()-Tartaric acid

()-Tartaric acid, C₄H₆O₆, crystallized from ethanol in space group P. The structure is characterized by five hydrogen bonds, including the formation of a centrosymmetric carbox­ylic acid dimer which forms infinite chains along the body diagonal. These chains form sheets via hydrogen bonding between α-hydroxyl groups. The sheets are connected through a bifurcated hydrogen bond. Structural comparisons are made with homochiral (2R,3R)-(+)-tartaric acid.

S1. Comment

Tartaric acid is an important additive in foods and pharmaceuticals. The structures of its various forms are of historical interest dating back to the work of Pasteur (1848, 1850). The study of the molecular packing and hydrogen bonding in tartaric acid and its derivatives is relevant to the development of approaches for crystal engineering (Aakeröy et al., 1992; Rychlewska & Warzajtis 2000). Furthermore, tartaric acid has often been cited as a case satisfying Wallach's rule [see references in Brock et al. (1991)], which states that racemic crystals tend to be denser than their chiral counterparts (Wallach 1895). The structure of the title compound, (I) (also known as DL-tartaric or racemic acid), has not been reported previously, although the structures of the homochiral [(+)-L-tartaric acid or (2R,3R)-(+)-tartaric acid, (II)] and meso forms have been determined (Stern & Beevers 1950; Okaya et al., 1966; Bootsma & Schoone 1967). Anhydrous (I) can be recrystallized from water above 346 K; however, the crystals obtained were of poor quality for structure determination (Parry, 1951). Consequently, Parry (1951) reported the structure of the hydrate. Very early reports of the structure of (I) were incomplete (Astbury, 1923; Gerstäker et al., 1927). An appropriate comparison of the crystallographic features of the homochiral and heterochiral crystal forms requires the structures of both anhydrous forms. As part of our investigation of the molecular basis for differences between the near-IR spectra of (I) and (II) (Patel et al., 2000), we have isolated a single-crystal of (I) from absolute ethanol and determined its crystal structure. We report here the crystal structure of (I) and also compare its hydrogen-bonding features to those of (II).

The refined molecule and labeling scheme for (I) are shown in Fig. 1. The structure is characterized by five hydrogen bonds (Table 2). Unique to the structure of (I), relative to (II), is the hydrogen-bonding pattern associated with the carboxylic acid groups and the formation of centrosymmetric dimers in the former (Fig. 2). Graph-set analysis (Bernstein et al., 1995) of the hydrogen bonds reveals four separate centrosymmetric rings between adjacent enantiomers formed by four of the hydrogen-bond motifs. The fifth motif is a helical C(5) chain formed between molecules of like chirality, propagating along the c axis. A combination of the two unique motifs associated with the carboxylic acid dimers (O4—H4···O3 and O1—H1···O2) forms a chain of rings, C²₂(14)[R²₂(8)R²₂(8)]. These twisted chains are crosslinked into sheets by the C(5) motif. Rings R²₂(12) and R²₂(10) result from O5—H5···O3 and O5—H5···O6 hydrogen bonds, respectively. Other binary graph sets form a variety of ladder and rail configurations with rings. The angle between the two planes formed by the carboxyl groups was 55.9 (1)°. Carbonyl–carbonyl interactions of the antiparallel motif (Allen et al., 1998) exist between C4—O3 carbonyl groups on adjacent molecules [O3···C4ⁱ = 3.009 (1) Å; symmetry code: (i) 1 - x, -y, -z] and similarly for C1—O2 carbonyl groups [O2···C1ⁱⁱ = 3.068 (1) Å; symmetry code: (ii) 2 - x, 1 - y, -z].

In constrast, for (II), carboxyl O atoms form hydrogen bonds with alcohol OH groups in addition to acidic OH groups on translationally related molecules in a head-to-tail arrangement along the a axis (Okaya et al., 1966). Carboxylic acid dimers are not present despite their propensity to form (Leiserowitz, 1976). Both (I) and (II) contain binary graph-set R²₁(5), formed among two α-hydroxyl groups and a carboxyl O atom. However, (II) features C(7) and C²₂(7) chains that form a ring R³₃(12) (Rychlewska et al., 1999; Rychlewska & Warzajtis, 2000). This feature links together three molecules and results in a more diffuse network in (II) than in (I). The impact of dimer formation and the altered hydrogen-bonding scheme in (I) is readily observed when comparing the splitting and shifting patterns of the ¹³C CP/MAS solid-state NMR and Raman spectra of the two forms (Patel et al., 2000). There are other short O···O contacts [O4···O2ⁱⁱⁱ = 2.858 (1) Å, O4···O1^iv = 3.007 (1) Å and O6···O6^v = 2.930 (2) Å; symmetry codes: (iii) -1 + x, y, -1 + z; (iv) 1 - x, 1 - y, -z; (v) 2 - x, -y, 1 - z] that are not hydrogen-bonding contacts, as the associated H atoms are involved in hydrogen bonds with other O atoms.

The calculated value of Δ% (Brock et al., 1991), a measure of the extent to which the racemate is denser than the homochiral form, was 2.2 for the tartaric acid pair. This value appears in the upper quartile for a wide range of structures examined by Brock et al. (1991) and is greater than the mean for pairs of chiral and racemic structures examined (0.92). The formation of dimers likely contributes to tighter packing in (I), as evidenced by its higher calculated density [1.796 versus 1.757 Mg m^-3 for (II)]. Thus, the crystal pair reasonably satisfies Wallach's rule, provided the inherent bias in comparing resolvable racemic/chiral pairs is recognized (Brock et al., 1991).

S2. Experimental

Compound (I) (Sigma, St. Louis, MO) was recrystallized from absolute ethanol by slow evaporation followed by vacuum drying at 373 K for 12 h. The X-ray powder diffraction patterns (D5000, Bruker AXS Inc., Madison, WI) of the recrystallized material, as well as the commercial bulk material, matched the pattern found in the ICDD for (I) (listed as DL-tartaric acid; Organic Databook 1989). The theoretically generated X-ray powder diffraction pattern (Materials Studio 2.0, Powder Diffraction Module, Accelrys, Princeton, NJ) from the structure reported here corresponded with the experimentally determined pattern of the commercial bulk sample, verifying the identity of the single-crystal form (pattern available in supplementary material). The true density of the commercial bulk sample was determined by helium pycnometry (MPY-2, Quantachrome, Boynton Beach, FL).

S3. Refinement

All H atoms were refined with isotropic displacement parameters [C—H = 0.88 (2)–0.93 (1) Å].

Computing details

Data collection: CAD-4 Operations Manual (Enraf-Nonius, 1977); cell refinement: CAD-4 Operations Manual; data reduction: MolEN (Fair, 1990); program(s) used to solve structure: SHELXTL (Sheldrick, 1997); program(s) used to refine structure: SHELXTL; molecular graphics: SHELXTL; software used to prepare material for publication: SHELXTL.

Figures

	Fig. 1. The molecular structure of (I), showing displacement ellipsoids at the 50% probability level.
	Fig. 2. Stereoview of the packing viewed down the c axis. Some of the hydrogen bonds are shown as dotted lines.

(2R/S,3R/S)-dihydroxy-1,4-butanedioic acid

Crystal data

C4H6O6	F(000) = 156
Mr = 150.09	Dx = 1.796 Mg m^−3 Dm = 1.786 Mg m^−3 Dm measured by He Pycnometry
Triclinic, P1	Melting point: 479 K
a = 6.580 (1) Å	Mo Kα radiation, λ = 0.71073 Å
b = 9.186 (1) Å	Cell parameters from 50 reflections
c = 4.8966 (7) Å	θ = 13.9–17.4°
α = 91.52 (1)°	µ = 0.18 mm^−1
β = 103.52 (1)°	T = 293 K
γ = 74.78 (1)°	Prism, colorless
V = 277.50 (7) Å^3	0.31 × 0.21 × 0.17 mm
Z = 2

Data collection

Enraf-Nonius CAD-4 diffractometer	Rint = 0.015
Radiation source: fine-focus sealed tube	θmax = 30.0°, θmin = 2.0°
Graphite monochromator	h = −9→9
θ–2θ scans	k = −12→12
3193 measured reflections	l = −6→6
1598 independent reflections	4 standard reflections every 120 min
1363 reflections with I > 2σ(I)	intensity decay: <2%

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)] = 0.033	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.101	All H-atom parameters refined
S = 1.06	w = 1/[σ^2(Fo^2) + (0.0537P)^2 + 0.0695P] where P = (Fo^2 + 2Fc^2)/3
1598 reflections	(Δ/σ)max = 0.012
115 parameters	Δρmax = 0.46 e Å^−3
0 restraints	Δρmin = −0.19 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 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
C1	0.89078 (16)	0.39473 (10)	0.1805 (2)	0.0213 (2)
O1	0.74120 (13)	0.48288 (10)	0.29074 (19)	0.0331 (2)
H1	0.804 (4)	0.529 (3)	0.434 (5)	0.082 (7)*
O2	1.08426 (12)	0.38222 (9)	0.25797 (16)	0.0276 (2)
C2	0.79394 (15)	0.30530 (11)	−0.05750 (19)	0.0202 (2)
H2	0.687 (2)	0.3739 (15)	−0.186 (3)	0.024 (3)*
O5	0.94702 (12)	0.22956 (9)	−0.20703 (15)	0.02443 (18)
H5	1.050 (3)	0.163 (2)	−0.091 (4)	0.053 (5)*
C3	0.69085 (16)	0.19626 (11)	0.06351 (19)	0.0205 (2)
H3	0.573 (2)	0.2528 (16)	0.129 (3)	0.024 (3)*
O6	0.84217 (14)	0.09436 (9)	0.26827 (16)	0.0283 (2)
H6	0.872 (3)	0.140 (2)	0.429 (4)	0.056 (5)*
C4	0.60465 (15)	0.10406 (11)	−0.17674 (19)	0.0202 (2)
O3	0.67218 (12)	−0.03252 (8)	−0.18357 (15)	0.02461 (19)
O4	0.45352 (14)	0.18895 (9)	−0.37348 (17)	0.0316 (2)
H4	0.409 (3)	0.132 (2)	−0.510 (4)	0.061 (6)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
C1	0.0248 (5)	0.0174 (4)	0.0193 (4)	−0.0066 (3)	−0.0005 (3)	−0.0034 (3)
O1	0.0270 (4)	0.0324 (4)	0.0369 (5)	−0.0080 (3)	0.0036 (3)	−0.0202 (3)
O2	0.0249 (4)	0.0289 (4)	0.0261 (4)	−0.0086 (3)	−0.0005 (3)	−0.0087 (3)
C2	0.0222 (4)	0.0187 (4)	0.0172 (4)	−0.0060 (3)	−0.0004 (3)	−0.0043 (3)
O5	0.0267 (4)	0.0262 (4)	0.0181 (3)	−0.0054 (3)	0.0032 (3)	−0.0049 (3)
C3	0.0231 (4)	0.0196 (4)	0.0171 (4)	−0.0066 (3)	0.0008 (3)	−0.0052 (3)
O6	0.0377 (4)	0.0242 (4)	0.0170 (3)	−0.0070 (3)	−0.0036 (3)	−0.0020 (3)
C4	0.0200 (4)	0.0222 (4)	0.0185 (4)	−0.0081 (3)	0.0024 (3)	−0.0052 (3)
O3	0.0275 (4)	0.0206 (3)	0.0226 (4)	−0.0066 (3)	0.0001 (3)	−0.0061 (3)
O4	0.0339 (4)	0.0234 (4)	0.0268 (4)	−0.0046 (3)	−0.0099 (3)	−0.0065 (3)

Geometric parameters (Å, º)

C1—O1	1.312 (1)	C3—C4	1.520 (1)
C1—O2	1.216 (1)	C3—H3	0.93 (1)
C1—C2	1.522 (1)	C3—O6	1.402 (1)
O1—H1	0.88 (2)	O6—H6	0.88 (2)
C2—C3	1.546 (1)	C4—O3	1.219 (1)
C2—H2	0.93 (1)	C4—O4	1.308 (1)
C2—O5	1.409 (1)	O4—H4	0.88 (2)
O5—H5	0.88 (2)
O2—C1—O1	125.3 (1)	O6—C3—C4	107.3 (1)
O2—C1—C2	122.9 (1)	O6—C3—C2	112.3 (1)
O1—C1—C2	111.8 (1)	C4—C3—C2	107.6 (1)
C1—O1—H1	109 (2)	O6—C3—H3	113 (1)
O5—C2—C1	112.2 (1)	C4—C3—H3	108 (1)
O5—C2—C3	112.3 (1)	C2—C3—H3	109 (1)
C1—C2—C3	108.9 (1)	C3—O6—H6	111 (1)
O5—C2—H2	106 (1)	O3—C4—O4	124.8 (1)
C1—C2—H2	108 (1)	O3—C4—C3	123.3 (1)
C3—C2—H2	110 (1)	O4—C4—C3	112.0 (1)
C2—O5—H5	108 (1)	C4—O4—H4	110 (1)
O2—C1—C2—O5	−10.8 (1)	O5—C2—C3—C4	−52.7 (1)
O1—C1—C2—O5	170.3 (1)	C1—C2—C3—C4	−177.6 (1)
O2—C1—C2—C3	114.2 (1)	O6—C3—C4—O3	−4.1 (1)
O1—C1—C2—C3	−64.8 (1)	C2—C3—C4—O3	117.0 (1)
O5—C2—C3—O6	65.2 (1)	O6—C3—C4—O4	176.8 (1)
C1—C2—C3—O6	−59.7 (1)	C2—C3—C4—O4	−62.1 (1)

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O4—H4···O3^i	0.88 (2)	1.78 (2)	2.660 (1)	173 (2)
O1—H1···O2^ii	0.88 (2)	1.80 (2)	2.675 (1)	175 (2)
O6—H6···O5^iii	0.88 (2)	1.96 (2)	2.841 (1)	177 (2)
O5—H5···O3^iv	0.88 (2)	2.09 (2)	2.962 (1)	170 (2)
O5—H5···O6^iv	0.88 (2)	2.48 (2)	2.975 (1)	116 (1)

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