On the stacking disorder of DL-norleucine

DL-Norleucine (2-amino­hexanoic acid, C₆H₁₃NO₂) forms a double-layer structure in all known phases (α, β, γ). The crystal structure of the β-phase was redetermined at 173 K. Diffraction patterns of the α- and β-phases frequently show diffuse streaks parallel to c*, which indicates a stacking disorder of the layers. A symmetry analysis was carried out to derive possible stacking sequences. Lattice-energy minimizations by force fields and by dispersion-corrected density functional theory (DFT-D) were performed on a set of ordered model structures with Z = 4, 8 and 16 with different stacking sequences. The calculated energies depend not only on the arrangement of neighbouring double layers, but also of next-neighbouring double layers. Stacking probabilities were calculated from the DFT-D energies. According to the calculated stacking probabilities large models containing 100 double layers were constructed. Their simulated diffraction patterns show sharp reflections for h + k = 2n and diffuse streaks parallel to c* through all reflections with h + k = 2n + 1. Experimental single-crystal X-ray diffraction revealed that at 173 K norleucine exists in the β-phase with stacking disorder. After reheating to room temperature, the investigated crystal showed a diffraction pattern with strong diffuse scattering parallel to c* through all reflections with h + k = 2n + 1, which is in good agreement with the simulated disordered structure.

Computing details

Program(s) used to refine structure: SHELXL2016/6 (Sheldrick, 2016).

(I)

Crystal data

C6H13NO2	F(000) = 576
Mr = 131.17	Dx = 1.195 Mg m^−3
Monoclinic, C2/c	Mo Kα radiation, λ = 0.71073 Å
a = 31.2310 (18) Å	Cell parameters from 8204 reflections
b = 4.7296 (4) Å	θ = 2.1–26.5°
c = 9.8739 (5) Å	µ = 0.09 mm^−1
β = 91.719 (5)°	T = 173 K
V = 1457.82 (17) Å^3	Plate, colourless
Z = 8	0.28 × 0.26 × 0.09 mm

Data collection

STOE IPDS II two-circle- diffractometer	1326 reflections with I > 2σ(I)
Radiation source: Genix 3D IµS microfocus X-ray source	Rint = 0.037
ω scans	θmax = 26.1°, θmin = 2.6°
Absorption correction: multi-scan X-Area (Stoe & Cie, 2001)	h = −38→38
Tmin = 0.370, Tmax = 1.000	k = −5→5
8204 measured reflections	l = −12→12
1451 independent reflections

Refinement

Refinement on F^2	17 restraints
Least-squares matrix: full	Hydrogen site location: mixed
R[F^2 > 2σ(F^2)] = 0.038	H atoms treated by a mixture of independent and constrained refinement
wR(F^2) = 0.117	w = 1/[σ^2(Fo^2) + (0.0743P)^2 + 0.9606P] where P = (Fo^2 + 2Fc^2)/3
S = 0.97	(Δ/σ)max = 0.001
1451 reflections	Δρmax = 0.20 e Å^−3
131 parameters	Δρmin = −0.19 e Å^−3

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	Occ. (<1)
O1	0.71594 (3)	−0.07663 (19)	0.80083 (9)	0.0273 (3)	0.950 (4)
O2	0.68563 (4)	0.2049 (3)	0.95311 (9)	0.0308 (3)	0.950 (4)
N1	0.70227 (4)	0.2984 (4)	0.60003 (12)	0.0236 (3)	0.950 (4)
H1N	0.6947 (5)	0.443 (4)	0.5384 (18)	0.034 (4)*	0.950 (4)
H2N	0.7296 (7)	0.325 (4)	0.6260 (18)	0.037 (4)*	0.950 (4)
H3N	0.7000 (6)	0.112 (5)	0.553 (2)	0.046 (6)*	0.950 (4)
C1	0.69433 (4)	0.1340 (3)	0.83407 (12)	0.0228 (3)	0.950 (4)
C2	0.67414 (4)	0.3110 (3)	0.71923 (12)	0.0231 (3)	0.950 (4)
H2	0.671506	0.511703	0.749761	0.028*	0.950 (4)
C3	0.62962 (4)	0.1938 (4)	0.68334 (14)	0.0275 (4)	0.950 (4)
H3A	0.611142	0.222502	0.761901	0.033*	0.950 (4)
H3B	0.632126	−0.012559	0.668684	0.033*	0.950 (4)
C4	0.60742 (4)	0.3243 (4)	0.55838 (14)	0.0321 (4)	0.950 (4)
H4A	0.605438	0.531494	0.570993	0.039*	0.950 (4)
H4B	0.625003	0.288853	0.478358	0.039*	0.950 (4)
C5	0.56276 (6)	0.2057 (8)	0.5316 (2)	0.0409 (6)	0.950 (4)
H5A	0.564447	−0.003153	0.528131	0.049*	0.950 (4)
H5B	0.544440	0.257430	0.607842	0.049*	0.950 (4)
C6	0.54197 (6)	0.3129 (5)	0.40014 (18)	0.0489 (5)	0.950 (4)
H6A	0.513360	0.229781	0.388218	0.073*	0.950 (4)
H6B	0.539564	0.519350	0.403630	0.073*	0.950 (4)
H6C	0.559582	0.258628	0.323876	0.073*	0.950 (4)
O1'	0.7160 (8)	0.583 (5)	0.800 (2)	0.058 (9)*	0.050 (4)
O2'	0.6849 (12)	0.313 (8)	0.952 (3)	0.071 (15)*	0.050 (4)
N1'	0.7010 (8)	0.191 (8)	0.593 (3)	0.019 (8)*	0.050 (4)
C1'	0.6939 (9)	0.372 (6)	0.830 (2)	0.048 (9)*	0.050 (4)
C2'	0.6739 (9)	0.198 (7)	0.717 (3)	0.057 (16)*	0.050 (4)
C3'	0.6288 (10)	0.297 (12)	0.681 (4)	0.08 (2)*	0.050 (4)
C4'	0.6072 (11)	0.180 (11)	0.554 (4)	0.062 (13)*	0.050 (4)
C5'	0.5617 (14)	0.278 (15)	0.525 (6)	0.06 (3)*	0.050 (4)
C6'	0.545 (2)	0.176 (18)	0.387 (6)	0.12 (3)*	0.050 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.0342 (5)	0.0236 (5)	0.0239 (5)	0.0040 (4)	−0.0018 (4)	0.0007 (3)
O2	0.0500 (7)	0.0253 (7)	0.0171 (5)	0.0020 (5)	0.0002 (4)	−0.0007 (4)
N1	0.0301 (8)	0.0213 (8)	0.0191 (6)	−0.0026 (5)	−0.0017 (4)	0.0010 (5)
C1	0.0292 (6)	0.0187 (6)	0.0203 (6)	−0.0033 (5)	−0.0018 (5)	0.0001 (5)
C2	0.0310 (7)	0.0200 (8)	0.0181 (6)	0.0004 (5)	−0.0003 (5)	−0.0008 (5)
C3	0.0299 (8)	0.0277 (9)	0.0249 (7)	0.0000 (5)	−0.0010 (5)	0.0021 (5)
C4	0.0343 (8)	0.0303 (9)	0.0313 (8)	−0.0003 (6)	−0.0069 (6)	0.0033 (6)
C5	0.0341 (11)	0.0453 (15)	0.0425 (12)	−0.0020 (7)	−0.0096 (6)	0.0045 (9)
C6	0.0391 (9)	0.0632 (14)	0.0435 (10)	0.0015 (8)	−0.0147 (7)	−0.0008 (9)

Geometric parameters (Å, º)

O1—C1	1.2526 (16)	C5—C6	1.521 (3)
O2—C1	1.2597 (15)	C5—H5A	0.9900
N1—C2	1.4908 (16)	C5—H5B	0.9900
N1—H1N	0.939 (19)	C6—H6A	0.9800
N1—H2N	0.89 (2)	C6—H6B	0.9800
N1—H3N	1.00 (2)	C6—H6C	0.9800
C1—C2	1.5302 (17)	O1'—C1'	1.257 (18)
C2—C3	1.5286 (18)	O2'—C1'	1.270 (18)
C2—H2	1.0000	N1'—C2'	1.509 (19)
C3—C4	1.5275 (18)	C1'—C2'	1.506 (18)
C3—H3A	0.9900	C2'—C3'	1.515 (19)
C3—H3B	0.9900	C3'—C4'	1.512 (19)
C4—C5	1.519 (2)	C4'—C5'	1.51 (2)
C4—H4A	0.9900	C5'—C6'	1.52 (2)
C4—H4B	0.9900
C2—N1—H1N	109.9 (10)	C5—C4—H4B	109.1
C2—N1—H2N	110.4 (11)	C3—C4—H4B	109.1
H1N—N1—H2N	107.7 (15)	H4A—C4—H4B	107.8
C2—N1—H3N	111.5 (12)	C6—C5—C4	113.1 (2)
H1N—N1—H3N	109.2 (15)	C6—C5—H5A	109.0
H2N—N1—H3N	108.1 (16)	C4—C5—H5A	109.0
O1—C1—O2	126.09 (12)	C6—C5—H5B	109.0
O1—C1—C2	117.02 (11)	C4—C5—H5B	109.0
O2—C1—C2	116.76 (12)	H5A—C5—H5B	107.8
N1—C2—C3	110.85 (11)	C5—C6—H6A	109.5
N1—C2—C1	108.89 (11)	C5—C6—H6B	109.5
C3—C2—C1	108.97 (12)	H6A—C6—H6B	109.5
N1—C2—H2	109.4	C5—C6—H6C	109.5
C3—C2—H2	109.4	H6A—C6—H6C	109.5
C1—C2—H2	109.4	H6B—C6—H6C	109.5
C2—C3—C4	115.37 (13)	O1'—C1'—O2'	123 (2)
C2—C3—H3A	108.4	O1'—C1'—C2'	118 (2)
C4—C3—H3A	108.4	O2'—C1'—C2'	119 (2)
C2—C3—H3B	108.4	N1'—C2'—C1'	113 (2)
C4—C3—H3B	108.4	N1'—C2'—C3'	111 (2)
H3A—C3—H3B	107.5	C1'—C2'—C3'	112 (2)
C5—C4—C3	112.57 (16)	C2'—C3'—C4'	118 (2)
C5—C4—H4A	109.1	C5'—C4'—C3'	116 (3)
C3—C4—H4A	109.1	C6'—C5'—C4'	112 (3)
O1—C1—C2—N1	−31.26 (17)	O1'—C1'—C2'—N1'	33 (4)
O2—C1—C2—N1	152.63 (13)	O2'—C1'—C2'—N1'	−153 (3)
O1—C1—C2—C3	89.76 (14)	O1'—C1'—C2'—C3'	−93 (4)
O2—C1—C2—C3	−86.35 (15)	O2'—C1'—C2'—C3'	82 (4)
N1—C2—C3—C4	−52.8 (2)	N1'—C2'—C3'—C4'	43 (6)
C1—C2—C3—C4	−172.65 (13)	C1'—C2'—C3'—C4'	170 (4)
C2—C3—C4—C5	−177.94 (17)	C2'—C3'—C4'—C5'	178 (5)
C3—C4—C5—C6	−174.50 (19)	C3'—C4'—C5'—C6'	173 (6)

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
N1—H1N···O2^i	0.939 (19)	1.886 (19)	2.801 (2)	164.3 (15)
N1—H2N···O1^ii	0.89 (2)	1.89 (2)	2.7717 (16)	171.1 (17)
N1—H3N···O1^iii	1.00 (2)	2.56 (2)	3.1759 (16)	119.7 (15)
N1—H3N···O2^iii	1.00 (2)	1.84 (2)	2.828 (2)	168.6 (18)
C2—H2···O1^iv	1.00	2.43	3.2677 (18)	140

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