NIR spectra simulation of thymol for better

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NIR spectra simulation of thymol for better understanding of the spectra forming factors, phase and concentration effects and PLS regression features

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Krzysztof B. Beć,1* Justyna Grabska,1,2 Christian G. Kirchler1 and Christian W. Huck1

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Institute of Analytical Chemistry and Radiochemistry, Leopold-Franzens University, Innrain 80/82, CCB-Center for Chemistry and Biomedicine, 6020-Innsbruck, Austria Faculty of Chemistry, University of Wrocław, F. Joliot-Curie 14, 50-383 Wrocław, Poland

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*Corresponding Author: K.B. Bed, email address: [email protected]

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Abstract

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Near-infrared spectroscopy (NIRS) is an effective analytical/quality control tool in various appliances, i.e. in phytopharmaceutical industry. While multivariate analysis gives NIRS the desired analytical performance level it lacks in providing deeper physical insights. Quantum mechanical (QM) simulation of NIR spectra is becoming feasible for complex molecules in the present days. The usefulness of QM simulation in NIRS surpasses that of IR region as NIR spectra are intrinsically complex due to anharmonic effects; yet QM investigations in NIR remain rare due to practical limitations. QM provides detailed band assignments, far exceeding the capability of classical spectroscopic methods, but also offers unveiling the influential factors in the chemometric models. In the present work we investigate NIR spectrum of thymol, a constituent of Thymi herba used in traditional medicine. Experimental part compares the NIR spectra of thymol in solid state, melted (neat liquid) and in CCl4 solution of different concentration. The analysis unveils the spectral regions of strongly varying sensitivity level to the sample state; two regions (6000-5600 cm-1 and 4490-4000 cm-1 ) are identified to remain largely invariant to the sample state. The band assignments and plotted density of modal contribution visualizes generalized and categorized factors which form the NIR spectrum of thymol. A principle relationship with the regression coefficients plot is established, demonstrating that the NIR bands which retain high insensitiveness to the intermolecular interactions give the most influence in the PLS regression model of thymol.

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Keywords: NIRS, spectra simulation, thymol, 5-Methyl-2-(propan-2-yl)phenol, phase transition, Thymi herba, phytopharmaceuticals, overtones, combination bands.

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1. Introduction

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Near-infrared spectroscopy (NIRS; 10,000-4000 cm-1) grows in importance as state-of-the-art quantitative analytical method due to a number of considerable advantages.1,2,3 It offers non-invasive capability, short analysis time, high throughput and high sample volume, is applicable to a wide range of sample types and retains a relative insensitiveness to their homogeneity levels while maintaining low operational cost.4,5 High compatibility with fiber probe instrumentation and recent breakthrough in developing miniaturized spectrometers largely boosted its final worthiness.5,6,7 Consequently, NIRS is an effective analytical/quality control tool in various appliances, i.e. in phytopharmaceutical industry. At the same time a complex nature of NIR spectra, resulting from a multitude of overlaying overtone and combination bands ruled by anharmonic effects decreases the inherent selectivity of the method.1-3 Extensive calibration and chemometric methods are needed; however, in the final outcome the sum of benefits typically outweighs the deficiencies of NIRS. Nevertheless, the difficulty in the interpretation of the spectral features forms a hindrance, putting NIRS apart from IR (mid-IR; 4000-400 cm-1) spectroscopy which coincidently features typically less complex spectra and wellestablished computational approaches which yield simulated IR spectra in a straightforward way. 1 Oppositely, truly useful simulation methods for NIRS should be described as still developing in the present time.1,8

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Unlike IR spectroscopy which may rely on harmonic approximation with good results,9,10 quantum mechanical (QM) simulation of NIR spectra necessarily requires anharmonic methods, in which the nature of molecular vibration (i.e. mode-mode correlations) is sufficiently described. 1,11 An overview of the theoretical background in the context of above factors may be found in recent literature;1,8,11 from the point of present introduction an essential notice is that the computational expense has been a practically limiting factor in theoretical NIRS for years. Consequently, spectral investigations utilizing QM simulations in NIR remain very rare unlike those in IR region, which contrarily can be nowadays described as routine. Substantial inherent complexity of NIR spectra makes QM simulations extremely useful, as classic spectral analysis often struggles to provide adequate explanation of the observed features.12

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NIRS rapidly gains favor in the analytical applications to raw materials among which pharmaceuticals of plant origin are frequently focused analytes. 13,14 The amount of feasibility studies exploring various conditions and methods in NIR quantitative analysis of medicinal herbs has been steadily increasing in the last few years. 13,14,15,16 Coherent with these trends an evaluation of quality control performances of Thymi herba based on NIR and ATR-IR (attenuated total reflection IR) spectroscopy hyphenated with multi-variate analytical (MVA) procedures has been reported recently.17 Thymi herba is a medicinal herb featuring a variety of therapeutic properties, mostly accounted with the antioxidant capacity of phenolic compounds embodied within. The study by Pezzei et al. focused on the quantification of two key chemicals involved, rosmarinic acid and thymol; these have been forming a typical area of interest of classical analytical studies in the past highlighting their importance for the medicinal properties of the drug.18,19 The former compound has already been investigated by us using methods of spectra simulation. 20 The latter one, thymol (IUPAC: 5-Methyl-2-(propan-2-yl)phenol; Fig. 1), is an antiseptic21 (antifungal22 and antibacterial23 ) substance figuring in the European Pharmacopeia;24 a number of other therapeutic effects (antispasmodic, 25 anti-inflammatory,26 immunomodulation,27 anti-oxidant28) has been reported as well. An essential oil of Thymi herba contains 30-70% of thymol. It is a traditional natural drug, although it can be found as the active compound of numerous industrially prepared cough medicines as well.29 Thymol forms an interesting subject of study from vibrational point of view as well. While

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being a close derivative of phenol which has been focused in our recent study,30 the spectrum of thymol is substantially enriched with NIR features. Following these features will allow drawing generalized conclusions about the factors standing behind formation of fine effects observable in NIR spectra of close derivatives. These correlations offer shedding more light onto the relationship between NIR spectral outlines and details of chemometric calibration models in the quantification procedures of thymol. 17

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Fig. 1. The optimized (DFT-B3LYP/SNST) molecular structure of thymol (refer to Supplementary Material for detailed structural parameters of the molecule).

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The present study aims at exploring NIR spectral features of thymol and their dependence on the sample state and concentration. Solid state and melted (neat liquid) as well as diluted (CCl4 solution) thymol will be investigated. The wavenumber regions featuring various level of sensitivity to the sample property will be observed. QM simulations of NIR bands will provide detailed band assignments throughout the entire spectral region. An analysis of mode contributions in the form of density maps will be performed. Such approach grants straightforward visualization of generalized and categorized contributions of vibrational modes, highlighting the major spectra forming factors. These analyses will be confronted with the most influential determinants in the chemometric calibration models allowing to draw conclusions about the relationship between these two fundamental for NIRS aspects.

2. Materials and methods 2.1 NIR spectral measurements Thymol was purchased from Sigma (T-0501; ≥99.5 % purity) and used without further purification. The measurement of NIR spectra of solid state and melted analyte was performed on Büchi NIRFlex N-500 FT‑NIR benchtop spectrometer controlled by the manufacturer’s NIRWare 1.4.3010 software. The solid sample was measured using Büchi solids device with a rotating cylinder and operating in diffuse reflectance mode and at room temperature. The spectrum of the melted analyte was acquired at the temperature of 60˚C (333 K), stabilized by the built-in sample temperature control unit of the spectrometer and using liquid cell accessory. Sealed quartz cuvette of 1 mm pathlength was employed for the melted sample. The following recording parameters were selected for solid and melted samples; spectral resolution, spectral range and scan number were 8 cm-1 (resulting in the interpolated 4 cm -1 of data spacing and 2 cm-1 of absolute accuracy), 10,000-

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4000 cm-1 and 32-64 (melted-solid), respectively. Spectra recordings were triplicated for each sample.

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Thymol in solution was prepared using CCl4 (carbon tetrachloride) a relatively inert solvent with negligible absorption throughout the entire NIR region. Varying concentration of the analyte (10-100 mg ml-1; 0.067-0.67 mol dm-3 ) was examined to account for the eventuality of concentration effect due to intermolecular interactions. These samples were measured using the PerkinElmer Spectrum 400 FT-IR/FT-NIR spectrometer operating in transmission mode. Sealed quartz cuvette with 2 mm optical pathlength was utilized. The following measurement parameters were set; 2 cm-1 (interpolated 0.5 cm-1 data spacing), 10,000-2000 cm-1 and 16, as the spectral resolution, spectral range and scan number, respectively. Measurements were repeated three times for each sample. The spectrometer allowed extending the investigation onto the wavenumber region of 4000-3650 cm-1 , which is populated by multiple combination bands and thus by its nature remains vibrationally indistinguishable from the proper NIR region (by concept down limited to 4000 cm-1, typically).1 The spectrum of diluted (10 mg ml-1) sample was processed with baseline correction; other spectra in this work presented adequate quality for qualitative assessment with no need for preprocessing of any kind.

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2.2 Quantum mechanical simulation of the NIR spectrum Since a fully anharmonic vibrational analysis induces a considerable computational cost on itself,31 it is crucial to employ a cost-effective method for the determination of the molecule’s ground state electronic structure, a preliminary step for obtaining all further properties of the system. In this role density functional theory (DFT) offers considerable advantages. In this work B3LYP (Becke, 3parameter, Lee-Yang-Parr) single-hybrid functional32 was selected, as it has repeatedly been reported to work well in anharmonic vibrational analysis.8,11,20,30 SNST basis set of triple- quality from SNS family33 was selected; it has been developed with spectroscopic appliances in mind and yields a good accuracy/cost balance for such purpose.8,31 Calculation of anharmonic frequencies is relatively sensitive to the accuracy of the approximation of the ground state structure.8 In order to obtain a desired precision, the molecular geometry optimization procedure was completed with tight convergence criteria. The resulting ground state geometry of thymol molecule which was further used in the calculations of the vibrational levels is presented in Fig. 1 and Table S1 (Supplementary Material). To increase the description quality of long-range interactions an empirical correction for dispersion was applied; in this role Grimme’s D3 damping function (GD3) 34 model was selected. Since the study focuses on solution phase a solvation model within self-consistent reaction field (SCRF) formalism35 was included. A conductor-like polarizable continuum model (CPCM) 36 solvent cavity model of CCl4 was applied; the approach has been reported to remain accurate in similar studies. 8,11 It is known that the solvent effect is easily observable in NIR spectra of comparable molecules.37,38 Relative simplicity and parameterization of SCRF framework may incorporate artificial effects on the results of vibrational analysis. A noticeable variability due to the solvent model has been observed in similar studies before;37,39 the dependence on particular molecular system inhibits effective generalization. Therefore, separate computations were performed in vacuum without implicit solvation model; a comparison and discussion of the results obtained in both ways will be provided in Section 3. Following the geometry optimization a vibrational analysis was performed, yielding harmonic frequencies and intensities of fundamental vibrations. The determined properties were subsequently used for the needs of fully anharmonic vibrational analysis by means of deperturbed second-order vibrational perturbation theory (DVPT2) 40 giving anharmonic frequencies and intensities of fundamental vibrations, as well as NIR modes - the first overtones and binary combinations. The latter ones were used for the purpose of simulation of NIR spectrum of thymol.

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The selected approach, including combination of B3LYP functional and SNST basis set have frequently been used in VPT2 (DVPT2/GVPT2) computations, including NIR spectra simulations with good results.8,30,41,42 The final simulation of NIR spectra involved convolution procedure in order to reflect the band broadening and band shape effects. For this intention a four-parameter Lorentz-Gauss product function was employed; this model gives good agreement with experimental vibrational bands in solution phase. 43,44 All QM calculation were performed with the use of Gaussian 09 D.01 suite of programs, 45 while the spectra simulation and processing, preparation of mode density maps and assembly of figures was carried out in MATLAB R2016b. 46

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3. Results and discussion

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3.1 The experimental NIR spectrum of thymol and its correspondence with sample state and concentration level

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The NIR spectra of thymol measured for solid state, melted (neat liquid; 333 K) and diluted (10-100 mg mL-1 CCl4) sample uncover a pattern of relationship to the sample state and concentration (Fig. 1). There exist a decisive difference between the spectral outlines of polycrystalline and melted thymol. The appearance of a broad structure (6800-5100 cm-1) as well as baseline elevation (5000-4000 cm-1 supposedly extending below this region) should be accounted to strong anharmonic effects, which arise in the ordered periodic structure of crystal. 47,48 These effects emerge due to highly symmetric hydrogen-bonding (HB) network of the OH group and have wellknown impact on IR spectra.47,48,49,50, The bands between 5000-4500 cm-1 wavenumbers also vary between solid and melted thymol, although more gradually. In the melted state the long-range ordering of the HB network is broken, although the concentration effect and short-range interaction through hydrogen-bonding are likely preserved. The dilution in an inert solvent introduces major difference in the regions of ca. 7000 cm -1 (2OH band) and 5000-4500 cm-1. However, once a reasonable isolation level of thymol molecules by the solvent is achieved (100 mg mL-1 CCl4 ) any further dilution (10 mg mL-1 CCl4 ) does not induce major changes. There are two spectral regions clearly independent of the sample state or concentration; 6000-5600 cm-1 and 4490-4000 cm-1 (Fig. 1). Even in the polycrystalline thymol these bands are largely invariant, although remain superimposed to the broad structures as explained earlier. The spectral features outlined in this paragraph will be further discussed with an aid of detailed band assignments and in the context of the relationship with the multi-variate quantification of thymol. 17

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Fig. 2. A set of the experimental NIR spectra of thymol; solid state and melted (neat liquid, 333 K) as well as diluted in -1 CCl4 (100 and 10 mg mL CCl4). Highlighted are the wavenumber regions qualitatively independent of sample phase and concentration; A: 6000-5600 cm-1; B: 4490-4000 cm-1.

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3.2 The simulated NIR spectrum of thymol; the role of solvation model, mode contributions and detailed band assignments

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The present limits of anharmonic QM spectra simulations prevent feasible studies of crystalline thymol.11 We will base our modeling on the thymol molecule placed in solvent cavity for direct comparison with the corresponding experimental data (soluted analyte; 100 mg mL-1 CCl4 ). The spectral cross-analysis presented above will allow following unambiguously the differences among the measured spectra. As explained in Section 2.2 the application of solvent model usually improves the results, but this may vary depending on given molecule. In the present study an incorporation of CPCM solvent model of CCl4 enhances the agreement with the experimental spectrum, as evidenced in Fig. 3.

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Fig. 3. Impact of implicit solvation model (SCRF/CPCM-CCl4) on the simulated (DVPT2//DFT-B3LYP/SNST+CPCM) NIR spectrum of thymol. The modeled spectral outlines compared with the experimental spectrum of thymol in solution (100 -1 mg mL CCl4).

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The accuracy of simulated NIR spectrum is lower when an isolated, placed in vacuum molecule is considered (Fig. 3). A good indicator could be formed by the less accurate position of the simulated 2OH peak, which arises from a highly anharmonic and sensitive mode which has often been focused on in physicochemical NIR studies. For the purpose of qualitative analysis of the entire NIR region, however, even minor bands play a role in drawing right conclusions. On top of an appearance of improper bands (i.e. strong bands at 5550 cm-1; 4245 cm-1; 3897 cm-1) the shape of the spectral outline is generally lower when the solvation model is omitted with the exception of 5300 4500 cm-1 region. Based on these observations for further reasoning the spectrum simulated with implicit solvent approximation will be employed.

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The computational approach assumed in this work involves modeling of the first overtone and binary combination bands. As investigated recently, these bands are responsible for the vast majority (ca. 80%) of spectral information emerging in NIR region.51 Inclusion of higher order modes requires a considerable increase in the usage of computational resources; however, it does not offer a momentous improvement of the quality of simulation. 51 Higher order overtones and ternary combinations are significantly weaker bands and what’s more the corresponding spectral information is “diffused” among weak, overlapping bands. 51 A possible general exception known in literature is the second overtone of C=O stretching mode, which may appear as a well resolved NIR band,52 obviously absent in the case of thymol. 12,53 Indeed, an overview of the theoretical outline and the modal contributions as compared with the experimental spectrum confirms that the simulation reflects the majority of the spectral features observed experimentally (Fig. 4).

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Fig. 4. The contributions of the first overtone and binary combination bands into the NIR spectral envelope of thymol in solution phase (100 mg mL-1 CCl4) as obtained through QM spectra simulation (DVPT2//DFT-B3LYP/SNST+CPCM).

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Fig. 5. The most probable band assignments in the experimental NIR spectrum of thymol in solution phase (100 mg mL-1 CCl4) based on comparative cross-analysis with the QM simulated NIR spectrum (DVPT2//DFT-B3LYP/SNST+CPCM). Band numbers correspond to those presented in Table 1.

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Spectra simulation provides a complete set of band assignments extending far beyond of the capabilities of classical spectroscopic methods. 8 Fig. 5 and Table 1 gather the major contributions of vibrational modes into the NIR spectrum of thymol. For sake of clarity, the experimental peaks have been ascribed following the most influential modes; high level of band overlapping (clearly evidenced in the simulation [Fig. 4]) makes elucidating concurrent minor contributions difficult. For the purpose of presenting deeper insights into the origin of the NIR spectrum of thymol a different approach will be applied as explained in Section 3.3. The overlapping is particularly noticeable in the lower NIR region, 4500-4000 cm-1; the spectral outline there may be described as a convolution of numerous weak binary combinations. Nevertheless, the model envelope resulting from the summed contributions reproduces the experimental spectrum reasonably well (Fig. 4). A considerable band overlay can be noticed between 6100-5600 cm-1 as well, where also first overtone bands appear influential. The agreement with the experimental spectrum is lower here, as the corresponding bands originate from highly anharmonic modes; the first overtone intensities are overestimated in the simulation. Similar feature has been reported for other molecules. 54 There exist some minor discrepancies in other subregions; i.e. the combination band of OH stretching and CH stretching is vastly overestimated in its height. However, these minor shortcomings may be identified effortlessly and do not inhibit comprehensive assignments (Fig. 5; Table 1). With the exception of highly anharmonic CH and CH3 stretching modes, the simulated peak wavenumbers remain remarkably correct (Table 1). The discrepancies do not exceed ca. 20 cm -1 in most cases; this translates to the error level of less than 0.5%. A relatively accurate position of the simulated 2OH band (underestimated by 9 cm-1 or 0.12 %), which is highly sensitive to the intermolecular interactions confirms that the concentration effects do not play a major role in the diluted thymol sample.

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Table 1. The proposed band assignments in the experimental NIR spectrum of thymol in solution phase (100 mg mL-1 CCl4). Band numbers correspond directly to those presented in Fig. 5. The listed contributions of the respective modes are limited to the most influential ones for sake of clarity.

Wavenumber / cm-1

Band number

Experimental

Calculated

Difference

1

7056

7047

-9

2OH

2

6488

6503

15

CHalkyl + OH

3

6072

6054

-18

2s CHring, s CHring + s CHring

4

~5972

5889

-83

2as CHring

5

5920

5873

-47

as CH3, as CH3 + as CH3 

6

5872

5832

-40

as CH3

7

5748

5751

3

s CH3, s CH3 + as CH3

8

5644

5676

32

CHalkyl

9

5236

5237

1

 ipCCring + OH

Major mode contribution

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10

5196

5186

-10

 ipCCring + OH

11

5128

5119

-9

 ipCHring + OH

12

5028

5041

13

 as CH3 + OH

13

4972

4990

18

 s CH3 + OH

14

4924

4937

13

 ipCHring + OH

15

4828

4855

27

 ipCHring + OH

16

4786, 4764

4793

-

 ipCHring + OH

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4700

4722

22

 ipOH + OH

18

4620

4616

-4

 ip,as CCring + as CHring

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4396

4387

-9

CH3 + as CH3 

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4320

4315, 4294

-

 s CH3 + as CH3;  s CH3 + as CH3,  as CH3 + s CH3 

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4260, 4236

4242

-

 s CH3 + s CH3 

22

4176

4197

21

 oopCHalkyl + CHalkyl

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4124

4155

31

 ipOH + as CHring

24

4072

4062

-10

 rockCH3 + s CHring

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3928

3976, 3908

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OH + OH, CCC + OH

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3828

3830

2

 rockCH3 + s CH3

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3764

3761

-3

C(CH3) 2 + OH

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3.3 An in-depth analysis of the origin of NIR spectrum of thymol and its relationship with PLS regression coefficient vector in quantification of thymol content

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With the aim at elucidating the generalized, mode-specific spectral contributions we have developed a density map of mode influence in the form of colormap (or heatmap) plot capable of highlighting the modes of interest in a straightforward way (Fig. 6). The color range corresponds to the square rooted intensity ratio of selected simulated bands to the total intensity of modeled spectrum at any given wavenumber i. The yielded value ranges from 0 (no contribution) to 1 (the NIR spectrum is influenced by the selected modes entirely). The square root allows elucidating less pronounced contributions. The density maps determined for various selections of modes-of-interest allow unequivocal and thorough analysis of the influential determinants in NIR spectrum. The most general classification into overtones and combinations (Fig. 6) brings an already known picture (Fig. 4); however, tuning the selection to a more specific selection yields insightful correspondences. In

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example, the combination bands involving OH stretching mode are one of the most decisive factors in forming NIR spectrum of thymol. Decomposing these into less general groups brings further details. I.e. OH + CH(ring) and OH + CH3 modes are relatively insignificant, while the combinations of OH and methyl deformations are highly influential only in a narrow wavenumber range (5080-4950 cm-1 ) and also appear between 4700 and 4600 cm -1 although with less impact. It can be easily assessed that the combinations of methyl stretching and deformation modes are largely responsible for the strong absorption region of 4450-4220 cm-1 (with peaks at 4396, 4320, 4260 and 4236 cm-1; Table 1). The distribution of the influence can be followed as well. In example, combinations of OH +CH3, CH3+CH3 and CH3+CH3 type remain highly localized in narrow wavenumber ranges. On the contrary, the combinations involving ring deformations (i.e. OH +ring and CH3+ring) can be described as diffused over wider regions along the wavenumber axis (Fig. 6). These projections allow for flexible yet straightforward generalizations and can be helpful for an indepth qualitative assessment of an NIR spectrum with highlight of categorized and grouped mode contributions.

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Taking advantage of recently analyzed NIR spectrum of phenol, 30 a brief comparison with present results may be made. Only few of thymol NIR features remain analogous with those of phenol; these bands stand apart from those of aliphatic linear and cyclic alcohols. 30 In example, the major 2OH peak appears at 7056 cm-1, near that of phenol (7052 cm-1); while in the other kinds of alcohols it tends to emerge at higher wavenumbers (7103-7073 cm-1).30 Likewise, the stretching modes of CH in ring (both first overtones and binary combinations) appear above 6000 cm-1 similar to phenol.30 In this regard, the discussed molecule keeps the vibrational properties common to phenols.30 However, while being a phenol derivative thymol features a substantial increase in the number of NIR bands in its spectrum. This should be mostly attributed to the addition of the methyl groups, as these are fairly influential particularly between 4450-3900 cm-1 but also in the 5900-5700 cm-1 region (Fig. 6). In the NIR spectrum of thymol a high separation on the wavenumber axis of the stretching modes C-H in ring and C-H in the isopropyl group should be noted as well, with the latter ones appearing below 5700 cm-1 (Fig. 5; Table 1). The two above factors enrich the spectrum of thymol as opposed to a relatively featureless phenol in the discussed region (6100-5600 cm-1).30

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-1

Fig. 6. The analysis of mode contribution into NIR spectrum of thymol (solution; 100 mg mL CCl4) based on the simulated data (DVPT2//DFT-B3LYP/SNST+CPCM). A: experimental and simulated outlines. B: contributions of selected modes as described on the figure.

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With the information set provided by the above analyses we can finally draw more general conclusions on the spectral correspondence to the sample state and concentration (Fig. 2, Section 3.1). The upper wavenumber region which remains largely invariant of these factors is mostly populated by the combinations and overtones involving C-H and CH3 stretching modes (region A in Fig. 2). In the region B (Fig. 2) the combinations of methyl stretching and deformation modes dominate (Fig. 6) with secondary influences from the combinations which involve ring deformations. These bands feature a relative insensitiveness to the sample state, preserving their position and bandshape as well as intensity in relation to other bands (Fig. 2). An exception should be mentioned, the absorption within the region B is relatively lower than in the region A for the solid state thymol; this is likely due to the superimposition of the broadened structure appearing in the region A and originating from ordered HB network which exists in crystalline phase (Fig. 2). The highest spectral variability develops between 5400-4500 cm-1, where decisive changes can be monitored with the sample melt and dilution (Fig. 2). A strong redshift and broadening of the entirety of the bands follows the transition from diluted to neat liquid (melted) sample and with even further aggregation with a single peak appearing at ca. 4600 cm-1. The discussed region is nearly exclusively formed by the combinations of OH stretching modes coupled to ring deformation, C-H (in ring) bending and methyl deformation modes (Fig. 5; Table 1). Cross-analysis with the aid of categorized combinations (Fig. 6) allows concluding that the high spectral variability is likely influenced by the specificity of OH mode. Its sensitivity to the intermolecular interactions manifests itself strongly in this case.

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A recent study has demonstrated the feasibility of quantification of thymol content in Thymi herba by employing multi-variate calibration based on NIR spectra of the natural sample.17 The constructed PLS regression coefficient vector has indicated a number of bands which introduce the highest influence on the calibration model for thymol. 17 These bands fall with no exception into the two “invariant” regions established in the present work. The influential wavenumbers [cm-1] have been reported as: 5860, 5760 (falling into the region A; Fig. 2) and 4476, 4418, 4392, 4368, 4220, 4128, 4092 (belonging in the region B; Fig. 2). 17 The major origin of these two groups can be summarized as overtones and combinations of CH3 and aromatic (region A) and combinations involvingCH3 (region B) modes. It can be concluded that the spectral information corresponding to the otherwise highly influential (in the sense of spectrum forming factor; Fig. 6) OH mode has not been recognized as being decisive in the quantification by PLS model.17 This includes a discrimination of the 5300-4500 cm-1 region. It may be argued that a “diffused” character (being spread along wide wavenumber regions) of these bands plays a role here. It should also be mentioned, that the impact of quantified molecule on its chemical surrounding through intermolecular interactions (i.e. HB or aromatic ring stacking in the case of thymol) creates a set of relevant spectral correlation which may likely be identified in the regression vector. Further studies could be aimed at simulation of these effects. The literature knows the concept of incorporating the band assignment in the chemometrics for improvement of the analytical performance of NIRS.55 However, the hindrance in utilization of such approaches has typically been imposed by lack of ability to obtain a detailed decomposition of an NIR spectrum; a barrier which may largely be removed by using spectra simulation. The correspondence of the linear spectra and the regression plots can also be found in the literature;56 however, most often such comparisons are facing similar limitations in their interpretation as the case described in the past sentence. The current preliminary study demonstrates the potential of QM in bringing deeper understanding of the relationship between the chemometric models and molecular and physiochemical background of the quantified sample.

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4. Summary QM simulation forms a major support tool as NIR spectra are inherently complex with strong band overlay; the anharmonic effects and sensitiveness to molecular interactions further inhibit the applicability of classical spectroscopic methods for an in-depth analysis of NIR data. By employing anharmonic calculations a complete decomposition of the NIR spectrum of thymol was possible, yielding comprehensive band assignments throughout the entire NIR region. The experimental study uncovered a patterned spectral variability in dependence of the sample state (solid and melted, neat liquid) and concentration (neat liquid and diluted in an inert solvent) . Spectral regions featuring high invariance to the sample property were identified. Further insights could be provided with the use of modal density plots; these allowed generalization, categorization and assessment of the spectrum forming factors and their straightforward visualization. The influential wavenumbers could be confronted with the major features of the regression coefficient vector in PLS quantification model of thymol content as reported recently. It was found that all the wavenumbers which have been identified as decisive in the PLS regression fall into the two “invariant” NIR spectral sub-regions of thymol as established in the present work. These regions are populated by the bands arising from CH3 and aromatic CH modes. Surprisingly, otherwise the most influential for the spectrum forming OH mode has been largely discriminated in the chemometric model. It was suggested that the sensitiveness of the OH mode to the intermolecular interactions, leading to a strong broadening of the corresponding bands may be accounted to the observed regularity. The presented study demonstrates the potential of gaining decisive advance in the capability of spectral analysis in the NIR region through utilization of QM spectra simulations.

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Acknowledgement

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

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