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.

Abstract

The five-membered heterocycle 1,3,5-trimethyl-1H-pyrazole, C₆H₁₀N₂ (1) crystallizes in space group Pnma with all non-hydrogen atoms of the mol­ecule on the crystallographic mirror plane. This arrangement has been recognized as favorable with respect to space filling by Kitaigorodskii and Wilson, pioneers in the field of crystal packing; Pnma represents a particularly rare space group for residues exclusively in a general position. Neighboring mol­ecules in 1 inter­act via non-classical C—H⋯N bonds in the plane and C—H⋯π contacts between adjacent layers. In Pnma, crystallographic inversion relates dipolar mol­ecules located on successive mirror planes and results in their head-to-tail arrangement. The inter­layer distance in the [010] direction is closely related to the van der Waals radii of C and N.

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 ▸, 1965 ▸, 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 ▸, 1951 ▸). An excellent summary of the close-packing 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 ▸.

Figure 1.

Displacement ellipsoid plot (Spek, 2020 ▸) of a mol­ecule in 1; ellipsoids are drawn at 70% probability, H atoms are shown as spheres of arbitrary radii. Selected distances (Å) and angles (°): N1—N2 1.358 (4), N2—C1 1.351 (4), C1—C2 1.360 (5), C2—C3 1.392 (4), N2—C4 1.448 (4), C3—N1—N2 104.2 (3), C1—C2—C3 106.6 (3).

Compared to other simple pyrazoles, this is a unique property as most of them do not crystallize in space groups exhibiting a mirror plane, e.g. 1H-pyrazole (space groups Pna2₁ and Pbcn; Sikora & Katrusiak, 2013 ▸), 3,5-dimethyl-1H-pyrazole (space group R c; Baldy et al., 1985 ▸) or 1,5-dimethyl-1H-pyrazole-3-carb­oxy­lic acid ethyl ester (P ; Schmidt et al., 2003 ▸). Intra­molecular distances and angles in these pyrazoles and 1 are very similar and adopt values within a narrow range (Table 1 ▸).

Table 1. Comparison of selected distances (Å) in 1 with two comparable structures denoted by their CSD refcodes (Groom et al., 2016 ▸).

Atom labels as in Fig. 1 ▸. For PYRZOL27, a Z′ of 2 is observed and only values for the first residue are listed here.

Compound	d(N1—N2)	d(N2—C1)	d(N1—C3)	d(C2—C3)	d(C1—C2)
1	1.358 (4)	1.351 (4)	1.336 (4)	1.392 (4)	1.360 (5)
PYRZOL27 a	1.357 (2)	1.338 (3)	1.334 (3)	1.391 (3)	1.373 (3)
ALOSEZ b	1.3464 (17)	1.3595 (14)	1.3415 (16)	1.3966 (15)	1.377 (2)

References: (a) Sikora & Katrusiak (2013 ▸); (b) Schmidt et al. (2003 ▸).

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).

Figure 2.

Packing in the (010) plane (Spek, 2020 ▸). Non-classical C—H⋯N contacts are shown as dashed lines: d(N⋯H ^a ) = 2.56 Å; ∠(C ^a —H ^a ⋯N) = 179°. Symmetry code: (a) −  + x,  − y,  − z.

Non-classical C—H⋯N hydrogen bonds represent the shortest directional contacts in the mirror plane and lead to chains along [100] (Fig. 2 ▸, right). This kind of inter­action is quite common for 4-unsubstituted pyrazoles and we only provide selected examples for comparison: ICEDUQ (Patra et al., 2004 ▸), LUNYID (Benisvy et al., 2009 ▸) and KITNOR (Kidwai et al., 2008 ▸) (Table 2 ▸).

Table 2. Comparison of N⋯H—C contacts (Å, °) observed in 1 and selected other pyrazoles.

Compound	d(N⋯H)	∠(N⋯H—C)
1	2.56	179
ICEDUQ a	2.852 (19)	177.3 (12)
LUNYID b	2.66	154
KITNOR c	2.458 (16)	156.2 (13)

References: (a) Patra et al. (2004 ▸); (b) Benisvy et al. (2009 ▸); (c) Kidwai et al. (2008 ▸).

A crystallographic center of inversion (Wyckoff position 4a) relates objects on the mirror planes at y = 0.25 and y = 0.75; the dipole moments of consecutive layers are therefore oriented in opposite directions, quite in agreement with early Nowacki (1943 ▸) ideas. The non-planar methyl groups in 1 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 five-membered ring of a neighbor. The shortest inter­atomic distance associated with this contact amounts to H4b⋯N2 ^a [symmetry code: (a) 1 − x, −  + y, 1 − z] = 2.65 Å.

Figure 3.

Short methyl C—H⋯π contacts about a center of inversion in 1 shown as dashed lines (Spek, 2020 ▸): d(Cg⋯H ^b ) = 2.586 Å; ∠(C ^b —H ^b ⋯Cg) = 140.97°. Symmetry code: (b) 1 − x, −y, 1 − z.

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—H⋯N hydrogen bond and the inter­layer meth­yl⋯π contact can clearly be perceived.

Figure 4.

Hirshfeld surface (Turner et al., 2017 ▸) about one 1,3,5-trimethyl-1H-pyrazole moiety in 1.

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.

Figure 5.

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).

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.

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 unit-cell parameter perpendicular to the mirror plane is c.

Compound	Formula	b (Å)	b/4 (Å)
1	C6H10N2	6.687 (11)	1.672
CIJZEB a	C4H4ClN3O2	6.1372 (5)	1.5343
CIJZEB01 b	C4H4ClN3O2	6.3050 (10)	1.5763
EQENUL c	C4H6BF3N2	6.635 (3)	1.659
FIFRAN d	C5H4N2O2	6.388 (2)	1.597
MURANT e†	C2H7N3O4	6.36 (2)	1.59
QOXVII f	C7H8N2O2	6.5670 (7)	1.6418
VORDIR g	C4H6N2OS	6.4865 (4)	1.6216
WIQLOX h	C7H8N2O	6.722 (4)	1.681

References: (a) Kubicki & Wagner (2007a ▸); (b) Kubicki & Wagner (2007b ▸); (c) Takao & Ikeda (2008 ▸); (d) Rybalova et al. (1998 ▸); (e) Bryden (1957 ▸); (f) Nawrot et al. (2001 ▸); (g) Konstanti­nova et al. (2014 ▸); (h) Aldabbagh et al. (1999 ▸).

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.

Database survey

For all database searches, version 5.42 of the CSD (Groom et al., 2016 ▸), including all updates until September 2021 were used. The examples compiled in 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) is readily available by the Knorr pyrazole synthesis using 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_σ = 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 CH₃ 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.

Table 4. Experimental details.

Crystal data
Chemical formula	C6H10N2
M r	110.16
Crystal system, space group	Orthorhombic, P n m a
Temperature (K)	100
a, b, c (Å)	11.205 (19), 6.687 (11), 8.373 (15)
V (Å3)	627.3 (19)
Z	4
Radiation type	Mo Kα
μ (mm−1)	0.07
Crystal size (mm)	0.21 × 0.10 × 0.09
Data collection
Diffractometer	Bruker APEX CCD
Absorption correction	Multi-scan (SADABS; Krause et al., 2015 ▸)
T min, T max	0.657, 0.745
No. of measured, independent and observed [I > 2σ(I)] reflections	6665, 648, 366
R int	0.138
Refinement
R[F 2 > 2σ(F 2)], wR(F 2), S	0.047, 0.119, 0.87
No. of reflections	648
No. of parameters	50
H-atom treatment	H-atom parameters constrained
Δρmax, Δρmin (e Å−3)	0.26, −0.23

Computer programs: SMART (Bruker, 2001 ▸), SAINT-Plus (Bruker, 2009 ▸), SHELXT2014/5 (Sheldrick, 2015a ▸), SHELXL2019/2 (Sheldrick, 2015b ▸), PLATON (Spek, 2020 ▸) and Mercury (Macrae at al., 2020 ▸).

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 non-hydrogen atoms should be associated with a residue volume of approximately 150 ų. The unit cell of 1 will therefore contain four pyrazole mol­ecules, necessarily in special positions. Wyckoff positions 4a and 4b require 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!

Supplementary Material

CCDC reference: 2203895

Additional supporting information: crystallographic information; 3D view; checkCIF report

supplementary crystallographic information

Crystal data

C6H10N2	Dx = 1.166 Mg m−3
Mr = 110.16	Mo Kα radiation, λ = 0.71073 Å
Orthorhombic, Pnma	Cell parameters from 263 reflections
a = 11.205 (19) Å	θ = 3.0–19.7°
b = 6.687 (11) Å	µ = 0.07 mm−1
c = 8.373 (15) Å	T = 100 K
V = 627.3 (19) Å3	Block, colorless
Z = 4	0.21 × 0.10 × 0.09 mm
F(000) = 240

Data collection

Bruker APEX CCD diffractometer	648 independent reflections
Radiation source: microsource	366 reflections with I > 2σ(I)
Multilayer optics monochromator	Rint = 0.138
ω scans	θmax = 25.9°, θmin = 3.0°
Absorption correction: multi-scan (SADABS; Krause et al., 2015)	h = −13→13
Tmin = 0.657, Tmax = 0.745	k = −8→8
6665 measured reflections	l = −10→10

Refinement

Refinement on F2	Hydrogen site location: mixed
Least-squares matrix: full	H-atom parameters constrained
R[F2 > 2σ(F2)] = 0.047	w = 1/[σ2(Fo2) + (0.0645P)2] where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.119	(Δ/σ)max < 0.001
S = 0.87	Δρmax = 0.26 e Å−3
648 reflections	Δρmin = −0.23 e Å−3
50 parameters	Extinction correction: SHELXL-2019/2 (Sheldrick 2015b), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
0 restraints	Extinction coefficient: 0.011 (4)
Primary atom site location: dual

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.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
N1	0.4912 (2)	0.250000	0.6988 (3)	0.0289 (7)
N2	0.5279 (2)	0.250000	0.5442 (3)	0.0249 (6)
C1	0.6481 (3)	0.250000	0.5301 (4)	0.0236 (7)
C2	0.6912 (3)	0.250000	0.6820 (3)	0.0260 (8)
H2	0.772711	0.250000	0.713077	0.031*
C3	0.5924 (3)	0.250000	0.7829 (4)	0.0265 (7)
C4	0.4409 (3)	0.250000	0.4164 (3)	0.0327 (9)
H4A	0.360267	0.250000	0.461847	0.049*
H4B	0.451701	0.130335	0.350369	0.049*
C5	0.7079 (3)	0.250000	0.3728 (4)	0.0342 (8)
H5A	0.794608	0.250000	0.388049	0.051*
H5B	0.684366	0.369665	0.312985	0.051*
C6	0.5878 (3)	0.250000	0.9617 (4)	0.0380 (9)
H6A	0.504403	0.250000	0.996905	0.057*
H6B	0.628021	0.369665	1.002625	0.057*

Atomic displacement parameters (Ų)

	U11	U22	U33	U12	U13	U23
N1	0.0378 (16)	0.0195 (13)	0.0295 (16)	0.000	0.0012 (14)	0.000
N2	0.0297 (15)	0.0182 (13)	0.0268 (15)	0.000	−0.0012 (12)	0.000
C1	0.0238 (16)	0.0149 (15)	0.032 (2)	0.000	0.0009 (14)	0.000
C2	0.0263 (17)	0.0177 (15)	0.034 (2)	0.000	−0.0025 (16)	0.000
C3	0.0356 (17)	0.0166 (14)	0.0274 (18)	0.000	−0.0035 (17)	0.000
C4	0.038 (2)	0.0228 (15)	0.037 (2)	0.000	−0.0104 (16)	0.000
C5	0.040 (2)	0.0275 (16)	0.035 (2)	0.000	0.0047 (16)	0.000
C6	0.048 (2)	0.0349 (17)	0.031 (2)	0.000	0.0033 (17)	0.000

Geometric parameters (Å, º)

N1—C3	1.336 (4)	C4—H4A	0.9800
N1—N2	1.358 (4)	C4—H4B	0.9800
N2—C1	1.351 (4)	C4—H4Bi	0.9800
N2—C4	1.448 (4)	C5—H5A	0.9800
C1—C2	1.360 (5)	C5—H5B	0.9800
C1—C5	1.478 (4)	C5—H5Bi	0.9800
C2—C3	1.392 (4)	C6—H6A	0.9800
C2—H2	0.9500	C6—H6B	0.9800
C3—C6	1.498 (5)	C6—H6Bi	0.9800
C3—N1—N2	104.2 (3)	N2—C4—H4Bi	109.47 (10)
C1—N2—N1	112.7 (2)	H4A—C4—H4Bi	109.5
C1—N2—C4	127.3 (3)	H4B—C4—H4Bi	109.5
N1—N2—C4	120.0 (3)	C1—C5—H5A	109.5
N2—C1—C2	105.8 (3)	C1—C5—H5B	109.5
N2—C1—C5	122.0 (3)	H5A—C5—H5B	109.5
C2—C1—C5	132.2 (3)	C1—C5—H5Bi	109.47 (11)
C1—C2—C3	106.6 (3)	H5A—C5—H5Bi	109.5
C1—C2—H2	126.7	H5B—C5—H5Bi	109.5
C3—C2—H2	126.7	C3—C6—H6A	109.5
N1—C3—C2	110.8 (3)	C3—C6—H6B	109.5
N1—C3—C6	119.9 (3)	H6A—C6—H6B	109.5
C2—C3—C6	129.4 (3)	C3—C6—H6Bi	109.47 (10)
N2—C4—H4A	109.5	H6A—C6—H6Bi	109.5
N2—C4—H4B	109.5	H6B—C6—H6Bi	109.5
H4A—C4—H4B	109.5

Symmetry code: (i) x, −y+1/2, z.

Comparison of selected distances in 1 with two comparable structures.

For PYRZOL27 a Z' of 2 is observed and only values for the first residue have been taken into account.

Compound	d(N—N)	d1(N═C)	d2(N═C)	d1(C═C)	d2(CC)
1	1.358 (4)	1.351 (4)	1.336 (4)	1.392 (4)	1.360 (5)
PYRZOL27	1.357 (2)	1.338 (3)	1.334 (3)	1.391 (3)	1.373 (3)
ALOSEZ	1.3464 (17)	1.3595 (14)	1.3415 (16)	1.3966 (15)	1.377 (2)

Funding Statement

Funding for this research was provided by: RWTH Graduiertenförderung (scholarship to SvT).