Structural studies of two capsaicinoids: dihydrocapsaicin and nonivamide. ¹³C and ¹⁵N MAS NMR supported by genetic algorithm and GIAO DFT calculations

Abstract

Capsaicinoids are alkaloid type capsaicin analogs with prospective pharmacological activity. However their solid state conformations have not been studied yet. As part of the study, cross polarization (CP) magic angle spinning (MAS) solid state ¹³C and ¹⁵N NMR spectra of dihydrocapsaicin (DHCAP) and nonivamide (NVA) were recorded. Solid state chemical shifts differ from their solution counterparts; remarkable differences occur for carbons C2′, C6′ and C7′ linked to C1′ in DHCAP and with methylene carbons C4–C8 in NVA. The doubling of some resonances in the spectra of solid NVA indicates that there are two molecules in the crystallographic asymmetric unit. DFT GIAO calculations of shielding constants were performed for several geometric isomers, including molecules with different orientations of aliphatic chain with respect to aromatic ring. Low-energy conformers were found by genetic algorithm methodology. Comparison of experimental ¹³C chemical shifts with theoretical (GIAO DFT) shielding parameters was helpful in predicting the most reliable geometry in the solid state. Cross polarization time constants T_CP and relaxation times in the rotating frame T^H_1ρ were obtained from variable-contact cross-polarization experiments. T^H_1ρ are longer in the order: NVA < CAP < DHCAP.

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Introduction

Capsaicin (8-methyl-N-vanillyl-6-nonenamide) is a pungent alkaloid found in chili pepper fruit. Over the last decades, it has been described as a multipotent bioactive compound.¹ According to these studies, many new capsaicin analogs with expected biological activity were sought. Nonivamide (NVA) and dihydrocapsaicin (DHCAP) (Fig. 1) are two derivatives of capsaicin (CAP)^2,3 which can be found as a component of analgesic drugs or pepper spray;⁴ they are also used in pain-killer cream and patches.

Fig. 1 Structure of (a) dihydrocapsaicin (DHCAP) and (b) nonivamide (NVA) with numbering of carbon atoms.

Pharmacological properties of potential drug substances, crucial for modern pharmaceutical sciences, are widely studied using spectroscopic and theoretical methods. The biological activity of a compound defined by the affinity of a small-molecule ligand towards the macromolecular receptor can be explored using in silico methods, like the molecular docking approach. The docking process involves prediction of multiple structural conformations in a binding pocket as a basic step. However, solid state conformation analysis is also very important, because the majority of dosage forms are solid dosage forms and solid state conformation is connected with pharmacokinetic properties of an API (Active Pharmaceutical Ingredient). Therefore, low energy conformations of capsaicinoids, as well as their solid-state structure are of interest and should be studied in detail.

Crystallographic data for nonivamide and dihydrocapsaicin do not exist. Since all our attempts to obtain single crystals of capsaicinoids suitable for XRD measurement have been unsuccessful, solid-state NMR is proposed as a method for structure determination for these substances. NMR spectroscopy supported by theoretical calculations was used as the main method of structural studies. This approach was previously applied by us in the study on capsaicin structure⁵ and the results were compared with PXRD data. To the best of our knowledge, this work is the first to focus on the solid-state structure of nonivamide and dihydrocapsaicin. Our results may be a step towards determination of the conformation – bioavailability relationship, because neither the conformations nor the crystal structures of these capsaicinoids have been described before.

Methods

Materials

NVA (nonivamide) and DHCAP (dihydrocapsaicin) were purchased from Sigma-Aldrich (Aldrich no. V9130 and M1022 respectively).

¹³C CPMAS NMR spectroscopy

The ¹³C and ¹⁵N magic angle spinning (MAS) NMR spectra of solid samples were recorded on a Bruker DRX-400 Advance spectrometer using a Bruker PH MAS VTN 400WB BL4 probehead. Samples packed in a 4 mm ZrO₂ rotor were spun at 10 kHz (¹³C) and 5 kHz (¹⁵N). Contact time of 2.5 ms, repetition time of 10 s and spectral width of 20 kHz were used for accumulation of 200 scans for standard ¹³C MAS experiments. For the acquisition of ¹⁵N MAS spectra these parameters were: 5 ms, 10 s and 12 000 scans, respectively. ¹³C chemical shifts were calibrated indirectly through the glycine CO signal recorded at 176.0 ppm, relative to TMS. ¹⁵N chemical shifts were calibrated through the glycine NH signal δ ¹⁵N 10.0 ppm and referenced to nitromethane δ ¹⁵N = 380.2 ppm (liquid NH₃ δ ¹⁵N = 0). Solid-state NMR cross-polarization (CP) ¹H–¹³C experiments were performed with contact times in the range from 25 μs to 18 ms.

Genetic algorithm

A conformational search was carried for each molecule using genetic algorithm (GA) with multimodal optimization. Special software (ALJAR05) was developed for the calculations and used as described earlier.⁶ Each conformation was first optimized using molecular mechanics (MMFF94 force field) to classify the conformers found by the genetic algorithm methodology.

GIAO DFT calculations

Further calculations of NMR shielding constants were performed using the DFT method with the B3LYP functional and the 6-311G(d,p) basis set (Gaussian 09 software⁷). Values of chemical shifts for each conformation were obtained in two ways: (i) by calculating TMS carbon atoms shielding constants and using the equation δ_iso = σ_TMS − σ_iso and (ii) by converting shielding constants with scaling factors.⁸ The model conformers were verified by comparing calculated shielding constants with experimental MAS NMR chemical shifts. For ¹⁵N NMR, the reference molecule nitromethane was also optimized and its isotropic NMR shielding constants were calculated.

Results and discussion

¹³C CPMAS NMR

¹H and ¹³C NMR spectra of NVA and DHCAP (in CDCl₃ solutions) were measured and assigned. The chemical shifts were in agreement with those reported previously by Gómez-Calvario et al.^{9 13}C CPMAS NMR spectra were recorded for both solids and are illustrated in Fig. 2.

Fig. 2 ¹³C CPMAS NMR spectra of (a) DHCAP and (b) NVA.

Resonances in the solid-state spectra were assigned by comparison with liquid-state chemical shifts and the results are collected in Table 1.

Table 1 ¹³C NMR chemical shifts of NVA and DHCAP in CDCl₃ (δ, ppm, ref. TMS) (δ_sol), solid-state (δ_ss) and differences δ_sol − δ_ss > 1.5 ppm

DHCAP				NVA
C atom no.	δsol	δss	Δ	C atom no.	δsol	δss	Δ
1′	130.82	128.59	2.23	1′	129.94	130.48/131.14
2′	111.19	107.77	3.42	2′	110.74	111.66/112.92	—/−2.18
3′	147.22	147.19		3′	146.70	145.41
4′	145.62	145.44		4′	145.19	143.46/145.41	1.73/—
5′	114.88	114.82		5′	114.37	115.48
6′	121.23	117.39	3.84	6′	120.86	121.85/122.65	—/−1.79
7′	43.99	40.4	3.63	7′	43.76	43.9
8′	56.39	53.6	2.76	8′	55.98	54.8/56.6
1	173.38	176.3	−2.9	1	173.53	171.9	1.5
2	37.32	37.3		2	36.55	36.08
3	26.30	28.7	−2.3	3	25.88	26.58
4	29.85	31.5	−1.6	4	29.29	33.75	−4.46
5	30.11	31.6	−1.5	5	29.14	33.75	−4.61
6	27.72	28.7		6	29.14	33.75	−4.61
7	39.43	40.4		7	22.63	24.58	−1.95
8	28.41	28.7		8	31.79	33.75	−1.96
9	23.10	24.0		9	14.08	15.46
10	23.10	23.0		—	—	—	—

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The ¹³C signals in the solid-state spectrum of DHCAP were assigned first on the basis of liquid-state chemical shifts and the results are collected in Table 1. The assignments were further confirmed by the calculation of shielding constants. The signals of carbons C1 and C7′ bound to nitrogen might be slightly broader due to the interaction with quadrupolar 14 N nuclei but the effect was not observed in the spectra recorded with spinning speed of 10 kHz. Significant differences between chemical shifts in solution and solid state (Δ = δ_sol − δ_ss > 1.5 ppm) are observed for both compounds, but for different carbon atoms.

For DHCAP, the differences appear for aromatic carbons C1′, C2′, C6′ and also for C7′and C8′. Similar differences were noticed earlier for capsaicin.⁵ All three neighbors of C1′ exhibit an increase of shielding (3.4–3.8 ppm) in the solid state, suggesting the presence of steric hindrance. Molecular modeling shows that the rotation about C1′–C7′ bond is crucial and results in intramolecular interactions of C7′–H with either C2′–H or C6′–H. Significant values of Δ may be due to the locking of this fragment into a particular conformation, for example one of the C7′–H located closer to C6′–H and OCH₃ group near aliphatic chain (Fig. 1).

Considering the NVA molecule, the most remarkable differences in chemical shifts (ca. −4.5 ppm) are observed for methylene carbons C4, C5 and C6 of the chain. The signals of four aromatic carbons (1′, 2′, 3′, 6′) and OCH₃ (C8′) appear as doublets. The presence of split resonances indicates that two different molecules coexist in an asymmetric part of a unit cell of solid NVA. An attempt to assign the resonances to particular conformer was made. It is possible that one of them is similar to DHCAP, with OCH₃ group near aliphatic chain as suggested by comparable values of Δ. But for the second conformer these differences are smaller suggesting that this molecule has aliphatic chain oriented far from aromatic ring and therefore may be less hindered.

On the basis of ¹³C CPMAS NMR and theoretical B3LYP/6-31G** calculations we could characterize the structure of conformers in solid phase. The chemical shifts for some conformers with different orientations of aliphatic chain, hydroxy and methoxy groups have been calculated by GIAO DFT. In solids, the rotation of hydroxy and methoxy groups is usually frozen, revealing specific environments with different chemical shifts, best seen for aromatic carbons ortho to the substituent. Better correlations between the measured and the calculated δ_ii values confirmed the existence of conformers with “anticlockwise” orientation of OH and OCH₃ groups, e.g. with OCH₃ pointing to C2′ and OH towards OCH₃ oxygen (Fig. 1).

Besides conformational effects, ¹³C CPMAS chemical shifts reflect intermolecular interactions in solids. The formation of H-bonds results in changes of the chemical shift (deshielding) of carbonyl carbons. In CDCl₃ only weak interactions with the solvent occur, whereas in the solid state the C=O⋯HN and/or C=O⋯HO bonds should affect the δ_ss value. In DHCAP, chemical shift of C1=O for solution is 173.38 ppm, and for solid state 176.28 ppm. The deshielding (Δ = 2.9 ppm) confirms the formation of intermolecular hydrogen bonds. For NVA, the difference of chemical shift between solution and solid state is +1.5 ppm and an increase of shielding suggest absence of hydrogen bond-type interaction involving C=O group.

¹⁵N MAS NMR

¹³C CPMAS spectra of solid NVA and DHCAP indicate that DHCAP has only one molecule in an asymmetric part of a unit cell, whereas NVA may have two. ¹⁵N MAS NMR spectra provide confirmation of these findings. In ¹⁵N MAS NMR spectrum of DHCAP a narrow singlet appears at −259.3 ppm, whereas in the spectrum of NVA a doublet is visible at −257.2/−258.2 ppm (Fig. 3).

Fig. 3 ¹⁵N MAS NMR spectra of (a) DHCAP and (b) NVA.

The value of ¹⁵N chemical shift for both compounds is typical for aliphatic and aromatic amides.¹⁰ In both solids, hydrogen bonds may be formed by the OH⋯O=C or NH⋯O=C interaction. The NH⋯O=C interaction should be reflected in ¹⁵N MAS chemical shift. If DHCAP is stabilized by NH⋯O=C H-bonds, and NVA is not, their ¹⁵N chemical shifts would be significantly different. The relationship between ¹⁵N MAS chemical shift and hydrogen bond-type interactions via NH group has been previously described and the effect of H-bond formation is estimated as ca. 8 ppm.¹¹ The ¹⁵N signals of DHCAP and NVA have almost the same chemical shift, values differ only by 1–2 ppm suggesting similar type of intermolecular interactions. Thus, one can assume that molecules of NVA and DHCAP are not linked by NH⋯O=C bonds. The deshielding of C=O in ¹³C MAS spectrum of DHCAP can be explained rather by OH⋯O=C interactions.

GIAO DFT calculations were performed for an isolated molecule of DHCAP and NVA and the values of ¹⁵N NMR chemical shift (−256.0 and −254.6 ppm, respectively) are in agreement with experimental data.

Cross-polarization dynamics

It seemed worth to check if DHCAP and NVA exhibit distinct cross-polarization dynamics. Therefore, a series of ¹³C CPMAS spectra with various contact times were recorded. According to the classic I-S model¹² the signal intensity in CP spectra is a function of contact time t:

I(t) = A(1 − T_CP/T^H_1ρ) − 1[exp(−t/T^H_1ρ) − exp(−t/T_CP)] (1)

where A is the intensity amplitude. The progress of cross-polarization is characterized by the time constant T_CP and the decrease in intensity for longer contact times t is due to the effects of ¹H spin–spin relaxation in the rotating frame, T^H_1ρ. Both parameters are specific for functional groups and differ for protonated and quaternary carbons.¹³ The values of T_CP and T^H_1ρ for dihydrocapsaicin, capsaicin and nonivamide are given in Table 2. Selected spectra of DHCAP and NVA recorded with varying contact times, are illustrated in Fig. 4a and b.

Table 2 Cross-polarization kinetic parameters: T_CP and T_1ρ for dihydrocapsaicin, capsaicin⁵ and nonivamide (nd – no data from cited publication)

Parameter	DHCAP		CAP^5		NVA
	Mean value ± SD [ms]	Range of values [ms]	Mean value ± SD [ms]	Range of values [ms]	Mean value ± SD [ms]	Range of values [ms]
Quaternary carbons C1′, C3′, C4′
TCP	0.87 ± 0.24	0.65–1.13	0.95 ± 0.22	0.71–1.23	0.71 ± 0.08	0.64–0.80
T^H1ρ	159 ± 15	143–172	154 ± 35	124–192	31 ± 8	24–40
Tdf	0.95 ± 0.43	0.58–1.42	Nd	nd	0.87 ± 0.38	0.59–1.43
C1=O
TCP	0.69	—	0.67	—	1.14	—
T^H1ρ	122	—	107	—	35	—
Tdf (I-I*-S)	0.61	—	Nd	nd	0.52	—
C–H aromatic (C2′, C5′, C6′) and C8 in DHCAP
TCP	0.51 ± 0.09	0.45–0.65	0.42 ± 0.05	0.35–0.47	0.42 ± 0.08	0.33–0.49
T^H1ρ	200 ± 58	150–250	149 ± 20	117–160	39 ± 7	35–48
Tdf (I-I*-S)	0.42 ± 0.11	0.30–0.53	Nd	nd	0.29 ± 0.03	0.23–0.30
CH2 (C2–C7) i C7′
TCP	0.38 ± 0.11	0.30–0.60	0.27 ± 0.12	0.2–0.47	0.20 ± 0.06	0.15–0.3
T^H1ρ	148 ± 23	128–180	129 ± 15	115–148	23 ± 4	21–33
Tdf (I-I*-S)	0.35 ± 0.11	0.20–0.50	Nd	nd	0.10 ± 0.09	0.05–0.31
CH3 groups
TCP	1.62 ± 0.05	1.58–1.65	0.85 ± 0	—	0.32	—
T^H1ρ	160 ± 14	150–170	160 ± 14	150–170	31	—
Tdf (I-I*-S)	2.00 ± 0.00	2.00	Nd	nd	0.23	—
OCH3 groups
TCP	0.68	—	0.45	—	0.50	—
T^H1ρ	180	—	180	—	35	—
Tdf (I-I*-S)	0.30	—	Nd	nd	0.32 ± 0.01	0.31–0.33

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Fig. 4 ¹³C NMR spectra of (a) DHCAP and (b) NVA, recorded with variable CP contact times.

T_CP is governed by dipolar coupling¹² and is long for carbons without adjacent hydrogens. Quaternary carbon atoms of DHCAP and NVA have average T_CP values of 0.87 and 0.7 ms respectively. T_CP for CH groups is shorter (0.42–0.51 ms). Assuming that the average value of 0.42 ms is typical for CH carbons (Table 2), then 0.20 ms should be expected for CH₂ and even lower value for CH₃. The values for methyl carbons of 0.32–1.62 ms are longer than those expected without intramolecular dynamics, evidencing that methyl groups are fairly mobile. T_CP increases with increasing mobility of the structural fragment bearing this carbon, and the fast rotation is typical for methyl groups.¹⁴ In the ¹³C CPMAS spectra of DHCAP separate signals of two methyl groups appeared, therefore we were able to characterize particular carbons. The values of T_CP are 1.58 and 1.65 ms for C9 and C10, respectively, indicating that their interaction with intra- or intermolecular does not differ.

Relaxation times T^H_1ρ are influenced by the short-range spatial proximity between protons and also reflect molecular dynamics. It seemed interesting to check if the two molecules present in an asymmetric part of a unit cell of solid NVA exhibit distinct cross-polarization dynamics. Inspection of the spectra in Fig. 4, in which the doublets (C2′, C3′, C6′) of almost equal intensity are seen, as well as an analysis of T_CP and T^H_1ρ values indicated that the behaviour of these two conformations is quite similar.

Fig. 5 shows the plot of signal intensity vs. contact time for methyl groups of NVA and DHCAP. Two signals of OCH₃ groups in NVA are characterized by long decay, similar to DHCAP. The T^H_1ρ values obtained for CH₃ groups (both from the aliphatic chain and methoxy groups) are the same for DHCAP and CAP.

Fig. 5 Cross-polarization kinetics for methyl carbons of (a) DHCAP and (b) NVA. Signal intensity in arbitrary units (a.u), contact time in ms. The fitted functions have long T^H_1ρ.

The plot of signal intensity vs. contact time for carbonyl carbons C1 is illustrated in Fig. 6; the shape of fitted functions is distinct: steeper for NVA and plane for DHCAP.

Fig. 6 Cross-polarization kinetics for C1=O carbon of (a) DHCAP and (b) NVA. The fitted functions have different T_1ρ values. Signal intensity in arbitrary units (a.u), contact time in ms. Fitting using eqn (1) gives T^H_1ρ = 122 ms for DHCAP and 35 ms for NVA. (T_CP = 0.61 ms and 0.52 ms, respectively).

Unfortunately, no reliable data on cross-polarization dynamics can be provided on particular methylene carbons (except C7′) because of signal overlapping.

It is difficult to predict in advance which model will be better for the quantification of a particular CP signal. Therefore, we decided to analyze CP data in accordance with the I-I*S model. Intensity decays were described by Kolodziejski and Klinowski¹² by the following equation:

I(t) = I₀[1 − ½ exp(−t/T_df) − ½ exp(−[/]t/T_df)exp(−½t²/T₂²)],

where T_df is the proton spin-diffusion constant. T_df values for DHCAP and NVA are collected in Table 2.

Relaxation time in the rotating frame is frequently averaged over all protons by spin diffusion and is indicative for separation of molecules or some domains (e.g. aliphatic and aromatic) by missing intimate spin contact. T_df are long for quaternary carbon atoms. C4′ and C3′ which are the most distant from aliphatic chain carbon atoms have the longest T_df (0.85 and 1.42 ms for DHCAP, 0.82 and 1.42 ms for NVA, respectively). There are no significant differences in T_df values for aromatic ring carbon atoms. However, the CH₃ groups of the aliphatic chain of DHCAP and NVA differ in proton spin-diffusion constant. Methyl groups of DHCAP require longer spin-diffusion, which may be caused by fast rotation of isopropyl chain termination, as it was described earlier for CAP.⁵ Shorter T_df value indicates that the CH₃ group of NVA may be less rotating. The average relaxation times in the rotating frame for solid capsaicinoids decrease in the order: DHCAP > CAP > NVA. Although the differences may be the result of different phenomena, including intramolecular mobility and intermolecular interactions, the lowest values for NVA (Table 2) suggest that solid NVA is more tightly packed and the chain has less space for dynamics.

T^H_1ρ relaxation times are considered to be a probe of crystallinity degrees. For crystalline samples, T^H_1ρ takes longer values than for amorphous samples.¹⁵ It may suggest that NVA has a more disordered network compared to DHCAP and CAP. However, line broadening characteristic for amorphous solids is not observed neither in DHCAP nor NVA ¹³C CPMAS spectra.

Cross-polarisation dynamic parameters were analyzed for the common pharmaceutical excipients.¹⁵ Branched polymers of cellulose (methylcellulose, ethylcellulose, hydroxypropylmethylcellulose) have mean T^H_1ρ value of 20 ms, which is similar to NVA. For some crystalline compounds, T^H_1ρ values were significantly higher, for example olanzapine form II (T_1ρ = ∞).¹⁶ The molecular dynamics of solid β-carotene were studied by means of ¹³C CPMAS NMR.¹⁷ The T_CP average value of 0.79 ms was found for methine carbons and 0.65–0.78 ms for methylene carbons, which indicated that these groups must be in a flexible molecular fragment. The relaxation times T^H_1ρ were very long (the CP curves ended in a plateau).

Genetic algorithm search

Low-energy conformations for NVA and DHCAP should be found for further molecular modelling, and simple DFT optimization is not efficient enough. For flexible compounds like NVA and DHCAP, systematical conformational searching (grid search) is extremely time consuming and is not recommended. A relatively new methodology of conformational analysis capable of locating minimum energy structures on conformational potential energy surfaces are evolutionary algorithms (GA) based on the concepts of biological evolution. A ‘population’ of possible solutions to the problem is first created with each solution being scored using a ‘fitness function’ that indicates how good they are. The population evolves over time and allows you to receive better solutions. Of the various types of evolutionary algorithm, the genetic algorithm (GA) is the most well-known. The idea of GA is based on the genetic principles of heredity transferred to the field of quantum chemistry. The best adapted, low-energy conformations are selected and promoted to the next generations.

In our research for DHCAP and NVA 11 torsion angles were defined (Fig. 7) and listed in Table 5. The GA calculations with MMFF94 force field were carried out using two different dielectric constants (ε = 1.0, ε = 4.0). The higher ε value mimics the more polar surrounding of the molecule. The purpose was to verify how electrostatic interactions affect the optimal arrangements of the aliphatic chain. A set of low-energy conformers was obtained differing by ca. 1 kcal mol⁻¹ (genetic algorithm procedures yielded ca 30 low-energy conformers for each compound). Then shielding constants calculation was carried out using DFT methods⁷ for each conformation. The calculated NMR shielding constants were converted into chemical shifts, allowing easier comparison with experimental data. The next step was to verify the agreement between experimental solid-state and theoretical NMR data (mainly in aliphatic chain region). Selected results are collected in Tables 3 and 4.

Fig. 7 Torsion angles of (a) DHCAP and (b) NVA selected for GA calculations.

Table 3 Chemical shifts calculated by GIAO DFT for selected DHCAP conformers from GA (R²-tail shows correlation to experimental ¹³C CPMAS data of aliphatic chain carbons, E1, E4 – dielectric constants, 01, 02… – conformer number)

	E1-01	E1-03	E1-04	E1-06	E1-08	E4-01	E4-03	E4-05	E4-07	E4-08
C1′	141.00	141.30	139.14	141.05	140.92	140.99	140.38	141.28	138.10	140.73
C2′	116.36	116.14	113.71	116.24	115.31	116.76	117.99	115.89	114.13	115.86
C3′	154.14	154.43	154.27	154.17	154.69	154.49	154.20	154.25	152.45	154.14
C4′	155.12	153.41	155.19	155.27	155.25	154.99	153.91	154.71	154.56	155.81
C5′	118.71	118.49	119.79	119.66	119.65	119.40	119.15	118.97	121.57	119.18
C6′	126.56	126.38	128.08	126.62	126.56	126.75	126.73	126.38	128.23	126.32
C7′	47.81	47.82	46.29	47.87	47.54	47.79	48.89	47.63	48.47	47.44
C8′	57.37	57.07	56.80	56.92	56.39	57.54	57.07	57.28	57.03	56.95
C1	178.39	178.72	176.74	179.03	178.31	178.35	179.22	178.90	177.29	178.91
C2	42.16	43.16	40.68	36.32	38.94	41.99	41.46	43.02	43.00	39.77
C3	34.10	33.31	30.74	25.75	24.80	34.29	28.80	30.48	32.87	26.14
C4	34.26	34.95	31.90	31.16	29.05	32.42	38.73	35.93	34.17	29.59
C5	37.70	36.82	31.19	27.95	30.45	36.32	35.51	36.08	36.34	29.55
C6	34.50	33.98	30.87	28.98	28.10	33.48	36.24	32.79	32.90	28.04
C7	44.88	43.10	39.72	43.15	41.59	42.48	44.50	45.62	45.02	41.67
C8	36.04	36.59	29.77	31.45	36.65	36.82	36.02	36.45	35.62	36.34
C9	22.14	26.44	20.89	20.79	22.17	22.69	26.42	26.34	22.51	22.02
C10	26.98	22.58	26.71	26.50	26.99	26.31	22.28	22.30	28.45	26.87
R^2-tail	0.907	0.878	0.924	0.841	0.723	0.857	0.822	0.911	0.934	0.758

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Table 4 Chemical shifts calculated by GIAO DFT for selected NVA conformers from GA (R²-tail shows correlation to experimental ¹³C CPMAS data of aliphatic chain carbons, E1, E3 – dielectric constants, 01, 02… – conformer number)

	E1-01	E1-03	E1-04	E1-05	E1-10	E4-04	E4-07	E4-08	E4-09	E4-10
C1′	140.99	141.27	140.79	141.18	140.90	141.21	140.90	142.68	141.18	138.04
C2′	115.88	116.82	116.58	117.02	115.86	117.33	114.92	118.60	117.02	115.11
C3′	154.53	154.78	154.59	154.17	154.15	154.06	154.50	156.75	154.17	152.85
C4′	154.61	155.17	154.29	154.42	155.61	154.68	154.60	153.71	154.42	154.59
C5′	119.04	119.62	119.17	119.08	119.58	119.24	119.50	117.94	119.08	121.82
C6′	126.69	126.79	126.66	126.78	126.61	126.58	127.07	124.18	126.78	129.16
C7′	48.03	48.03	48.24	47.76	47.39	48.21	47.29	47.78	47.75	49.21
C8′	57.71	57.37	57.33	57.07	56.84	57.32	57.23	57.04	57.07	56.93
C1	179.05	178.74	178.54	178.76	179.17	178.80	177.68	178.42	178.76	176.89
C2	37.60	42.58	41.97	42.71	41.93	42.14	40.95	41.87	42.71	43.12
C3	30.26	31.40	34.13	30.73	34.14	34.34	27.35	33.66	30.74	31.13
C4	32.45	30.13	30.93	29.08	34.92	32.35	28.71	32.11	29.08	35.98
C5	34.84	34.33	30.24	34.55	33.50	35.75	30.22	36.14	34.55	35.81
C6	37.63	31.74	28.10	28.27	31.21	36.48	29.08	35.52	28.27	36.03
C7	39.32	34.84	30.49	32.91	34.37	36.82	31.74	36.78	32.91	39.29
C8	29.46	30.07	21.62	27.95	23.59	30.13	26.48	30.16	27.95	29.73
C9	16.84	16.60	13.40	14.57	13.16	16.49	17.25	16.77	14.57	17.69
R^2-tail	0.914	0.787	0.653	0.733	0.813	0.902	0.753	0.866	0.733	0.947

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For each dielectric constant the best conformation was chosen (based on R²-tail values). Energies and dihedral angles of selected conformers are listed in Table 5.

Table 5 Torsional angles and energy values (kcal mol⁻¹) calculated with MMFF94 force field at two different dielectric constants (ε = 1.0, ε = 4.0) obtained by GA for the low-energy conformers of DHCAP and NVA

Torsion angle	DHCAP-E1	DHCAP-E4	NVA-E1	NVA-E4
α (°)	−0.5	1.5	−0.9	1.8
β (°)	−0.4	0.4	−0.4	0.5
γ (°)	−69.6	118.2	−75.2	112.7
θ (°)	125.2	146.7	93	155.9
ι (°)	146.3	97.5	137.7	−133.5
κ (°)	−67.8	66.7	−67.6	−174.8
λ (°)	−177.5	176	−66.8	−177
μ (°)	178	66.5	−176.9	−66.3
ν (°)	64.5	176	179.9	−176.4
ξ (°)	60.7	175.3	−179.7	−180
τ (°)	60.1	63.8	−179.9	−179.8
ΔE	1.28	2.43	0.08	1.1
R^2	0.997	0.997	0.999	0.999
R^2-tail	0.924	0.934	0.914	0.947
MAE (TMS)	4.08	5.34	4.53	4.87
MAE (SF)	2.62	2.00	1.86	1.45

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Shielding constants are usually recalculated to chemical shifts by comparison to theoretical shielding constant of TMS (δ_iso = σ_TMS − σ_iso). However, there is a number of publications describing the converting of shielding constants with scaling factors (SF).^18,19 Empirical scaling enables achieving high-accuracy theoretical chemical shifts. In this approach, the systematic error was decreased by scaling factors determined via linear regression analyses of experimental and computed chemical shift data. It was proposed as a rewarding method.

The selected low-energy conformers (Fig. 8) differ mainly in the geometry of the aliphatic chain. Their isotropic ¹³C shielding constants σ_iso were compared with the experimental δ_{CPMAS NMR} values. The correlation of the calculated isotropic shielding with each set of resonances in the MAS spectrum is satisfactory because R² > 0.99. As a criterion of the quality of conformers, the R² factor and the minimal absolute error (MAE) between theoretical and experimental data can be applied. However, the R² criterion used to determine the quality of fitting is not sensitive enough to make selection, therefore R²-tail (which compares only the aliphatic chain carbons chemical shifts) and MAE were added as rewarding parameters. For both molecules, the two best conformations were chosen for each method of chemical shift conversion: DHCAP-E1, DHCAP-E4 and NVA-E1, NVA-E4 (see Tables 3 and 4).

Fig. 8 The selected low-energy conformers of DHCAP and NVA and their overlapped structures.

The differences between chemical shifts calculated according to the TMS shielding constant and using scaling factors are visible at the first sight. The MAE is lower for these obtained by SF almost by half. The traditional approach in NMR calculations is calculating shielding constants for a reference molecule.²⁰ However, the utilizing of a single molecule reference compound may lead to a systematic error. In the case of SF, isotropic shielding constants are plotted against known experimental chemical shifts for a numerous set of small organic molecules.²¹ and a strong linear correlation was observed.

The traditional approach, e.g. calculations of the isotropic shielding constant of TMS, allowed the selection of the best conformations: DHCAP-E1 and NVA-E1. DHCAP-E1 fulfils both criteria: the highest R²-tail value (0.924) and the lowest MAE (4.08). For NVA the highest R²-tail (0.933) and the lowest MAE (4.53) were also obtained for E1. However, when scaling factors were used, the best results were obtained for calculations with ε = 4.0. The R²-tail was 0.934 and 0.910 and MAE 2.00 and 1.45 for DHCAP-E4 and NVA-E4, respectively. These four low-energy conformers, which show the best agreement between theoretical and experimental chemical shifts, are illustrated in Fig. 8. The aromatic part of DHCAP and NVA has the same structure in all conformers, with OCH₃ group pointing to C2′ and OH directed to oxygen at C3′. The most interesting structural part of both studied molecules is the flexible aliphatic chain.

Both GA-conformers of DHCAP have a bent chain, as it was found earlier for capsaicin.⁵ However, in one of them it is bent towards the methoxyl group (E1), which may cause steric hindrance, whereas in the second – in the opposite direction (E4). The hindrance should influence the CP kinetic parameters. The CP parameters of DHCAP for both CH₃ and OCH₃ group are longer than CP parameters of CAP. It may suggest increased mobility of these groups, which is possible in the absence of the steric hindrance (E4). Summarized GA and CPMAS NMR data recommend that the most probable conformation of DHCAP is DHCAP E4. It is bent as capsaicin conformation, but in the opposite direction.

Both GA conformers of NVA, which have the best fitting parameters to experimental NMR data, have different geometries of aliphatic chain. The NVA-E1 has a bent and the NVA-E4 extended aliphatic chain. Split resonances (doublets) in ¹³C and ¹⁵N MAS NMR spectra suggest that solid NVA sample contains two different molecules in the crystallographic unit. Taking into account the conformers obtained by GA, we suppose that the molecules coexisting in the solid may differ by the orientation of aliphatic chain. However, to confirm such assumption crystallographic data are required.

Conclusions

The solid-state structure of DHCAP and NVA were investigated. Since there is no crystallographic data and single crystals suitable for XRD were not obtained, ¹³C and ¹⁵N MAS NMR supported by genetic algorithm and GIAO DFT calculations were used for solid state structural studies. To the best of our knowledge this work is the first that focuses on solid state of DHCAP and NVA. DHCAP shows numerous similarities in NMR and GA data to these obtained for CAP.⁵ Conformation with a bent aliphatic chain is probable in solid DHCAP, however the chain is not close to the methoxyl group. The molecular network of capsaicinoids is not stabilized by NH⋯O=C intermolecular hydrogen bonds, more probable is OH⋯O=C interaction in DHCAP and CAP but not in NVA. Solid state of NVA is characterized by the presence of two conformers, with bent and extended aliphatic chain.

Conflicts of interest

There are no conflicts to declare.

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