An Example of Polynomial Expansion: The Reaction of 3(5)-Methyl-1H-Pyrazole with Chloroform and Characterization of the Four Isomers

The reaction in phase-transfer catalyzed conditions of 3(5)-methyl-1H-pyrazole with chloroform affords four isomers 333, 335, 355 and 555 in proportions corresponding to the polynomial expansion (a + b)3, with a = 0.6 and b = 0.4, a and b being 3-methyl and 5-methyl proportions. The up (u) and down (d) conformation of the pyrazolyl rings with regard to the Csp3–H atom was established by X-ray crystallography and by 1H-, 13C- and 15N-NMR in solution combined with gauge-including atomic orbitals (GIAO)/B3LYP/6-311++G(d,p) calculations. A comparison with other X-ray structures of tris-pyrazolylmethanes was carried out.

The reaction was reported again in 1999 and, surprisingly, the only isolated isomer (17% yield) was the 335 isomer ( 1 H, CDCl 3 , Csp 3 -H: 8.21 ppm) [7]. In 2012 the more hindered 555 derivative was prepared from tri(pyrazol-1-yl)methane (tpzm) by alkylation of the lithium derivative ( 1 H, CDCl 3 , Csp 3 -H: 8.31 ppm) [8]. Finally, the reaction was repeated again in 2012 and, although the yields of different isomers were not discussed, using the information concerning the 1 H-NMR of the Csp 3 -H proton from this and others papers the relative yields of the four isomers can be determined ( Figure 2) [8,9]. The authors also demonstrated that the mixture of the four isomers could be isomerized under the action of p-toluenesulfonic acid to a mixture of 333 and 335 in a 2:1 ratio (crude yield 82%), proving that they are the most stable isomers. The utility of the 333 ligand prompted Anwander et al. to prepare it from the mixture and isolate it by recrystallization [10]. The authors point out that the 333 isomer, δ = 8.13 ppm, represents approximately 22% of the crude. From the data of Figure 2 reported and from the integration (total 2.324) it is easy to determine the proportions: 333, δ = 8.13 ppm, 22%; 335, δ = 8.21 ppm, 43%; 355, δ = 8.26 ppm, 28.5%; and 555, δ = 8.32 ppm, 6.5%.

Results and Discussion
We decided to repeat the reaction shown in Figure 1 to determine if it was possible to isolate other isomers and establish their structures, and to discuss their conformations.

Chemistry
The synthesis of N,N',N"-3(5)-trimethylpyrazolylmethanes was performed following the protocol described by Juliá et al. for the synthesis of N,N',N"-triazolylmethanes (see Section 3.2) [3]. The percentages were determined by 1 H-NMR using the signals of the Csp 3 -H atom in CDCl 3 at 400 MHz (Table 1): 21.8% 333, 47.8% 335, 25.2% 355 and 5.2% 555. These percentages correspond to (a + b) 3 for a = 0.60 and b = 0.40 (21.6%; 43.2%; 28.8%; 6.4%) with a little worse agreement than the literature results [8]. Tables S1 to S4. In CDCl 3 equilibration between isomers occurs that can be due to the presence of DCl, although we keep the solvent over Ag wire. For this reason, only the "fast" 1 H-NMR experiments are reported in this solvent (see later). To avoid the problems encountered with deuterochloroform we move to another solvent. We select hexadeuterobenzene because in this solvent (in earlier work C 6 H 6 was used) the methyl groups of pyrazoles have rather different 1 H-NMR chemical shifts [22,24].    The methyl groups appear in C 6 D 6 at~2.10 (3-methyl) and~1.85 ppm (5-methyl), very close to the values reported in the literature, 2.25 and 1.80 ppm, respectively [22][23][24]. These values together with the relative intensities allow an immediate identification of the four isomers by 1 H-NMR.
Another useful criterion is that 3 J HH has a value of 1.8 Hz between H3 and H4 protons and 2.6 Hz between H3 and H4 protons. When a methyl group was involved, then 4 J H4Me5 > 4 J H4Me3 [22][23][24].
The GIAO calculated chemical shifts reported in the ESI agree well with the experimental values. To determine the major conformers, the problem is that the variation of chemical shift inter-conformers are small compared with the variation within each isomer that results in correlation coefficients R = 1.000 or 0.999 in most cases (correlation coefficient matrix). However, considering not only R 2 , but also an intercept as small as possible and a slope as close to 1.00 as possible, the results of Table 3 were obtained. They are not all consistent but clear preferences are observed. We have tried a mixture of the conformations of lower energy; for the 335 isomer we have preferred the udd (12.6 kJ·mol -1 ) to the uuu (12.1 kJ·mol -1 ).
In the case of the 555 isomers, the regression leads to a negative coefficient for the uud isomer that does not have a physical meaning, which indicates that the only isomer present is the udd isomer.
The mixtures (sum ≈ 1.00) correspond to about 3/4 of the lower energy isomers and 1/4 of the higher energy ones for 335 and 355; in the case of the 333 isomer there is 95% of the uud isomer.
We found that a solution of an almost pure sample of the 335 isomer in CDCl 3 slowly isomerizes into the more stable 333 isomer ( Figure 4). This could be due to the presence of DCl in the solvent produced by photodecomposition of CDCl 3 , and is related to the already reported isomerization in acid media [9]. The mechanism should proceed by protonation of one of the pyrazoles (formation of a pyrazolium salt), leaving this ring as neutral 3(5)-methyl-1H-pyrazole, and the resulting carbocation reacting with 3(5)-methyl-1H-pyrazole.

Crystallography
The crystal structure of 335 presents one independent molecule in its asymmetric unit with two of their pyrazole N2 atoms pointing to the CH direction and the third one pointing into the opposite direction; therefore, these molecules present an uud conformation displaying HCN1N2 dihedral angles of 39.0(6) • , 17.6(7) • and −168.1(3) • . As the crystal space group contains inversion centers, both enantiomers coexist in a 1:1 ratio.
A summary of the crystal data and structure refinement is included in the ESI as Table S1. Table 4 contains geometrical parameters of 3(5)-methylpyrazolylmethane isomers, the one recorded in the Cambridge Structural Database (CSD) [21] and the new one reported in this manuscript. A view of their molecule structure with their atom labeling is depicted in Figure 3.  There are no significant differences in the observed geometry parameters for the pyrazole rings for the 3-methyl rings in both 333 and 335 isomers; however, the 5-methyl ring in 335 presents unusual geometries, especially for the intra-ring bond angles, N2-C3-C4, C3-C4-C5 and C4-C5-N1, and also for the N1-C5-C6 and C4-C5-C6 angles. There is not any apparent reason to justify this, but X-ray data collected for other crystals showed a possible occupancy disorder of the two isomers, 335 and 333. Therefore, pz_C can, overall, be of 5-methylpyrazolyl with high occupancy and 3-methylpyrazolyl at low occupancy. It also justifies the difference peaks observed around the pz_C ring ( Figure 5). A disorder model has been able to be refined with a crystal collected at low temperature but, due to the problems in reaching refinement convergence with the data, and the many geometrical restraints and constraints that were necessary, we do not think that it adds any knowledge to the results presented in this manuscript. Both compounds present a twist of the pz-planes describing a propeller structure independently of the N2 position (up or down).
Compound 335 forms dimers through weak CH···N hydrogen bonds (C1-H···N2(B), C6(B)-H···N2(A)) that expand into chains along (1-10) axis by C5(B)-H···N2(C) contacts. Saturating the three N-acceptors in the molecules, these chains join to form (001) layers by C-H···π-pz non-bonded interactions (C3(C)-H···π-pz(A), C4(C)-H···π-pz(B)). Methyl groups of pyrazoles A and B point out of these layers forming lines along the b-direction with an a-axis separation between methyl lines where a methyl line, from a consecutive layer, fits as a zipper to pack the layers and to build the crystal. C6(A)-H···π-pz(C) and van der Waal interactions glue the layers ( Figure 6).  All trispyrazolylmethane molecules display a propeller structure with a wide range of twisting in their pyrazole planes, from 3 • to 68 • . The most frequent conformations are udd (observed in 10 structures) and uud (observed in seven structures).

Theoretical Calculations
The geometries of the two most relevant isomers are depicted in Figure 8 while the energies are reported in Table 5.   The isomers' stability decreases in the order 333 (0.0) > 335 (1.7) > 355 (17.9) > 555 (23.8 kJ·mol −1 ), in agreement with the experimental results; this is the thermodynamic order that is unrelated to the kinetic order of the percentages measured on the crude. The acid-catalyzed isomerization from the crude leads to a mixture of 333 and 335 which have very close energies (Figure 7) [8]. Concerning the up/down isomerism, the most stable are the uud ones (333, 335), the ddu one (355) and the udd one (555). The 355 uud is 9.9 kJ·mol −1 above the 355 ddu and the 555 uud is 5.9 kJ·mol −1 above the 555 udd one.
Concerning the calculated geometries, the most interesting parameters are the torsion angles (Table 6). The chemical shifts we have used for the interpolations (Equations (1-3)) have been obtained transforming the absolute shielding calculated with the B3LYP/6-311++G(d,p)/GIAO methods for the gas phase and then transformed through empirical equations to chemical shifts (see Section 3.5). These δ values do not correspond to the gas phase but to solution, because the empirical equations were established using gas phase σ and solution δ.
When comparing the experimental chemical shifts in solution to the GIAO calculated ones, remember that the four 3/5 isomers correspond to different molecules that are stable in the NMR time scale. On the other hand, the up/down rotational isomers are separated by low rotational barriers and in solution only averaged signals will be observed.

Experimental
High-resolution mass spectra were recorded on a Quadrupole Time-of-Flight (QTOF) mass spectrometer under Electrospray Ionization (ESI) conditions.
Only the 335 isomer was isolated pure in enough quantity; the 355 was isolated in a very small amount only enough to measure its melting point and record its exact mass; the two other isomers, 333 and 555 only as mixtures of two isomers enriched in one of them.

NMR Spectroscopy
Solution NMR spectra were recorded on a 9.4 Tesla Bruker spectrometer (Bruker Española S.A., Madrid, Spain), 400.13 MHz for 1 H, 100.62 MHz for 13 C and 40.54 MHz for 15 N) at 300 K with a 5-mm inverse detection H-X probe equipped with a z-gradient coil. Chemical shifts (δ in ppm) are given from internal solvents: CDCl 3 7.26 for 1 H; C 6 D 6 7.16 for 1 H and 128.39 for 13 C. Nitromethane was used as external reference for 15 N. Coupling constants (J in Hz) are accurate to ±0.2 Hz for 1 H and ±0.6 Hz for 13 C. CDCl 3 contains 0.5 wt% silver wire as stabilizer.
Typical parameters for 1 H-NMR spectra were spectral width 4000 Hz and pulse width 9.5 µs at an attenuation level of 0 dB. Typical parameters for 13 C-NMR spectra were spectral width 21 kHz, pulse width 10.6 µs at an attenuation level of −6 dB and relaxation delay 2 s. WALTZ 16 was used for broadband proton decoupling; the FIDs were multiplied by an exponential weighting (lb = 2 Hz) before Fourier transformation. In some cases, for resolution enhancement processing a Gaussian multiplication of the FID prior to Fourier transformation was applied.
Selected parameters for ( 1 H-13 C) gs-HMQC and gs-HMBC spectra were: spectral width 4000 Hz for 1 H and 20 kHz for 13 C, 1024 × 256 data set, number of scans 2 (HMQC) or 4 (HMBC) and relaxation delay 1s. In the gs-HMQC experiments GARP modulation of 13 C was used for decoupling. The FIDs were processed using zero filling in the F1 domain and a sine-bell window function in both dimensions was applied prior to Fourier transformation.
Selected parameters for gs-HMBC spectra were: spectral width 4000 Hz for 1 H and 15 kHz for 15 N, 2048 × 1024 data set, number of scans 4, relaxation delay 1s. In the gs-HMBC delays of 60 and 100 ms for the evolution of the 15 N-1 H long-range coupling were used. The FIDs were processed using zero filling in the F1 domain and a sine-bell window function in both dimensions was applied prior to Fourier transformation.
From initial data collected at room temperature, a possible occupancy disorder of the two isomers, 335 and 333 was identified. Data collected at 150 K of a different crystal allowed us to build a disorder model that showed a mixture of these two isomers. Due to the many problems to refine this disordered model and to reach convergence, we kept the best data for the work presented in this manuscript. It corresponds to data collected at room temperature and it shows the lowest proportion of the 333 isomer (so it could be omitted).
Using Olex2 (v1.2, Durham University, Durham, UK) [26], the structure was solved with the ShelXS (v4-2016, Universität Göttingen, Göttingen, Germany) [27] structure solution program using Direct Methods and refined with the ShelXL (v4-2016, Universität Göttingen, Göttingen, Germany) [28] refinement package using Least Squares minimization. A summary of the crystal data and structure refinement is included in Table S5. For the visualization and analysis of crystal structures the Mercury program was used [29].

Conclusions
The accuracy of the polynomial expansion (a + b) 3 is extraordinary because it was unexpected. It implies that the ratios of the reactivity of the chlorine atoms with 3(5)-methyl-1H-pyrazole are the same for CHCl 3 , CH(Mepz)Cl 2 and CH(Mepz) 2 Cl. This work reported the first systematic study of the structure of the four tris[3(5)-methyl]pyrazol-1-ylmethanes, a series of ligands used in coordination chemistry.
The solid-solution [40] structure of the 335 isomer, actually a mixture of 335 (major) and 333 (minor) isomers, results from the isomerization of the 335 isomer into the 333 isomer during the crystallization process. In the crystallization batch there are different crystals but a clear predominance of the 335 isomer is always found by crystallography.