2,4-Diamino-6-methyl-1,3,5-triazine ethanol solvate

Xiao, Z.-H.

doi:10.1107/S1600536808000159

organic compounds

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ISSN: 2056-9890

Volume 64| Part 2| February 2008| Page o411

doi:10.1107/S1600536808000159

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2,4-Diamino-6-methyl-1,3,5-triazine ethanol solvate

Zun-Hong Xiao ^a ^*

^aSchool of Physics and Chemistry Science, Guizhou Normal University, Guiyang, 550001, People's Republic of China.
^*Correspondence e-mail: xzh729@126.com

(Received 23 December 2007; accepted 2 January 2008; online 9 January 2008)

The crystal structure of the title compound, C₄H₇N₅·C₂H₆O, is determined by extensive hydrogen bonding. A sequence of dimeric associations, formed by N—H(amino)⋯N(ring), connects the triazine rings into a molecular tape. Molecules are linked into a supramolecular structure by N—H⋯O and O—H⋯O hydrogen bonds. The asymmetric unit consists of two formula units.

Related literature

For general background, see: Sebenik et al. (1989 ); Tashiro & Oiwa (1981 ).

Experimental

Crystal data

C₄H₇N₅·C₂H₆O
M_r = 171.21
Triclinic, $[P \overline 1]$
a = 8.3860 (6) Å
b = 9.1514 (6) Å
c = 11.9104 (9) Å
α = 88.703 (1)°
β = 87.614 (2)°
γ = 76.668 (2)°
V = 888.56 (11) Å³
Z = 4
Mo Kα radiation
μ = 0.09 mm⁻¹
T = 273 (2) K
0.34 × 0.26 × 0.21 mm

Data collection

Bruker SMART CCD area-detector diffractometer
Absorption correction: multi-scan (SADABS; Bruker, 2005 ) T_min = 0.975, T_max = 0.985
7627 measured reflections
3111 independent reflections
2619 reflections with I > 2σ(I)
R_int = 0.017

Refinement

R[F² > 2σ(F²)] = 0.042
wR(F²) = 0.118
S = 1.07
3111 reflections
223 parameters
H-atom parameters constrained
Δρ_max = 0.25 e Å⁻³
Δρ_min = −0.19 e Å⁻³

Table 1
Hydrogen-bond geometry (Å, °)

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
N4—H4B⋯N7ⁱ	0.86	2.11	2.9666 (18)	171
N5—H5D⋯N8ⁱⁱ	0.86	2.19	3.0132 (19)	159
N5—H5E⋯O2ⁱⁱⁱ	0.86	2.29	3.0071 (19)	142
N10—H10A⋯O2^iv	0.86	2.10	2.9337 (18)	163
O2—H2⋯O1^v	0.82	1.90	2.7185 (18)	174
Symmetry codes: (i) x-1, y, z; (ii) x, y-1, z; (iii) -x+1, -y, -z+1; (iv) -x+1, -y+1, -z+1; (v) x, y, z+1.

Data collection: SMART (Bruker, 2002 ); cell refinement: SAINT (Bruker, 2002); data reduction: SAINT; 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 ); software used to prepare material for publication: WinGX (Farrugia, 1999 ).

Supporting information

Crystal structure: contains datablocks global, I. DOI: 10.1107/S1600536808000159/bq2061sup1.cif

Structure factors: contains datablock I. DOI: 10.1107/S1600536808000159/bq2061Isup2.hkl

checkCIF report

Comment top

Triazine compounds are used in pharmaceutical industry as coupling agents for the synthesis of peptides and as side chain of antibiotics, as well as in formulating bactericides and fungicides. 2,4-Diamino-6-methyl-1,3,5-triazine (acetoguanamine) is used as an intermediate for pharmaceuticals and as a modifier and flexibilizer of formaldehyde resins (Sebenik et al., 1989, Tashiro et al., 1981).

The crystal structure of the title compound (Fig. 1) consists of triazine and solvate ethanol molecule. The amino groups are coplanar with the ring plane, the dihedral angle between the triazine ring (C2,N2,C4,N1,C3,N3) and the ring (C8,N7,C9,N8,C10,N6) is 12.73 (7)°. A lot of hydrogen bonds are observed (Table 1), each NH₂ group acts as a donor in hydrogen bond with the ring nitrogen atoms of neighboring molecules, these contacts and the cross-linking interactions stabilize the crystal packing.

Related literature top

For general background, see: Sebenik et al. (1989); Tashiro & Oiwa (1981).

Experimental top

2,4-diamino-6-methyl-1,3,5-triazine (0.625 g, 0.05 mol) was added to a stirred solvent of ethanol (100 ml) at 50°C for 3 h. After cooling to room temperature, the mixture was filtered. The filtrate was set aside for one week to obtain colorless crystals.

Computing details top

Data collection: SMART (Bruker, 2002); cell refinement: SAINT (Bruker, 2002); data reduction: SAINT (Bruker, 2002); 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); software used to prepare material for publication: WinGX (Farrugia, 1999).

Figures top

Fig. 1. The molecular structure of (I) showing the atom-labeling scheme. Displacement ellipsoids are drawn at the 50% probability level.

2,4-Diamino-6-methyl-1,3,5-triazine ethanol solvate top

Crystal data top

C₄H₇N₅·C₂H₆O	Z = 4
M_r = 171.21	F(000) = 368.0
Triclinic, P1	D_x = 1.280 Mg m⁻³
Hall symbol: -P 1	Mo Kα radiation, λ = 0.71073 Å
a = 8.3860 (6) Å	Cell parameters from 3111 reflections
b = 9.1514 (6) Å	θ = 1.7–25.0°
c = 11.9104 (9) Å	µ = 0.09 mm⁻¹
α = 88.703 (1)°	T = 273 K
β = 87.614 (2)°	Block, colorless
γ = 76.668 (2)°	0.34 × 0.26 × 0.21 mm
V = 888.56 (11) Å³

Data collection top

Bruker CCD area-detector diffractometer	3111 independent reflections
Radiation source: fine-focus sealed tube	2619 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.017
ϕ and ω scans	θ_max = 25.0°, θ_min = 1.7°
Absorption correction: multi-scan (SADABS; Bruker, 2005)	h = −9→9
T_min = 0.975, T_max = 0.985	k = −10→10
7627 measured reflections	l = −12→14

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)] = 0.042	Hydrogen site location: inferred from neighbouring sites
wR(F²) = 0.118	H-atom parameters constrained
S = 1.07	w = 1/[σ²(F_o²) + (0.0597P)² + 0.2811P] where P = (F_o² + 2F_c²)/3
3111 reflections	(Δ/σ)_max < 0.001
223 parameters	Δρ_max = 0.25 e Å⁻³
0 restraints	Δρ_min = −0.19 e Å⁻³

Crystal data top

C₄H₇N₅·C₂H₆O	γ = 76.668 (2)°
M_r = 171.21	V = 888.56 (11) Å³
Triclinic, P1	Z = 4
a = 8.3860 (6) Å	Mo Kα radiation
b = 9.1514 (6) Å	µ = 0.09 mm⁻¹
c = 11.9104 (9) Å	T = 273 K
α = 88.703 (1)°	0.34 × 0.26 × 0.21 mm
β = 87.614 (2)°

Data collection top

Bruker CCD area-detector diffractometer	3111 independent reflections
Absorption correction: multi-scan (SADABS; Bruker, 2005)	2619 reflections with I > 2σ(I)
T_min = 0.975, T_max = 0.985	R_int = 0.017
7627 measured reflections

Refinement top

R[F² > 2σ(F²)] = 0.042	0 restraints
wR(F²) = 0.118	H-atom parameters constrained
S = 1.07	Δρ_max = 0.25 e Å⁻³
3111 reflections	Δρ_min = −0.19 e Å⁻³
223 parameters

Special details top

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 (Å²) top

	x	y	z	U_iso*/U_eq
C1	0.0454 (2)	0.41963 (19)	0.15635 (15)	0.0388 (4)
H1A	−0.0653	0.4778	0.1527	0.058*
H1B	0.0892	0.3946	0.0817	0.058*
H1C	0.1110	0.4770	0.1920	0.058*
C2	0.04756 (19)	0.27874 (17)	0.22268 (13)	0.0290 (4)
C3	−0.07229 (18)	0.14537 (17)	0.34835 (13)	0.0258 (3)
C4	0.18337 (18)	0.04532 (17)	0.27722 (13)	0.0268 (3)
C5	0.6644 (3)	0.2978 (3)	0.0124 (2)	0.0651 (6)
H5A	0.7394	0.2012	0.0089	0.098*
H5B	0.7212	0.3716	0.0348	0.098*
H5C	0.6200	0.3244	−0.0602	0.098*
C6	0.5286 (2)	0.2917 (2)	0.09584 (17)	0.0486 (5)
H6A	0.5730	0.2628	0.1691	0.058*
H6B	0.4548	0.3900	0.1019	0.058*
C7	0.3737 (2)	0.18852 (18)	0.49621 (15)	0.0342 (4)
H7A	0.4172	0.1132	0.4412	0.051*
H7B	0.2683	0.1765	0.5241	0.051*
H7C	0.4469	0.1780	0.5572	0.051*
C8	0.35597 (18)	0.34072 (16)	0.44340 (12)	0.0254 (3)
C9	0.47170 (18)	0.50943 (16)	0.34763 (12)	0.0244 (3)
C10	0.20147 (18)	0.56977 (16)	0.39979 (12)	0.0255 (3)
N1	0.05944 (15)	0.02890 (14)	0.34824 (11)	0.0279 (3)
N2	0.18531 (16)	0.17023 (15)	0.21443 (11)	0.0299 (3)
N3	−0.08554 (15)	0.27267 (14)	0.28518 (11)	0.0284 (3)
N4	−0.20112 (16)	0.13534 (15)	0.41484 (11)	0.0323 (3)
H4A	−0.1984	0.0563	0.4559	0.039*
H4B	−0.2871	0.2079	0.4167	0.039*
N6	0.20797 (15)	0.43256 (14)	0.44771 (11)	0.0273 (3)
N7	0.49186 (15)	0.37128 (13)	0.39648 (10)	0.0268 (3)
N8	0.32886 (15)	0.61343 (14)	0.34805 (11)	0.0274 (3)
N9	0.05530 (15)	0.66659 (15)	0.40412 (12)	0.0336 (3)
H9A	0.0442	0.7546	0.3742	0.040*
H9B	−0.0276	0.6409	0.4368	0.040*
N10	0.60412 (15)	0.54140 (15)	0.29698 (11)	0.0309 (3)
H10A	0.5979	0.6276	0.2650	0.037*
H10B	0.6959	0.4759	0.2962	0.037*
O1	0.44204 (16)	0.18580 (16)	0.06094 (10)	0.0475 (4)
H1	0.3607	0.1897	0.1024	0.071*
C11	0.0989 (3)	0.1326 (3)	0.89654 (19)	0.0599 (6)
H11A	0.1324	0.1124	0.9725	0.090*
H11B	0.0321	0.0655	0.8769	0.090*
H11C	0.0370	0.2344	0.8900	0.090*
C12	0.2460 (2)	0.1100 (2)	0.81971 (17)	0.0495 (5)
H12A	0.3036	0.0053	0.8237	0.059*
H12B	0.2103	0.1310	0.7434	0.059*
N5	0.31467 (16)	−0.06868 (15)	0.26948 (12)	0.0353 (3)
H5D	0.3180	−0.1490	0.3091	0.042*
H5E	0.3961	−0.0619	0.2249	0.042*
O2	0.35702 (16)	0.19983 (16)	0.84251 (11)	0.0461 (3)
H2	0.3769	0.1931	0.9095	0.069*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
C1	0.0392 (10)	0.0326 (9)	0.0423 (10)	−0.0051 (7)	0.0017 (8)	0.0095 (8)
C2	0.0299 (8)	0.0272 (8)	0.0294 (8)	−0.0059 (7)	−0.0023 (6)	0.0018 (6)
C3	0.0241 (8)	0.0242 (8)	0.0282 (8)	−0.0041 (6)	−0.0011 (6)	−0.0001 (6)
C4	0.0250 (8)	0.0267 (8)	0.0281 (8)	−0.0051 (6)	−0.0004 (6)	0.0010 (6)
C5	0.0531 (13)	0.0762 (16)	0.0747 (16)	−0.0344 (12)	0.0045 (11)	0.0046 (12)
C6	0.0485 (11)	0.0488 (11)	0.0516 (12)	−0.0174 (9)	0.0003 (9)	−0.0063 (9)
C7	0.0298 (9)	0.0250 (8)	0.0454 (10)	−0.0028 (7)	0.0032 (7)	0.0040 (7)
C8	0.0248 (8)	0.0233 (8)	0.0269 (8)	−0.0032 (6)	0.0004 (6)	−0.0019 (6)
C9	0.0251 (8)	0.0230 (7)	0.0242 (8)	−0.0037 (6)	0.0001 (6)	−0.0011 (6)
C10	0.0237 (8)	0.0244 (8)	0.0270 (8)	−0.0028 (6)	−0.0012 (6)	−0.0002 (6)
N1	0.0247 (7)	0.0251 (7)	0.0313 (7)	−0.0019 (5)	0.0038 (5)	0.0036 (5)
N2	0.0293 (7)	0.0285 (7)	0.0311 (7)	−0.0062 (6)	0.0035 (5)	0.0031 (6)
N3	0.0257 (7)	0.0258 (7)	0.0321 (7)	−0.0030 (5)	0.0003 (5)	0.0039 (5)
N4	0.0258 (7)	0.0250 (7)	0.0419 (8)	0.0007 (5)	0.0089 (6)	0.0058 (6)
N6	0.0237 (7)	0.0234 (7)	0.0334 (7)	−0.0032 (5)	0.0008 (5)	0.0007 (5)
N7	0.0241 (7)	0.0228 (7)	0.0312 (7)	−0.0013 (5)	0.0016 (5)	0.0015 (5)
N8	0.0251 (7)	0.0239 (7)	0.0309 (7)	−0.0016 (5)	0.0009 (5)	0.0026 (5)
N9	0.0223 (7)	0.0269 (7)	0.0478 (9)	0.0005 (5)	0.0038 (6)	0.0078 (6)
N10	0.0237 (7)	0.0253 (7)	0.0411 (8)	−0.0017 (5)	0.0039 (6)	0.0054 (6)
O1	0.0477 (8)	0.0614 (9)	0.0398 (7)	−0.0274 (7)	0.0112 (6)	−0.0083 (6)
C11	0.0513 (12)	0.0746 (15)	0.0606 (14)	−0.0303 (11)	0.0095 (10)	−0.0034 (11)
C12	0.0453 (11)	0.0601 (13)	0.0463 (11)	−0.0190 (10)	0.0023 (9)	−0.0044 (9)
N5	0.0260 (7)	0.0298 (7)	0.0455 (8)	0.0005 (6)	0.0105 (6)	0.0072 (6)
O2	0.0461 (8)	0.0581 (8)	0.0391 (7)	−0.0241 (6)	0.0010 (6)	0.0112 (6)

Geometric parameters (Å, º) top

C1—C2	1.494 (2)	C8—N7	1.3327 (19)
C1—H1A	0.9600	C9—N10	1.3300 (19)
C1—H1B	0.9600	C9—N8	1.3471 (19)
C1—H1C	0.9600	C9—N7	1.3571 (19)
C2—N3	1.327 (2)	C10—N9	1.3364 (19)
C2—N2	1.340 (2)	C10—N8	1.3459 (19)
C3—N4	1.332 (2)	C10—N6	1.3580 (19)
C3—N1	1.3466 (19)	N4—H4A	0.8600
C3—N3	1.3576 (19)	N4—H4B	0.8600
C4—N5	1.332 (2)	N9—H9A	0.8600
C4—N1	1.346 (2)	N9—H9B	0.8600
C4—N2	1.355 (2)	N10—H10A	0.8600
C5—C6	1.490 (3)	N10—H10B	0.8600
C5—H5A	0.9600	O1—H1	0.8200
C5—H5B	0.9600	C11—C12	1.482 (3)
C5—H5C	0.9600	C11—H11A	0.9600
C6—O1	1.417 (2)	C11—H11B	0.9600
C6—H6A	0.9700	C11—H11C	0.9600
C6—H6B	0.9700	C12—O2	1.415 (2)
C7—C8	1.494 (2)	C12—H12A	0.9700
C7—H7A	0.9600	C12—H12B	0.9700
C7—H7B	0.9600	N5—H5D	0.8600
C7—H7C	0.9600	N5—H5E	0.8600
C8—N6	1.3285 (19)	O2—H2	0.8200

C2—C1—H1A	109.5	N10—C9—N7	116.38 (13)
C2—C1—H1B	109.5	N8—C9—N7	124.41 (13)
H1A—C1—H1B	109.5	N9—C10—N8	118.57 (13)
C2—C1—H1C	109.5	N9—C10—N6	116.26 (13)
H1A—C1—H1C	109.5	N8—C10—N6	125.17 (13)
H1B—C1—H1C	109.5	C4—N1—C3	114.56 (13)
N3—C2—N2	125.90 (14)	C2—N2—C4	114.89 (13)
N3—C2—C1	117.42 (14)	C2—N3—C3	114.50 (13)
N2—C2—C1	116.68 (14)	C3—N4—H4A	120.0
N4—C3—N1	117.82 (13)	C3—N4—H4B	120.0
N4—C3—N3	116.89 (13)	H4A—N4—H4B	120.0
N1—C3—N3	125.28 (13)	C8—N6—C10	114.35 (12)
N5—C4—N1	117.59 (14)	C8—N7—C9	114.99 (12)
N5—C4—N2	117.68 (13)	C10—N8—C9	114.81 (12)
N1—C4—N2	124.72 (14)	C10—N9—H9A	120.0
C6—C5—H5A	109.5	C10—N9—H9B	120.0
C6—C5—H5B	109.5	H9A—N9—H9B	120.0
H5A—C5—H5B	109.5	C9—N10—H10A	120.0
C6—C5—H5C	109.5	C9—N10—H10B	120.0
H5A—C5—H5C	109.5	H10A—N10—H10B	120.0
H5B—C5—H5C	109.5	C6—O1—H1	109.5
O1—C6—C5	109.36 (17)	C12—C11—H11A	109.5
O1—C6—H6A	109.8	C12—C11—H11B	109.5
C5—C6—H6A	109.8	H11A—C11—H11B	109.5
O1—C6—H6B	109.8	C12—C11—H11C	109.5
C5—C6—H6B	109.8	H11A—C11—H11C	109.5
H6A—C6—H6B	108.3	H11B—C11—H11C	109.5
C8—C7—H7A	109.5	O2—C12—C11	114.80 (17)
C8—C7—H7B	109.5	O2—C12—H12A	108.6
H7A—C7—H7B	109.5	C11—C12—H12A	108.6
C8—C7—H7C	109.5	O2—C12—H12B	108.6
H7A—C7—H7C	109.5	C11—C12—H12B	108.6
H7B—C7—H7C	109.5	H12A—C12—H12B	107.5
N6—C8—N7	126.22 (13)	C4—N5—H5D	120.0
N6—C8—C7	117.53 (13)	C4—N5—H5E	120.0
N7—C8—C7	116.25 (13)	H5D—N5—H5E	120.0
N10—C9—N8	119.21 (13)	C12—O2—H2	109.5

N5—C4—N1—C3	−177.19 (14)	N7—C8—N6—C10	−0.8 (2)
N2—C4—N1—C3	3.9 (2)	C7—C8—N6—C10	178.93 (13)
N4—C3—N1—C4	178.53 (14)	N9—C10—N6—C8	−178.84 (13)
N3—C3—N1—C4	−0.9 (2)	N8—C10—N6—C8	2.1 (2)
N3—C2—N2—C4	−0.2 (2)	N6—C8—N7—C9	−1.2 (2)
C1—C2—N2—C4	178.97 (14)	C7—C8—N7—C9	179.03 (13)
N5—C4—N2—C2	177.66 (14)	N10—C9—N7—C8	−177.94 (13)
N1—C4—N2—C2	−3.4 (2)	N8—C9—N7—C8	2.4 (2)
N2—C2—N3—C3	2.9 (2)	N9—C10—N8—C9	179.85 (13)
C1—C2—N3—C3	−176.34 (14)	N6—C10—N8—C9	−1.1 (2)
N4—C3—N3—C2	178.33 (14)	N10—C9—N8—C10	179.00 (13)
N1—C3—N3—C2	−2.3 (2)	N7—C9—N8—C10	−1.3 (2)

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
N4—H4B···N7ⁱ	0.86	2.11	2.9666 (18)	171
N5—H5D···N8ⁱⁱ	0.86	2.19	3.0132 (19)	159
N5—H5E···O2ⁱⁱⁱ	0.86	2.29	3.0071 (19)	142
N10—H10A···O2^iv	0.86	2.10	2.9337 (18)	163
O2—H2···O1^v	0.82	1.90	2.7185 (18)	174

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

Experimental details

Crystal data
Chemical formula	C₄H₇N₅·C₂H₆O
M_r	171.21
Crystal system, space group	Triclinic, P1
Temperature (K)	273
a, b, c (Å)	8.3860 (6), 9.1514 (6), 11.9104 (9)
α, β, γ (°)	88.703 (1), 87.614 (2), 76.668 (2)
V (Å³)	888.56 (11)
Z	4
Radiation type	Mo Kα
µ (mm⁻¹)	0.09
Crystal size (mm)	0.34 × 0.26 × 0.21

Data collection
Diffractometer	Bruker CCD area-detector diffractometer
Absorption correction	Multi-scan (SADABS; Bruker, 2005)
T_min, T_max	0.975, 0.985
No. of measured, independent and observed [I > 2σ(I)] reflections	7627, 3111, 2619
R_int	0.017
(sin θ/λ)_max (Å⁻¹)	0.595

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.042, 0.118, 1.07
No. of reflections	3111
No. of parameters	223
H-atom treatment	H-atom parameters constrained
Δρ_max, Δρ_min (e Å⁻³)	0.25, −0.19

Computer programs: SMART (Bruker, 2002), SAINT (Bruker, 2002), SHELXS97 (Sheldrick, 2008), SHELXL97 (Sheldrick, 2008), ORTEP-3 for Windows (Farrugia, 1997), WinGX (Farrugia, 1999).

Hydrogen-bond geometry (Å, º) top

D—H···A	D—H	H···A	D···A	D—H···A
N4—H4B···N7ⁱ	0.86	2.11	2.9666 (18)	170.5
N5—H5D···N8ⁱⁱ	0.86	2.19	3.0132 (19)	159.0
N5—H5E···O2ⁱⁱⁱ	0.86	2.29	3.0071 (19)	141.5
N10—H10A···O2^iv	0.86	2.10	2.9337 (18)	162.5
O2—H2···O1^v	0.82	1.90	2.7185 (18)	174.1

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

Acknowledgements

This work was supported by the Nomarch Education Foundation of Guizhou, China (No. 2004–07).

References

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