3,3′:5,6-Di-O-isopropyl­idene-3-C-hydroxy­methyl-d-allono-1,4-lactone: an organic structure containing large unoccupied voids

Simone, M.; Fleet, G.W.J.; Watkin, D.J.

doi:10.1107/S1600536807002061

organic compounds

CRYSTALLOGRAPHIC
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ISSN: 2056-9890

Volume 63| Part 2| February 2007| Pages o799-o801

https://doi.org/10.1107/S1600536807002061

3,3′:5,6-Di-O-isopropylidene-3-C-hydroxymethyl-D-allono-1,4-lactone: an organic structure containing large unoccupied voids

Michela Simone,^a ^* George W. J. Fleet ^a and David J. Watkin ^b

^aDepartment of Organic Chemistry, Chemical Research Laboratory, Oxford University, Mansfield Road, Oxford OX1 3TA, England, and ^bDepartment of Chemical Crystallography, Chemical Research Laboratory, Oxford University, Mansfield Road, Oxford OX1 3TA, England
^*Correspondence e-mail: michela_simone@yahoo.co.uk

(Received 6 December 2006; accepted 15 January 2007; online 19 January 2007)

The Kiliani reaction of D-hamamelose with sodium cyanide, followed by acetonation, affords crystalline 3,3′:5,6-di-O-isopropylidene-3-C-hydroxymethyl-D-allono-1,4-lactone, C₁₃H₂₀O₇, a carbon-branched sugar with potential as an enantiomerically pure carbohydrate scaffold. The lactone has one single free hydroxyl group unprotected, with six other functional groups protected in a single step as ketals or esters. The resulting crystal structure is unusual in that it contains large voids (544 Å³) within which there is no evidence of included solvent.

Comment

At present, there are very few accessible branched carbohydrate scaffolds (Lichtenthaler & Peters, 2004 ; Bols, 1996 ) for use in the synthesis of complex enantiomerically pure targets (Simone et al., 2005 ). The reactions of calcium oxide on Amadori 1-deoxyamino-ketoses (Hotchkiss et al., 2006 ) and the Kiliani reaction of cyanide with ketoses (Hotchkiss et al., 2004 ; Soengas et al., 2005 ) allow the preparation of 2-C-methyl and 2-C-hydroxymethyl lactones in relatively short sequences. However, syntheses of carbohydrates bearing a carbon branch at C-3 are very rare (Bream et al., 2006 ). One approach to such chirons is the Kiliani cyanide reaction on 2-C-hydroxymethyl sugars [such as hamamelose (1)] to produce 3-C-hydroxymethyl lactones [such as (2) and (4)]. The experimental details for the Kiliani reaction of D-hamamelose (1) with cyanide to give a mixture of the two branched sugar lactones (2) and (4), followed by treatment with dimethoxypropane to afford a separable mixture of the two diacetonides (3) and (5), have been reported in a previous paper (Parker et al., 2006 ).

A significant number of ambiguities arise from the formation of possible lactones, the sites for the formation of cyclic ketals and the sizes of both the lactone and ketal rings. This is an area in which X-ray crystallography is needed to have any confidence at all in the structures of diacetonides obtained by this short procedure. The crystal structure of the altrono-diacetonide (5), formed from the lactone (4) derived by cyclization of the branched C-3′ hydroxymethyl group on to the carboxylic acid, has been established by X-ray crystallography (Parker et al., 2006). This paper firmly assigns the structure of the second crystalline product as the branched allono-lactone (3) formed from lactone formation from the C-4 hydroxyl group; the absolute configuration of (3) is determined by the use of D-ribose as the starting material for the synthesis. It is noteworthy that both lactones (3) and (5) have only the C-2 hydroxyl group unprotected; the sequence provides access to two sugars with seven functional groups but with six of the them protected in one simple step.

The component molecules have no unusual torsion angles, and show no evidence of internal strain. The relatively large anisotropic displacement parameters for the methyl groups and O atoms in the acetonide protecting group may indicate some ring fluxion (Fig. 1).

The crystal structure is unusual in that it contains substantial voids (544 Å³) within which there is no evidence for included solvent (Fig. 2). The voids are big enough to have contained dichloromethane, but the maximum residual electron density is only 0.2 e Å⁻³. We do not know if the voids in the dry crystals ever contained solvent, though generally solvent loss from organic crystals is associated with either a total loss of crystallinity, or at least a degradation of the crystal quality. In this case the crystals remained glass-clear.

The structure consists of a tight helix (Fig. 3), involving O—H⋯Oⁱ hydrogen bonds (Table 1), which runs parallel to the c axis at (½, ½, z). The main parts of the molecule hang off this backbone like leaves from a tree. The tips of the `leaves' of four separate helices meet to form a second helix at (0, 0, z). The `leaves' of each pair of adjacent hydrogen-bonded helices (separated by $[z\over2]$ because of the 4₁ axis) interleave along (0, 0, z), but there is no evidence for particularly strong interactions at these points.

Figure 1
The molecular structure of the title compound with displacement ellipsoids drawn at the 50% probability level. H atoms are shown as spheres of arbitary radius.

Figure 2
Packing diagam of the title compound viewed along c. The residual electron density in the void has a maximum value of 0.22 e Å⁻³. Hydrogen bonds are drawn as dotted lines

Figure 3
Oblique packing diagram of the title compound, showing the hydrogen-bonded helix which is the main structural feature. The ends of one turn of the helix are coloured blue and purple. Operators involved in forming the helix are: (i) x, y, z + 1; (ii) −y + 1, x, z + $[{1\over 4}]$ ; (iii) −x + 1, −y + 1, z + $[{1\over 2}]$ ; (iv) y, −x + 1, z − $[{1\over 4}]$ ; (v) y, −x + 1, z + $[{3\over 4}]$ . Hydrogen bonds are drawn as dotted lines.

Experimental

The title compound, (3), was crystallized by dissolving it in dichloromethane, adding a few drops of cyclohexane and allowing the slow competitive evaporation of the two solvents until needle-like colourless crystals formed [m.p. 353 K (dichloromethane/cyclohexane)]. MS–ES⁻ (m/z): 287.2 ([M − H]⁻, 15%); HRMS (MS ES⁺): found 311.1101 [M + Na]⁺ C₁₃H₂₀NaO₇ requires 311.1101; [α]_D²³: +5.5 (c 1.25 in chloroform); ν_max (thin film): 3445 (br, OH), 2989 (CH₂, CH₃), 1800 (C=O) cm⁻¹; δ_H (C₆D₆, 400 MHz): 1.20, 1.31, 1.36, 1.38 [12H, 4 × s, 2 × C(CH₃)₂], 3.30–3.40 (1H, br s, OH-2), 3.51 (1H, ddd, J_H-5,H-4 = 8.5 Hz, J_H-5,H-6 = 6.7 Hz, J_H-5,H-6′ = 5.3 Hz, H-5), 3.75 (1H, dd, J_H-6,H-6′ = 9.5 Hz, J_H-6,H-5 = 6.6 Hz, H-6), 3.82 (1H, dd, J_H-6′,H-6 = 9.5 Hz, J_H-6′,H-5 = 5.3 Hz, H-6′), 3.97 (1H, d, J_H-3,H-3′ = 10.0 Hz H-3), 4.20 (1H, s, H-2), 4.26 (1H, d, J_H-4,H-5 = 8.6 Hz, H-4), 4.55 (1H, d, J_H-3′,H-3 = 10.0 Hz, H-3′); δ_C (C₆D₆, 100 MHz): 24.8, 25.5, 26.5, 26.9 [2 × C(CH₃)₂], 65.3 (C-3′), 65.8 (C-6), 67.0 (C-2), 73.7 (C-5), 84.9 (C-3), 85.0 (C-4), 110.7, 111.2 [2 × C(CH₃)₂], 173.2 (C=O).

Crystal data

C₁₃H₂₀O₇
M_r = 288.30
Tetragonal, P 4₁
a = 14.1641 (4) Å
c = 9.2045 (3) Å
V = 1846.62 (10) Å³
Z = 4
D_x = 1.037 Mg m⁻³
Mo Kα radiation
μ = 0.08 mm⁻¹
T = 150 K
Needle, colourless
0.44 × 0.12 × 0.10 mm

Data collection

Nonius KappaCCD diffractometer
ω scans
Absorption correction: multi-scan (DENZO/SCALEPACK; Otwinowski & Minor, 1997 ) T_min = 0.96, T_max = 0.99
21907 measured reflections
2229 independent reflections
1802 reflections with I > 3σ(I)
R_int = 0.068
θ_max = 27.6°

Refinement

Refinement on F
R[F² > 2σ(F²)] = 0.046
wR(F²) = 0.044
S = 1.04
1802 reflections
181 parameters
H-atom parameters constrained
w = [1 − (F_o − F_c)²/36σ²(F)]²/[1.09T₀(x) + 0.255T₁(x) + 0.726T₂(x)] where T_i are Chebychev polynomials and x = F_c/F_max (Prince, 1982 ; Watkin, 1994 ) Modified Chebychev polynomial (Watkin, 1994; Prince, 1982)
(Δ/σ)_max = 0.010
Δρ_max = 0.22 e Å⁻³
Δρ_min = −0.21 e Å⁻³

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
O2—H1⋯O2ⁱ	0.80	1.91	2.679 (2)	160
Symmetry code: (i) $[-y+1, x, z+{\script{1\over 4}}]$ .

In the absence of significant anomalous scattering, Friedel pairs were merged and the absolute configuration assigned from the starting materials The H atoms were all located in a difference map, but those attached to C atoms were repositioned geometrically. The H atoms were initially refined with soft restraints on the bond lengths and angles to regularize their geometry [C—H = 0.93–0.98, O—H = 0.82 Å and U_iso(H) = 1.2 or 1.5 times U_eq(parent atom)], after which the positions were refined with riding constraints.

Data collection: COLLECT (Nonius, 2001 ).; cell refinement: DENZO/SCALEPACK (Otwinowski & Minor, 1997); data reduction: DENZO/SCALEPACK; program(s) used to solve structure: SIR92 (Altomare et al., 1994 ); program(s) used to refine structure: CRYSTALS (Betteridge et al., 2003 ); molecular graphics: CAMERON (Watkin et al., 1996 ); software used to prepare material for publication: CRYSTALS.

Supporting information

Crystal structure: contains datablocks 3, global. DOI: https://doi.org/10.1107/S1600536807002061/sj2196sup1.cif

Structure factors: contains datablock 3. DOI: https://doi.org/10.1107/S1600536807002061/sj21963sup2.hkl

Computing details top

Data collection: COLLECT (Nonius, 2001).; cell refinement: DENZO/SCALEPACK (Otwinowski & Minor, 1997); data reduction: DENZO/SCALEPACK; program(s) used to solve structure: SIR92 (Altomare et al., 1994); program(s) used to refine structure: CRYSTALS (Betteridge et al., 2003); molecular graphics: CAMERON (Watkin et al., 1996); software used to prepare material for publication: CRYSTALS.

3,3':5,6-di-O-isopropylidene-3-C-hydroxymethyl-D-allono-1,4-lactone top

Crystal data top

C₁₃H₂₀O₇	D_x = 1.037 Mg m⁻³
M_r = 288.30	Mo Kα radiation, λ = 0.71073 Å
Tetragonal, P4₁	Cell parameters from 21907 reflections
Hall symbol: P 4w	θ = 5–28°
a = 14.1641 (4) Å	µ = 0.08 mm⁻¹
c = 9.2045 (3) Å	T = 150 K
V = 1846.62 (10) Å³	Needle, colourless
Z = 4	0.44 × 0.12 × 0.10 mm
F(000) = 616

Data collection top

Nonius KappaCCD diffractometer	1802 reflections with I > 3σ(I)
Graphite monochromator	R_int = 0.068
ω scans	θ_max = 27.6°, θ_min = 5.2°
Absorption correction: multi-scan (DENZO/SCALEPACK; Otwinowski & Minor, 1997)	h = −12→13
T_min = 0.96, T_max = 0.99	k = 0→18
21907 measured reflections	l = 0→11
2229 independent reflections

Refinement top

Refinement on F	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Hydrogen site location: inferred from neighbouring sites
R[F² > 2σ(F²)] = 0.046	H-atom parameters constrained
wR(F²) = 0.044	Modified Chebychev polynomial (Watkin, 1994; Prince, 1982) with coefficients 1.09 0.255 0.726 and Robust Weighting (Prince, 1982); W = [weight][1-(δF/6σF)²]²
S = 1.04	(Δ/σ)_max = 0.010
1802 reflections	Δρ_max = 0.22 e Å⁻³
181 parameters	Δρ_min = −0.21 e Å⁻³
1 restraint

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

	x	y	z	U_iso*/U_eq
C1	0.40908 (17)	0.29983 (17)	0.2555 (3)	0.0322
C2	0.50778 (16)	0.34055 (15)	0.2595 (2)	0.0292
C3	0.56325 (17)	0.26748 (16)	0.1741 (2)	0.0306
C4	0.51393 (17)	0.17588 (17)	0.2218 (3)	0.0340
C5	0.54440 (19)	0.13445 (17)	0.3650 (3)	0.0384
C6	0.4755 (2)	0.06101 (19)	0.4243 (4)	0.0493
O1	0.33445 (12)	0.34056 (13)	0.2657 (2)	0.0401
O2	0.51303 (12)	0.43275 (11)	0.20539 (19)	0.0336
O3	0.54536 (12)	0.28276 (12)	0.02234 (18)	0.0340
O4	0.41413 (12)	0.20543 (12)	0.2386 (2)	0.0367
O5	0.62892 (15)	0.08096 (13)	0.3439 (3)	0.0522
O6	0.53620 (16)	0.00210 (14)	0.5075 (3)	0.0579
C7	0.67037 (18)	0.27177 (18)	0.1852 (3)	0.0356
O8	0.69994 (13)	0.24162 (13)	0.0446 (2)	0.0409
C8	0.63374 (18)	0.27831 (18)	−0.0555 (3)	0.0356
C9	0.6603 (2)	0.3780 (2)	−0.1031 (3)	0.0434
C10	0.6248 (2)	0.2097 (2)	−0.1803 (3)	0.0477
C11	0.6237 (2)	−0.0037 (2)	0.4304 (3)	0.0510
C12	0.6225 (4)	−0.0873 (2)	0.3307 (5)	0.0805
C13	0.7021 (3)	−0.0043 (3)	0.5393 (4)	0.0793
H1	0.5317	0.4678	0.2677	0.0507*
H21	0.5308	0.3403	0.3595	0.0347*
H41	0.5201	0.1275	0.1480	0.0411*
H51	0.5523	0.1854	0.4369	0.0454*
H61	0.4264	0.0889	0.4849	0.0586*
H62	0.4459	0.0254	0.3444	0.0580*
H71	0.6906	0.3361	0.2042	0.0413*
H72	0.6947	0.2293	0.2595	0.0417*
H91	0.7203	0.3782	−0.1548	0.0642*
H92	0.6673	0.4189	−0.0191	0.0647*
H93	0.6102	0.4041	−0.1660	0.0643*
H101	0.6850	0.2058	−0.2287	0.0703*
H102	0.5776	0.2310	−0.2491	0.0705*
H103	0.6073	0.1473	−0.1420	0.0706*
H121	0.6216	−0.1447	0.3883	0.1191*
H122	0.6795	−0.0864	0.2731	0.1185*
H123	0.5676	−0.0845	0.2679	0.1184*
H131	0.6983	−0.0602	0.6003	0.1178*
H132	0.7623	−0.0033	0.4884	0.1177*
H133	0.6982	0.0510	0.5999	0.1178*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
C1	0.0403 (13)	0.0401 (12)	0.0161 (8)	−0.0017 (10)	0.0017 (9)	0.0035 (9)
C2	0.0405 (12)	0.0301 (11)	0.0169 (9)	0.0024 (9)	−0.0033 (9)	0.0022 (9)
C3	0.0429 (13)	0.0302 (11)	0.0188 (10)	−0.0015 (9)	−0.0003 (9)	0.0012 (8)
C4	0.0432 (13)	0.0297 (11)	0.0292 (11)	−0.004 (1)	0.0058 (9)	−0.0041 (9)
C5	0.0508 (14)	0.0277 (11)	0.0368 (12)	0.0027 (10)	0.0091 (11)	0.0047 (10)
C6	0.0598 (17)	0.0355 (13)	0.0526 (17)	0.0019 (12)	0.0124 (14)	0.0173 (13)
O1	0.0380 (9)	0.0546 (10)	0.0278 (8)	0.0050 (8)	0.0042 (7)	0.0055 (8)
O2	0.0501 (10)	0.0280 (8)	0.0228 (7)	−0.0023 (7)	−0.0088 (7)	0.0007 (6)
O3	0.0403 (9)	0.0442 (9)	0.0174 (7)	−0.0029 (7)	0.0011 (6)	0.0016 (7)
O4	0.0390 (9)	0.0369 (9)	0.0343 (9)	−0.0044 (7)	0.0035 (7)	0.0001 (7)
O5	0.0550 (12)	0.0410 (10)	0.0606 (13)	0.0091 (9)	0.0166 (10)	0.0154 (9)
O6	0.0734 (13)	0.0437 (10)	0.0566 (13)	0.0090 (10)	0.0162 (12)	0.0237 (10)
C7	0.0403 (13)	0.0397 (13)	0.0269 (11)	0.0011 (10)	0.0059 (10)	0.0042 (10)
O8	0.0432 (10)	0.0476 (10)	0.0319 (9)	0.0031 (8)	0.0084 (7)	0.0024 (8)
C8	0.0410 (13)	0.0407 (13)	0.0250 (11)	−0.0021 (10)	0.0054 (10)	0.0018 (10)
C9	0.0471 (15)	0.0496 (15)	0.0335 (12)	−0.0063 (12)	0.0070 (11)	0.0057 (12)
C10	0.0611 (17)	0.0499 (15)	0.0320 (13)	0.0003 (13)	0.0107 (12)	−0.0074 (12)
C11	0.0686 (19)	0.0385 (14)	0.0458 (15)	0.0130 (13)	0.0028 (14)	0.0082 (12)
C12	0.120 (3)	0.0417 (17)	0.080 (3)	0.0111 (19)	0.011 (2)	−0.0076 (18)
C13	0.078 (2)	0.103 (3)	0.057 (2)	0.011 (2)	−0.0075 (19)	0.011 (2)

Geometric parameters (Å, º) top

C1—C2	1.513 (3)	O6—C11	1.430 (4)
C1—O1	1.208 (3)	C7—O8	1.426 (3)
C1—O4	1.348 (3)	C7—H71	0.972
C2—C3	1.519 (3)	C7—H72	0.974
C2—O2	1.400 (3)	O8—C8	1.413 (3)
C2—H21	0.976	C8—C9	1.526 (4)
C3—C4	1.538 (3)	C8—C10	1.510 (4)
C3—O3	1.436 (2)	C9—H91	0.974
C3—C7	1.522 (4)	C9—H92	0.971
C4—C5	1.506 (4)	C9—H93	0.987
C4—O4	1.482 (3)	C10—H101	0.963
C4—H41	0.968	C10—H102	0.970
C5—C6	1.527 (4)	C10—H103	0.984
C5—O5	1.430 (3)	C11—C12	1.499 (5)
C5—H51	0.986	C11—C13	1.497 (5)
C6—O6	1.422 (4)	C12—H121	0.972
C6—H61	0.975	C12—H122	0.965
C6—H62	0.985	C12—H123	0.970
O2—H1	0.803	C13—H131	0.972
O3—C8	1.444 (3)	C13—H132	0.972
O5—C11	1.441 (3)	C13—H133	0.964

C2—C1—O1	128.7 (2)	C3—C7—H72	112.0
C2—C1—O4	109.39 (19)	O8—C7—H72	110.4
O1—C1—O4	121.9 (2)	H71—C7—H72	110.5
C1—C2—C3	101.88 (18)	C7—O8—C8	106.66 (18)
C1—C2—O2	113.35 (18)	O3—C8—O8	105.54 (17)
C3—C2—O2	115.11 (18)	O3—C8—C9	108.4 (2)
C1—C2—H21	109.2	O8—C8—C9	111.4 (2)
C3—C2—H21	108.2	O3—C8—C10	109.5 (2)
O2—C2—H21	108.8	O8—C8—C10	108.3 (2)
C2—C3—C4	101.08 (18)	C9—C8—C10	113.4 (2)
C2—C3—O3	108.02 (18)	C8—C9—H91	110.9
C4—C3—O3	108.96 (19)	C8—C9—H92	110.4
C2—C3—C7	117.0 (2)	H91—C9—H92	107.3
C4—C3—C7	117.86 (19)	C8—C9—H93	109.7
O3—C3—C7	103.63 (18)	H91—C9—H93	109.9
C3—C4—C5	116.7 (2)	H92—C9—H93	108.6
C3—C4—O4	103.00 (18)	C8—C10—H101	108.4
C5—C4—O4	106.95 (19)	C8—C10—H102	110.7
C3—C4—H41	110.8	H101—C10—H102	109.1
C5—C4—H41	108.2	C8—C10—H103	109.1
O4—C4—H41	111.1	H101—C10—H103	109.7
C4—C5—C6	113.3 (2)	H102—C10—H103	109.8
C4—C5—O5	109.1 (2)	O5—C11—O6	105.7 (2)
C6—C5—O5	102.86 (19)	O5—C11—C12	108.6 (3)
C4—C5—H51	109.5	O6—C11—C12	109.9 (3)
C6—C5—H51	109.4	O5—C11—C13	109.7 (3)
O5—C5—H51	112.6	O6—C11—C13	108.2 (3)
C5—C6—O6	101.9 (2)	C12—C11—C13	114.4 (3)
C5—C6—H61	112.6	C11—C12—H121	109.1
O6—C6—H61	111.2	C11—C12—H122	108.5
C5—C6—H62	110.7	H121—C12—H122	108.8
O6—C6—H62	111.0	C11—C12—H123	110.0
H61—C6—H62	109.3	H121—C12—H123	110.4
C2—O2—H1	109.9	H122—C12—H123	110.1
C3—O3—C8	108.84 (18)	C11—C13—H131	110.5
C4—O4—C1	110.04 (17)	C11—C13—H132	109.1
C5—O5—C11	108.8 (2)	H131—C13—H132	109.8
C6—O6—C11	106.9 (2)	C11—C13—H133	109.8
C3—C7—O8	102.68 (19)	H131—C13—H133	109.0
C3—C7—H71	110.1	H132—C13—H133	108.5
O8—C7—H71	110.9

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
O2—H1···O2ⁱ	0.80	1.91	2.679 (2)	160

Symmetry code: (i) −y+1, x, z+1/4.

Acknowledgements

Financial support [to MS] provided through the European Community's Human Potential Programme under contract HPRN-CT-2002–00173 is gratefully acknowledged.

References

Altomare, A., Cascarano, G., Giacovazzo, G., Guagliardi, A., Burla, M. C., Polidori, G. & Camalli, M. (1994). J. Appl. Cryst. 27, 435. CrossRef Web of Science IUCr Journals Google Scholar
Betteridge, P. W., Carruthers, J. R., Cooper, R. I., Prout, K. & Watkin, D. J. (2003). J. Appl. Cryst. 36, 1487. Web of Science CrossRef IUCr Journals Google Scholar
Bols, M. (1996). Carbohydrate Building Blocks. New York: John Wiley & Sons. Google Scholar
Bream, R., Watkin, D., Soengas, R., Eastwick-Field, V. & Fleet, G. W. J. (2006). Acta Cryst. E62, o977–o979. CSD CrossRef IUCr Journals Google Scholar
Hotchkiss, D. J., Jenkinson, S. F., Storer, R., Heinz, T. & Fleet, G. W. J. (2006). Tetrahedron Lett. 47, 315–318. Web of Science CrossRef CAS Google Scholar
Hotchkiss, D. J., Soengas, R., Simone, M. I., van Ameijde, J., Hunter, S., Cowley, A. R. & Fleet, G. W. J. (2004). Tetrahedron Lett. 45, 9461–9464. Web of Science CrossRef CAS Google Scholar
Lichtenthaler, F. W. & Peters, S. (2004). C. R. Chim. 7, 65–90. Web of Science CrossRef CAS Google Scholar
Nonius (2001). COLLECT. Nonius BV, Delft, The Netherlands. Google Scholar
Otwinowski, Z. & Minor, W. (1997). Methods in Enzymology, Vol. 276, Macromolecular Crystallography, Part A, edited by C. W. Carter Jr and R. M. Sweet, pp. 307–326. New York: Academic Press. Google Scholar
Parker, S. G., Watkin, D. J., Simone, M. I. & Fleet, G. W. J. (2006). Acta Cryst. E62, o3961–o3963. Web of Science CSD CrossRef IUCr Journals Google Scholar
Prince, E. (1982). Mathematical Techniques in Crystallography and Materials Science. New York: Springer-Verlag. Google Scholar
Simone, M. I., Soengas, R., Newton, C. R., Watkin, D. J. & Fleet, G. W. J. (2005). Tetrahedron Lett. 46, 5761–5765. Web of Science CSD CrossRef CAS Google Scholar
Soengas, R., Izumori, K., Simone, M. I., Watkin, D. J., Skytte, U. P., Soetaert, W. & Fleet, G. W. J. (2005). Tetrahedron Lett. 46, 5755–5759. Web of Science CrossRef CAS Google Scholar
Watkin, D. (1994). Acta Cryst. A50, 411–437. CrossRef CAS Web of Science IUCr Journals Google Scholar
Watkin, D. J., Prout, C. K. & Pearce, L. J. (1996). CAMERON. Chemical Crystallography Laboratory, Oxford, England. Google Scholar

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