Phase-transition-induced twinning in the 1:1 adduct of hexamethylenetetramine and azelaic acid

The title compound, C₆H₁₂N₄C₉H₁₆O₄, undergoes several thermotropic phase transitions. The crystalline structure is layered, with sheets of azelaic acid linked to sheets of hexamethylenetetramine by hydrogen bonds. In the room-temperature phase, the azelaic acid molecules are disordered. By lowering the temperature, this disorder partially disappears. The ordering is clearly observed in reciprocal space where on the rods of diffuse scattering, present in the room-temperature phase, a series of superstructure reflections emerges. This phase transition leads to twin-lattice quasi-symmetry (TLQS) twinning. The structure of this twinned phase is explored in this paper. There are two orientational domains linked by a mirror plane which relates disordered orientations of the acid molecules above the phase transition. A single domain has space group . The structure has been solved and refined on the complete set of data to R₁ = 0.0469. The chains remain partially disordered, showing two acid groups with unequal population: the major form corresponding to a carboxylic acid and the minor to a carboxylate. The ordering of the structure, when going through the phase transition, is interpreted in terms of stabilization by C—H...O hydrogen bonding. A least-squares estimator of the twinning volume ratio is developed that gives an expression for the twinning ratio in terms of the intensities of nonoverlapping reflections. The twinning ratio obtained in the structure refinement compares very well with that obtained from this estimator.

Computing details

Data collection: EXPOSE (STOE & CIE GmbH (1997) IPDS 2.87 Software Manual); cell refinement: INDEX, CELL (STOE & CIE GmbH (1997) IPDS 2.87 Software Manual); data reduction: PROFILE, EMS, INTEGRATE (STOE & CIE GmbH (1997) IPDS 2.87 Software Manual), XPREP Version 5.04, Siemens Analytical X-ray Insts. (1996) and home written programs; program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: XP Version 5.04, Siemens Analytical X-ray Insts. (1996).

(I)

Crystal data

C6H12N4·C9H16O4	Z = 4
Mr = 328.41	F(000) = 712
Monoclinic, P21/c	Dx = 1.244 Mg m^−3
a = 5.8907 (7) Å	Mo Kα radiation, λ = 0.71073 Å
b = 26.071 (2) Å	µ = 0.09 mm^−1
c = 11.8868 (11) Å	T = 258 K
β = 106.118 (9)°	Platelet, colourless
V = 1753.8 (3) Å^3	0.3 × 0.2 × 0.02 mm

Data collection

Stoe IPDS imaging plate system diffractometer	1443 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	Rint = see _diffrn_special_details
Graphite monochromator	θmax = 20.8°, θmin = 2.4°
oscillation scans	h = −5→5
6256 measured reflections	k = −25→25
1443 independent reflections	l = −11→11

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.047	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.136	H atoms treated by a mixture of independent and constrained refinement
S = 1.15	Calculated w = 1/[σ^2(Fo^2) + (0.0908P)^2 + 0.0702P] where P = (Fo^2 + 2Fc^2)/3
1443 reflections	(Δ/σ)max = 0.001
246 parameters	Δρmax = 0.17 e Å^−3
8 restraints	Δρmin = −0.12 e Å^−3

Special details

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F² against ALL reflections. The structure is non-merohedral twin. All reflections, i.e. both common and single domain reflections are used in the refinement. The refinement was performed using the HKLF 5 option in SHELXL. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. 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)
O1A	−0.025 (7)	0.875 (2)	0.098 (4)	0.108 (12)	0.29 (4)
O1B	−0.056 (2)	0.8552 (4)	0.0475 (16)	0.076 (3)	0.71 (4)
O2A	0.291 (7)	0.8681 (16)	0.048 (4)	0.090 (11)	0.29 (4)
O2B	0.310 (2)	0.8795 (6)	0.0680 (14)	0.075 (4)	0.71 (4)
H2O	0.3406	0.8557	0.1214	0.112*	0.71 (4)
C11	0.0823 (9)	0.88405 (15)	0.0257 (4)	0.0509 (12)
C12	0.0111 (8)	0.92394 (16)	−0.0675 (4)	0.0568 (13)
H12A	0.0357	0.9101	−0.1389	0.068*
H12B	0.1164	0.9530	−0.0446	0.068*
C13	−0.2383 (8)	0.94317 (15)	−0.0946 (4)	0.0575 (13)
H13A	−0.2578	0.9624	−0.0281	0.069*
H13B	−0.3452	0.9141	−0.1068	0.069*
C14	−0.3034 (9)	0.97712 (18)	−0.2026 (5)	0.0692 (15)
H14A	−0.1861	1.0041	−0.1919	0.083*
H14B	−0.2920	0.9567	−0.2690	0.083*
C15	−0.5437 (8)	1.00182 (18)	−0.2334 (4)	0.0607 (12)
H15A	−0.5499	1.0265	−0.1732	0.073*
H15B	−0.6623	0.9758	−0.2354	0.073*
C16	−0.6007 (9)	1.02870 (18)	−0.3506 (4)	0.0666 (15)
H16A	−0.4717	1.0519	−0.3502	0.080*
H16B	−0.6058	1.0031	−0.4105	0.080*
C17	−0.8278 (9)	1.05880 (16)	−0.3857 (4)	0.0596 (14)
H17A	−0.8190	1.0869	−0.3312	0.072*
H17B	−0.9577	1.0368	−0.3814	0.072*
C18	−0.8753 (8)	1.07994 (17)	−0.5081 (4)	0.0569 (13)
H18A	−0.7358	1.0984	−0.5134	0.068*
H18B	−0.8967	1.0512	−0.5620	0.068*
C19	−1.0829 (9)	1.11470 (15)	−0.5487 (5)	0.0546 (12)
O3A	−1.237 (8)	1.1182 (16)	−0.499 (5)	0.072 (9)	0.29 (4)
O3B	−1.178 (4)	1.1367 (7)	−0.486 (2)	0.088 (5)	0.71 (4)
O4A	−1.119 (6)	1.1335 (18)	−0.652 (4)	0.078 (11)	0.29 (4)
O4B	−1.130 (2)	1.1250 (7)	−0.6618 (14)	0.067 (4)	0.71 (4)
H4O	−1.2724	1.1373	−0.6868	0.101*	0.71 (4)
N1	0.4557 (6)	0.79563 (12)	0.2069 (3)	0.0460 (9)
H1	0.3891	0.8230	0.1622	0.055*	0.29 (4)
N2	0.4336 (6)	0.70364 (11)	0.2341 (3)	0.0449 (9)
H2	0.3519	0.6746	0.2058	0.054*	0.29 (4)
N3	0.8159 (6)	0.74534 (13)	0.2758 (3)	0.0495 (10)
N4	0.5608 (7)	0.75981 (13)	0.4034 (3)	0.0509 (10)
C1	0.3276 (8)	0.74864 (15)	0.1633 (4)	0.0486 (10)
H1A	0.3282	0.7432	0.0826	0.058*
H1B	0.1645	0.7522	0.1648	0.058*
C2	0.7049 (7)	0.78895 (16)	0.2057 (4)	0.0507 (12)
H2A	0.7106	0.7841	0.1256	0.061*
H2B	0.7930	0.8198	0.2356	0.061*
C3	0.4510 (9)	0.80276 (16)	0.3295 (4)	0.0566 (13)
H3A	0.5338	0.8342	0.3600	0.068*
H3B	0.2885	0.8062	0.3319	0.068*
C4	0.6794 (8)	0.69955 (16)	0.2305 (4)	0.0548 (13)
H4A	0.7522	0.6701	0.2764	0.066*
H4B	0.6825	0.6939	0.1503	0.066*
C5	0.8048 (8)	0.75397 (17)	0.3963 (5)	0.0589 (12)
H5A	0.8938	0.7846	0.4271	0.071*
H5B	0.8783	0.7253	0.4448	0.071*
C6	0.4308 (7)	0.71313 (15)	0.3560 (4)	0.0483 (12)
H6A	0.2685	0.7163	0.3590	0.058*
H6B	0.5010	0.6841	0.4042	0.058*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1A	0.098 (17)	0.16 (3)	0.08 (2)	0.007 (19)	0.044 (17)	0.057 (19)
O1B	0.065 (4)	0.069 (5)	0.084 (9)	−0.014 (3)	0.007 (5)	0.036 (4)
O2A	0.116 (17)	0.09 (2)	0.100 (17)	0.062 (18)	0.086 (17)	0.028 (14)
O2B	0.066 (5)	0.054 (5)	0.092 (8)	−0.008 (4)	0.003 (5)	0.033 (5)
C11	0.058 (3)	0.041 (3)	0.053 (4)	−0.004 (2)	0.015 (3)	0.002 (2)
C12	0.071 (3)	0.046 (2)	0.052 (3)	−0.002 (2)	0.014 (3)	0.010 (2)
C13	0.071 (3)	0.043 (2)	0.060 (3)	0.004 (2)	0.020 (3)	0.006 (2)
C14	0.085 (4)	0.064 (3)	0.061 (4)	0.015 (3)	0.023 (3)	0.018 (2)
C15	0.074 (3)	0.054 (2)	0.055 (3)	0.010 (2)	0.019 (3)	0.009 (2)
C16	0.080 (4)	0.061 (3)	0.061 (4)	0.012 (3)	0.023 (3)	0.014 (2)
C17	0.075 (3)	0.045 (2)	0.060 (4)	0.010 (2)	0.022 (3)	0.006 (2)
C18	0.070 (3)	0.049 (2)	0.052 (3)	0.011 (2)	0.017 (3)	0.002 (2)
C19	0.071 (4)	0.038 (2)	0.059 (4)	0.004 (2)	0.025 (3)	−0.003 (2)
O3A	0.081 (15)	0.07 (2)	0.071 (18)	0.031 (14)	0.037 (13)	0.023 (17)
O3B	0.129 (13)	0.079 (9)	0.066 (5)	0.048 (8)	0.044 (8)	0.004 (8)
O4A	0.101 (18)	0.09 (2)	0.077 (14)	−0.003 (12)	0.074 (15)	0.014 (13)
O4B	0.082 (7)	0.062 (5)	0.050 (5)	0.039 (5)	0.006 (5)	0.008 (3)
N1	0.051 (2)	0.0436 (19)	0.045 (3)	0.0034 (17)	0.0157 (18)	0.0069 (16)
N2	0.047 (2)	0.0436 (19)	0.044 (3)	−0.0037 (16)	0.0125 (18)	−0.0031 (16)
N3	0.038 (2)	0.063 (2)	0.049 (3)	0.0004 (17)	0.0128 (18)	0.0026 (18)
N4	0.057 (2)	0.058 (2)	0.040 (3)	−0.0041 (19)	0.017 (2)	−0.0025 (18)
C1	0.045 (3)	0.058 (3)	0.040 (3)	0.001 (2)	0.007 (2)	0.000 (2)
C2	0.049 (3)	0.058 (3)	0.047 (3)	−0.005 (2)	0.017 (2)	0.005 (2)
C3	0.070 (3)	0.049 (2)	0.056 (4)	0.001 (2)	0.026 (3)	−0.008 (2)
C4	0.060 (3)	0.054 (3)	0.055 (3)	0.015 (2)	0.023 (3)	0.002 (2)
C5	0.050 (3)	0.071 (3)	0.048 (4)	−0.008 (2)	0.002 (2)	0.003 (2)
C6	0.046 (3)	0.056 (3)	0.046 (3)	−0.002 (2)	0.018 (2)	0.007 (2)

Geometric parameters (Å, º)

N1—C1	1.457 (5)	C15—C16	1.512 (6)
N1—C3	1.477 (6)	C15—H15A	0.9700
N1—C2	1.482 (5)	C15—H15B	0.9700
N1—H1	0.9100	C16—C17	1.507 (6)
N2—C4	1.464 (5)	C16—H16A	0.9700
N2—C6	1.475 (6)	C16—H16B	0.9700
N2—C1	1.477 (5)	C17—C18	1.507 (6)
N2—H2	0.9100	C17—H17A	0.9700
N3—C2	1.454 (6)	C17—H17B	0.9700
N3—C4	1.457 (6)	C18—C19	1.490 (6)
N3—C5	1.469 (7)	C18—H18A	0.9700
N4—C3	1.459 (6)	C18—H18B	0.9700
N4—C6	1.464 (5)	C19—O3B	1.20 (2)
N4—C5	1.471 (6)	C19—O3A	1.22 (5)
O1A—C11	1.22 (3)	C19—O4A	1.29 (4)
O1B—C11	1.190 (11)	C19—O4B	1.322 (15)
O2A—C11	1.25 (3)	O4B—H4O	0.8700
O2B—C11	1.298 (14)	C1—H1A	0.9700
O2B—H2O	0.8700	C1—H1B	0.9700
C11—C12	1.492 (6)	C2—H2A	0.9700
C12—C13	1.500 (6)	C2—H2B	0.9700
C12—H12A	0.9700	C3—H3A	0.9700
C12—H12B	0.9700	C3—H3B	0.9700
C13—C14	1.518 (7)	C4—H4A	0.9700
C13—H13A	0.9700	C4—H4B	0.9700
C13—H13B	0.9700	C5—H5A	0.9700
C14—C15	1.505 (6)	C5—H5B	0.9700
C14—H14A	0.9700	C6—H6A	0.9700
C14—H14B	0.9700	C6—H6B	0.9700
C11—O2B—H2O	109.5	O3B—C19—C18	124.9 (12)
O1B—C11—O1A	37 (3)	O3A—C19—C18	123 (2)
O1B—C11—O2A	115.7 (19)	O4A—C19—C18	116.5 (14)
O1A—C11—O2A	117 (2)	O4B—C19—C18	112.0 (8)
O1B—C11—O2B	123.6 (9)	C19—O4B—H4O	109.5
O1A—C11—O2B	113 (2)	C1—N1—C3	107.9 (3)
O2A—C11—O2B	17 (2)	C1—N1—C2	108.3 (3)
O1B—C11—C12	122.2 (7)	C3—N1—C2	108.3 (4)
O1A—C11—C12	124.2 (17)	C1—N1—H1	110.7
O2A—C11—C12	116.7 (17)	C3—N1—H1	110.7
O2B—C11—C12	113.5 (8)	C2—N1—H1	110.7
C11—C12—C13	116.7 (4)	C4—N2—C6	108.7 (3)
C11—C12—H12A	108.1	C4—N2—C1	107.9 (3)
C13—C12—H12A	108.1	C6—N2—C1	108.0 (3)
C11—C12—H12B	108.1	C4—N2—H2	110.7
C13—C12—H12B	108.1	C6—N2—H2	110.7
H12A—C12—H12B	107.3	C1—N2—H2	110.7
C12—C13—C14	112.3 (4)	C2—N3—C4	108.3 (4)
C12—C13—H13A	109.1	C2—N3—C5	107.8 (3)
C14—C13—H13A	109.1	C4—N3—C5	108.4 (3)
C12—C13—H13B	109.1	C3—N4—C6	108.0 (4)
C14—C13—H13B	109.1	C3—N4—C5	108.8 (3)
H13A—C13—H13B	107.9	C6—N4—C5	107.9 (3)
C15—C14—C13	117.1 (4)	N1—C1—N2	111.7 (3)
C15—C14—H14A	108.0	N1—C1—H1A	109.3
C13—C14—H14A	108.0	N2—C1—H1A	109.3
C15—C14—H14B	108.0	N1—C1—H1B	109.3
C13—C14—H14B	108.0	N2—C1—H1B	109.3
H14A—C14—H14B	107.3	H1A—C1—H1B	107.9
C14—C15—C16	112.1 (4)	N3—C2—N1	112.0 (3)
C14—C15—H15A	109.2	N3—C2—H2A	109.2
C16—C15—H15A	109.2	N1—C2—H2A	109.2
C14—C15—H15B	109.2	N3—C2—H2B	109.2
C16—C15—H15B	109.2	N1—C2—H2B	109.2
H15A—C15—H15B	107.9	H2A—C2—H2B	107.9
C17—C16—C15	116.7 (4)	N4—C3—N1	111.8 (3)
C17—C16—H16A	108.1	N4—C3—H3A	109.3
C15—C16—H16A	108.1	N1—C3—H3A	109.3
C17—C16—H16B	108.1	N4—C3—H3B	109.3
C15—C16—H16B	108.1	N1—C3—H3B	109.3
H16A—C16—H16B	107.3	H3A—C3—H3B	107.9
C16—C17—C18	111.7 (4)	N3—C4—N2	112.2 (3)
C16—C17—H17A	109.3	N3—C4—H4A	109.2
C18—C17—H17A	109.3	N2—C4—H4A	109.2
C16—C17—H17B	109.3	N3—C4—H4B	109.2
C18—C17—H17B	109.3	N2—C4—H4B	109.2
H17A—C17—H17B	107.9	H4A—C4—H4B	107.9
C19—C18—C17	116.8 (4)	N3—C5—N4	112.4 (3)
C19—C18—H18A	108.1	N3—C5—H5A	109.1
C17—C18—H18A	108.1	N4—C5—H5A	109.1
C19—C18—H18B	108.1	N3—C5—H5B	109.1
C17—C18—H18B	108.1	N4—C5—H5B	109.1
H18A—C18—H18B	107.3	H5A—C5—H5B	107.9
O3B—C19—O3A	28.1 (18)	N4—C6—N2	111.7 (3)
O3B—C19—O4A	116 (2)	N4—C6—H6A	109.3
O3A—C19—O4A	119 (3)	N2—C6—H6A	109.3
O3B—C19—O4B	122.4 (13)	N4—C6—H6B	109.3
O3A—C19—O4B	121 (3)	N2—C6—H6B	109.3
O4A—C19—O4B	11 (3)	H6A—C6—H6B	107.9
C13—C12—C11—O1A	−18 (4)	C14—C15—C16—C17	−174.7 (4)
C13—C12—C11—O2A	−180 (2)	C15—C16—C17—C18	−175.1 (4)
C13—C12—C11—O1B	27.2 (12)	C16—C17—C18—C19	−174.2 (4)
C13—C12—C11—O2B	−161.7 (9)	C17—C18—C19—O3A	−15 (3)
C11—C12—C13—C14	−171.1 (4)	C17—C18—C19—O4A	179 (2)
C12—C13—C14—C15	−175.7 (4)	C17—C18—C19—O3B	18.9 (16)
C13—C14—C15—C16	−172.3 (4)	C17—C18—C19—O4B	−170.7 (10)

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O2B—H2O···N1	0.87	1.89	2.730 (16)	163
O4B—H4O···N2^i	0.87	1.98	2.699 (14)	140
C2—H2A···O1B^ii	0.97	2.63	3.157 (14)	115
C3—H3B···O3B^iii	0.97	2.58	3.19 (2)	121
C5—H5A···O3B^iv	0.97	2.62	3.58 (2)	170
C5—H5B···O1B^v	0.97	2.40	3.345 (15)	163
C12—H12A···O4B^vi	0.97	2.74	3.706 (18)	176
N1—H1···O2A	0.91	1.76	2.65 (4)	165
N1—H1···O1A	0.91	2.71	3.46 (3)	140
N2—H2···O3A^vii	0.91	2.79	3.51 (5)	138
N2—H2···O4A^vii	0.91	1.72	2.59 (4)	160
C2—H2B···O1A^ii	0.97	2.62	3.21 (4)	120
C6—H6B···O2A^viii	0.97	2.74	3.38 (4)	124
C2—H2A···N4^ix	0.97	2.79	3.682 (6)	154
C1—H1B···N3^x	0.97	2.74	3.622 (6)	152
C6—H6A···N3^x	0.97	2.68	3.580 (6)	154

Symmetry codes: (i) −x−1, y+1/2, −z−1/2; (ii) x+1, y, z; (iii) −x−1, −y+2, −z; (iv) −x, −y+2, −z; (v) x+1, −y+3/2, z+1/2; (vi) −x−1, −y+2, −z−1; (vii) −x−1, y−1/2, −z−1/2; (viii) x, −y+3/2, z+1/2; (ix) x, −y+3/2, z−1/2; (x) x−1, y, z.