Anharmonicity and Spectra–Structure Correlations in MIR and NIR Spectra of Crystalline Menadione (Vitamin K3)

Mid-infrared (MIR) and near-infrared (NIR) spectra of crystalline menadione (vitamin K3) were measured and analyzed with aid of quantum chemical calculations. The calculations were carried out using the harmonic approach for the periodic model of crystal lattice and the anharmonic DVPT2 calculations applied for the single molecule model. The theoretical spectra accurately reconstructed the experimental ones permitting for reliable assignment of the MIR and NIR bands. For the first time, a detailed analysis of the NIR spectrum of a molecular system based on a naphthoquinone moiety was performed to elucidate the relationship between the chemical structure of menadione and the origin of the overtones and combination bands. In addition, the importance of these bands during interpretation of the MIR spectrum was demonstrated. The overtones and combination bands contribute to 46.4% of the total intensity of menadione in the range of 3600–2600 cm−1. Evidently, these bands play a key role in shaping of the C-H stretching region of MIR spectrum. We have shown also that the spectral regions without fundamentals may provide valuable structural information. For example, the theoretical calculations reliably reconstructed numerous overtones and combination bands in the 4000–3600 and 2800–1800 cm−1 ranges. These results, provide a comprehensive origin of the fundamentals, overtones and combination bands in the NIR and MIR spectra of menadione, and the relationship of these spectral features with the molecular structure.


Introduction
Vitamins play an important role in living organisms, therefore are subject of numerous experimental and theoretical studies [1,2]. The investigations cover the fundamental chemical and biological processes involving vitamins, e.g., electron transfer reactions [3] as well as their biochemical activity in living organisms [4]. However, equally important are studies on the physical and chemical properties of vitamins. Different experimental methods were used to examine the correlation between the properties and the biochemical functions of vitamins, e.g., interactions of vitamins with the chemical environment and solubility in various solvents [5,6] their antioxidant potentials [7] photosensitivity and photostability [8] and the relationships between their molecular structure and chemical stability [9].
Among numerous experimental methods, vibrational spectroscopy is particularly powerful tool since it provides detailed information on changes at a molecular level. Fundamental vibrations of vitamins were intensively examined by various spectroscopic techniques, i.e., mid-infrared (MIR; i.e., infrared, IR), far-infrared (FIR), terahertz (THz) and Raman. For example, attenuated total reflectance terahertz (ATR-THz) spectroscopy spectra were simulated using a single-molecule with the geometry extracted from the crystalline structure and then optimized in vacuum. As demonstrated recently, such approach is feasible due to local character of the vibrational modes in the NIR region [33,44]. Numerous studies have been devoted to investigations of hydrogen bonding effects in MIR spectra [20,22,[45][46][47]. Recently, increases the interest in studying weak interactions, such as CH···O hydrogen bonding [48,49]. However, the investigations of these interactions in NIR spectra have been started not long ago [44,[50][51][52][53][54]. The CH···O hydrogen bonding is very weak, and therefore difficult to observe in MIR spectra. On the other hand, electrical anharmonicity leads to increased intensity of NIR bands of X-H group involved in weak hydrogen bonding [55,56]. The first overtone of the carbonyl group is located in MIR region, while the second overtone appears in NIR region [39]. Therefore, simultaneous examination of MIR and NIR spectra of menadione in a well-defined crystalline phase is expected to yield helpful information on the CH···O=R interactions in vibrational spectra.
The aim of this work was providing a detailed assignment of all fundamental bands as well as overtones and combination bands of menadione in the crystalline state. On the basis of these assignments, we elucidated the spectra-structure correlation in MIR and NIR regions. These correlations give an opportunity for study of the structure and interactions of menadione in different environments. Besides, information included in this work has a great potential in analytical applications.

Comparison of Experimental and Theoretical (Harmonic Approximation within Periodic Model) MIR Spectra
Comparing the experimental ATR-IR and DRIFT (diffuse reflectance infrared Fourier transform) spectra one can notice obvious differences resulting from the specificity of each method (Figures S1 and S2 in Supplementary Materials). Firstly, the measured spectral intensity in DRIFT spectrum is close to optimal, as the concentration of menadione could be easily adjusted by mixing with KBr. Furthermore, the penetration depth in ATR method depends on optical properties of the sample and ATR crystal and is reduced towards the shorter wavelengths (i.e., higher wavenumbers). This effect is easily seen in the normalized spectra ( Figure S2). As a result, the spectral features in the high frequency region of ATR-IR spectrum (4000-1800 cm −1 ) are very weak. In contrast, this spectral region is much better developed in the DRIFT spectrum. Therefore, we used DRIFT spectrum of menadione for further discussion.
Regardless of the method used (i.e., B3LYP/"Gatti" or B3LYP/TZVP), the MIR spectra in the 3400-2800 cm −1 region ( Figure S3) are poorly reconstructed by harmonic calculations and numerous bands are missing. Evidently, the contributions from the anharmonic vibrations (overtones and combination bands) in this spectral region are significant, and therefore, harmonic spectra calculated by periodic B3LYP/"Gatti" and B3LYP/TZVP methods do not provide basis for reliable bands assignments.
In contrast, the harmonic spectra in the 1800-400 cm −1 range ( Figure 1) obtained by B3LYP/"Gatti" and B3LYP/TZVP methods are similar to each other, and resemble the DRIFT spectra. In spite of some differences in the peak positions and relative intensities both simulated spectra develop the same spectral features. This means that the anharmonic modes have minor contribution in this spectral range. Hence, one can conclude that the fundamental bands observed in IR spectrum of crystalline menadione can be reliably identified by the periodic harmonic calculations ( Figure 1 and Table 1). In addition, we briefly investigated whether any spectral changes appear upon increasing the sample temperature from room temperature to the temperature of ca. 363 K ( Figure S4 in Supplementary Materials), below melting point of menadione at 380 K. From Figure S4 it is evident that the spectra recorded at room and elevated temperatures are similar, indicating that the crystalline structure of menadione is very stable and dominates in the solid sample. Therefore, the crystalline model considered in this work is representative for the wider range of experimental conditions. the crystalline structure of menadione is very stable and dominates in the solid sample. Therefore, the crystalline model considered in this work is representative for the wider range of experimental conditions. Figure 1. Spectrum of crystalline menadione in the 1800-400 cm −1 range together with the harmonic spectra calculated by periodic DFT (B3LYP/"Gatti" and B3LYP/TZVP). The detailed band assignments are presented in Table 1.   Table 1. for each calculated spectrum (i.e., B3LYP/"Gatti" and B3LYP/TZVP); (c) ν-stretching; δ-in-plane bending; γ-out-of-plane bending; ρ-rocking. Figure 2 and Table 2 reveal that much better reconstruction of the spectra of menadione in the 3600-2600 cm −1 region was obtained by anharmonic calculations. It is of note that only relatively narrow spectral range (3100-2900 cm −1 ) originates from the fundamental transitions, while outside this range dominate the combination and overtone modes ( Figure 2). To obtain quantitative information on the contributions from different vibrational modes, we calculated the integral intensities of the theoretical anharmonic spectrum in the 3600-2600 cm −1 region. It is of note that the fundamental bands contribute only to 53.6% of the total integral intensity in this region, while the contributions from the combination and overtone bands are 34.8% and 11.6%, respectively. This illustrates very well the importance of the non-fundamental transitions in this fragment of the spectrum of menadione. The distinct peaks at 3310 and 3272 cm −1 , as well as broader absorption structures observed at ca. 3183-3126 cm −1 and 2892-2813 cm −1 (including a better resolved peak at 2842 cm −1 ) originate solely from the first overtones and binary combination bands ( Figure 2 and Table 2). The significant contribution from the anharmonic vibrations in this spectral region is the main reason of poor agreement between the harmonic spectra and the experimental ones (discussed in Section 2.1). This is another example of great impact of the non-fundamental peaks on the νC-H region of MIR spectrum [40]. Note, as DVPT2 calculations offer anharmonic transition intensities as well, the IR spectra calculated with this method improve the accuracy not only of the positions of the calculated fundamental bands but also their intensities, as compared with harmonic calculations.

Overtones and Combination Bands in MIR Spectrum of Menadione
The presence of the first overtones and binary combination bands is clearly manifested in the regions of MIR spectra free from the fundamental bands such as 4000-3600 cm −1 ( Figure 3A) or 2800-1800 cm −1 ( Figure 3B). The corresponding band assignments are collected in Tables 3 and 4. These spectral regions are often neglected during the routine studies. In principle, both regions belong to IR range, however, they include only the bands from non-fundamental transitions (overtones and combinations), just like NIR spectra. In the case of simple deuterated compounds, the range of MIR spectrum without fundamentals may cover the range from 4000 to 2300 cm −1 [42,43]. Figure 3B reveals that in the 2800-1800 cm −1 range appears a lot of peaks that may be interpreted with aid of the anharmonic calculations. It is of note that below 2000 cm −1 the highest frequency fundamental band is observed at 1664 cm −1 and it originates from a mixed δ(ring) and νC=O vibration.  Table 2. The presence of the first overtones and binary combination bands is clearly manifested in the regions of MIR spectra free from the fundamental bands such as 4000-3600  Table 2. vibration. The domination of anharmonic transitions is clearly seen in the 2800-1800 cm −1 region. The bands due to the first overtones are less numerous than the combination bands. Yet, they clearly appear in the experimental MIR spectrum of menadione, e.g., at 2747, 2655 or 2625, and 2008 cm −1 ( Figure 3B and Table 4). In the range of 2010-1800 cm −1 , occur few sharp peaks of relatively high intensity, originating mainly from the combination bands involving γC-H vibrations. In addition, the overtones of γC-H modes contribute to this range, but this contribution is much smaller.    Table 2) and assignments of the fundamental bands in the 4000-3600 cm −1 range for crystalline menadione.

Experimental Position
Calc   Table 2) and assignments of the fundamental bands in the 2800-1800 cm −1 range for crystalline menadione.  The domination of anharmonic transitions is clearly seen in the 2800-1800 cm −1 region. The bands due to the first overtones are less numerous than the combination bands. Yet, they clearly appear in the experimental MIR spectrum of menadione, e.g., at 2747, 2655 or 2625, and 2008 cm −1 ( Figure 3B and Table 4). In the range of 2010-1800 cm −1 , occur few sharp peaks of relatively high intensity, originating mainly from the combination bands involving γC-H vibrations. In addition, the overtones of γC-H modes contribute to this range, but this contribution is much smaller.

NIR Spectrum of Menadione
Most of bands in NIR spectrum of crystalline menadione is located in two spectral regions: 6100-5700 cm −1 ( Figure 4A) and 4800-4100 cm −1 ( Figure 4B). Outside these regions are observed only extremely weak bands from the higher order overtones and combination bands. To estimate the relative importance of the overtones and combination bands in the NIR range, we calculated integral intensity values for the theoretical spectrum. It appears that in the 7000-4000 cm −1 range the binary combinations and the first overtones contribute to 70% and 30% of total intensity, respectively. Evidently, the combination bands are the main component of the NIR spectrum of crystalline menadione.  As can be seen ( Figure 5) most of bands contribute to 4800-4000 cm −1 and 6200-5700 cm −1 regions, confirming direct observation from the spectra. Interestingly, the extent of the overlap of peaks in the 4400-4000 cm −1 region is noticeable greater than that in the 4000-3600 cm −1 range ( Figure 3A), despite similar origin of the major contributing bands, i.e., δring + νCH and δCH + νCH (see Figures 3 and 5, Table 3). Obviously, the degree of The 6100-5700 cm −1 region is contributed mainly by the first overtones, while the contribution from the binary combinations is visible at 6022 cm −1 ( Figure 4A). The other higher frequency combinations (e.g., 6094 cm −1 ) in the theoretical spectra are less clear in the experimental spectrum. Some of these bands appear as not resolved shoulders.
As shown, NIR spectra of even relatively simple molecules are complex and consist of numerous overlapped bands [57]. This feature of NIR spectra is well demonstrated in the case of crystalline menadione. In Figure 4, the experimental and calculated NIR spectra are compared. For the theoretical spectra, the contributions from all individual overtones and combination bands are also shown. Evidently, the degree of overlap of various bands is significantly higher than that observed in the MIR spectrum ( Figure 1). Consequently, the structural information included in the NIR spectrum is obscured and difficult to present in the table with the individual band assignments. Therefore, to better reflect this intrinsic complexity of NIR line shape and present the assignments in a clear way, the contributions from selected vibrational modes to NIR spectra are shown in form of color maps.
As can be seen ( Figure 5) most of bands contribute to 4800-4000 cm −1 and 6200-5700 cm −1 regions, confirming direct observation from the spectra. Interestingly, the extent of the overlap of peaks in the 4400-4000 cm −1 region is noticeable greater than that in the 4000-3600 cm −1 range ( Figure 3A), despite similar origin of the major contributing bands, i.e., δring + νCH and δCH + νCH (see Figures 3 and 5, Table 3). Obviously, the degree of overlap of NIR bands rapidly increases with the size of the molecule [40,58]. However, NIR spectrum of menadione consist of relatively sharp and well-resolved peaks, as compared with smaller molecules such as crystalline melamine [33], butyl alcohols [59] or ethanol in CCl 4 [60,61]. Therefore, menadione offers an opportunity to elucidate reliable spectra-structure correlations in the NIR region.
As expected, the major contribution to NIR spectra originates from the first overtones of the aromatic C-H stretching modes absorbing above 5900 cm −1 ( Figure 4A). However, the presence of the methyl group is clearly seen in the 5900-5600 cm −1 range. The two 2ν as CH 3 bands (of different symmetry, i.e., 2ν as CH 3 and 2ν as 'CH 3 according to Pulay's convention [62]) appear at 5895 and 5817 cm −1 . It seems that the former band has an underestimated intensity, and probably it corresponds to the sharp peak at 5887 cm −1 in the experimental spectrum. Interestingly, the 2ν s CH 3 vibration has only a minor contribution at 5799 cm −1 .
In the spectral region from 4780 to 4600 cm −1 appears a series of sharp peaks with a relatively small extent of overlap ( Figure 4B). The pronounced absorbance at 4719 cm −1 corresponds to the combination band (νC=O, δring) + νCH, while the peaks at 4646 cm −1 and 4631 cm −1 are due to the other combinations (δring, δCH) + νCH. The prominent intensity of these combination bands and relatively good separation reflects strong coupling between the vibrational modes. This may result from the localization of the modes in a rigid and symmetric ring structure. Similar peaks have been recently observed in polymers having six-membered aromatic rings [63] and in NIR spectra of other systems with aromatic rings [64]. Interestingly, the combinations of ring in-plane deformation with C=O stretching vibrations are more pronounced for menadione than those for the six-membered rings [63]. Further studies are necessary to better understand the impact of the C=O bonds in the aromatic ring on presence of this characteristic pattern in NIR spectra. The presence of a series of strong and isolated combination bands in this spectral range may evidence the presence of aromatic rings in the sample.

Experimental
Menadione of high purity (>98%) purchased from Sigma Aldrich (St. Louis, MO, USA) was used as received. MIR spectra were measured by attenuated total reflection (ATR) and diffuse reflectance (DRIFT) techniques on a Nicolet iS50 FT-IR/NIR spectrometer (Thermo Fisher Scientific, Waltham, MA, USA) using KBr beamsplitter and DTGS/KBr detector. IR spectra were measured in the 4000-400 cm −1 range with a resolution of 2 cm −1 and 512 scans were accumulated. DRIFT spectra were measured with the Collector accessory. The sample was mixed with dry KBr to obtain approx. 2% (w/w) solid solution. The sample was prepared directly before the spectral measurements. ATR-IR spectra were acquired by ATR Smart Golden Gate accessory (single reflection, 45 • incident angle) with diamond internal reflection element (IRE). Next, the spectra were subjected to ATR correction using the refractive index of the IRE and the sample. NIR spectra were measured on Nicolet iS50 spectrometer (Thermo Fisher Scientific, Waltham, MA, USA), with CaF 2 beamsplitter and DTGS/KBr detector. The spectra were collected in the 10,000-4000 cm −1 range with resolution of 4 cm −1 and 256 scans were accumulated.

Computational Procedures
The simulation of MIR spectra of crystalline menadione was based on harmonic analysis in three-dimensional periodic representation of crystal structure of menadione using Crystal 09 software (Aethia Srl, Turin, Italy) [65]. An infinite 3D models of crystal lattice was constructed by defining the primitive cell based on the experimental structural data obtained from the Cambridge Structural Database (CSD) (Figure 6) [66]. At first, an unconstrained and full geometry optimization involving both the atomic centers and cell parameters was performed. The following parameters were set throughout the geometry and vibrational computing steps. The Monkhorst-Pack reciprocal space was sampled over a shrinking factor of eight. The self-consistent field (SCF) procedure was iteratively converged with a tolerance of 10 −13 atomic units per unit cell. The truncation of Coulomb and exchange sums in direct space was controlled by setting the Gaussian overlap tolerance criteria to 10 −8 , 10 −8 , 10 −8 , 10 −8 , and 10 −16 . To accelerate the convergence of the SCF procedure, a linear mixing of Fock matrices by 25% between adjacent steps and an energy shifting of 0.8 Hartree for the first SCF cycle were employed. The electron integrals were numerically calculated over a dense (XL) integration grid. The periodic Density Functional Theory (DFT) computations were performed with the use of B3LYP (Becke, three-parameter, Lee-Yang-Parr) [67] single-hybrid density functional, as implemented in Crystal 09 software. The calculations were performed using two different basis sets. In the first one, we applied the basis sets for the respective atomic centers: 3-1p1G for hydrogen, and 6-31d1G for carbon and oxygen. As these basis sets were proposed by Gatti et al. [68], for clarity we refer them as "Gatti" basis sets. The second kind of calculations used triple-ζ valence basis set with polarization (TZVP), applied uniformly for all atomic centers (C, O, H). An application of the TZVP basis set substantially increased the computational time. Harmonic vibrational frequencies and intensities were obtained at the Gamma point in each case. The frequencies were numerically calculated by Crystal 09. To ensure the high stability of this procedure, numerical derivation (the second derivatives of the potential energy) was based on two-point finite difference scheme. The convergence criterion for the vibrational analysis was successfully achieved, as the sonic modes of the crystal lattice approached near zero values (not exceeding −0.5 cm −1 ).
Harmonic vibrational frequencies and intensities were obtained at the Gamma point in each case. The frequencies were numerically calculated by Crystal 09. To ensure the high stability of this procedure, numerical derivation (the second derivatives of the potential energy) was based on two-point finite difference scheme. The convergence criterion for the vibrational analysis was successfully achieved, as the sonic modes of the crystal lattice approached near zero values (not exceeding −0.5 cm −1 ). Simulations of NIR spectra required multi-modal anharmonic computations in order to yield data on binary combinations, which are the most important factors in this spectral region [69]. For this purpose, we applied Deperturbed Vibrational Second-Order Perturbation Theory (DVPT2), and the calculations were performed with Gaussian 16 Rev. B.02 software [70]. Computations of NIR spectra were carried out using DFT approach at B3LYP/SNST [71] level of theory, and additionally refined by applying Grimme's third version of empirical correction for dispersion with Becke-Johnson damping (GD3BJ) [72]. The considered system is not expected to be appreciably impacted by the dispersion forces, but the modern variants of the dispersion correction should be commonly used with DFT [73], as the gain in accuracy is achieved whenever geometry optimization is performed [74][75][76]. The accuracy of the calculated anharmonic frequencies and intensities is known to be sensitive to the precision of the optimized geometry [77]. The calculations were based on the model of a single molecule in vacuum ( Figure S5 in Supplementary Materials). The initial atomic coordinates were extracted from the experimental crystalline structure and subsequently optimized to the local minimum energy. The geometry optimization was performed with very tight convergence criteria. Superfine grids were used for the evaluation of two-electron integrals and solving coupled perturbed Hartree-Fock equations.
The modelling of the MIR and NIR band shapes was carried out by using product of Lorentz-Gauss (Cauchy-Gauss) functions [51,78]. To improve the agreement between the Simulations of NIR spectra required multi-modal anharmonic computations in order to yield data on binary combinations, which are the most important factors in this spectral region [69]. For this purpose, we applied Deperturbed Vibrational Second-Order Perturbation Theory (DVPT2), and the calculations were performed with Gaussian 16 Rev. B.02 software [70]. Computations of NIR spectra were carried out using DFT approach at B3LYP/SNST [71] level of theory, and additionally refined by applying Grimme's third version of empirical correction for dispersion with Becke-Johnson damping (GD3BJ) [72]. The considered system is not expected to be appreciably impacted by the dispersion forces, but the modern variants of the dispersion correction should be commonly used with DFT [73], as the gain in accuracy is achieved whenever geometry optimization is performed [74][75][76]. The accuracy of the calculated anharmonic frequencies and intensities is known to be sensitive to the precision of the optimized geometry [77]. The calculations were based on the model of a single molecule in vacuum ( Figure S5 in Supplementary Materials). The initial atomic coordinates were extracted from the experimental crystalline structure and subsequently optimized to the local minimum energy. The geometry optimization was performed with very tight convergence criteria. Superfine grids were used for the evaluation of two-electron integrals and solving coupled perturbed Hartree-Fock equations.
The modelling of the MIR and NIR band shapes was carried out by using product of Lorentz-Gauss (Cauchy-Gauss) functions [51,78]. To improve the agreement between the harmonic spectra calculated in periodic conditions with the experimental MIR spectra, we applied a single-parameter scaling based on Yoshida's wavenumber linear scaling (WLS) method [79]. Such an approach was found to yield helpful improvement of the calculated peak positions in our earlier works in which calculations of IR spectra of crystalline systems were performed [33,41]. No frequency scaling was applied to the anharmonic spectra.

Conclusions
A detailed vibrational analysis of MIR and NIR spectra of crystalline menadione (i.e., vitamin K 3 ) was performed with the use of harmonic approximation applied to a periodic model of a crystal lattice and anharmonic DVPT2 calculations applied to an isolated molecule. The combination of different theoretical approaches made possible for successful reconstruction of the experimental spectra and enabled reliable band assignments. For the first time, a detailed analysis of the NIR spectrum of a molecule with naphthoquinone moiety was performed, and new spectra-structure relationships were elucidated. Our results evidence the great importance of overtones and combination bands in the interpretation of MIR spectrum of crystalline menadione. It was estimated that these non-fundamental bands contribute to 46.4% of the total integral intensity in the 3600-2600 cm −1 region. Evidently, they are significant factors influencing the spectral line shape. As shown, the overtones and combination bands absorbing in the regions of MIR spectrum without the fundamental bands (4000-3600 and 2800-1800 cm −1 ) provide useful structural information. Using a color map, we presented in a clear way the contribution to NIR intensity from different vibrational modes. As shown, the NIR spectrum is dominated by the combination bands, while the first overtones (from νC-H) significantly contribute only in the 6000-5800 cm −1 range. The total contribution to the NIR intensity from the combination modes and first overtones was estimated to be 70% and 30%, respectively. This work provides solid basis for comprehensive interpretation of NIR and MIR spectra of crystalline menadione, and establish new relationships between these two spectral regions.
Supplementary Materials: The following are available online, Figure S1. Untreated experimental ATR and DRIFT IR spectra of crystalline menadione in region of 4000-400 cm −1 ; Figure S2. Normalized experimental ATR-IR and DRIFT spectra of crystalline menadione in region of 4000-400 cm −1 ; Figure S3. IR (DRIFT) spectrum of crystalline menadione in the 3400-2800 cm −1 region together with the harmonic spectra calculated by periodic DFT (B3LYP/"Gatti" and B3LYP/TZVP); Figure S4. Experimental ATR spectra of crystalline menadione in region of 4000-400 cm −1 measured in room temperature (bottom) and at around 373 K. Figure S5. The molecule of menadione optimized at B3LYP-GD3BJ/SNST level of theory; Table S1. Geometrical parameters in Cartesian coordinates of menadione optimized at B3LYP-GD3BJ/SNST level of theory; Table S2. Potential energy distributions over the internal coordinates of menadione resulting from harmonic analysis performed at B3LYP-GD3BJ/SNST level of theory.