Trimethylpyrazole: a simple heterocycle reflecting Kitaigorodskii’s packing principle

The title compound represents a textbook example for the arrangement of small molecules and space-group symmetry: in space group Pnma the mirror planes should be occupied to ensure efficient space filling.


Introduction
Aleksander Kitaigorodskii was already working on his principle of close packing in the 1940s, at a time when structure analysis via single-crystal diffraction was still not fast and routine. We recall that about 20 years later, in 1965, the archives of the Cambridge Crystallographic Data Centre comprised only 3000 structures. Kitaigorodskii's finding that void space in crystals is in general unfavorable enabled him to rank certain space groups as more or less suitable for close packing. It took considerable time before Kitaigorodskii's ideas were appreciated in the western world (Kitaigorodskii, 1961(Kitaigorodskii, , 1965(Kitaigorodskii, , 1973. The term symmorphic refers to space groups that exhibit a special position with the same symmetry as the crystal class (Chapuis et al., 2022). A. J. C. Wilson expanded these original ideas (Wilson, 1993a) and coined the term antimorphic space groups (Wilson, 1993b), which only possess symmetry elements associated with a favorable packing, i.e. screw axes, glide planes and inversion centers. In contrast to Kitaigorodskii, W. Nowacki explained the statistical preference for certain space groups by their ability to form a favorable dipole arrangement rather than an efficient packing (Nowacki, 1943(Nowacki, , 1951). An excellent summary of the closepacking principle and its consequences for space-group frequencies, together with other packing criteria, was published by Brock & Dunitz (1994).
In this contribution, we present the crystal structure of the simple heterocycle 1,3,5-trimethyl-1H-pyrazole (1) in space group Pnma and describe its crystal packing in the context of Kitaigorodskii's and Wilson's ideas.

Results and Discussion
All non-hydrogen atoms in 1 occupy a crystallographic mirror plane in space group Pnma (Wyckoff position 4c), resulting in a strictly planar scaffold. A displacement ellipsoid plot of a heterocyclic molecule is shown in Fig. 1.
Pnma, the space-group type adopted by the title compound, plays a central role in the concepts of Kitaigorodskii and Wilson. We cite literally from Wilson (1991): 'The space-group type Pnma is particularly interesting, as Kitaigorodskii (1965) predicted that it would be popular because it would permit close-packing of molecules with inherent mirror symmetry [ . . . ] The structures published in Acta Crystallographica C were checked, and all were found to consist of molecules possessing and using inherent mirror planes.' The 1965 article cited in Wilson's statement above refers to the Russian version of Organic Chemical Crystallography (Kitaigorodskii, 1961). The heterocyclic molecule in 1 is a candidate par excellence for Pnma: It not only matches the required site symmetry but all of its non-hydrogen atoms are located on this mirror plane, providing an efficient in-plane arrangement (Fig. 2, left).
Atom labels as in Fig. 1. For PYRZOL27, a Z 0 of 2 is observed and only values for the first residue are listed here.
Compound  (13) provide the most relevant interlayer contacts. Fig. 3 shows the head-to-tail arrangement of two molecules, with a methyl H atom pointing towards the center of gravity of the fivemembered ring of a neighbor. The shortest interatomic distance associated with this contact amounts to H4bÁ Á ÁN2 a [symmetry code: (a) 1 À x, À 1 2 + y, 1 À z] = 2.65 Å . The Hirshfeld surface (Spackman & Jayatilaka, 2009) about one pyrazole moiety is shown in Fig. 4. It has been mapped with the dimensionless interaction-sensitive quantity d norm ; red areas indicate short contacts. Both the C-HÁ Á ÁN hydrogen bond and the interlayer methylÁ Á Á contact can clearly be perceived.
The stacking of efficiently packed layers of which only the methyl H atoms protrude leads to a simple relationship between the lattice parameter in the stacking direction, i.e. unit-cell parameter b in the standard setting of space group Pnma, and the van der Waals radii of the partaking atoms. Fig. 5 provides a sketch of the situation.
Kitaigorodskii himself had determined van der Waals radii (r vdW ) of 1.8 Å for carbon and of 1.58 Å for nitrogen (Kitaigorodskii, 1973); values of 1.7 for C and 1.55 for N have been suggested by Batsanov (1995). The unit-cell parameter b for our title compound 1 amounts to approximately 6.7 Å , closely matching the expected fourfold van der Waals radius of the non-hydrogen atoms involved. Table 3 shows additional examples for small and planar organic molecules crystallizing in the same space group type and with a similar cell parameter b.
These examples share the same construction principle: The individual flat molecules are arranged in the crystallographic mirror plane, and for symmetry reasons dipole directions alternate between consecutive layers along b.  Table 3 were restricted to entries with space group Pnma crystallizing in unit cells similar to 1, with a tolerance of 0.7 Å for each unit-cell parameter. These conditions were met by seventeen entries; eight of these show a packing analogous to that of 1.

Synthesis and crystallization
The target compound 1,3,5-trimethyl-1H-pyrazole (1)    View of the unit cell of 1 along c (Spek, 2020), methyl groups omitted. The radii of the atoms essentially denote their van der Waals radii (r vdW ). Table 3 Other structures showing the same motif as 1; r vdW (C) = 1.7 Å ; r vdW (N) = 1.55 Å (Batsanov, 1995). † For MURANT the non-standard setting Pbnm was chosen, so the shown unitcell parameter perpendicular to the mirror plane is c.

Compound
Formula b (Å ) b/4 (Å )  (2008)  acetylacetone and methylhydrazine (Knorr, 1883;Stanovnik & Svete, 2002). Alternatively, the compound may be purchased from common vendors. The single crystal for the reported structure was obtained from the reaction mixture. It is soluble in a wide range of common solvents; single crystals may also be grown via recrystallization from a solution in diethyl ether at 243 K. The small crystal size as well as the fast growth and the absence of any heavy atom restricted diffraction data to a limited resolution. The result is a comparatively high agreement factor of symmetry-related reflections (R int = 13.77%) and agreement factor considering the intensity of reflections (R = 7.07%).

Refinement details
Crystal data, data collection parameters and convergence results for the single crystal X-ray diffraction experiment have been summarized in Table 4. Non-hydrogen atoms were assigned anisotropic displacement parameters. H atoms were introduced into calculated positions and treated as riding with C-H = 0.98 Å and U iso (H) = 1.5U eq (C) for methyl and with C-H = 0.95 Å and U iso (H) = 1.2U eq (C) for the heteroaryl H atom. Tentative refinement of a model in which the methyl conformations were chosen to best match local difference-Fourier maxima leads to split positions, but for each CH 3 group one H atom is located very close to the crystallographic mirror plane. We therefore decided to constrain the y coordinate of these almost in-plane hydrogens to fit the special position.

Conclusion and outlook
What else can we learn from the packing of the simple heterocycle 1 in space group Pnma. Space filling is unexceptional; according to the well-known Kempster-Lipson rule (Kempster & Lipson, 1972) a molecule with eight nonhydrogen atoms should be associated with a residue volume of approximately 150 Å 3 . The unit cell of 1 will therefore contain four pyrazole molecules, necessarily in special positions. Wyckoff positions 4a and 4b require 1 symmetry and can be excluded whereas 4c appears compatible with the molecular symmetry. Harker vectors are subtended by atoms related by crystallographic symmetry. All Harker peaks and all Patterson cross peaks (Glusker et al., 1994;Viterbo, 2002) derived for occupied 4c positions should be characterized by a Patterson coordinate of 0.0 or 0.5 in the [010] direction. The Patterson function for 1 perfectly matches this expectation: The highest Patterson peak with a v coordinate unequal to 0.0 or 0.5 has an intensity of less than 5% of the trivial origin peak. Our trimethylpyrazole represents a well-suited example for teaching basic concepts of crystallography such as space groups, Wyckoff positions, packing rules, and popular short contacts! Data collection: SMART (Bruker, 2001); cell refinement: SAINT-Plus (Bruker, 2009); data reduction: SAINT-Plus (Bruker, 2009); program(s) used to solve structure: SHELXT2014/5 (Sheldrick, 2015a); program(s) used to refine structure: SHELXL2019/2 (Sheldrick, 2015b); molecular graphics: PLATON (Spek, 2020) and Mercury (Macrae et al., 2020). Special details Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.