N′-Cyclo­dodecyl­idene­pyridine-4-carbohydrazide

Lemmerer, A.; Bernstein, J.; Kahlenberg, V.

doi:10.1107/S1600536812011774

organic compounds

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ISSN: 2056-9890

Volume 68| Part 4| April 2012| Page o1205

doi:10.1107/S1600536812011774

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N′-Cyclododecylidenepyridine-4-carbohydrazide

Andreas Lemmerer,^a ^* Joel Bernstein ^b and Volker Kahlenberg ^c

^aMolecular Sciences Institute, School of Chemistry, University of the Witwatersrand, Johannesburg, PO Wits 2050, South Africa, ^bFaculty of Science, NYU Abu Dhabi, PO Box 129188, Abu Dhabi, United Arab Emirates, and ^cInstitute of Mineralogy and Petrography, University of Innsbruck, Innsbruck 6020, Austria
^*Correspondence e-mail: andreas.lemmerer@wits.ac.za

(Received 7 March 2012; accepted 19 March 2012; online 28 March 2012)

The title compound, C₁₈H₂₇N₃O, is a derivative of the antituberculosis drug isoniazid (systematic name: pyridine-4-carbohydrazidei). The crystal structure consists of repeating C(4) chains along the b axis, formed by N—H⋯O hydrogen bonds with adjacent amide functional groups that are related by a b-glide plane. The cyclododecyl ring has the same approximately `square' conformation, as seen in the parent hydrocarbon cyclododecane.

Related literature

For hydrogen-bonding motifs, see: Bernstein et al. (1995 ). For cycloalkane ring conformations, see: Dale (1966 ).

Experimental

Crystal data

C₁₈H₂₇N₃O
M_r = 301.43
Orthorhombic, P b c a
a = 14.8450 (6) Å
b = 8.0980 (4) Å
c = 27.3910 (11) Å
V = 3292.8 (2) Å³
Z = 8
Cu Kα radiation
μ = 0.60 mm⁻¹
T = 100 K
0.44 × 0.34 × 0.2 mm

Data collection

Oxford Diffraction Xcalibur Ruby Gemini ultra diffractometer
Absorption correction: multi-scan (CrysAlis PRO; Oxford Diffraction, 2006 $[Oxford Diffraction (2006). CrysAlis PRO. Oxford Diffraction Ltd, Abingdon, England.]$ ) T_min = 0.779, T_max = 0.890
23848 measured reflections
2931 independent reflections
2535 reflections with I > 2σ(I)
R_int = 0.048

Refinement

R[F² > 2σ(F²)] = 0.040
wR(F²) = 0.111
S = 1.08
2931 reflections
203 parameters
H atoms treated by a mixture of independent and constrained refinement
Δρ_max = 0.17 e Å⁻³
Δρ_min = −0.20 e Å⁻³

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
N1—H1⋯O1ⁱ	0.88 (2)	2.15 (2)	3.0122 (15)	164.7 (16)
Symmetry code: (i) $[-x+{\script{3\over 2}}, y+{\script{1\over 2}}, z]$ .

Data collection: CrysAlis PRO (Oxford Diffraction, 2006 $[Oxford Diffraction (2006). CrysAlis PRO. Oxford Diffraction Ltd, Abingdon, England.]$ ); cell refinement: CrysAlis PRO; data reduction: CrysAlis PRO; program(s) used to solve structure: SHELXS97 (Sheldrick, 2008 ); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ORTEP-3 for Windows (Farrugia, 1997 ) and DIAMOND (Brandenburg, 1999 ); software used to prepare material for publication: WinGX (Farrugia, 1999 ) and PLATON (Spek, 2009 ).

Supporting information

Crystal structure: contains datablocks global, I. DOI: 10.1107/S1600536812011774/fj2532sup1.cif

Supporting information file. DOI: 10.1107/S1600536812011774/fj2532Isup2.mol

Structure factors: contains datablock I. DOI: 10.1107/S1600536812011774/fj2532Isup3.hkl

Supporting information file. DOI: 10.1107/S1600536812011774/fj2532Isup4.cml

checkCIF report

Comment top

Fig. 1 shows the atomic numbering scheme of the title compound. The amide functional groups form a torsion angle of 38.54 (17)° with the pyridine ring. Fig. 2 shows the C(4) (Bernstein et al., 1995) hydrogen bonded ring formed with adjacent amide functional groups, leading to a chain along the b-axis. The cyclododecyl ring has a square conformation, as seen in the related cycloalkane C₁₂H₂₄ ring (Dale, 1966).

Related literature top

For hydrogen-bonding motifs, see: Bernstein et al. (1995). For cycloalkane ring conformations, see: Dale (1966).

Experimental top

A stoichiometric amount in the ratio of 1:1 of isonicotinic acid hydrazide to cyclododecanone was dissolved in 5 ml of methanol. The solution was refluxed for a few hours, and left to cool to room temperature. Colourless, block-like crystals were harvested after slow evaporation over a few days at ambient conditions.

Structure description top

For hydrogen-bonding motifs, see: Bernstein et al. (1995). For cycloalkane ring conformations, see: Dale (1966).

Computing details top

Data collection: CrysAlis PRO (Oxford Diffraction, 2006); cell refinement: CrysAlis PRO (Oxford Diffraction, 2006); data reduction: CrysAlis PRO (Oxford Diffraction, 2006); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ORTEP-3 for Windows (Farrugia, 1997) and DIAMOND (Brandenburg, 1999); software used to prepare material for publication: WinGX (Farrugia, 1999) and PLATON (Spek, 2009).

Figures top

	Fig. 1. The asymmetric unit of (I) showing the atomic numbering scheme. Displacement ellipsoids are shown at the 50% probability level.
	Fig. 2. Hydrogen bonding chain showing the C(4) hydrogen bonded chains. Intermolecular N—H···O hydrogen bonds are shown as dashed red lines.

N'-Cyclododecylidenepyridine-4-carbohydrazide top

Crystal data top

C₁₈H₂₇N₃O	F(000) = 1312
M_r = 301.43	D_x = 1.216 Mg m⁻³
Orthorhombic, Pbca	Cu Kα radiation, λ = 1.5418 Å
Hall symbol: -P 2ac 2ab	Cell parameters from 9464 reflections
a = 14.8450 (6) Å	θ = 3.0–67.5°
b = 8.0980 (4) Å	µ = 0.60 mm⁻¹
c = 27.3910 (11) Å	T = 100 K
V = 3292.8 (2) Å³	Block, colourless
Z = 8	0.44 × 0.34 × 0.2 mm

Data collection top

Oxford Diffraction Xcalibur Ruby Gemini ultra diffractometer	2535 reflections with I > 2σ(I)
ω scans	R_int = 0.048
Absorption correction: multi-scan (CrysAlis PRO; Oxford Diffraction, 2006)	θ_max = 67.0°, θ_min = 3.2°
T_min = 0.779, T_max = 0.890	h = −17→16
23848 measured reflections	k = −9→9
2931 independent reflections	l = −32→32

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	H atoms treated by a mixture of independent and constrained refinement
R[F² > 2σ(F²)] = 0.040	w = 1/[σ²(F_o²) + (0.0722P)² + 0.6785P] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.111	(Δ/σ)_max = 0.001
S = 1.08	Δρ_max = 0.17 e Å⁻³
2931 reflections	Δρ_min = −0.20 e Å⁻³
203 parameters

Crystal data top

C₁₈H₂₇N₃O	V = 3292.8 (2) Å³
M_r = 301.43	Z = 8
Orthorhombic, Pbca	Cu Kα radiation
a = 14.8450 (6) Å	µ = 0.60 mm⁻¹
b = 8.0980 (4) Å	T = 100 K
c = 27.3910 (11) Å	0.44 × 0.34 × 0.2 mm

Data collection top

Oxford Diffraction Xcalibur Ruby Gemini ultra diffractometer	2931 independent reflections
Absorption correction: multi-scan (CrysAlis PRO; Oxford Diffraction, 2006)	2535 reflections with I > 2σ(I)
T_min = 0.779, T_max = 0.890	R_int = 0.048
23848 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.040	0 restraints
wR(F²) = 0.111	H atoms treated by a mixture of independent and constrained refinement
S = 1.08	Δρ_max = 0.17 e Å⁻³
2931 reflections	Δρ_min = −0.20 e Å⁻³
203 parameters

Special details top

Experimental. Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm in CrysAlisPro.

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.

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

	x	y	z	U_iso*/U_eq
C1	0.83538 (9)	0.67344 (15)	0.71252 (5)	0.0140 (3)
C2	0.77610 (9)	0.76355 (16)	0.74142 (5)	0.0151 (3)
H2	0.713	0.7447	0.7397	0.018*
C3	0.81105 (9)	0.88164 (16)	0.77286 (5)	0.0171 (3)
H3	0.7701	0.9417	0.7927	0.02*
C4	0.95549 (9)	0.82425 (17)	0.74991 (5)	0.0185 (3)
H4	1.0183	0.8447	0.7527	0.022*
C5	0.92753 (9)	0.70136 (16)	0.71813 (5)	0.0157 (3)
H5	0.9702	0.6374	0.7005	0.019*
C6	0.80631 (9)	0.54546 (16)	0.67606 (4)	0.0131 (3)
C7	0.65632 (8)	0.52936 (16)	0.57794 (5)	0.0144 (3)
C8	0.61244 (9)	0.69684 (16)	0.57370 (5)	0.0160 (3)
H8A	0.6251	0.7436	0.541	0.019*
H8B	0.6386	0.7721	0.5984	0.019*
C9	0.50972 (9)	0.68614 (17)	0.58126 (5)	0.0179 (3)
H9A	0.4828	0.7957	0.5746	0.022*
H9B	0.4843	0.607	0.5574	0.022*
C10	0.48338 (9)	0.63169 (18)	0.63275 (5)	0.0208 (3)
H10A	0.5026	0.7177	0.6562	0.025*
H10B	0.5163	0.5289	0.6408	0.025*
C11	0.38197 (9)	0.60107 (18)	0.63905 (5)	0.0221 (3)
H11A	0.3691	0.5856	0.6742	0.027*
H11B	0.349	0.7008	0.6281	0.027*
C12	0.34546 (9)	0.45158 (17)	0.61105 (5)	0.0202 (3)
H12A	0.2788	0.4539	0.6123	0.024*
H12B	0.3636	0.4613	0.5764	0.024*
C13	0.37813 (10)	0.28492 (17)	0.63069 (5)	0.0219 (3)
H13A	0.4364	0.3016	0.6475	0.026*
H13B	0.3343	0.2447	0.6552	0.026*
C14	0.39013 (10)	0.15214 (17)	0.59157 (6)	0.0224 (3)
H14A	0.3336	0.1432	0.5726	0.027*
H14B	0.4004	0.0446	0.6078	0.027*
C15	0.46814 (9)	0.18511 (17)	0.55621 (5)	0.0190 (3)
H15A	0.4653	0.1034	0.5294	0.023*
H15B	0.4601	0.2961	0.5417	0.023*
C16	0.56119 (9)	0.17631 (16)	0.57975 (5)	0.0178 (3)
H16A	0.5722	0.0615	0.5906	0.021*
H16B	0.5615	0.2476	0.6091	0.021*
C17	0.63832 (9)	0.22928 (17)	0.54617 (5)	0.0178 (3)
H17A	0.6962	0.1979	0.5615	0.021*
H17B	0.6333	0.1683	0.515	0.021*
C18	0.63976 (9)	0.41420 (17)	0.53531 (5)	0.0168 (3)
H18A	0.687	0.4349	0.5105	0.02*
H18B	0.5813	0.4443	0.5204	0.02*
N1	0.73263 (7)	0.58502 (14)	0.64919 (4)	0.0148 (3)
H1	0.7106 (12)	0.686 (2)	0.6498 (6)	0.024 (4)*
N2	0.89901 (8)	0.91633 (14)	0.77697 (4)	0.0191 (3)
N3	0.70898 (7)	0.47642 (14)	0.61174 (4)	0.0148 (3)
O1	0.84951 (6)	0.41677 (11)	0.67137 (3)	0.0159 (2)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
C1	0.0179 (6)	0.0130 (6)	0.0113 (6)	0.0000 (5)	−0.0025 (5)	0.0028 (5)
C2	0.0164 (6)	0.0153 (6)	0.0136 (6)	0.0009 (5)	−0.0012 (5)	0.0028 (5)
C3	0.0202 (7)	0.0163 (6)	0.0147 (6)	0.0022 (5)	−0.0002 (5)	0.0004 (5)
C4	0.0180 (6)	0.0203 (7)	0.0171 (6)	−0.0029 (5)	−0.0012 (5)	0.0013 (5)
C5	0.0174 (7)	0.0160 (6)	0.0136 (6)	−0.0001 (5)	0.0007 (5)	0.0018 (5)
C6	0.0146 (6)	0.0135 (6)	0.0113 (6)	−0.0011 (5)	0.0014 (5)	0.0015 (5)
C7	0.0128 (6)	0.0164 (7)	0.0141 (6)	−0.0024 (5)	0.0012 (5)	−0.0004 (5)
C8	0.0169 (7)	0.0164 (6)	0.0146 (6)	−0.0010 (5)	−0.0031 (5)	0.0005 (5)
C9	0.0166 (7)	0.0182 (7)	0.0190 (7)	0.0013 (5)	−0.0023 (5)	−0.0009 (5)
C10	0.0189 (7)	0.0257 (7)	0.0178 (7)	−0.0006 (6)	0.0011 (5)	−0.0046 (6)
C11	0.0189 (7)	0.0247 (7)	0.0227 (7)	0.0018 (6)	0.0041 (6)	−0.0035 (6)
C12	0.0160 (6)	0.0228 (7)	0.0220 (7)	0.0016 (5)	0.0001 (5)	−0.0004 (6)
C13	0.0215 (7)	0.0240 (7)	0.0201 (7)	0.0010 (6)	0.0031 (6)	0.0033 (6)
C14	0.0208 (7)	0.0186 (7)	0.0278 (8)	−0.0017 (5)	0.0007 (6)	0.0002 (6)
C15	0.0200 (7)	0.0179 (7)	0.0192 (7)	−0.0008 (5)	−0.0015 (5)	−0.0034 (5)
C16	0.0203 (7)	0.0141 (6)	0.0192 (7)	0.0007 (5)	−0.0027 (5)	0.0002 (5)
C17	0.0174 (6)	0.0182 (7)	0.0177 (7)	0.0016 (5)	−0.0028 (5)	−0.0048 (5)
C18	0.0172 (6)	0.0197 (7)	0.0134 (6)	−0.0012 (5)	−0.0008 (5)	−0.0018 (5)
N1	0.0168 (5)	0.0131 (6)	0.0145 (5)	0.0014 (4)	−0.0039 (4)	−0.0029 (4)
N2	0.0234 (6)	0.0178 (6)	0.0161 (6)	−0.0027 (5)	−0.0025 (5)	−0.0003 (4)
N3	0.0159 (5)	0.0157 (5)	0.0127 (5)	−0.0020 (4)	−0.0007 (4)	−0.0027 (4)
O1	0.0165 (5)	0.0145 (5)	0.0166 (5)	0.0011 (3)	0.0001 (4)	−0.0001 (4)

Geometric parameters (Å, º) top

C1—C2	1.3905 (19)	C11—C12	1.532 (2)
C1—C5	1.3950 (18)	C11—H11A	0.99
C1—C6	1.5026 (17)	C11—H11B	0.99
C2—C3	1.3875 (19)	C12—C13	1.5317 (19)
C2—H2	0.95	C12—H12A	0.99
C3—N2	1.3404 (18)	C12—H12B	0.99
C3—H3	0.95	C13—C14	1.529 (2)
C4—N2	1.3447 (19)	C13—H13A	0.99
C4—C5	1.3857 (19)	C13—H13B	0.99
C4—H4	0.95	C14—C15	1.533 (2)
C5—H5	0.95	C14—H14A	0.99
C6—O1	1.2304 (16)	C14—H14B	0.99
C6—N1	1.3567 (17)	C15—C16	1.5262 (18)
C7—N3	1.2853 (17)	C15—H15A	0.99
C7—C8	1.5091 (18)	C15—H15B	0.99
C7—C18	1.5144 (18)	C16—C17	1.5301 (19)
C8—C9	1.5414 (18)	C16—H16A	0.99
C8—H8A	0.99	C16—H16B	0.99
C8—H8B	0.99	C17—C18	1.5268 (19)
C9—C10	1.5286 (19)	C17—H17A	0.99
C9—H9A	0.99	C17—H17B	0.99
C9—H9B	0.99	C18—H18A	0.99
C10—C11	1.5354 (19)	C18—H18B	0.99
C10—H10A	0.99	N1—N3	1.3961 (15)
C10—H10B	0.99	N1—H1	0.88 (2)

C2—C1—C5	118.21 (12)	C13—C12—H12A	108.7
C2—C1—C6	123.96 (12)	C11—C12—H12A	108.7
C5—C1—C6	117.82 (12)	C13—C12—H12B	108.7
C3—C2—C1	118.59 (12)	C11—C12—H12B	108.7
C3—C2—H2	120.7	H12A—C12—H12B	107.6
C1—C2—H2	120.7	C14—C13—C12	114.23 (12)
N2—C3—C2	124.11 (12)	C14—C13—H13A	108.7
N2—C3—H3	117.9	C12—C13—H13A	108.7
C2—C3—H3	117.9	C14—C13—H13B	108.7
N2—C4—C5	123.89 (13)	C12—C13—H13B	108.7
N2—C4—H4	118.1	H13A—C13—H13B	107.6
C5—C4—H4	118.1	C13—C14—C15	114.11 (11)
C4—C5—C1	118.65 (12)	C13—C14—H14A	108.7
C4—C5—H5	120.7	C15—C14—H14A	108.7
C1—C5—H5	120.7	C13—C14—H14B	108.7
O1—C6—N1	124.31 (12)	C15—C14—H14B	108.7
O1—C6—C1	120.26 (11)	H14A—C14—H14B	107.6
N1—C6—C1	115.42 (11)	C16—C15—C14	114.11 (12)
N3—C7—C8	128.15 (12)	C16—C15—H15A	108.7
N3—C7—C18	116.66 (12)	C14—C15—H15A	108.7
C8—C7—C18	115.09 (11)	C16—C15—H15B	108.7
C7—C8—C9	111.48 (11)	C14—C15—H15B	108.7
C7—C8—H8A	109.3	H15A—C15—H15B	107.6
C9—C8—H8A	109.3	C15—C16—C17	114.22 (11)
C7—C8—H8B	109.3	C15—C16—H16A	108.7
C9—C8—H8B	109.3	C17—C16—H16A	108.7
H8A—C8—H8B	108	C15—C16—H16B	108.7
C10—C9—C8	113.16 (11)	C17—C16—H16B	108.7
C10—C9—H9A	108.9	H16A—C16—H16B	107.6
C8—C9—H9A	108.9	C18—C17—C16	113.74 (11)
C10—C9—H9B	108.9	C18—C17—H17A	108.8
C8—C9—H9B	108.9	C16—C17—H17A	108.8
H9A—C9—H9B	107.8	C18—C17—H17B	108.8
C9—C10—C11	113.64 (12)	C16—C17—H17B	108.8
C9—C10—H10A	108.8	H17A—C17—H17B	107.7
C11—C10—H10A	108.8	C7—C18—C17	117.13 (11)
C9—C10—H10B	108.8	C7—C18—H18A	108
C11—C10—H10B	108.8	C17—C18—H18A	108
H10A—C10—H10B	107.7	C7—C18—H18B	108
C12—C11—C10	114.72 (11)	C17—C18—H18B	108
C12—C11—H11A	108.6	H18A—C18—H18B	107.3
C10—C11—H11A	108.6	C6—N1—N3	116.91 (11)
C12—C11—H11B	108.6	C6—N1—H1	120.5 (12)
C10—C11—H11B	108.6	N3—N1—H1	120.4 (12)
H11A—C11—H11B	107.6	C3—N2—C4	116.42 (12)
C13—C12—C11	114.10 (12)	C7—N3—N1	118.17 (11)

C5—C1—C2—C3	2.74 (18)	C11—C12—C13—C14	−146.98 (12)
C6—C1—C2—C3	−178.29 (12)	C12—C13—C14—C15	68.58 (16)
C1—C2—C3—N2	0.7 (2)	C13—C14—C15—C16	67.05 (16)
N2—C4—C5—C1	1.9 (2)	C14—C15—C16—C17	−173.04 (11)
C2—C1—C5—C4	−3.94 (18)	C15—C16—C17—C18	70.36 (15)
C6—C1—C5—C4	177.03 (11)	N3—C7—C18—C17	33.46 (17)
C2—C1—C6—O1	−140.43 (13)	C8—C7—C18—C17	−149.87 (11)
C5—C1—C6—O1	38.54 (17)	C16—C17—C18—C7	64.33 (15)
C2—C1—C6—N1	41.05 (17)	O1—C6—N1—N3	−4.55 (19)
C5—C1—C6—N1	−139.98 (12)	C1—C6—N1—N3	173.91 (10)
N3—C7—C8—C9	−110.81 (15)	C2—C3—N2—C4	−2.77 (19)
C18—C7—C8—C9	72.97 (14)	C5—C4—N2—C3	1.44 (19)
C7—C8—C9—C10	64.83 (15)	C8—C7—N3—N1	−2.22 (19)
C8—C9—C10—C11	−173.28 (11)	C18—C7—N3—N1	173.95 (11)
C9—C10—C11—C12	68.04 (16)	C6—N1—N3—C7	−161.67 (12)
C10—C11—C12—C13	68.83 (16)

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
N1—H1···O1ⁱ	0.88 (2)	2.15 (2)	3.0122 (15)	164.7 (16)

Symmetry code: (i) −x+3/2, y+1/2, z.

Experimental details

Crystal data
Chemical formula	C₁₈H₂₇N₃O
M_r	301.43
Crystal system, space group	Orthorhombic, Pbca
Temperature (K)	100
a, b, c (Å)	14.8450 (6), 8.0980 (4), 27.3910 (11)
V (Å³)	3292.8 (2)
Z	8
Radiation type	Cu Kα
µ (mm⁻¹)	0.60
Crystal size (mm)	0.44 × 0.34 × 0.2

Data collection
Diffractometer	Oxford Diffraction Xcalibur Ruby Gemini ultra
Absorption correction	Multi-scan (CrysAlis PRO; Oxford Diffraction, 2006)
T_min, T_max	0.779, 0.890
No. of measured, independent and observed [I > 2σ(I)] reflections	23848, 2931, 2535
R_int	0.048
(sin θ/λ)_max (Å⁻¹)	0.597

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.040, 0.111, 1.08
No. of reflections	2931
No. of parameters	203
H-atom treatment	H atoms treated by a mixture of independent and constrained refinement
Δρ_max, Δρ_min (e Å⁻³)	0.17, −0.20

Computer programs: CrysAlis PRO (Oxford Diffraction, 2006), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), ORTEP-3 for Windows (Farrugia, 1997) and DIAMOND (Brandenburg, 1999), WinGX (Farrugia, 1999) and PLATON (Spek, 2009).

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
N1—H1···O1ⁱ	0.88 (2)	2.15 (2)	3.0122 (15)	164.7 (16)

Symmetry code: (i) −x+3/2, y+1/2, z.

Acknowledgements

This work was supported in part by grant No. 2004118 from the United States–Israel Binational Science Foundation (Jerusalem). AL thanks the South African National Research Foundation for a postdoctoral scholarship (SFP2007070400002) and the Oppenheimer Memorial Trust for financial support, and the Molecular Sciences Institute for infrastucture support.

References

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