Non-centrosymmetric racemates: space-group frequencies and conformational similarities between crystallographically independent molecules

Dalhus, B.; Görbitz, C.H.

doi:10.1107/S0108768100002172

Non-centrosymmetric racemates: space-group frequencies and conformational similarities between crystallographically independent molecules

DL-Allylglycine (DL-2-amino-4-pentenoic acid, C₅H₉NO₂) yields crystals with Pca2₁ symmetry and two crystallographically independent yet pseudo-inversion-related enantiomers. The distribution among the common space groups of other crystalline racemates with more than one molecule in the asymmetric unit has been established. The conformational similarities between crystallographically independent enantiomers in 114 non-centrosymmetric racemates were quantified using the r.m.s. deviation for a molecular superposition. The analysis shows that in the majority of crystals the conformations of the crystallographically independent molecules are very similar with mean r.m.s. deviation = 0.190 Å. In almost 80% of the structures the mean r.m.s. deviations is in the interval 0-0.2 Å. It is estimated that racemates constitute 23% of the centrosymmetric organic structures in the Cambridge Structural Database.

Keywords: Non-centrosymmetric racemates; Space-group frequencies; Conformation; DL-Allylglycine.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768100002172/os0044sup1.cif Contains datablocks I, global
	Structure factor file (CIF format) https://doi.org/10.1107/S0108768100002172/os0044Isup2.hkl Contains datablock I
	Text file https://doi.org/10.1107/S0108768100002172/os0044sup3.txt Supplementary material
	Portable Document Format (PDF) file https://doi.org/10.1107/S0108768100002172/os0044sup4.pdf Supplementary material

CCDC reference: 148920

Computing details top

Data collection: SMART (Siemens, 1995); cell refinement: Saint (Siemens, 1995); data reduction: Saint (Siemens, 1995); program(s) used to solve structure: SHELXTL (Sheldrick, 1994); program(s) used to refine structure: SHELXTL (Sheldrick, 1994); molecular graphics: Sybyl 6.4 (Tripos, 1997).

DL-2-amino-4-pentenoic acid top

Crystal data top

C₅H₉NO₂	D_x = 1.287 Mg m⁻³
M_r = 115.13	Mo Kα radiation, λ = 0.71073 Å
Orthorhombic, Pca2₁	Cell parameters from 5506 reflections
a = 9.8588 (5) Å	θ = 2.4–39.7°
b = 4.8125 (3) Å	µ = 0.10 mm⁻¹
c = 25.0546 (13) Å	T = 150 K
V = 1188.73 (11) Å³	Plate, colorless
Z = 8	0.40 × 0.40 × 0.10 mm
F(000) = 496

Data collection top

Siemens Smart CCD Diffractometer	7312 independent reflections
Radiation source: fine-focus sealed tube	6251 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.037
ω–scans	θ_max = 40.1°, θ_min = 3.3°
Absorption correction: multi-scan Sadabs, Sheldrick (1996)	h = −17→17
T_min = 0.961, T_max = 0.990	k = −8→8
26563 measured reflections	l = −45→43

Refinement top

Refinement on F²	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F² > 2σ(F²)] = 0.044	Hydrogen site location: inferred from neighbouring sites
wR(F²) = 0.111	H atoms treated by a mixture of independent and constrained refinement
S = 1.05	w = 1/[σ²(F_o²) + (0.070P)²] where P = (F_o² + 2F_c²)/3
7312 reflections	(Δ/σ)_max < 0.001
177 parameters	Δρ_max = 0.46 e Å⁻³
1 restraint	Δρ_min = −0.29 e Å⁻³

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
O1A	0.09520 (6)	0.56822 (12)	0.18784 (3)	0.01745 (10)
O2A	−0.06823 (6)	0.31216 (14)	0.22600 (3)	0.02104 (12)
N1A	0.28759 (7)	0.18606 (15)	0.20740 (3)	0.01549 (11)
H1A	0.3265 (16)	0.346 (4)	0.2094 (7)	0.024 (4)*
H2A	0.3416 (18)	0.073 (4)	0.2167 (7)	0.031 (4)*
H3A	0.2706 (14)	0.162 (3)	0.1739 (6)	0.011 (3)*
C1A	0.05368 (7)	0.36671 (15)	0.21479 (3)	0.01362 (11)
C2A	0.16103 (7)	0.17524 (15)	0.23957 (3)	0.01352 (11)
H4A	0.1263 (5)	−0.018 (3)	0.24026 (3)	0.016*
C3A	0.18821 (8)	0.27327 (18)	0.29687 (3)	0.01810 (13)
H5A	0.2200 (4)	0.462 (2)	0.29575 (4)	0.022*
H6A	0.1042 (10)	0.27207 (18)	0.3162 (2)	0.022*
C4A	0.28927 (12)	0.1015 (2)	0.32668 (4)	0.02662 (18)
H7A	0.2697 (4)	−0.098 (4)	0.33148 (9)	0.032*
C5A	0.40348 (12)	0.2001 (3)	0.34706 (5)	0.0387 (3)
H8A	0.4270 (4)	0.406 (3)	0.34282 (9)	0.046*
H9A	0.4683 (10)	0.070 (2)	0.3671 (3)	0.046*
O1B	0.70017 (6)	−0.07034 (13)	0.10500 (3)	0.01816 (11)
O2B	0.86465 (6)	0.18270 (14)	0.06682 (3)	0.02159 (13)
N1B	0.50974 (6)	0.31731 (15)	0.08508 (3)	0.01513 (11)
H1B	0.4681 (15)	0.150 (3)	0.0767 (6)	0.017 (3)*
H2B	0.4546 (15)	0.458 (3)	0.0732 (6)	0.019 (3)*
H3B	0.5315 (17)	0.346 (3)	0.1160 (7)	0.023 (4)*
C1B	0.74251 (7)	0.13005 (15)	0.07796 (3)	0.01383 (11)
C2B	0.63630 (7)	0.32251 (15)	0.05285 (3)	0.01361 (11)
H4B	0.6683 (6)	0.494 (3)	0.05168 (4)	0.016*
C3B	0.60759 (9)	0.22035 (19)	−0.00413 (3)	0.01938 (14)
H5B	0.6935 (10)	0.2103 (2)	−0.0236 (2)	0.023*
H6B	0.5704 (4)	0.032 (2)	−0.00223 (4)	0.023*
C4B	0.51141 (12)	0.3988 (2)	−0.03492 (4)	0.02719 (18)
H7B	0.5425 (5)	0.637 (4)	−0.04219 (12)	0.033*
C5B	0.39443 (13)	0.3126 (4)	−0.05470 (5)	0.0405 (3)
H8B	0.3643 (5)	0.110 (3)	−0.04929 (10)	0.049*
H9B	0.3336 (9)	0.448 (2)	−0.0755 (3)	0.049*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
O1A	0.0183 (2)	0.0149 (2)	0.0191 (3)	−0.00016 (18)	−0.00234 (19)	0.00355 (18)
O2A	0.0113 (2)	0.0183 (3)	0.0336 (3)	−0.00062 (18)	0.0001 (2)	0.0019 (2)
N1A	0.0127 (2)	0.0162 (3)	0.0175 (3)	0.0028 (2)	−0.00074 (19)	−0.0022 (2)
C1A	0.0122 (2)	0.0126 (3)	0.0161 (3)	0.00054 (19)	−0.0017 (2)	−0.0017 (2)
C2A	0.0123 (2)	0.0114 (3)	0.0168 (3)	0.0004 (2)	−0.0014 (2)	0.0002 (2)
C3A	0.0201 (3)	0.0191 (3)	0.0151 (3)	0.0032 (2)	−0.0012 (2)	−0.0006 (2)
C4A	0.0357 (5)	0.0234 (4)	0.0207 (4)	0.0075 (3)	−0.0100 (3)	−0.0018 (3)
C5A	0.0274 (5)	0.0577 (8)	0.0310 (6)	0.0096 (5)	−0.0110 (4)	−0.0056 (5)
O1B	0.0193 (2)	0.0154 (2)	0.0198 (3)	0.00033 (18)	−0.00210 (19)	0.00385 (18)
O2B	0.0115 (2)	0.0193 (3)	0.0339 (4)	0.00027 (18)	−0.0003 (2)	0.0016 (2)
N1B	0.0123 (2)	0.0168 (3)	0.0163 (3)	0.00222 (19)	−0.00113 (19)	−0.0017 (2)
C1B	0.0121 (2)	0.0122 (3)	0.0172 (3)	0.0007 (2)	−0.0021 (2)	−0.0006 (2)
C2B	0.0128 (2)	0.0121 (3)	0.0160 (3)	−0.0001 (2)	−0.0012 (2)	0.0004 (2)
C3B	0.0212 (3)	0.0204 (4)	0.0165 (3)	0.0023 (3)	−0.0005 (3)	−0.0011 (2)
C4B	0.0365 (5)	0.0243 (4)	0.0208 (4)	0.0045 (4)	−0.0098 (3)	−0.0012 (3)
C5B	0.0298 (5)	0.0629 (9)	0.0288 (6)	0.0106 (5)	−0.0089 (4)	−0.0090 (5)

Geometric parameters (Å, º) top

O1A—C1A	1.2505 (9)	O1B—C1B	1.2503 (10)
O2A—C1A	1.2619 (10)	O2B—C1B	1.2618 (10)
N1A—C2A	1.4862 (10)	N1B—C2B	1.4864 (10)
N1A—H1A	0.860 (17)	N1B—H1B	0.930 (15)
N1A—H2A	0.797 (18)	N1B—H2B	0.916 (15)
N1A—H3A	0.863 (14)	N1B—H3B	0.815 (16)
C1A—C2A	1.5345 (10)	C1B—C2B	1.5330 (10)
C2A—C3A	1.5349 (11)	C2B—C3B	1.5364 (11)
C2A—H4A	0.9918	C2B—H4B	0.8841
C3A—C4A	1.4946 (12)	C3B—C4B	1.4938 (13)
C3A—H5A	0.9594	C3B—H5B	0.9792
C3A—H6A	0.9593	C3B—H6B	0.9792
C4A—C5A	1.3244 (17)	C4B—C5B	1.3220 (17)
C4A—H7A	0.9865	C4B—H7B	1.1989
C5A—H8A	1.0246	C5B—H8B	1.0281
C5A—H9A	1.0246	C5B—H9B	1.0281

C2A—N1A—H1A	112.0 (11)	C2B—N1B—H1B	105.2 (9)
C2A—N1A—H2A	112.2 (13)	C2B—N1B—H2B	108.1 (9)
H1A—N1A—H2A	107.2 (16)	H1B—N1B—H2B	107.7 (13)
C2A—N1A—H3A	111.1 (9)	C2B—N1B—H3B	107.0 (12)
H1A—N1A—H3A	105.2 (15)	H1B—N1B—H3B	118.5 (15)
H2A—N1A—H3A	108.8 (16)	H2B—N1B—H3B	109.9 (15)
O1A—C1A—O2A	126.39 (7)	O1B—C1B—O2B	126.40 (7)
O1A—C1A—C2A	117.28 (6)	O1B—C1B—C2B	117.41 (7)
O2A—C1A—C2A	116.23 (7)	O2B—C1B—C2B	116.09 (7)
N1A—C2A—C1A	109.80 (6)	N1B—C2B—C1B	109.89 (6)
N1A—C2A—C3A	110.48 (6)	N1B—C2B—C3B	110.17 (6)
C1A—C2A—C3A	108.32 (6)	C1B—C2B—C3B	108.29 (6)
N1A—C2A—H4A	109.4	N1B—C2B—H4B	109.5
C1A—C2A—H4A	109.4	C1B—C2B—H4B	109.5
C3A—C2A—H4A	109.4	C3B—C2B—H4B	109.5
C4A—C3A—C2A	114.44 (7)	C4B—C3B—C2B	114.39 (7)
C4A—C3A—H5A	108.7	C4B—C3B—H5B	108.7
C2A—C3A—H5A	108.7	C2B—C3B—H5B	108.7
C4A—C3A—H6A	108.7	C4B—C3B—H6B	108.7
C2A—C3A—H6A	108.7	C2B—C3B—H6B	108.7
H5A—C3A—H6A	107.6	H5B—C3B—H6B	107.6
C5A—C4A—C3A	124.13 (11)	C5B—C4B—C3B	124.55 (12)
C5A—C4A—H7A	117.9	C5B—C4B—H7B	117.7
C3A—C4A—H7A	117.9	C3B—C4B—H7B	117.7
C4A—C5A—H8A	120.0	C4B—C5B—H8B	120.0
C4A—C5A—H9A	120.0	C4B—C5B—H9B	120.0
H8A—C5A—H9A	120.0	H8B—C5B—H9B	120.0

O1A—C1A—C2A—N1A	−26.27 (9)	O1B—C1B—C2B—N1B	26.94 (9)
O2A—C1A—C2A—N1A	157.17 (7)	O2B—C1B—C2B—N1B	−156.59 (7)
O1A—C1A—C2A—C3A	94.45 (8)	O1B—C1B—C2B—C3B	−93.45 (8)
O2A—C1A—C2A—C3A	−82.11 (8)	O2B—C1B—C2B—C3B	83.02 (9)
N1A—C2A—C3A—C4A	−60.95 (10)	N1B—C2B—C3B—C4B	63.23 (10)
C1A—C2A—C3A—C4A	178.75 (7)	C1B—C2B—C3B—C4B	−176.55 (8)
C2A—C3A—C4A—C5A	120.91 (12)	C2B—C3B—C4B—C5B	−120.03 (12)

Hydrogen bonds in DL-allylglycine. top

N-H···O	N-H	H···O^a	H···O^b	N···O	N-H···O^a

DL-allylglycine
N1A-H1A···O2Aⁱ	0.86 (2)	1.99 (2)	1.824	2.841 (1)	170 (2)
N1A-H2A···O2Aⁱⁱ	0.80 (2)	2.07 (2)	1.852	2.826 (1)	159 (2)
N1A-H3A···O1Bⁱⁱⁱ	0.86 (1)	1.91 (1)	1.749	2.763 (1)	168 (1)
N1B-H1B···O2Bⁱⁱⁱ	0.93 (1)	1.91 (1)	1.813	2.837 (1)	172 (1)
N1B-H2B···O2B^iv	0.92 (2)	1.95 (2)	1.844	2.836 (1)	162 (1)
N1B-H3B···O1Aⁱ	0.82 (2)	1.95 (2)	1.737	2.764 (1)	175 (2)

Notes: (a) With experimental N-H distance; (b) With N-H distance normalized to 1.03Å (Taylor & Kennard, 1983).

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

Distribution of 1263 selected racemates among 5560 organic structures in centrosymmetric space groups. top

Space group	Racemates	Racemates	Overall in CSD
		with Z_eff>Z₀ ^a	with Z_eff>Z₀ ^a

P-1	336	69 (20.5%)	15.5%
P2₁/c	721	52 (7.2%)	7.9%
C2/c	96	3 (3.1%)	4.5%
Pbca	85	2 (2.4%)	4.2%
Others	25 ^b	–	–

Notes: (a) Z_eff = reported Z value, Z₀ = standard Z value given in International Tables for Crystallography (Vol A, 1996). (b) P2/c (1), Pcca (1), Pccn (1), Pbcn (5), Pnma (1), P4₂/n (4), I4₁/a (4), R-3 (4), R-3c (3) and Unknown (1).

Racemates in non-centrosymmetric space groups which do have symmetry operations of the second kind. top

Space group	Racemates	Racemates	Overall in CSD
		with Z_eff>Z₀ ^a	with Z_eff>Z₀ ^a

Pc	39	13 (33.3%)	28.5%
Cc	136	14 (10.3%)	15.0%
Pca2₁	147	45 (30.6%)	27.9%
Pna2₁	233	34 (14.6%)	12.8%
Fdd2	35	1 (2.9%)	<0.5%
Others	42 ^b	3 (6.8%)	–

Note: (a) Z_eff = reported Z value, Z₀ = standard Z value given in International Tables for Crystallography (Vol A, 1996). (b) Pnc2 (1), Pba2 (1), Pnn2 (2), Aba2 (4), Iba2 (14), P-4 (1), I-4 (8), I4₁cd (2), P-42₁c (8) and R3c (1).

Racemates in space groups which do not have symmetry operations of the second kind. top

Space group	Racemates

P1	1
P21	11
P2₁2₁2₁	4
P3₁21	1

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