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Acta Crystallogr Sect E Struct Rep Online. 2010 November 1; 66(Pt 11): o2712.
Published online 2010 October 2. doi:  10.1107/S1600536810038225
PMCID: PMC3008973

Bis(homopiperazine-1,4-diium) cyclo­tetra­phosphate–telluric acid (1/2)

Abstract

The title compound, 2C5H14N2 2+·P4O12 4−·2Te(OH)6, involves doubly protonated homopiperazinium cations, cyclo­tetra­phosphate anions and telluric acid mol­ecules. The framework possesses very large channels wherein the organic cations reside. A network of O—H(...)O, N—H(...)O and C—H(...)O hydrogen bonds consolidates the crystal packing.

Related literature

For the properties of materials containing telluric acid, see: Chabchoub et al. (2006 [triangle]); Khemakhem, (1999 [triangle]). For related structures containing phosphate rings and telluric acid, see: Averbuch-Pouchot & Durif (1987a [triangle],b [triangle]); Durif et al. (1982 [triangle]). For hydrogen bonding, see: Blessing (1986 [triangle]); Brown (1976 [triangle]). For deviations in four-membered phosphate rings having the same An external file that holds a picture, illustration, etc.
Object name is e-66-o2712-efi3.jpg inter­nal symmetry, see: Durif (1995 [triangle]); A similar conformation for the same organic mol­ecule was observed in (C5H14N2)(H2AsO4)2, see: Wilkinson & Harrison (2006 [triangle]). For the synthesis, see: Ondik (1964 [triangle]).

An external file that holds a picture, illustration, etc.
Object name is e-66-o2712-scheme1.jpg

Experimental

Crystal data

  • C5H14N2 2+·0.5P4O12 4−·Te(OH)6
  • M r = 489.77
  • Monoclinic, An external file that holds a picture, illustration, etc.
Object name is e-66-o2712-efi4.jpg
  • a = 20.826 (3) Å
  • b = 8.3600 (13) Å
  • c = 17.030 (8) Å
  • β = 101.65 (3)°
  • V = 2903.9 (14) Å3
  • Z = 8
  • Ag Kα radiation
  • λ = 0.56083 Å
  • μ = 1.24 mm−1
  • T = 293 K
  • 0.2 × 0.18 × 0.16 mm

Data collection

  • Enraf–Nonius CAD-4 diffractometer
  • 8219 measured reflections
  • 6346 independent reflections
  • 4847 reflections with I > 2σ(I)
  • R int = 0.027
  • 2 standard reflections every 120 min intensity decay: 5%

Refinement

  • R[F 2 > 2σ(F 2)] = 0.033
  • wR(F 2) = 0.084
  • S = 1.01
  • 6346 reflections
  • 223 parameters
  • 12 restraints
  • H atoms treated by a mixture of independent and constrained refinement
  • Δρmax = 1.99 e Å−3
  • Δρmin = −1.19 e Å−3

Data collection: CAD-4 EXPRESS (Enraf–Nonius, 1994 [triangle]); cell refinement: CAD-4 EXPRESS; data reduction: XCAD4 (Harms & Wocadlo, 1996 [triangle]); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008 [triangle]); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008 [triangle]); molecular graphics: ORTEP-3 for Windows (Farrugia, 1997 [triangle]); software used to prepare material for publication: WinGX (Farrugia, 1999 [triangle]).

Table 1
Hydrogen-bond geometry (Å, °)

Supplementary Material

Crystal structure: contains datablocks I, global. DOI: 10.1107/S1600536810038225/bv2159sup1.cif

Structure factors: contains datablocks I. DOI: 10.1107/S1600536810038225/bv2159Isup2.hkl

Additional supplementary materials: crystallographic information; 3D view; checkCIF report

supplementary crystallographic information

Comment

Materials containing telluric acid exhibit many interesting physical properties such as ferroelectricity and protonic conduction (Chabchoub et al.,2006; Khemakhem, 1999). On the chemical plane, telluric acid has the property to form adduct compounds with many kinds of phosphates and was extensively investigated during the past thirty years. With cyclotriphosphate, several adduct compounds of telluric acid have been identified whereas with cyclotetraphosphate only three inorganic telluric acid-adduct compounds are reported: (NH4)4P4O12.Te(OH)6.2H2O (Durif et al.,1982), K4P4O12.Te(OH)6.2H2O and Rb4P4O12.Te(OH)6.2H2O (Averbuch-Pouchot & Durif, 1987a b). In the present work, we report the first telluric acid-adduct compound of an organic cyclotetraphosphate (C5H14N2)2P4O12.2Te(OH)6 (I). The configuration of different components of (I) is shown in Figure 1. In the crystal structure of this compound, P4O124- and Te(OH)6 form an anionic three-dimensional framework. The negative charge of this is compensated by the diprotonated amine (C5H14N2)2+. Figure 2 shows the total atomic arrangement projected along the [1 0 1] direction. This projection shows that the inorganic entities form very large channels wherein the organic cations are located. The telluric acid molecules Te(OH)6 are linked pair-wise by two symmetric strong O—H···O hydrogen bonds, with an O···O distance of 2.695 (3) Å, into dimers where the Te···Te distance is 5.102 (5) Å. The tellurium atom is surrounded by six OH groups in a rather regular octahedral arrangement as indicated by the Te-O distances ranging from 1.905 (2) to 1.916 (2) Å, the cis and trans O-Te-O angles which are found in the 87.4 (1)-92.94 (9) ° and 175.03 (9)-178.8 (1)° ranges, respectively, and Te—O—H angles ranging from 107 (3) to 116 (3)°. Each Te(OH)6 dimer is linked to six P4O12 rings and two homopiperazinium (C5H14N2)2+ through a three-dimensional hydrogen bonding network O—H···O and N—H···O (Fig. 3). The P4O12 ring anions are centrosymmetric and are built by only two crystallographically independent PO4 tetrahedra with P-O distances ranging from 1.477 (2) to 1.605 (2) Å and O-P-O angles ranging from 103.9 (1) to 120.2 (2)° with a mean value (109.22°) very close to the ideal value (109.28°). In spite of these large ranges in P-O distances and O-P-O angles, which can be explained by different environments of oxygen atoms, the PO4 tetrahedron is described by regular oxygen atom arrangement with the phosphorus atom shifted by 0.122 and 0.149 Å from the centre of gravity . The cyclic anion is distorted as evidenced by P—P—P angles (81.60 (1) and 98.40 (1)°) which show a pronounced deviation from the ideal value (90°). Such deviation is commonly observed in tetramembered phosphoric rings having the same -1 internal symmetry (Durif, 1995). Only one homopiperazinium cation (C5H14N2)2+ exists in the asymmetric unit and adopts a chair conformation as evidenced by the mean deviation (±0.0251 Å) from the least square plane defined by the four constituent atoms N1, N2, C1 and C3 and the remaining atoms C2, C4 and C5 displaced from the plane by 0.7495 (3), 0.6175 (3) and -0.2661 (3) Å, respectively. A similar conformation for the same organic molecule was observed in (C5H14N2)(H2AsO4)2 (Wilkinson & Harrison, 2006) with important difference that the "seat" chair was defined by one N atom and three C atoms rather than two N atoms and two C atoms as found here. The organic and inorganic components exert between them different interactions (electrostatic, hydrogen bonds and Van der Waals) to form a stable three-dimensional network. The examination of the hydrogen-bond scheme shows the existence of four strong hydrogen bonds with distances O···O ranging from 2.686 (3) to 2.722 (3) Å. The other bonds are weaker, with O(N,C)···O distances falling from 2.739 (3) to 3.265 (4) Å (Blessing, 1986; Brown, 1976).

Experimental

Crystals of the title compound were prepared by adding ethanolic solution (5 ml) of homopiperazine (10 mmol) dropwise to an aqueous solution of cyclotetraphosphoric acid (5 mmol, 20 ml). The obtained solution was added to an aquous solution of telluric acid (10 mmol, 15 ml). Good quality of colourless prisms were obtained after a slow evaporation during few days at ambient temperature. The cyclotetraphosphoric acid H4P4O12, was produced from Na4P4O12.4H2O, prepared according to the Ondik process (Ondik, 1964), through an ion-exchange resin in H-state (Amberlite IR 120).

Refinement

All H atoms of the organic molecule were positioned geometrically and treated as riding on their parent atoms, [N–H = 0.89, C–H = 0.96 Å (CH3) with Uiso(H) = 1.5Ueq and C–H =0.96 Å (Ar–H), with Uiso(H) = 1.5Ueq]. The H-atoms of telluric acid, located in difference Fourier maps, were refined with a distance restraint of O-H = 0.86 (2) Å; their temperature factors were refined.

Figures

Fig. 1.
An ORTEP view of (I) with the atom-labelling scheme. Displacement ellipsoids are drawn at the 50% probability level. H atoms are represented as small spheres of arbitrary radii. [Symmetry codes: (i) 1/2 - x, 1/2 - y, 1 - z].
Fig. 2.
Projection of (I) along [1 0 1] direction. Some hydrogen atoms are omitted for clarity.
Fig. 3.
A perspective view of the atomic arrangement of (I).

Crystal data

C5H14N22+·0.5P4O124·Te(OH)6F(000) = 1936
Mr = 489.77Dx = 2.241 Mg m3
Monoclinic, C2/cAg Kα radiation, λ = 0.56083 Å
Hall symbol: -C 2ycCell parameters from 25 reflections
a = 20.826 (3) Åθ = 9.0–10.9°
b = 8.3600 (13) ŵ = 1.24 mm1
c = 17.030 (8) ÅT = 293 K
β = 101.65 (3)°Prism, colourless
V = 2903.9 (14) Å30.2 × 0.18 × 0.16 mm
Z = 8

Data collection

Enraf–Nonius CAD-4 diffractometerRint = 0.027
Radiation source: Enraf Nonius FR590θmax = 27.0°, θmin = 2.1°
graphiteh = −33→33
Non–profiled ω scansk = 0→13
8219 measured reflectionsl = −5→27
6346 independent reflections2 standard reflections every 120 min
4847 reflections with I > 2σ(I) intensity decay: 5%

Refinement

Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.033Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.084H atoms treated by a mixture of independent and constrained refinement
S = 1.01w = 1/[σ2(Fo2) + (0.0482P)2] where P = (Fo2 + 2Fc2)/3
6346 reflections(Δ/σ)max = 0.001
223 parametersΔρmax = 1.99 e Å3
12 restraintsΔρmin = −1.19 e Å3

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 (Å2)

xyzUiso*/Ueq
C50.17222 (12)0.3358 (3)0.92873 (16)0.0227 (5)
H5A0.17820.22470.94500.027*
H5B0.19090.40140.97470.027*
C40.20920 (13)0.3672 (3)0.86247 (18)0.0253 (5)
H4A0.18800.45380.82910.030*
H4B0.25350.40100.88600.030*
H3−0.0202 (13)0.058 (5)0.080 (2)0.060 (14)*
H4−0.0415 (18)0.298 (4)0.1851 (19)0.039 (11)*
H10.1244 (7)0.217 (4)0.2504 (13)0.027 (9)*
H60.0994 (18)0.505 (3)0.1086 (14)0.053 (13)*
H2−0.0171 (9)0.333 (4)0.0087 (11)0.024 (8)*
H50.1230 (13)0.094 (3)0.068 (2)0.047 (12)*
Te10.053963 (7)0.257312 (16)0.128185 (8)0.01399 (4)
P10.35495 (3)0.28147 (6)0.49522 (3)0.01199 (9)
P20.26836 (3)0.30733 (7)0.61119 (3)0.01214 (9)
O100.32281 (8)0.22730 (19)0.56907 (10)0.0161 (3)
O70.29316 (8)0.3056 (2)0.42301 (10)0.0167 (3)
O90.39402 (8)0.1419 (2)0.47840 (11)0.0199 (3)
O10.08267 (8)0.2069 (2)0.23924 (11)0.0200 (3)
O110.25530 (8)0.4740 (2)0.58395 (11)0.0197 (3)
N20.21224 (11)0.2239 (2)0.81152 (15)0.0223 (4)
H2A0.24220.24190.78120.027*
H2B0.22640.14040.84380.027*
O4−0.02504 (9)0.3469 (2)0.15028 (12)0.0239 (4)
O60.09666 (11)0.4585 (2)0.15090 (12)0.0273 (4)
O80.38702 (8)0.4392 (2)0.51103 (11)0.0197 (3)
O120.28855 (8)0.2710 (2)0.69789 (10)0.0217 (3)
O20.02429 (9)0.3119 (3)0.01751 (11)0.0229 (4)
O50.13208 (8)0.1739 (3)0.10185 (12)0.0254 (4)
C30.14949 (14)0.1782 (3)0.75778 (16)0.0268 (5)
H3A0.15640.08130.72920.032*
H3B0.13680.26210.71830.032*
N10.10076 (10)0.3697 (3)0.90552 (13)0.0211 (4)
H1A0.08170.33400.94510.025*
H1B0.09550.47650.90310.025*
C20.09384 (13)0.1504 (3)0.80154 (17)0.0245 (5)
H2C0.05950.09110.76650.029*
H2D0.10990.08410.84810.029*
O30.01479 (9)0.0496 (2)0.11451 (13)0.0253 (4)
C10.06439 (13)0.3009 (4)0.82876 (18)0.0289 (5)
H1C0.06190.38120.78710.035*
H1D0.01990.27750.83440.035*

Atomic displacement parameters (Å2)

U11U22U33U12U13U23
C50.0248 (11)0.0218 (10)0.0203 (11)0.0009 (9)0.0014 (9)−0.0054 (9)
C40.0217 (10)0.0176 (10)0.0379 (15)−0.0035 (8)0.0093 (10)−0.0031 (10)
Te10.01393 (6)0.01490 (6)0.01358 (6)0.00039 (5)0.00382 (4)0.00058 (5)
P10.0102 (2)0.0138 (2)0.0119 (2)−0.00096 (16)0.00219 (17)−0.00043 (17)
P20.0121 (2)0.0149 (2)0.0091 (2)−0.00041 (17)0.00137 (17)−0.00098 (18)
O100.0179 (7)0.0176 (7)0.0150 (7)0.0030 (5)0.0081 (6)0.0033 (5)
O70.0144 (6)0.0184 (7)0.0153 (7)−0.0029 (5)−0.0016 (5)0.0042 (6)
O90.0178 (7)0.0238 (8)0.0187 (8)0.0042 (6)0.0051 (6)−0.0050 (6)
O10.0178 (7)0.0266 (8)0.0151 (7)0.0017 (6)0.0023 (6)0.0054 (6)
O110.0218 (8)0.0140 (7)0.0224 (8)0.0010 (6)0.0023 (7)−0.0022 (6)
N20.0252 (9)0.0183 (8)0.0275 (11)0.0030 (7)0.0152 (9)0.0046 (7)
O40.0236 (8)0.0291 (9)0.0213 (8)0.0106 (7)0.0101 (7)0.0080 (7)
O60.0435 (11)0.0192 (8)0.0191 (9)−0.0103 (8)0.0060 (8)−0.0019 (7)
O80.0191 (7)0.0189 (7)0.0198 (8)−0.0068 (6)0.0010 (6)−0.0013 (6)
O120.0173 (7)0.0394 (10)0.0084 (6)−0.0014 (7)0.0021 (6)0.0014 (6)
O20.0170 (7)0.0376 (10)0.0142 (7)0.0013 (7)0.0034 (6)0.0046 (7)
O50.0146 (7)0.0335 (10)0.0282 (10)0.0016 (7)0.0045 (7)−0.0091 (8)
C30.0350 (13)0.0285 (12)0.0182 (11)0.0024 (10)0.0083 (10)−0.0008 (10)
N10.0248 (9)0.0209 (9)0.0197 (10)0.0009 (7)0.0094 (8)−0.0039 (7)
C20.0254 (11)0.0217 (11)0.0261 (12)−0.0026 (9)0.0042 (10)−0.0058 (9)
O30.0218 (8)0.0196 (8)0.0326 (11)−0.0040 (6)0.0009 (8)0.0022 (7)
C10.0222 (11)0.0325 (13)0.0306 (14)0.0044 (10)0.0021 (10)−0.0068 (11)

Geometric parameters (Å, °)

C5—N11.488 (3)O7—P2i1.6033 (17)
C5—C41.512 (4)O1—H10.855 (13)
C5—H5A0.9700N2—C31.486 (4)
C5—H5B0.9700N2—H2A0.9000
C4—N21.488 (3)N2—H2B0.9000
C4—H4A0.9700O4—H40.846 (18)
C4—H4B0.9700O6—H60.830 (17)
Te1—O51.9050 (18)O2—H20.862 (16)
Te1—O61.9050 (18)O5—H50.874 (17)
Te1—O11.9119 (19)C3—C21.517 (4)
Te1—O31.9124 (18)C3—H3A0.9700
Te1—O41.9130 (18)C3—H3B0.9700
Te1—O21.916 (2)N1—C11.488 (4)
P1—O81.4784 (17)N1—H1A0.9000
P1—O91.4831 (17)N1—H1B0.9000
P1—O71.6028 (18)C2—C11.513 (4)
P1—O101.6046 (18)C2—H2C0.9700
P2—O111.4766 (18)C2—H2D0.9700
P2—O121.4825 (19)O3—H30.840 (19)
P2—O7i1.6033 (17)C1—H1C0.9700
P2—O101.6052 (17)C1—H1D0.9700
N1—C5—C4113.7 (2)P1—O10—P2132.59 (11)
N1—C5—H5A108.8P1—O7—P2i131.58 (11)
C4—C5—H5A108.8Te1—O1—H1107.4 (15)
N1—C5—H5B108.8C3—N2—C4115.5 (2)
C4—C5—H5B108.8C3—N2—H2A108.4
H5A—C5—H5B107.7C4—N2—H2A108.4
N2—C4—C5112.5 (2)C3—N2—H2B108.4
N2—C4—H4A109.1C4—N2—H2B108.4
C5—C4—H4A109.1H2A—N2—H2B107.5
N2—C4—H4B109.1Te1—O4—H4116 (3)
C5—C4—H4B109.1Te1—O6—H6110.3 (17)
H4A—C4—H4B107.8Te1—O2—H2109.4 (13)
O5—Te1—O689.15 (9)Te1—O5—H5110.6 (16)
O5—Te1—O192.34 (9)N2—C3—C2113.6 (2)
O6—Te1—O187.36 (8)N2—C3—H3A108.8
O5—Te1—O390.15 (9)C2—C3—H3A108.8
O6—Te1—O3175.03 (9)N2—C3—H3B108.8
O1—Te1—O387.75 (9)C2—C3—H3B108.8
O5—Te1—O4177.38 (9)H3A—C3—H3B107.7
O6—Te1—O489.95 (9)C1—N1—C5117.7 (2)
O1—Te1—O490.08 (8)C1—N1—H1A107.9
O3—Te1—O490.96 (8)C5—N1—H1A107.9
O5—Te1—O288.67 (9)C1—N1—H1B107.9
O6—Te1—O291.96 (9)C5—N1—H1B107.9
O1—Te1—O2178.78 (8)H1A—N1—H1B107.2
O3—Te1—O292.94 (9)C1—C2—C3114.8 (2)
O4—Te1—O288.91 (8)C1—C2—H2C108.6
O8—P1—O9119.45 (10)C3—C2—H2C108.6
O8—P1—O7106.91 (10)C1—C2—H2D108.6
O9—P1—O7109.72 (10)C3—C2—H2D108.6
O8—P1—O10110.71 (10)H2C—C2—H2D107.5
O9—P1—O10105.15 (10)Te1—O3—H3107 (3)
O7—P1—O10103.86 (9)N1—C1—C2115.1 (2)
O11—P2—O12120.22 (11)N1—C1—H1C108.5
O11—P2—O7i111.00 (9)C2—C1—H1C108.5
O12—P2—O7i106.65 (10)N1—C1—H1D108.5
O11—P2—O10110.78 (10)C2—C1—H1D108.5
O12—P2—O10106.01 (10)H1C—C1—H1D107.5
O7i—P2—O10100.20 (9)

Symmetry codes: (i) −x+1/2, −y+1/2, −z+1.

Hydrogen-bond geometry (Å, °)

D—H···AD—HH···AD···AD—H···A
O1—H1···O12i0.86 (2)1.85 (2)2.686 (3)165 (2)
N1—H1B···O4ii0.902.152.898 (3)140
N1—H1B···O9iii0.902.423.002 (3)123
N1—H1A···O2iv0.901.892.763 (3)162
O2—H2···O9v0.86 (2)1.83 (2)2.688 (3)172 (3)
N2—H2A···O120.901.892.769 (3)167
N2—H2B···O11vi0.901.852.739 (3)172
O3—H3···O8v0.84 (3)2.05 (3)2.881 (3)170 (4)
O4—H4···O1vii0.85 (3)1.85 (3)2.695 (3)175 (3)
O5—H5···O8viii0.87 (3)1.85 (3)2.719 (3)172 (3)
O6—H6···O9ix0.83 (3)1.90 (2)2.722 (3)171 (3)
C2—H2C···O1x0.972.603.162 (3)117
C4—H4B···O5i0.972.433.256 (4)142
C5—H5B···O11xi0.972.313.265 (4)168

Symmetry codes: (i) −x+1/2, −y+1/2, −z+1; (ii) −x, −y+1, −z+1; (iii) −x+1/2, y+1/2, −z+3/2; (iv) x, y, z+1; (v) x−1/2, −y+1/2, z−1/2; (vi) −x+1/2, y−1/2, −z+3/2; (vii) −x, y, −z+1/2; (viii) −x+1/2, y−1/2, −z+1/2; (ix) −x+1/2, y+1/2, −z+1/2; (x) x, −y, z+1/2; (xi) x, −y+1, z+1/2.

Footnotes

Supplementary data and figures for this paper are available from the IUCr electronic archives (Reference: BV2159).

References

  • Averbuch-Pouchot, M. T. & Durif, A. (1987a). Acta Cryst. C43, 1245–1247.
  • Averbuch-Pouchot, M. T. & Durif, A. (1987b). C. R. Acad. Sci. Ser. 2, 304, 269–271.
  • Blessing, R. H. (1986). Acta Cryst. B42, 613–621.
  • Brown, I. D. (1976). Acta Cryst. A32, 24–31.
  • Chabchoub, N., Darriet, J. & Khemakhem, H. (2006). J. Solid State Chem.1792, 164–2173.
  • Durif, A. (1995). In Crystal Chemistry of Condensed Phosphates New York: Plenum Press.
  • Durif, A., Averbuch-Pouchot, M. T. & Guitel, J. C. (1982). J. Solid State Chem.41, 153–159.
  • Enraf–Nonius (1994). CAD-4 EXPRESS Enraf–Nonius, Delft, The Netherlands.
  • Farrugia, L. J. (1997). J. Appl. Cryst.30, 565.
  • Farrugia, L. J. (1999). J. Appl. Cryst.32, 837–838.
  • Harms, K. & Wocadlo, S. (1996). XCAD4 University of Marburg, Germany.
  • Khemakhem, H. (1999). Ferroelectrics, 234, 47–59.
  • Ondik, H. M. (1964). Acta Cryst.17, 1139–1145.
  • Sheldrick, G. M. (2008). Acta Cryst. A64, 112–122. [PubMed]
  • Wilkinson, H. S. & Harrison, W. T. A. (2006). Acta Cryst. E62, m1397–m1399.

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