(–)-Gibberic acid: hydrogen-bonding pattern of the monohydrate of a non-­racemic tetracyclic δ-keto acid derivative of gibberellin A₃

In the the title compound, 1,7-di­methyl-8-oxo-4bα,7α-gibba-1,3,4a(10a)-triene-10β-carboxyl­ic acid monohydrate, C₁₈H₂₀O₃·H₂O, the water of hydration accepts a hydrogen bond from the carboxyl and donates hydrogen bonds to the carboxyl carbonyl and the ketone in two different screw-related neighbors, which are mutually translational, yielding a complex three-dimensional hydrogen-bonding array.

S1. Comment

Our interest in the crystal structures of keto carboxylic acids concerns their five known hydrogen-bonding modes (Coté et al., 1996; Lalancette et al., 1999; Thompson et al., 2001). The dimeric arrangement typical of functionally unelaborated acids is also dominant among keto acids overall. However, intermolecular acid-to-ketone patterns provide a sizable minority of cases and actually predominate when centrosymmetric arrangements are precluded. We report here the structure and hydrogen-bonding pattern of the monohydrate of gibberic acid, (I), a δ-keto acid derived from gibberellic acid (gibberellin A₃). The gibberellins are an important family of diterpenoid plant growth factors first isolated from cultures of the fungus Gibberella fujikuroi in the late 1930 s (Mander, 1992). The degradation leading to (I) involves separate acid-catalyzed processes which aromatize the A-ring by hydrolysis, decarboxylation and dehydration and which rearrange the bridged C/D ring system (Stork et al., 1965). \sch

Both the structure (Cross et al., 1961) and stereochemistry (Hartsuck & Lipscomb, 1963; McCapra et al., 1966) of gibberellic acid and of (I) have long been firmly established. Nevertheless, at least two major reference sources provide structures for (I) in which the stereochemistry assigned to C4b is incorrect, showing instead the stereochemistry for epigibberic acid (Buckingham, 1982; Connolly & Hill, 1991).

Fig. 1 shows the asymmetric unit for (I), with its Chemical Abstracts `gibbane' numbering (Budavari, 1989), which differs from the alternative `gibberellin' numbering often used (Mander, 1992). The H atoms at C4b and C10, as well as the ketone bridge, all lie on the `lower' α face of the molecule. The molecule has no conformational flexibility and the only available rotations involve the methyl groups and the carboxyl, which is turned so that its C ═ O is toward the β face. The carboxyl is hydrogen bonded to a water of hydration, which in turn donates hydrogen bonds to two different C ═O groups in separate neighboring molecules (see below). Fig. 1 shows this water molecule, arbitrarily, in its hydrogen-bonding relationship to the carboxyl OH.

Because the carboxyl is not dimerized but hydrogen bonded to another species, it shows no disorder. Averaging of C—O bond lengths and C—C—O angles by disorder is common in carboxyl dimers (Leiserowitz, 1976), but is not seen in catemers and other hydrogen-bonding arrangements whose geometry cannot support the mechanisms responsible for such averaging. In (I), these carboxyl C—O bond lengths are 1.213 (5) and 1.323 (4) Å, with carboxyl C—C—O angles of 124.7 (4) and 111.1 (4)°. Our own survey of 56 keto acid structures which are not acid dimers gives average values of 1.20 (1) and 1.32 (2) Å, and 124.5 (14) and 112.7 (17)°, for these lengths and angles, in accord with typical values of 1.21 and 1.31 Å, and 123 and 112°, cited for highly ordered dimeric carboxyls (Borthwick, 1980). No rotational disorder was observed for either methyl group.

Fig. 2 illustrates the packing arrangement with its hydrogen bonding, which adheres to a recurrent pattern among hydrated keto acids. The carboxyl donates its hydrogen bond to the water molecule [O···O 2.603 (4) Å], which in turn donates hydrogen bonds to the carbonyls of a ketone [O···O 2.903 (4) Å] and a carboxyl [O···O 2.831 (4) Å] in separate adjacent molecules, in this instance, both screw-related to the first but mutually translational. Thus, each water molecule participates in hydrogen bonds to three separate gibberic acid molecules, while each of them participates in hydrogen bonds to three separate water molecules, producing a complex three-dimensional network.

We characterize the geometry of hydrogen bonding to carbonyls using a combination of the H···O ═C angle and the H···O ═C—X torsional angle. These describe the approach of the H atom to the O atom in terms of its deviation from, respectively, C ═O axiality (ideal = 120°) and planarity with the carbonyl (ideal = 0°). In (I), these criteria are applicable to two of the three hydrogen bonds present. Approach angles for the water-to-acid hydrogen bond are 135.0 (13) and -35.4 (18)°, and for the water-to-ketone hydrogen bond 131.8 (13) and -9.3 (17)°. No C—H···O close contacts were found within the 2.7 Å range we usually employ for such non-bonded packing interactions (Steiner, 1997).

The solid-state (KBr) infrared spectrum of (I) displays C ═O absorptions at 1719 and 1701 cm^-1 for hydrogen-bonded ketone and carboxyl groups, respectively. In CHCl₃ solution, where the ketone is presumably not hydrogen bonded, these bands appear at 1737 and 1711 cm^-1.

S2. Experimental

Commercial `90%+ pure' gibberellic acid, obtained from Acros Organics/Fisher Scientific, Springfield, NJ, USA, was treated with refluxing 1.75 M HCl as described by Cross (1954). Recrystallization of isolated (I) from formic acid yielded the material used, which loses water below its m.p. of 427 K. The higher-melting (ca 545 K) anhydrous form gave only micro-needles, unsuitable for X-ray analysis.

S3. Refinement

All H atoms for (I) were found in electron-density difference maps but were placed in calculated positions and allowed to refine as riding models, except for the two H atoms of the water molecule, the positional parameters of which were allowed to refine, but with their isotropic displacement parameters fixed at 0.08 Ų. C—H distances were fixed at 0.93 (phenyl), 0.98 (methine), 0.97 (methylene) or 0.96 Å (methyl), and O—H was fixed at 0.82 Å.

Computing details

Data collection: XSCANS (Siemens, 1996); cell refinement: XSCANS; data reduction: XSCANS; program(s) used to solve structure: SHELXS97 (Sheldrick, 1997b); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997b); molecular graphics: SHELXL97; software used to prepare material for publication: SHELXL97.

Figures

	Fig. 1. The molecular structure of the asymmetric unit of (I), with its gibbane numbering. The water of hydration is shown, arbitrarily, in its hydrogen-bonding relationship to the carboxyl OH. Displacement ellipsoids are drawn at the 20% probability level and H atoms are shown as small spheres of arbitrary radii.
	Fig. 2. A partial packing diagram with extracellular molecules, illustrating the complex three-dimensional hydrogen-bonding arrangement for (I). All carbon-bound H atoms have been removed for clarity, but some peripheral water molecules are shown.

1,7-dimethyl-8-oxo-4 bα,7α-gibba-1,3,4a(10a)-triene-10β-carboxylic acid monohydrate

Crystal data

C18H20O3·H2O	Dx = 1.269 Mg m^−3
Mr = 302.36	Melting point: 427 K
Monoclinic, P21	Mo Kα radiation, λ = 0.71073 Å
a = 8.841 (3) Å	Cell parameters from 35 reflections
b = 6.283 (3) Å	θ = 2.3–14.5°
c = 14.646 (4) Å	µ = 0.09 mm^−1
β = 103.45 (2)°	T = 293 K
V = 791.2 (5) Å^3	Parallelepiped, colorless
Z = 2	0.28 × 0.10 × 0.08 mm
F(000) = 324

Data collection

Siemens P4 diffractometer	1021 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	Rint = 0.071
Graphite monochromator	θmax = 25.0°, θmin = 2.4°
2θ/θ scans	h = −10→10
Absorption correction: numerical (SHELXTL; Sheldrick, 1997a)	k = −7→7
Tmin = 0.98, Tmax = 0.99	l = −17→17
3208 measured reflections	3 standard reflections every 97 reflections
1517 independent reflections	intensity decay: variation < 1.5%

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: inferred from neighbouring sites
R[F^2 > 2σ(F^2)] = 0.041	H atoms treated by a mixture of independent and constrained refinement
wR(F^2) = 0.084	w = 1/[σ^2(Fo^2) + (0.0247P)^2] where P = (Fo^2 + 2Fc^2)/3
S = 1.00	(Δ/σ)max < 0.001
1517 reflections	Δρmax = 0.19 e Å^−3
208 parameters	Δρmin = −0.13 e Å^−3
1 restraint	Extinction correction: SHELXL97 (Sheldrick, 1997b), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
Primary atom site location: structure-invariant direct methods	Extinction coefficient: 0.041 (4)

Special details

Experimental. 'crystal mounted on glass fiber using epoxy resin'

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
O1	1.0936 (3)	−0.0343 (4)	0.3644 (2)	0.0707 (10)
O2	0.5899 (3)	0.6755 (4)	0.34957 (18)	0.0556 (8)
O3	0.5610 (3)	0.3247 (4)	0.3671 (2)	0.0584 (8)
O4	0.5808 (3)	0.4101 (5)	0.5434 (2)	0.0644 (9)
C1	0.5423 (4)	0.7749 (6)	0.1311 (2)	0.0440 (10)
C2	0.5783 (5)	0.9092 (6)	0.0640 (3)	0.0551 (12)
C3	0.7099 (5)	0.8875 (7)	0.0311 (3)	0.0628 (12)
C4	0.8112 (5)	0.7238 (6)	0.0622 (3)	0.0551 (11)
C4A	0.7799 (4)	0.5848 (6)	0.1292 (2)	0.0454 (10)
C4B	0.8615 (4)	0.3826 (6)	0.1658 (2)	0.0487 (10)
C5	1.0363 (5)	0.3533 (9)	0.1760 (3)	0.0722 (13)
C6	1.1399 (4)	0.4105 (7)	0.2707 (3)	0.0631 (13)
C7	1.0665 (4)	0.3534 (6)	0.3542 (3)	0.0459 (10)
C8	1.0124 (4)	0.1230 (6)	0.3391 (2)	0.0507 (11)
C9	0.8410 (4)	0.1173 (5)	0.2930 (3)	0.0472 (11)
C9A	0.8090 (4)	0.3482 (5)	0.2585 (2)	0.0388 (9)
C10	0.6398 (4)	0.4323 (5)	0.2330 (2)	0.0376 (9)
C10A	0.6474 (4)	0.6118 (5)	0.1643 (2)	0.0371 (9)
C11	0.9141 (4)	0.4709 (5)	0.3389 (2)	0.0419 (9)
C12	0.5914 (4)	0.4945 (7)	0.3210 (3)	0.0436 (10)
C13	1.1788 (4)	0.3904 (7)	0.4482 (3)	0.0653 (13)
C14	0.3936 (4)	0.8093 (7)	0.1631 (3)	0.0623 (12)
H3	0.5618	0.3576	0.4213	0.067 (14)*
H4AA	0.537 (5)	0.334 (8)	0.577 (3)	0.080*
H4BB	0.668 (4)	0.432 (7)	0.581 (3)	0.080*
H2	0.5098	1.0190	0.0403	0.066*
H3A	0.7308	0.9840	−0.0125	0.075*
H4B	0.8112	0.2700	0.1231	0.058*
H4	0.8996	0.7061	0.0387	0.066*
H5A	1.0552	0.2056	0.1629	0.087*
H5B	1.0675	0.4390	0.1285	0.087*
H6A	1.1612	0.5621	0.2720	0.076*
H6B	1.2382	0.3362	0.2783	0.076*
H9A	0.7798	0.0795	0.3377	0.057*
H9B	0.8189	0.0175	0.2411	0.057*
H10	0.5706	0.3201	0.2007	0.045*
H11A	0.9257	0.6179	0.3216	0.050*
H11B	0.8731	0.4673	0.3949	0.050*
H13A	1.2096	0.5372	0.4535	0.098*
H13B	1.2689	0.3022	0.4529	0.098*
H13C	1.1289	0.3552	0.4979	0.098*
H14A	0.4147	0.8947	0.2189	0.093*
H14B	0.3523	0.6742	0.1760	0.093*
H14C	0.3192	0.8808	0.1146	0.093*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.0552 (18)	0.0398 (16)	0.106 (2)	0.0082 (15)	−0.0038 (16)	−0.0003 (16)
O2	0.0641 (19)	0.0575 (17)	0.0482 (16)	0.0078 (16)	0.0191 (14)	−0.0048 (14)
O3	0.0651 (19)	0.0632 (18)	0.0514 (18)	−0.0035 (17)	0.0229 (14)	0.0102 (16)
O4	0.0549 (18)	0.082 (2)	0.0570 (19)	−0.0117 (18)	0.0142 (13)	0.0098 (16)
C1	0.053 (2)	0.042 (2)	0.0319 (19)	−0.004 (2)	0.0002 (18)	0.0000 (18)
C2	0.074 (3)	0.043 (2)	0.042 (2)	0.003 (2)	0.000 (2)	0.010 (2)
C3	0.091 (3)	0.056 (3)	0.040 (2)	−0.012 (3)	0.012 (2)	0.013 (2)
C4B	0.049 (2)	0.054 (2)	0.043 (2)	0.003 (2)	0.0118 (17)	−0.002 (2)
C4	0.066 (3)	0.055 (2)	0.049 (3)	−0.008 (2)	0.022 (2)	0.002 (2)
C4A	0.055 (2)	0.045 (2)	0.036 (2)	−0.008 (2)	0.0092 (18)	−0.0019 (19)
C5	0.063 (3)	0.092 (3)	0.070 (3)	0.003 (3)	0.033 (2)	0.005 (3)
C6	0.053 (2)	0.065 (3)	0.075 (3)	−0.002 (2)	0.023 (2)	−0.001 (3)
C7	0.038 (2)	0.0373 (19)	0.058 (2)	−0.005 (2)	0.0030 (19)	−0.004 (2)
C8	0.053 (3)	0.043 (2)	0.053 (3)	0.001 (2)	0.008 (2)	−0.001 (2)
C9A	0.041 (2)	0.0328 (18)	0.0421 (19)	0.0003 (18)	0.0085 (17)	0.0006 (18)
C9	0.043 (2)	0.036 (2)	0.060 (2)	−0.0013 (19)	0.0051 (19)	−0.004 (2)
C10A	0.042 (2)	0.037 (2)	0.0304 (19)	−0.005 (2)	0.0046 (17)	−0.0026 (17)
C10	0.036 (2)	0.036 (2)	0.039 (2)	−0.0048 (18)	0.0064 (16)	−0.0038 (17)
C11	0.045 (2)	0.0351 (18)	0.045 (2)	0.0019 (19)	0.0109 (17)	−0.0018 (19)
C12	0.037 (2)	0.051 (2)	0.042 (2)	−0.001 (2)	0.0084 (18)	0.007 (2)
C13	0.051 (2)	0.056 (2)	0.078 (3)	−0.002 (2)	−0.006 (2)	−0.007 (2)
C14	0.059 (3)	0.061 (3)	0.063 (3)	0.013 (2)	0.006 (2)	0.006 (2)

Geometric parameters (Å, º)

O1—C8	1.227 (4)	C10A—C10	1.524 (5)
O2—C12	1.213 (5)	O3—H3	0.8200
O3—C12	1.323 (4)	O4—H4AA	0.84 (5)
C1—C2	1.388 (5)	O4—H4BB	0.85 (4)
C1—C10A	1.393 (5)	C2—H2	0.9300
C1—C14	1.511 (5)	C3—H3A	0.9300
C2—C3	1.365 (5)	C4B—H4B	0.9800
C3—C4	1.370 (5)	C4—H4	0.9300
C4—C4A	1.389 (5)	C5—H5A	0.9700
C4A—C10A	1.394 (5)	C5—H5B	0.9700
C4B—C4A	1.498 (5)	C6—H6A	0.9700
C4B—C5	1.528 (5)	C6—H6B	0.9700
C4B—C9A	1.549 (5)	C9—H9A	0.9700
C5—C6	1.516 (5)	C9—H9B	0.9700
C6—C7	1.555 (5)	C10—H10	0.9800
C7—C11	1.507 (5)	C11—H11A	0.9700
C7—C13	1.517 (4)	C11—H11B	0.9700
C7—C8	1.525 (5)	C13—H13A	0.9600
C8—C9	1.510 (5)	C13—H13B	0.9600
C9A—C11	1.529 (4)	C13—H13C	0.9600
C9A—C9	1.541 (5)	C14—H14A	0.9600
C9A—C10	1.547 (5)	C14—H14B	0.9600
C10—C12	1.501 (5)	C14—H14C	0.9600
C2—C1—C10A	116.8 (4)	C1—C2—H2	118.5
C2—C1—C14	119.5 (3)	C2—C3—H3A	119.9
C10A—C1—C14	123.7 (3)	C4—C3—H3A	119.9
C3—C2—C1	122.9 (4)	C4A—C4B—H4B	105.9
C2—C3—C4	120.2 (4)	C5—C4B—H4B	105.9
C3—C4—C4A	118.9 (4)	C9A—C4B—H4B	105.9
C4—C4A—C10A	120.4 (4)	C3—C4—H4	120.5
C4—C4A—C4B	128.9 (4)	C4A—C4—H4	120.5
C10A—C4A—C4B	110.3 (3)	C6—C5—H5A	108.2
C4A—C4B—C5	122.0 (3)	C4B—C5—H5A	108.2
C4A—C4B—C9A	102.3 (3)	C6—C5—H5B	108.2
C5—C4B—C9A	113.6 (3)	C4B—C5—H5B	108.2
C6—C5—C4B	116.3 (4)	H5A—C5—H5B	107.4
C5—C6—C7	113.0 (3)	C5—C6—H6A	109.0
C11—C7—C13	115.7 (3)	C7—C6—H6A	109.0
C11—C7—C8	101.8 (3)	C5—C6—H6B	109.0
C13—C7—C8	113.2 (3)	C7—C6—H6B	109.0
C11—C7—C6	107.0 (3)	H6A—C6—H6B	107.8
C13—C7—C6	112.0 (3)	C8—C9—H9A	111.3
C8—C7—C6	106.2 (3)	C9A—C9—H9A	111.3
O1—C8—C9	124.9 (3)	C8—C9—H9B	111.3
O1—C8—C7	125.4 (3)	C9A—C9—H9B	111.3
C9—C8—C7	109.6 (3)	H9A—C9—H9B	109.2
C11—C9A—C9	100.9 (2)	C12—C10—H10	109.3
C11—C9A—C10	113.2 (3)	C10A—C10—H10	109.3
C9—C9A—C10	119.6 (3)	C9A—C10—H10	109.3
C11—C9A—C4B	110.7 (3)	C7—C11—H11A	111.1
C9—C9A—C4B	110.4 (3)	C9A—C11—H11A	111.1
C10—C9A—C4B	102.2 (3)	C7—C11—H11B	111.1
C8—C9—C9A	102.3 (3)	C9A—C11—H11B	111.1
C12—C10—C10A	116.1 (3)	H11A—C11—H11B	109.1
C12—C10—C9A	109.6 (3)	C7—C13—H13A	109.5
C10A—C10—C9A	102.9 (3)	C7—C13—H13B	109.5
C1—C10A—C4A	120.7 (3)	H13A—C13—H13B	109.5
C1—C10A—C10	130.3 (3)	C7—C13—H13C	109.5
C4A—C10A—C10	108.9 (3)	H13A—C13—H13C	109.5
C7—C11—C9A	103.3 (3)	H13B—C13—H13C	109.5
O2—C12—O3	124.1 (4)	C1—C14—H14A	109.5
O2—C12—C10	124.7 (4)	C1—C14—H14B	109.5
O3—C12—C10	111.1 (4)	H14A—C14—H14B	109.5
C12—O3—H3	109.5	C1—C14—H14C	109.5
H4AA—O4—H4BB	101 (4)	H14A—C14—H14C	109.5
C3—C2—H2	118.5	H14B—C14—H14C	109.5
C10A—C1—C2—C3	−0.4 (5)	C10—C9A—C9—C8	−162.0 (3)
C14—C1—C2—C3	−179.5 (4)	C4B—C9A—C9—C8	79.9 (3)
C1—C2—C3—C4	2.0 (6)	C2—C1—C10A—C4A	−1.4 (5)
C2—C3—C4—C4A	−1.7 (5)	C14—C1—C10A—C4A	177.7 (3)
C3—C4—C4A—C10A	0.0 (5)	C2—C1—C10A—C10	−176.5 (3)
C3—C4—C4A—C4B	172.4 (3)	C14—C1—C10A—C10	2.6 (5)
C5—C4B—C4A—C4	33.6 (5)	C4—C4A—C10A—C1	1.6 (5)
C9A—C4B—C4A—C4	161.8 (3)	C4B—C4A—C10A—C1	−172.1 (3)
C5—C4B—C4A—C10A	−153.4 (3)	C4—C4A—C10A—C10	177.7 (3)
C9A—C4B—C4A—C10A	−25.1 (3)	C4B—C4A—C10A—C10	4.0 (4)
C4A—C4B—C5—C6	92.2 (5)	C1—C10A—C10—C12	−45.9 (4)
C9A—C4B—C5—C6	−30.9 (6)	C4A—C10A—C10—C12	138.6 (3)
C4B—C5—C6—C7	36.2 (6)	C1—C10A—C10—C9A	−165.5 (3)
C5—C6—C7—C11	−58.3 (5)	C4A—C10A—C10—C9A	19.0 (3)
C5—C6—C7—C13	173.9 (4)	C11—C9A—C10—C12	−38.1 (4)
C5—C6—C7—C8	49.9 (4)	C9—C9A—C10—C12	80.6 (4)
C11—C7—C8—O1	−162.5 (4)	C4B—C9A—C10—C12	−157.2 (3)
C13—C7—C8—O1	−37.6 (6)	C11—C9A—C10—C10A	85.9 (3)
C6—C7—C8—O1	85.7 (5)	C9—C9A—C10—C10A	−155.4 (3)
C11—C7—C8—C9	14.2 (4)	C4B—C9A—C10—C10A	−33.1 (3)
C13—C7—C8—C9	139.1 (3)	C13—C7—C11—C9A	−161.1 (3)
C6—C7—C8—C9	−97.6 (4)	C8—C7—C11—C9A	−37.9 (4)
C4A—C4B—C9A—C11	−85.5 (3)	C6—C7—C11—C9A	73.3 (3)
C5—C4B—C9A—C11	47.8 (4)	C9—C9A—C11—C7	47.7 (4)
C4A—C4B—C9A—C9	163.6 (3)	C10—C9A—C11—C7	176.7 (3)
C5—C4B—C9A—C9	−63.0 (4)	C4B—C9A—C11—C7	−69.2 (3)
C4A—C4B—C9A—C10	35.3 (3)	C10A—C10—C12—O2	−16.0 (5)
C5—C4B—C9A—C10	168.7 (3)	C9A—C10—C12—O2	99.9 (4)
O1—C8—C9—C9A	−168.6 (4)	C10A—C10—C12—O3	168.5 (3)
C7—C8—C9—C9A	14.6 (4)	C9A—C10—C12—O3	−75.6 (3)
C11—C9A—C9—C8	−37.2 (4)