Fig. S3 in Supporting Information for additional details).

Another consideration should be aimed at the role of conformational flexibility. The two discussed OH stretching vibrations have extensively been investigated in the past. However, often these studies focused on cyclic dimers of simpler carboxylic acids; frequently such molecular systems are rigid (i.e. formic acid, acetic acid, benzoic acid82-85). In contrary, the molecules studied in the present work feature extensive levels of flexibility which as it was explained forced us to base the study on arbitrarily selected conformers. However, it would be interesting to assess how the potential curve changes between extreme cases. 34 ACS Paragon Plus Environment

Page 34 of 44

Page 35 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


For this reason, we have resolved the vibrational problem for low-symmetry, highly packed cyclic dimer of palmitic acid in addition to the previously discussed centrosymmetric C2h conformation (Fig. S1 in Supporting Information). The difference in the potential curve among high- and low-symmetry conformations is extensive (Figure 9). The lower symmetry case features a significantly more distinct local minimum. As expected, the difference propagates onto the corresponding energy eigenstates (Figure S3 in SI). A brief observation may be reported on the known problem of energy spacing between the fundamental vibrational levels of symmetric and antisymmetric OH stretching in the cyclic dimers. Since it may be difficult to obtain the splitting value experimentally, 86 calculated data are helpful here. In the long-chain fatty acids, ∆ν(Bu-Ag) difference may vary noticeably being influenced by the conformational isomerism. In the case of palmitic acid these were determined to be 359 and 372 cm-1 for the high-symmetry and low-symmetry systems, respectively, resulting in variability of 13 cm-1. The above observations remain preliminary, as a number of factors would need to be additionally considered to bring a more comprehensive picture in the case of complex molecules. Further studies would need to be aimed at exploring the vibrational differences in the cyclic hydrogen bonded bridge of long-chain fatty acids.

4. Conclusions Recent advances in the field of anharmonic quantum chemical methods have opened a new era in NIR spectroscopy as simulations of NIR spectra of rather complicated compounds become possible. This introduces far-reaching possibilities and prospects for NIR spectroscopy. Here, we have verified this 35 ACS Paragon Plus Environment


potential by investigating long chain fatty acids, biosignificant molecules surpassing in complexity the usual objects of theoretical spectroscopy studies. Six compounds were successfully analysed, three with a saturated alkyl chain and tree with an unsaturated one. Successful reproductions of experimental NIR spectra of these fatty acids by the anharmonic DFT calculations, including explanation of the concentration effects, provide rich information about band assignments and the relevant spectra-structure correlations. The present work may be considered as a feasibility study of NIR spectra simulation of biomolecules with good accuracy and manageable demand for computational resource. DVPT2 allows efficient simulation of NIR spectra but highly anharmonic (i.e. OH stretching) modes may be represented less accurately. Therefore, a detailed study of the anharmonic potential curves of the OH stretching modes was carried out for the cyclic dimers of palmitic and linoleic acids. Differences in the quartic anharmonicity and the shape of the potential curves were uncovered for the saturated and unsaturated molecules. An influence of the conformational isomerism on the shape of the symmetric OH stretching potential was observed. The low-symmetry, folded dimer exhibits a more pronounced double-minimum curve; the spacing between the energy levels (symmetric and antisymmetric OH stretching) also differs accordingly between different conformations. By performing an anharmonic computational study it is possible to explain in detail the reasons of the spectral difference between saturated and unsaturated LCFAs, and to unambiguously correlate the spectral features with molecular properties. Further advance will be aimed at the molecules which interact more strongly with their biochemical environment, and thus their 36 ACS Paragon Plus Environment

Page 36 of 44

Page 37 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


actual spectral data remains difficult for interpretation.

Supporting Information This article contains Supporting Information (additional figures and tables).

Acknowledgement Calculations have been carried out in Wroclaw Centre for Networking and Supercomputing (http:/www.wcss.pl), under grant no. 375



References 1

Ozaki, Y.; Huck, C. W.; Beć, K. B. Near infrared spectroscopy and its applications. Gupta, V. P. Ed.; Molecular and laser spectroscopy, Elsevier, 2017. 2 Siesler, H. W.; Ozaki, Y.; Kawata, S.; Heise, H. M. Eds.; Near-infrared spectroscopy, Wiley-VCH, Weinheim, 2002. 3 Ozaki, Y.; McClure, W. F.; Christy, A. A. Eds.; Near-infrared spectroscopy in food science and technology, Wiley-Interscience, Hoboken, NJ, USA, 2007. 4 Czarnecki, M. A.; Morisawa, Y.; Futami, Y.; Ozaki, Y. Advances in molecular structure and interaction studies using near-infrared spectroscopy. Chem. Rev. 2015, 115, 9707–9744. 5 Ishigaki, M.; Kawasaki, S.; Ishikawa, D.; Ozaki, Y. Near-infrared spectroscopy and imaging studies of fertilized fish eggs: in vivo monitoring of egg growth at the molecular level. Scientific Reports 2016, 6:20066, 1-10. 6 Ishigaki, M.; Yasui, Y.; Puangchit, P.; Kawasaki, S.; Ozaki, Y. In vivo monitoring of the growth of fertilized eggs of medaka fish (Oryzias latipes) by near-infrared spectroscopy and near-Infrared imaging—a marked change in the relative content of weakly hydrogen-bonded water in egg yolk just before hatching. Molecules 2016, 21, 1003-1017. 7 Šašić, S.; Segtnan, V. H.; Ozaki, Y. Self-modeling curve resolution study of temperature-dependent near-infrared spectra of water and the investigation of water structure. J. Phys. Chem. A 2002, 106, 760−766. 8 Czarnecki, M. A. Near-infrared spectroscopic study of hydrogen bonding in chiral and racemic octan-2-ol. J. Phys. Chem. A 2003, 107, 1941−1944. 9 Iwamoto, R. Infrared and near-infrared study of the interaction of amide C=O with water in ideally inert medium. J. Phys. Chem. A 2010, 114, 7398−7407. 10 Howard, D. L.; Kjaergaard, H. G. Vapor phase near infrared spectroscopy of the hydrogen bonded methanol−trimethylamine complex. J. Phys. Chem. A 2006, 110, 9597−9601. 11 Türker-Kaya, S.; Huck C. W. A Review of mid-infrared and near-infrared imaging: principles, concepts and applications in plant tissue analysis. Molecules 2017, 22, 168-188. 12 Pezzei, C.; Brunner, A.; Bonn, G. K.; Huck, C. W. Fourier transform infrared imaging analysis in discrimination studies of bladder cancer. Analyst 2013, 138, 5719-5725. 13 Wiercigroch, E.; Staniszewska-Ślęzak, E.; Szkaradek, K.; Wójcik, T.; Ozaki, Y.; Barańska, M.; Małek, K. FT-IR Spectroscopic imaging of endothelial cells response to tumor necrosis factor-α: to follow markers of inflammation using standard and high-magnification resolution. Anal. Chem. 2018, 90, 3727–3736. 14 Wróbel, T. P.; Vichi, A.; Barańska, M.; Kazarian, S. Micro-attenuated total reflection Fourier transform infrared (Micro ATR FT-IR) spectroscopic imaging with variable Angles of incidence. Appl. Spectrosc. 2015, 69, 1170-1174. 15 Beć, K. B.; Futami, Y.; Wójcik, M. J.; Ozaki, Y. A spectroscopic and theoretical study in the near-infrared region of low concentration aliphatic alcohols. Phys. Chem. Chem. Phys. 2016, 38 ACS Paragon Plus Environment

Page 38 of 44

Page 39 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


18, 13666−13682. 16 Kirchler, C. G.; Pezzei, C. K.; Beć, K. B.; Mayr, S.; Ishigaki, M.; Ozaki, Y.; Huck, C. W. Critical evaluation of spectral information of benchtop vs. portable near-infrared spectrometers: Quantum chemistry and two-dimensional correlation spectroscopy for a better understanding of PLS regression models of the rosmarinic acid content in Rosmarini folium. Analyst 2017, 142, 455-464. 17 Grabska, J.; Beć, K. B.; Ozaki, Y.; Huck, C. W. Temperature drift of conformational equilibria of butyl alcohols studied by near-infrared spectroscopy and fully anharmonic DFT. J. Phys. Chem. A 2017, 121, 1950−1961. 18 Beć, K. B.; Grabska, J.; Ozaki, Y.; Hawranek, J. P.; Huck, C. W. Influence of non-fundamental modes on mid-infrared spectra of aliphatic ethers. A fully anharmonic DFT study. J. Phys. Chem. A 2017, 121, 1412−1424. 19 Bloino, J.; Biczysko, M.; Barone, V. Anharmonic effects on vibrational spectra intensities: infrared, Raman, vibrational circular dichroism, and Raman optical activity. J. Phys. Chem. A 2015, 119, 11862–11874. 20 Barone, V.; Biczysko, M.; Bloino, J. Fully anharmonic IR and Raman spectra of medium-size molecular systems: accuracy and interpretation. Phys. Chem. Chem. Phys. 2014, 16, 1759– 1787. 21 Šebek, J.; Pele, L.; Potma, E. O.; Gerber, R. B. Raman spectra of long chain hydrocarbons: anharmonic calculations, experiment and implications for imaging of biomembranes. Phys. Chem. Chem. Phys. 2011, 13, 12724–12733. 22 Wojciechowski, P.; Helios, K.; Michalska, D. Theoretical anharmonic Raman and infrared spectra with vibrational assignments for monofluoroaniline isomers. Vib. Spectr. 2011, 57, 126–134. 23 Beć, K. B.; Grabska, J.; Huck, C. W.; Ozaki, Y.; Hawranek, J. P. Computational and quantum chemical study on high-frequency dielectric function of tert-butylmethyl ether in mid-infrared and near-infrared regions. J. Mol. Liq. 2016, 224, 1189–1198. 24 Yagi, K. Development of molecular vibrational structure theory with an explicit account of anharmonicity. Mol. Sci. 2016, 10, A0085. 25 Yagi, K.; Thomsen, B. Infrared spectra of protonated water clusters, H+(H2O)4, in Eigen and Zundel forms studied by vibrational quasi-degenerate perturbation theory. J. Phys. Chem. A 2017, 121, 2386–2398. 26 Biczysko, M.; Bloino, J.; Carnimeo, I.; Panek, P.; Barone, V. Fully ab initio IR spectra for complex molecular systems from perturbative vibrational approaches: glycine as a test case. J. Mol. Struct. 2012, 1009, 74-82. 27 Thomsen, B.; Kawakami, T.; Shigemoto, I.; Sugita, Y.; Yagi, Y. Weight-averaged anharmonic vibrational analysis of hydration structures of polyamide 6. J. Phys. Chem. B 2017, 121, 6050– 6063. 28 Zielińska, A.; Nowak, I. Fatty acids in vegetable oils and their importance in cosmetic industry, Chemik 2014, 68, 103-110. 29 Moghis Ahmad (Ed.) Fatty Acids, Academic Press and AOCS Press, 2017. 30 Białek, A.; Białek, M.; Jelińska, M.; Tokarz, A., Fatty acid profile of new promising 39 ACS Paragon Plus Environment


unconventional plant oils for cosmetic use. Int. J. Cosmet. Sci. 2016, 38, 382-8. 31 Rabasco Alvarez, A. M.; Gonzalez Rodriguez, M. L. Lipids in pharmaceutical and cosmetic preparations. Grasas y Aceites 2000, 51, 74-96. 32 Wood, J. D.; Richardson, R. I.; Nute, G. R.; Fisher, A. V.; Campo, M. M.; Kasapidou, E.; Sheard, P. R.; Enser, M. Effects of fatty acids on meat quality: a review. Meat Science 2003, 66, 21–32. 33 Albuquerque, M. L. S.; Guedes, I.; Alcantara, P.; Moreira, S. G. C.; Neto, N. M. B.; Correa, D. S.; Zilio, S. C. Characterization of buriti (Mauritia flexuosa L.) oil by absorption and emission spectroscopies. J. Braz. Chem. Soc. 2005, 16, 1113-1117. 34 Bonini, M.; Fratini, E.; Baglioni, P. SAXS Study of chain-like structures formed by magnetic nanoparticles. Mater. Sci. Eng. C Biomim. Supramol. Syst. 2007, 27, 1377-1381. 35 Simakova, I.; Simakova, O.; Maki-Arvela, P.; Simakov, A.; Estrada, M.; Murzin, D. Y. Deoxygenation of palmitic and stearic acid over supported Pd catalysts: effect of metal dispersion. Appl. Catal. A Gen. 2009, 355, 100-108. 36 Sari, A. Thermal reliability test of some fatty acids as PCMs used for solar thermal latent heat storage applications. Energy Convers. Manag. 2003, 44, 2277-2287. 37 Sari, A. Eutectic mixtures of some fatty acids for low temperature solar heating applications: Thermal properties and thermal reliability. Appl. Therm. Eng. 2005, 25, 2100-2107. 38

Kaneko, F.; Yamazaki, K.; Kitagawa, K.; Kikyo, T.; Kobayashi, M.; Kitagawa, Y.; Matsuura, Y.;

Sato, K.; Suzuki, M. Structure and crystallization behavior of the β phase of oleic acid. J. Phys.

Chem. B 1997, 101, 1803-1809. 39

Moreno, E.; Cordobilla, R.; Calvet, T.; Cuevas-Diarte, M. A.; Gbabode, G.; Negrier, P.; Mondieig, D.; Oonk H. A. J. Polymorphism of even saturated carboxylic acids from n-decanoic to n-eicosanoic acid. New J. Chem. 2007, 31, 947-957. 40 Czamara, K.; Majzner, K.; Pacia, M. Z.; Kochan, K.; Kaczora, A.; Barańska, M. Raman spectroscopy of lipids: a review. J. Raman Spectrosc. 2015, 46, 4–20. 41 de Sousa, F. F.; Nogueira, C. E. S.; Freire, P. T. C.; Moreira, S. G. C.; Teixeira, A. M. R.; de Menezes, A. S.; Mendes Filho, J.; Saraiva, G. D. Conformational change in the C form of palmitic acid investigated by Raman spectroscopy and X-ray diffraction. Spectrochmica Acta A 2016, 161, 162–169. 42 Muik, B.; Lendl, B.; Molina-Diaz, A.; Ayora-Cañada, M. J. Reagent-free determination of free fatty acid content in olive oil and olives by Fourier transform Raman spectrometry. Anal. Chim. Acta 2003, 487, 211-220. 43 Paré, C.; Lafleur, M. Formation of liquid ordered lamellar phases in the palmitic acid/cholesterol system. Langmuir 2001, 17, 5587-5594. 44 Zerbi, G.; Conti, G.; Minoni, G.; Pison, S.; Bigotto, A. Premelting phenomena in fatty acids: an infrared and Raman study. J. Phys. Chem. 1987, 91, 2386-2393. 40 ACS Paragon Plus Environment

Page 40 of 44

Page 41 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


45

S. Mishra, D. Chaturvedi, N. Kumar, P. Tandon, H.W. Siesler. An ab initio and DFT study of structure and vibrational spectra of γ form of Oleic acid: Comparison to experimental data. Chem. Phys. Lipids. 2010, 163, 207-217. 46 Shreve, O. D.; Heether, M. R.; Knight, H.B.; Swern, D. Infrared absorption spectra some long-chain fatty acids, esters, and alcohols. Analitical Chemistry 1950, 22, 1498-1451. 47 Vogel-Weill, C.; Corset, J. Infrared and Raman spectra of stearic acid and a series of form C fatty acids: skeletal modes, coupling of longitudinal acoustic modes (LAM1, LAM3) with in-plane modes of the hydrogen-bonded dimer below 700 cm−1. Spectrochim. Acta A 1995, 51, 2357-2377. 48 Unger, M.; Chaturvedi, D.; Mishra, S.; Tandon, P.; Siesler, H. W. Two-dimensional correlation analysis of temperature-dependent FT-IR spectra of oleic acid. Spectrosc. Lett. 2012, 46, 21-27. 49 Che Man, Y. B.; Moh, M. H. Determination of free fatty acids in palm oil by near-infrared reflectance spectroscopy. JAOCS 1998, 75, 557-562. 50 Ozaki, Y.; Liu, Y.; Czarnecki, M. A.; Noda, I. FT-NIR spectroscopy of some long-chain fatty acids and alkohols. Macromol. Symp. 1995, 94, 51-59. 51 Iwahashi, M.; Hachiya, N.; Hayashi, Y.; Matsuzawa, H.; Liu, Y.; Czarnecki, M. A.; Ozaki, Y.; Horiuchi, T.; Suzuki, M. Self-association of cis-9-octadecen-1-ol in the pure liquid state and in decane solutions as observed by viscosity, self-diffusion, nuclear magnetic resonance, electron spin resonance and near-infrared spectroscopic measurements. J. Phys. Chem. 1995, 99, 4155-4161. 52 Iwahashi, M.; Suzuki, M.; Czarnecki, M. A.; Liu, Y.; Ozaki, Y. Near-IR molar absorption coefficient for the OH-stretching mode of cis-9-octadecenoic acid and dissociation of the acid dimers in the pure liquid state. J. Chem. Soc. Faraday Trans. 1995, 91, 697-701. 53 Góra, R. W.; Grabowski, S. J.; Leszczyński, J. Dimers of formic acid, acetic acid, formamide and pyrrole-2-carboxylic acid: an ab initio study. J. Phys. Chem. A 2005, 109, 6397–6405. 54 Pi, F.; Kaneko, F.; Iwahashi, M.; Suzuki, M.; Ozaki, Y. Solid-state low temperature → middle temperature phase transition of linoleic acid studied by FTIR spectroscopy. J. Phys. Chem. B 2011, 115, 6289–6295. 55 Max, J. J.; Chapados, C. Infrared spectroscopy of aqueous carboxylic acids: malic acid. J. Phys. Chem. A 2002, 106, 6452–6461. 56 Matsuzawa, H.; Tsuda, M.; Minami, H.; Iwahashi, M. Dynamic molecular behavior and cluster structure of octanoic acid in its liquid and CCl4 solution. Food Nutr. Sci. 2013, 4, 25-32. 57 Al-Lahham, S. H.; Peppelenbosch, M. P.; Roelofsen, H.; Vonk, R. J.; Venema, K. Biological effects of propionic acid in humans; metabolism, potential applications and underlying mechanisms. Biochimica et Biophysica Acta (BBA) - Molecular and Cell Biology of Lipids 2010, 1801, 1175–1183. 58 Lehmann, D.; Radomski, N.; Lütke-Eversloh, T. New insights into the butyric acid metabolism of Clostridium acetobutylicum. Appl. Microbiol. Biotechnol. 2012, 96, 1325-1339. 59 Suckling, K. E.; Suckling, C. J. Biological Chemistry: The Molecular Approach to Biological Systems; Cambridge University Press, 1980. 41 ACS Paragon Plus Environment


60 Ushijima, T.; Takahashi, M.; Ozaki, Y. Acetic, propionic, and oleic acid as the possible factors influencing the predominant residence of some species of Propionibacterium and coagulase-negative Staphylococcus on normal human skin. Can. J. Microbiol. 1984, 30, 647−652. 61 Lassila, T.; Hokkanen, J.; Aatsinki, S.-M.; Mattila, S.; Turpeinen, M.; Tolonen, A. Toxicity of carboxylic acid-containing drugs: the role of acyl migration and CoA conjugation. Investigated. Chem. Res. Toxicol. 2015, 28, 2292–2303. 62 Thiam, A. R.; Farese Jr, R. V.; Walther, T. C. The biophysics and cell biology of lipid droplets. Nature Reviews Molecular Cell Biology 2013, 14, 775–786. 63 Ishigaki, M.; Nakanishi, A.; Hasunuma, T.; Kondo, A.; Morishima, T.; Okuno, T.; Ozaki, Y. High-speed scanning for the quantitative evaluation of glycogen concentration in bioethanol feedstock synechocystis sp. PCC6803 using a near-infrared hyperspectral imaging system with a new near-infrared spectral camera. Appl. Spectrosc. 2017, 71, 463-471. 64 Huck, C. W.; Huck-Pezzei, V. A.; Ozaki, Y. Critical review upon the role and potential of fluorescence and near-infrared imaging and absorption spectroscopy in cancer related cells, serum, saliva, urine and tissue analysis. Curt. Med. Chem. 2016, 23, 1-24. 65 Grabska, J.; Ishigaki, M.; Beć, K. B.; Wójcik, M. J.; Ozaki, Y. Structure and near-infrared spectra of saturated and unsaturated carboxylic acids. An insight from anharmonic DFT calculations. J. Phys. Chem. A 2017, 121, 3437−3451. 66 Grabska, J.; Beć, K. B.; Ishigaki, M.; Wójcik, M. J.; Ozaki, Y. Spectra-structure correlations of saturated and unsaturated medium-chain fatty acids. Near-infrared and anharmonic DFT study of hexanoic acid and sorbic acid. Spectrochim. Acta A 2017, 185, 35–44. 67 Becke, A. D. Density‐functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 1993, 98, 5648-5652. 68 Kesharwani, M. K.; Brauer, B.; Martin, J. M. L. Frequency and zero-point vibrational energy scale factors for double-hybrid density functionals (and other selected methods): Can anharmonic force fields be avoided? J. Phys. Chem. A 2015, 119, 1701-1714. 69 Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, Revision E.01; Gaussian, Inc.: Wallingford, CT 2009. 70 Schuler, M. J.; Hofer, T. S.; Huck, C. W. Assessing the predictability of anharmonic vibrational modes at the example of hydroxyl groups – ad hoc construction of localised modes and the influence of structural solute–solvent motifs. Phys. Chem. Chem. Phys. 2017, 19, 11990-12001. 71 Beć, K. B.; Futami, Y.; Wójcik, M. J.; Nakajima, T.; Ozaki, Y. Spectroscopic and computational study of acetic acid and its cyclic dimer in the near-infrared region. J. Phys. Chem. A 2016, 120, 6170-6183. 72 Holman, R. T.; Edmondson, P. R. Near-infrared spectra of fatty acids and some related substances. Anal. Chem. 1956, 28, 1533−1538. 73 Weyer, L. G.; Lo, S.-C. Spectra structure correlation in the near infrared. In Handbook of 42 ACS Paragon Plus Environment

Page 42 of 44

Page 43 of 44 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Vibrational Spectroscopy; Chalmers, J. M., Griffiths, P. R., Eds.; John Wiley & Sons: 2002. 74 Puangchit, P.; Ishigaki, M.; Yasui, Y.; Kajita, M.; Ritthiruangdej, P.; Ozaki, Y. Non-staining visualization of embryogenesis and energy metabolism in medaka fish eggs using near-infrared spectroscopy and imaging. Analyst 2017, 142, 4765-4772. 75 Beć, K. B.; Grabska, J.; Ozaki, Y. Advances in anharmonic methods and their applications to vibrational spectroscopies. Wójcik, M. J.; Nakatsuji, H.; Kirtman, B.; Ozaki, Y. Eds.; Frontiers of Quantum Chemistry. Springer, 2017. 76 Grabska, J.; Czarnecki, M. A.; Beć, K. B.; Ozaki, Y. Spectroscopic and quantum mechanical calculation study of the effect of isotopic substitution on NIR spectra of methanol. J. Phys. Chem. A 2017, 121, 7925–7936. 77 Beć, K. B Grabska, J.; Czarnecki, M. A. Spectra-structure correlations in NIR region: Spectroscopic and anharmonic DFT study of n-hexanol, cyclohexanol and phenol. Spectrochim. Acta A 2018, 197C, 176-184. 78 Yagi, K.; Keçeli, M.; Hirata, S. Optimized coordinates for anharmonic vibrational structure theories. J. Chem. Phys. 2012, 137, 204118. 79 Thomsen, B.; Yagi, K.; Christiansen. O. A simple state-average procedure determining optimal coordinates for anharmonic vibrational calculations. Chem. Phys. Lett. 2014, 610– 611, 288-297. 80 Chocholoušová, J.; Vacek, J.; Hobza, P. Acetic acid simer in the gas phase, nonpolar solvent, microhydrated environment, and dilute and concentrated acetic acid: Ab Initio quantum chemical and molecular dynamics simulations. J. Phys. Chem. A 2003, 107, 3086−3092. 81 Fletcher, A. N.; Heller, C. A. Self-association of alcohols in nonpolar solvents. J. Phys. Chem. 1967, 71, 3742-3756. 82 Mackeprang, K.; Xu, Z. H.; Maroun, Z.; Meuwly, M.; Kjaergaard, H. G. Spectroscopy and dynamics of double proton transfer in formic acid dimer. Phys. Chem. Chem. Phys. 2016, 18, 24654-62. 83 Farfán, P.; Echeverri, A.; Diaz, E.; Tapia, J. D.; Gómez, S.; Restrepo, A. Dimers of formic acid: Structures, stability, and double proton transfer. J. Chem. Phys. 2017, 147, 044312-8. 84 Durlak, P.; Berski, S.; Latajka, Z. Car-Parrinello and path integral molecular dynamics study of the hydrogen bond in the acetic acid dimer in the gas phase. J. Mol. Model. 2011, 17, 2995-3004. 85 Godbeer, A. D.; Al-Khalili, J.; Stevenson, P. D. Environment-induced dephasing versus von Neumann measurements in proton tunneling. Phys. Rev. A 2014, 90, 012102-8. 86 Florio, G. M.; Zwier, T. S.; Myshakin, E. M.; Jordan, K. D.; Sibert III, E. L. Theoretical modeling of the OH stretch infrared spectrum of carboxylic acid dimers based on first-principles anharmonic couplings. J. Chem. Phys. 2003, 118, 1735-1746.



203x114mm (192 x 192 DPI)

ACS Paragon Plus Environment

Page 44 of 44

NIR Spectra Simulations by Anharmonic DFT-Saturated and

Recommend Documents