Isomorphism and solid solution as shown by an accurate high-resolution diffraction experiment

High-resolution crystal structure determination and spherical and multipolar refinement enabled an organic solid solution of 1-(4′-chlorophenyl)-2-methyl-4-nitro-1H-imidazole-5-carbonitrile and 5-bromo-1-(4′-chlorophenyl)-2-methyl-4-nitro-1H-imidazole to be found, which would not normally be revealed using only standard resolution data (ca 0.8 Å), as the disordered part is only visible at high resolution. Therefore, this new structure would have been reported as just another polymorphic form, even more reasonably as isostructural with other derivatives. To the best of our knowledge this is the first example of organic solid solution modelled via charge density Hansen–Coppens formalism and analysed by means of quantum theory of atoms in molecules (QTAIM) theory.

S1. Experimental

S1.1. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1.

S2. Results and discussion

Computing details

Program(s) used to refine structure: MoPro (J. Appl. Cryst. 2005, 38, 38-54).

Figures

(I)

Crystal data

C10.98H7Br0.02ClN3.98O2	F(000) = 537.8
Mr = 263.93	Dx = 1.550 Mg m^−3
Monoclinic, P21/n	Mo Kα radiation, λ = 0.7107 Å
Hall symbol: -P 2yn	Cell parameters from 29906 reflections
a = 9.3618 (2) Å	θ = 3.1–53.2°
b = 9.6497 (2) Å	µ = 0.41 mm^−1
c = 12.9909 (2) Å	T = 100 K
β = 105.428 (2)°	Plate, colourless
V = 1131.29 (4) Å^3	0.78 × 0.60 × 0.15 mm
Z = 4

Data collection

Xcalibur, Eos diffractometer	10032 independent reflections
Radiation source: Enhance (Mo) X-ray Source	10015 reflections with > 2.0σ(I)
Graphite monochromator	θmax = 53.3°, θmin = 3.1°
Detector resolution: 16.1544 pixels mm^-1	h = −21→20
Absorption correction: analytical CrysAlis PRO, Agilent Technologies, Version 1.171.35.4 (release 09-12-2010 CrysAlis171 .NET) (compiled Dec 9 2010,10:47:41) Analytical numeric absorption correction using a multifaceted crystal model based on expressions derived by R.C. Clark & J.S. Reid. (Clark, R. C. & Reid, J. S. (1995). Acta Cryst. A51, 887-897)	k = 0→21
Tmin = 0.816, Tmax = 0.952	l = 0→29
104943 measured reflections

Refinement

Refinement on F	27 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F^2 > 2σ(F^2)] = 0.021	Secondary atom site location: difference Fourier map
wR(F^2) = 0.022	Hydrogen site location: inferred from neighbouring sites
S = 1.12	H-atom parameters constrained
10032 reflections	Weighting scheme based on measured s.u.'s
477 parameters	(Δ/σ)max = 0.003

Special details

Refinement. Refinement of F¹ against reflections. The threshold expression of F² > σ(F²) is used for calculating R-factors(gt) and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R-factors based on ALL data will be even larger.

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
C1	0.71915 (3)	0.44793 (3)	0.75344 (2)	0.01131 (2)
C2	0.84128 (3)	0.38278 (3)	0.73277 (2)	0.01392 (2)
C3	0.86833 (3)	0.39882 (3)	0.63296 (2)	0.01489 (2)
C4	0.77406 (3)	0.48337 (3)	0.55774 (2)	0.01306 (2)
C5	0.65630 (3)	0.55373 (3)	0.58015 (2)	0.01384 (2)
C6	0.62685 (3)	0.53391 (3)	0.67857 (2)	0.01331 (2)
C7	0.57637 (3)	0.33046 (3)	0.86576 (2)	0.01258 (2)
C71	0.48373 (4)	0.24652 (3)	0.77730 (2)	0.01737 (2)
C8	0.66896 (3)	0.42395 (3)	1.01645 (2)	0.01295 (2)
C9	0.74268 (3)	0.48420 (3)	0.94911 (2)	0.01244 (1)
N1	0.68249 (3)	0.42148 (3)	0.85209 (2)	0.01167 (1)
N2	0.56687 (3)	0.33063 (3)	0.96562 (2)	0.01357 (2)
N8	0.69211 (3)	0.45406 (3)	1.12789 (2)	0.01603 (2)
O81	0.61294 (4)	0.39555 (4)	1.17567 (2)	0.02293 (3)
O82	0.78994 (5)	0.53705 (5)	1.16821 (3)	0.02337 (3)
CL1	0.79800 (2)	0.49908 (2)	0.43095 (1)	0.019172 (1)
H72	0.41362	0.31322	0.72122	0.03798
H71	0.41757	0.18040	0.81066	0.04218
H73	0.55160	0.18772	0.74017	0.03877
H6	0.53143	0.58139	0.69650	0.02815
H2	0.91314	0.32126	0.79523	0.03019
H3	0.95545	0.34280	0.61023	0.03351
H5	0.58701	0.62160	0.52114	0.03150
BR1a	0.8794 (2)	0.6396 (2)	0.9677 (1)	0.02149 (4)	0.02
C91b	0.85026 (3)	0.58946 (3)	0.96423 (2)	0.01565 (2)	0.98
N91b	0.93843 (3)	0.67627 (3)	0.97429 (2)	0.02309 (2)	0.98

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
C1	0.01156 (8)	0.01168 (8)	0.01126 (7)	0.00042 (6)	0.00400 (6)	0.00102 (6)
C2	0.01277 (8)	0.01528 (8)	0.01457 (8)	0.00309 (7)	0.00514 (7)	0.00355 (7)
C3	0.01396 (8)	0.01666 (9)	0.01579 (9)	0.00325 (7)	0.00696 (7)	0.00237 (7)
C4	0.01360 (8)	0.01476 (9)	0.01170 (7)	−0.000052 (7)	0.00486 (7)	0.00033 (6)
C5	0.01437 (8)	0.01541 (9)	0.01191 (7)	0.00279 (7)	0.00379 (7)	0.00237 (7)
C6	0.01344 (8)	0.01440 (9)	0.01285 (8)	0.00327 (7)	0.00481 (7)	0.00182 (7)
C7	0.01406 (8)	0.01263 (8)	0.01146 (7)	−0.00184 (7)	0.00412 (6)	0.000049 (6)
C71	0.0205 (1)	0.01665 (9)	0.01492 (8)	−0.00605 (8)	0.00463 (8)	−0.00204 (7)
C8	0.01324 (8)	0.01553 (9)	0.01023 (7)	0.00103 (7)	0.00342 (6)	0.00029 (7)
C9	0.01196 (7)	0.01375 (8)	0.01130 (7)	−0.00075 (6)	0.00254 (6)	−0.00045 (6)
N1	0.01267 (8)	0.01243 (8)	0.01040 (7)	−0.00153 (6)	0.00392 (6)	0.00013 (6)
N2	0.01464 (8)	0.01527 (9)	0.01168 (7)	−0.00079 (7)	0.00503 (7)	0.00110 (7)
N8	0.01629 (9)	0.0212 (1)	0.01029 (7)	0.00325 (8)	0.00300 (6)	−0.00014 (7)
O81	0.0254 (1)	0.0324 (2)	0.01330 (9)	0.0009 (1)	0.00908 (9)	0.00113 (9)
O82	0.0237 (1)	0.0305 (2)	0.0138 (1)	−0.0027 (1)	0.0014 (1)	−0.0048 (1)
CL1	0.02162 (3)	0.02538 (3)	0.01242 (2)	0.00053 (2)	0.00788 (2)	0.00033 (2)
H72	0.0383	0.0380	0.0309	−0.0017	−0.0027	0.0019
H71	0.0485	0.0461	0.0360	−0.0259	0.0185	−0.0024
H73	0.0398	0.0392	0.0407	−0.0028	0.0166	−0.0152
H6	0.0248	0.0344	0.0275	0.0115	0.0108	0.0037
H2	0.0285	0.0360	0.0260	0.0135	0.0071	0.0093
H3	0.0307	0.0420	0.0328	0.0140	0.0171	0.0030
H5	0.0328	0.0375	0.0232	0.0118	0.0058	0.0104
BR1a	0.0215 (2)	0.0201 (2)	0.0210 (2)	−0.0037 (2)	0.0022 (2)	0.0009 (2)
C91b	0.01391 (8)	0.01470 (9)	0.01682 (8)	−0.00277 (7)	0.00145 (6)	−0.00098 (7)
N91b	0.01940 (10)	0.01823 (9)	0.0289 (1)	−0.00787 (8)	0.00174 (8)	−0.00171 (8)

Geometric parameters (Å, º)

C1—N1	1.4351 (3)	C7—C71	1.4827 (3)
C1—C6	1.3907 (3)	C71—H72	1.059
C1—C2	1.3921 (4)	C71—H73	1.059
C2—C3	1.3944 (4)	C71—H71	1.059
C2—H2	1.083	C8—N8	1.4355 (3)
C3—C4	1.3930 (4)	C8—N2	1.3508 (4)
C3—H3	1.083	C8—C9	1.3786 (4)
C4—CL1	1.7270 (3)	C9—BR1a	1.944 (2)
C4—C5	1.3900 (4)	C9—N1	1.3764 (3)
C5—C6	1.3910 (4)	C9—C91b	1.4069 (4)
C5—H5	1.083	N8—O81	1.2240 (4)
C6—H6	1.083	N8—O82	1.2244 (5)
C7—N1	1.3725 (3)	C91b—N91b	1.1588 (4)
C7—N2	1.3238 (3)
C1—N1—C9	127.06 (2)	C7—C71—H72	109.2
C1—N1—C7	125.64 (3)	C7—C71—H73	110.3
C1—C6—C5	119.12 (3)	C7—C71—H71	107.3
C1—C6—H6	119.8	C71—C7—N1	122.93 (2)
C1—C2—C3	119.40 (3)	C71—C7—N2	125.61 (2)
C1—C2—H2	118.8	C8—N8—O81	117.95 (3)
C2—C1—N1	119.72 (3)	C8—N8—O82	117.32 (3)
C2—C1—C6	121.59 (3)	C8—C9—BR1a	132.09 (6)
C2—C3—C4	118.65 (3)	C8—C9—N1	104.09 (2)
C2—C3—H3	122.3	C8—C9—C91b	132.57 (3)
C3—C4—CL1	120.11 (3)	C9—C8—N8	126.00 (3)
C3—C4—C5	121.94 (3)	C9—C8—N2	112.31 (3)
C3—C2—H2	121.8	C9—C91b—N91b	178.50 (3)
C4—C5—C6	119.18 (3)	N1—C9—BR1a	123.28 (5)
C4—C5—H5	120.4	N1—C9—C91b	123.28 (2)
C4—C3—H3	118.9	N1—C7—N2	111.45 (2)
C5—C4—CL1	117.92 (2)	N2—C8—N8	121.68 (3)
C5—C6—H6	121.1	O81—N8—O82	124.73 (4)
C6—C1—N1	118.62 (2)	H72—C71—H73	110.4
C6—C5—H5	120.4	H72—C71—H71	109.0
C7—N1—C9	107.28 (2)	H71—C71—H73	110.5
C7—N2—C8	104.86 (2)
C1—N1—C9—BR1a	6.75 (6)	C7—N2—C8—N8	179.84 (2)
C1—N1—C9—C8	179.21 (2)	C7—N2—C8—C9	0.53 (2)
C1—N1—C9—C91b	1.65 (2)	C71—C7—N1—C9	178.03 (2)
C1—N1—C7—N2	−178.99 (2)	C71—C7—N2—C8	−178.56 (2)
C1—N1—C7—C71	−0.28 (2)	C8—N2—C7—N1	0.11 (2)
C1—C6—C5—C4	2.22 (2)	C8—C9—C91b—N91b	−168.85 (3)
C1—C6—C5—H5	−179.0	C9—N1—C7—N2	−0.69 (2)
C1—C2—C3—C4	1.85 (2)	C9—C8—N8—O81	176.97 (3)
C1—C2—C3—H3	−174.1	C9—C8—N8—O82	−2.89 (3)
C2—C1—N1—C9	83.31 (2)	N1—C9—C8—N8	179.80 (2)
C2—C1—N1—C7	−98.72 (2)	N1—C9—C8—N2	−0.93 (2)
C2—C1—C6—C5	0.86 (2)	N1—C9—C91b—N91b	7.94 (3)
C2—C1—C6—H6	178.8	N1—C7—C71—H72	−66.2
C2—C3—C4—CL1	−176.72 (2)	N1—C7—C71—H73	55.3
C2—C3—C4—C5	1.25 (2)	N1—C7—C71—H71	175.8
C3—C4—C5—C6	−3.31 (2)	N1—C1—C6—H6	1.7
C3—C4—C5—H5	177.9	N1—C1—C2—H2	−6.2
C3—C2—C1—N1	174.11 (2)	N2—C7—C71—H72	112.3
C3—C2—C1—C6	−2.93 (2)	N2—C7—C71—H73	−126.1
C4—C5—C6—H6	−175.6	N2—C7—C71—H71	−5.7
C4—C3—C2—H2	−177.8	N2—C8—N8—O81	−2.24 (3)
C5—C4—C3—H3	177.3	N2—C8—N8—O82	177.90 (4)
C5—C6—C1—N1	−176.21 (2)	N2—C8—C9—BR1a	170.57 (6)
C6—C1—N1—C9	−99.56 (2)	N2—C8—C9—C91b	176.31 (2)
C6—C1—N1—C7	78.42 (2)	N8—C8—C9—BR1a	−8.70 (6)
C6—C1—C2—H2	176.7	N8—C8—C9—C91b	−2.97 (3)
C6—C5—C4—CL1	174.70 (2)	CL1—C4—C5—H5	−4.1
C7—N1—C9—BR1a	−171.52 (7)	CL1—C4—C3—H3	−0.6
C7—N1—C9—C8	0.94 (2)	H6—C6—C5—H5	3.2
C7—N1—C9—C91b	−176.63 (2)	H2—C2—C3—H3	6.2

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
C5—H5···N91b^i	1.08	2.38	3.3687 (4)	151
C6—H6···O81^ii	1.08	2.41	3.3690 (4)	146

Symmetry codes: (i) x−1/2, −y+3/2, z−1/2; (ii) −x+1, −y+1, −z+2.