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Acta Crystallogr Sect E Struct Rep Online. 2009 August 1; 65(Pt 8): m998–m999.
Published online 2009 July 29. doi:  10.1107/S1600536809028797
PMCID: PMC2977137

Extensive hydrogen-bonding network and an unusual cation conformation in [tris­(hydroxy­meth­yl)methyl]­ammonium tetra­oxidorhenate(VII)

Abstract

The title compound, (C4H12NO3)[ReO4], contains two cations and two anions in the asymmetric unit, related by a non-crystallographic centre of symmetry. The crystal structure is stabilized by an extensive hydrogen-bonding network with the formation of puckered layers perpendicular to [001]. In the tris­(hydroxy­meth­yl)ammonium cations, intra­molecular O—H(...)O hydrogen bonds are present with the formation of an S 1 1(6) graph-set motif. The crystal structure is further consolid­ated by N—H(...)O hydrogen bonds.

Related literature

For related structures, see: Castellari & Ottani (1997 [triangle]); Eilerman & Rudman (1980 [triangle]); Hołyńska & Lis (2004 [triangle], 2008 [triangle]); Lock & Turner (1975 [triangle]); Marsh et al. (1998 [triangle]); Rudman et al. (1979 [triangle], 1983 [triangle]); Shakked et al. (1980 [triangle]); Tusvik et al. (1999 [triangle]). For the dielectric properties of rhenates(VII) with organic ammonium cations, see: Czarnecki & Małuszyńska (2000 [triangle]). For graph-set notation, see: Etter et al. (1990 [triangle]). For the synthesis of rhenic(VII) acid, see: Johnson et al. (1967 [triangle]).

An external file that holds a picture, illustration, etc.
Object name is e-65-0m998-scheme1.jpg

Experimental

Crystal data

  • (C4H12NO3)[ReO4]
  • M r = 372.35
  • Orthorhombic, An external file that holds a picture, illustration, etc.
Object name is e-65-0m998-efi1.jpg
  • a = 21.450 (5) Å
  • b = 6.867 (2) Å
  • c = 12.219 (4) Å
  • V = 1799.8 (9) Å3
  • Z = 8
  • Mo Kα radiation
  • μ = 13.51 mm−1
  • T = 110 K
  • 0.21 × 0.16 × 0.14 mm

Data collection

  • Oxford Diffraction KM-4-CCD diffractometer
  • Absorption correction: analytical (CrysAlis RED; Oxford Diffraction, 2006 [triangle]) T min = 0.104, T max = 0.268
  • 24604 measured reflections
  • 5888 independent reflections
  • 5084 reflections with I > 2σ(I)
  • R int = 0.029

Refinement

  • R[F 2 > 2σ(F 2)] = 0.020
  • wR(F 2) = 0.034
  • S = 1.02
  • 5888 reflections
  • 245 parameters
  • 1 restraint
  • H-atom parameters constrained
  • Δρmax = 2.00 e Å−3
  • Δρmin = −1.27 e Å−3

Data collection: CrysAlis CCD (Oxford Diffraction, 2006 [triangle]); cell refinement: CrysAlis RED (Oxford Diffraction, 2006 [triangle]); data reduction: CrysAlis RED; program(s) used to solve structure: SHELXS97 (Sheldrick, 2008 [triangle]); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008 [triangle]); molecular graphics: DIAMOND (Brandenburg & Putz, 2005 [triangle]) and SHELXTL-NT (Sheldrick, 2008 [triangle]); software used to prepare material for publication: SHELXL97.

Table 1
Selected geometric parameters (Å, °)
Table 2
Hydrogen-bond geometry (Å, °)

Supplementary Material

Crystal structure: contains datablocks I, global. DOI: 10.1107/S1600536809028797/ez2176sup1.cif

Structure factors: contains datablocks I. DOI: 10.1107/S1600536809028797/ez2176Isup2.hkl

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

Acknowledgments

Financial support from the Ministry of Science and Higher Education (project No. N204 130 32/3318) is acknowledged.

supplementary crystallographic information

Comment

The title compound was obtained as starting material for other syntheses (e.g. reaction with acethyl chloride - Hołyńska & Lis, 2008). It was chosen as the tris(hydroxymethyl)methylammonium cation gives rise to an extensive hydrogen bonding network, which allows for selective crystallization of products containing Re, reducing the risk of cocrystallization of impurities and crystal structure disorder. Moreover, rhenates(VII) with organic ammonium cations crystallizing in non-centrosymmetric space groups are promising materials with respect to their dielectric properties. For example, the previously discovered ferroelectric with a Curie temperature above room temperature is pyridinium rhenate(VII) (Czarnecki & Małuszyńska, 2000).

The title compound (1) is a product of the reaction of rhenic(VII) acid with tris(hydroxymethyl)methylamine (TRIS) in aqueous solution, comprising discrete tris(hydroxymethyl)methylammonium cations (protonated TRIS here denoted as TRISH+) and rhenate(VII) anions (Fig. 1, Scheme 1).

There are two symmetry-independent rhenate(VII) anions (containing atoms Re1 and Re2, respectively) with the expected (see e.g. Hołyńska & Lis, 2004 for example of rhenate(VII) anions in low symmetry environment) slightly distorted tetrahedral geometry. The Re—O bond lengths are listed in Table 1. Their values are consistent with those for other rhenates(VII), e.g. 1.723 (4) Å for potassium rhenate(VII) reported by Lock & Turner (1975). These bond lengths are not much affected by the presence of hydrogen bonds, as all rhenate(VII) O atoms participate in these interactions as acceptors (Table 2).

It is interesting to note that both symmetry-independent TRISH+ cations are of unusual conformation. Usually the cation symmetry is close to C3 (e.g. Rudman et al., 1983) or even exactly threefold (as in [TRISH]Cl appearing in a preliminary report by Rudman et al., 1979) with no intramolecular hydrogen bonds. In (1) both cations exhibit the presence of such intramolecular hydrogen bond (Table 2) with the formation of a S11(6) graph-set motif (Etter et al., 1990). The relevant N—C—C—O torsion angles are given in Table 1. Bond lengths characterizing the cations, among them the C—N bond length (which is longer than in the TRIS molecule - 1.477 (3) Å as reported for the neutral TRIS molecule by Eilerman & Rudman, 1980) are in accordance with the values reported for other structures (e.g. Castellari & Ottani, 1997). TRIS is a constituent of buffers used in biochemical studies in the pH range of 7–9 (Castellari & Ottani, 1997). Upon protonation it forms salts with biologically relevant anions (e.g. tris(hydroxymethyl)methylammonium deoxycholate reported by Tusvik et al., 1999), also a report on its interaction with nucleotides in the crystalline state is available (Shakked et al., 1980).

All cation ammonium and hydroxyl groups are donors in N—H···O or O—H···O hydrogen bonds, both to other TRISH+ cations or to rhenate(VII) anions. The shortest Re···Re distance is 4.210 (2) Å. Thus, puckered hydrogen-bonded layers perpendicular to [001] are formed (Fig. 2). The hydrogen bonding scheme stabilizing an individual layer is illustrated in Fig. 3.

Experimental

The title compound was obtained in the reaction of 0.19 g of tris(hydroxymethyl)methylamine (TRIS) with an excess of rhenic(VII) acid in aqueous solution, with slow evaporation leading to colourless crystals. The reaction was carried out in a quartz beaker. Rhenic(VII) acid was obtained according to the literature procedure (Johnson et al., 1967) in reaction of 0.3 g of metallic Re with an excess of a 30% aqueous hydrogen peroxide solution.

Refinement

The structure was solved by direct methods in the space group P1, and the present solution was obtained by switching to a higher symmetry. It was possible to end up in a false minimum in the Pca21 space group (e.g. with the following approximate coordinates for the Re atoms: 0.57, 0.024, 0.97 for Re1; 0.69, 0.51, 1.01 for Re2; see Marsh et al., 1998, for a review of some pitfalls connected with the Pca21 space group). All H atoms were generated geometrically and refined with Ueq=nUeq(parent atom), where n = 1.5 for hydroxyl H atoms, and n = 1.2 for the remaining H atoms. During the refinement, extinction was also taken into account. Furthermore, it was found that the structure is a racemic twin (with a refined BASF parameter value of 0.375 (6)). On the final difference Fourier map the highest peak of 2.00 e/Å3 was found at 0.62 Å from atom Re2. The crystal structure contains a pseudosymmetry centre at approximately (0.37, 0.73, 0.38).

Figures

Fig. 1.
The symmetry-independent part of (1). Thermal ellipsoids are drawn at 30% probability level. Hydrogen bonds are denoted with dashed lines.
Fig. 2.
Puckered hydrogen-bonded layers perpendicular to [001]. Hydrogen bonds are denoted with dashed lines.
Fig. 3.
One of the layers with hydrogen bonding scheme. Hydrogen bonds are denoted with dashed lines. Symmetry codes as in Table 2.

Crystal data

(C4H12NO3)[ReO4]F(000) = 1392
Mr = 372.35Dx = 2.748 Mg m3
Orthorhombic, Pca21Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2c -2acCell parameters from 20472 reflections
a = 21.450 (5) Åθ = 4.2–35.0°
b = 6.867 (2) ŵ = 13.51 mm1
c = 12.219 (4) ÅT = 110 K
V = 1799.8 (9) Å3Needle, colourless
Z = 80.21 × 0.16 × 0.14 mm

Data collection

Oxford Diffraction KM-4-CCD diffractometer5888 independent reflections
Radiation source: fine-focus sealed tube5084 reflections with I > 2σ(I)
graphiteRint = 0.029
ω scansθmax = 35.0°, θmin = 4.2°
Absorption correction: analytical (CrysAlis RED; Oxford Diffraction, 2006)h = −33→28
Tmin = 0.104, Tmax = 0.268k = −9→11
24604 measured reflectionsl = −14→19

Refinement

Refinement on F2Secondary atom site location: difference Fourier map
Least-squares matrix: fullHydrogen site location: inferred from neighbouring sites
R[F2 > 2σ(F2)] = 0.020H-atom parameters constrained
wR(F2) = 0.034w = 1/[σ2(Fo2) + (0.0119P)2] where P = (Fo2 + 2Fc2)/3
S = 1.02(Δ/σ)max = 0.002
5888 reflectionsΔρmax = 2.00 e Å3
245 parametersΔρmin = −1.27 e Å3
1 restraintExtinction correction: SHELXL97 (Sheldrick, 2008), Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4
Primary atom site location: structure-invariant direct methodsExtinction coefficient: 0.00101 (3)

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

xyzUiso*/Ueq
Re10.311748 (6)0.494021 (19)0.362409 (13)0.01257 (4)
O110.38162 (12)0.5562 (4)0.2998 (2)0.0266 (6)
O210.29045 (12)0.2623 (3)0.3220 (2)0.0217 (6)
O310.25389 (12)0.6547 (3)0.3237 (2)0.0204 (6)
O410.31950 (13)0.4971 (3)0.5010 (4)0.0192 (7)
Re20.431704 (6)0.975939 (17)0.393938 (10)0.01252 (4)
O120.43101 (13)0.9629 (4)0.2527 (4)0.0201 (7)
O220.48425 (12)0.8084 (4)0.4456 (2)0.0239 (6)
O320.35819 (12)0.9281 (4)0.4468 (2)0.0236 (6)
O420.45440 (14)1.2076 (3)0.4316 (2)0.0256 (6)
N10.54415 (13)0.4794 (3)0.3475 (3)0.0087 (7)
H1A0.57520.43300.39090.010*
H1B0.51160.39430.34780.010*
H1C0.53120.59690.37330.010*
C10.56824 (16)0.5031 (4)0.2313 (5)0.0108 (9)
C110.62070 (17)0.6555 (5)0.2341 (3)0.0158 (8)
H11A0.65830.59690.26740.019*
H11B0.63130.69420.15820.019*
O1110.60331 (12)0.8244 (3)0.2949 (2)0.0161 (5)
H1110.58820.90790.25230.024*
C210.59498 (17)0.3079 (5)0.1935 (3)0.0161 (8)
H21A0.60550.31690.11480.019*
H21B0.63410.28200.23400.019*
O2110.55315 (12)0.1482 (3)0.2097 (2)0.0190 (6)
H2110.51920.17150.17800.029*
C310.51492 (18)0.5698 (6)0.1573 (3)0.0171 (8)
H31A0.49770.69360.18580.020*
H31B0.53130.59470.08290.020*
O3110.46638 (12)0.4291 (4)0.1512 (2)0.0194 (6)
H3110.43690.46280.19220.029*
N20.19985 (14)0.0038 (3)0.4133 (3)0.0106 (7)
H2A0.23250.08810.41000.013*
H2B0.16790.05010.37180.013*
H2C0.2120−0.11450.38730.013*
C20.17844 (17)−0.0169 (5)0.5312 (5)0.0126 (9)
C120.15266 (17)0.1803 (5)0.5682 (3)0.0141 (7)
H12A0.11300.20600.52950.017*
H12B0.14360.17490.64760.017*
O1120.19500 (12)0.3372 (3)0.5474 (2)0.0174 (6)
H1120.22930.31380.57780.026*
C220.23218 (16)−0.0833 (5)0.6035 (3)0.0150 (7)
H22A0.2164−0.10760.67840.018*
H22B0.2489−0.20750.57480.018*
O2120.28111 (11)0.0562 (4)0.6084 (2)0.0205 (6)
H2120.30830.02880.56140.031*
C320.12571 (16)−0.1669 (5)0.5331 (3)0.0139 (7)
H32A0.1175−0.20670.60960.017*
H32B0.0872−0.10670.50380.017*
O3120.14087 (12)−0.3355 (3)0.4693 (2)0.0149 (5)
H3120.1612−0.41430.50800.022*

Atomic displacement parameters (Å2)

U11U22U33U12U13U23
Re10.01274 (6)0.01028 (5)0.01470 (9)−0.00034 (4)0.00299 (6)0.00074 (6)
O110.0195 (15)0.0232 (14)0.0373 (17)−0.0036 (11)0.0120 (13)−0.0001 (13)
O210.0299 (16)0.0150 (12)0.0201 (14)−0.0036 (10)0.0061 (12)0.0004 (10)
O310.0252 (15)0.0141 (12)0.0218 (14)0.0036 (10)0.0011 (12)−0.0006 (10)
O410.0268 (17)0.0171 (14)0.0137 (18)−0.0031 (10)−0.0014 (13)0.0013 (11)
Re20.01365 (7)0.01088 (5)0.01303 (8)−0.00034 (5)0.00093 (6)−0.00031 (8)
O120.0235 (16)0.0188 (12)0.0180 (18)−0.0037 (11)−0.0066 (12)−0.0068 (13)
O220.0284 (16)0.0237 (14)0.0195 (14)0.0086 (11)0.0016 (12)0.0010 (11)
O320.0176 (14)0.0194 (13)0.0336 (15)−0.0005 (10)0.0063 (11)0.0011 (12)
O420.0393 (17)0.0163 (12)0.0210 (15)−0.0084 (11)0.0083 (12)−0.0057 (10)
N10.0087 (13)0.0032 (10)0.014 (2)−0.0006 (9)0.0076 (14)0.0021 (11)
C10.0109 (18)0.0078 (15)0.014 (3)−0.0007 (13)0.0004 (14)0.0006 (11)
C110.0146 (19)0.0104 (16)0.022 (2)−0.0019 (13)0.0032 (15)−0.0018 (14)
O1110.0204 (14)0.0121 (12)0.0158 (13)−0.0001 (10)0.0032 (11)−0.0008 (9)
C210.0166 (19)0.0093 (16)0.022 (2)−0.0026 (13)0.0030 (16)−0.0016 (14)
O2110.0208 (15)0.0106 (11)0.0256 (16)−0.0020 (10)−0.0012 (12)0.0010 (11)
C310.016 (2)0.0167 (19)0.018 (2)0.0009 (15)0.0001 (15)0.0032 (15)
O3110.0127 (14)0.0207 (14)0.0250 (16)−0.0001 (11)−0.0028 (12)−0.0077 (12)
N20.0144 (13)0.0044 (12)0.013 (2)0.0016 (9)−0.0018 (13)−0.0049 (10)
C20.019 (2)0.0092 (17)0.010 (2)0.0024 (12)0.0001 (15)−0.0013 (13)
C120.0154 (19)0.0093 (15)0.0176 (19)0.0010 (12)0.0031 (14)−0.0003 (13)
O1120.0152 (14)0.0083 (11)0.0287 (16)−0.0024 (10)−0.0020 (12)−0.0010 (10)
C220.0139 (19)0.0131 (16)0.0182 (19)0.0004 (12)−0.0014 (14)0.0007 (14)
O2120.0124 (14)0.0215 (13)0.0276 (16)−0.0009 (10)−0.0023 (11)−0.0056 (12)
C320.0139 (19)0.0098 (16)0.018 (2)−0.0037 (12)0.0023 (15)−0.0022 (13)
O3120.0173 (14)0.0093 (11)0.0182 (14)0.0009 (9)−0.0011 (11)−0.0013 (9)

Geometric parameters (Å, °)

Re1—O111.736 (2)C31—O3111.423 (4)
Re1—O211.728 (2)C31—H31A0.9900
Re1—O311.727 (2)C31—H31B0.9900
Re1—O411.702 (5)O311—H3110.8400
Re2—O121.728 (4)N2—C21.519 (7)
Re2—O221.730 (3)N2—H2A0.9100
Re2—O321.736 (3)N2—H2B0.9100
Re2—O421.726 (2)N2—H2C0.9100
N1—C11.520 (7)C2—C221.522 (6)
N1—H1A0.9100C2—C321.530 (5)
N1—H1B0.9100C2—C121.531 (5)
N1—H1C0.9100C12—O1121.432 (4)
C1—C311.528 (6)C12—H12A0.9900
C1—C211.529 (5)C12—H12B0.9900
C1—C111.537 (4)O112—H1120.8400
C11—O1111.427 (4)C22—O2121.422 (4)
C11—H11A0.9900C22—H22A0.9900
C11—H11B0.9900C22—H22B0.9900
O111—H1110.8400O212—H2120.8400
C21—O2111.431 (4)C32—O3121.433 (4)
C21—H21A0.9900C32—H32A0.9900
C21—H21B0.9900C32—H32B0.9900
O211—H2110.8400O312—H3120.8400
O41—Re1—O31109.6 (2)O311—C31—H31A109.2
O41—Re1—O21108.7 (2)C1—C31—H31A109.2
O31—Re1—O21108.7 (2)O311—C31—H31B109.2
O41—Re1—O11110.6 (2)C1—C31—H31B109.2
O31—Re1—O11110.0 (2)H31A—C31—H31B107.9
O21—Re1—O11109.2 (2)C31—O311—H311109.5
O42—Re2—O12108.4 (2)C2—N2—H2A109.5
O42—Re2—O22109.4 (2)C2—N2—H2B109.5
O12—Re2—O22109.6 (2)H2A—N2—H2B109.5
O42—Re2—O32109.3 (2)C2—N2—H2C109.5
O12—Re2—O32110.8 (2)H2A—N2—H2C109.5
O22—Re2—O32109.3 (2)H2B—N2—H2C109.5
C1—N1—H1A109.5N2—C2—C22110.5 (3)
C1—N1—H1B109.5N2—C2—C32107.5 (4)
H1A—N1—H1B109.5C22—C2—C32110.5 (3)
C1—N1—H1C109.5N2—C2—C12107.8 (3)
H1A—N1—H1C109.5C22—C2—C12111.5 (4)
H1B—N1—H1C109.5C32—C2—C12108.9 (3)
N1—C1—C31109.3 (3)O112—C12—C2112.6 (3)
N1—C1—C21108.4 (3)O112—C12—H12A109.1
C31—C1—C21111.4 (4)C2—C12—H12A109.1
N1—C1—C11107.5 (4)O112—C12—H12B109.1
C31—C1—C11110.9 (3)C2—C12—H12B109.1
C21—C1—C11109.2 (3)H12A—C12—H12B107.8
O111—C11—C1111.9 (3)C12—O112—H112109.5
O111—C11—H11A109.2O212—C22—C2112.4 (3)
C1—C11—H11A109.2O212—C22—H22A109.1
O111—C11—H11B109.2C2—C22—H22A109.1
C1—C11—H11B109.2O212—C22—H22B109.1
H11A—C11—H11B107.9C2—C22—H22B109.1
C11—O111—H111109.5H22A—C22—H22B107.8
O211—C21—C1113.3 (3)C22—O212—H212109.5
O211—C21—H21A108.9O312—C32—C2111.6 (3)
C1—C21—H21A108.9O312—C32—H32A109.3
O211—C21—H21B108.9C2—C32—H32A109.3
C1—C21—H21B108.9O312—C32—H32B109.3
H21A—C21—H21B107.7C2—C32—H32B109.3
C21—O211—H211109.5H32A—C32—H32B108.0
O311—C31—C1112.0 (3)C32—O312—H312109.5
N1—C1—C11—O111−47.2 (4)N2—C2—C12—O112−51.4 (4)
N1—C1—C21—O21151.0 (4)N2—C2—C22—O21264.0 (4)
N1—C1—C31—O311−63.1 (4)N2—C2—C32—O31245.7 (4)

Hydrogen-bond geometry (Å, °)

D—H···AD—HH···AD···AD—H···A
N2—H2A···O210.912.032.858 (4)150
N2—H2B···O111i0.911.882.788 (4)173
N2—H2C···O31ii0.911.982.879 (4)169
O112—H112···O2120.842.122.773 (4)134
O112—H112···O410.842.492.942 (4)115
O212—H212···O32ii0.841.892.721 (4)168
O312—H312···O112ii0.841.922.704 (4)156
N1—H1A···O312iii0.911.832.738 (4)176
N1—H1B···O42ii0.912.052.872 (4)150
N1—H1C···O220.911.982.862 (4)164
O111—H111···O211iv0.841.892.681 (3)157
O211—H211···O3110.842.132.774 (4)134
O211—H211···O12ii0.842.542.960 (4)112
O311—H311···O110.841.882.714 (4)170

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

Footnotes

Supplementary data and figures for this paper are available from the IUCr electronic archives (Reference: EZ2176).

References

  • Brandenburg, K. & Putz, H. (2005). DIAMOND Crystal Impact GbR, Bonn, Germany.
  • Castellari, C. & Ottani, S. (1997). Acta Cryst. C53, 482–486.
  • Czarnecki, P. & Małuszyńska, H. (2000). J. Phys. Condens. Matter, 12, 4881–4892.
  • Eilerman, D. & Rudman, R. (1980). J. Chem. Phys.72, 5656–5666.
  • Etter, M. C., MacDonald, J. C. & Bernstein, J. (1990). Acta Cryst. B46, 256–262. [PubMed]
  • Hołyńska, M. & Lis, T. (2004). Acta Cryst. C60, m648–m650. [PubMed]
  • Hołyńska, M. & Lis, T. (2008). Acta Cryst. C64, i18–i20. [PubMed]
  • Johnson, N. P., Lock, C. J. L. & Wilkinson, G. (1967). Inorg. Synth.9, 145–148.
  • Lock, C. J. L. & Turner, G. (1975). Acta Cryst. B31, 1764–1765.
  • Marsh, R. E., Schomaker, V. & Herbstein, F. H. (1998). Acta Cryst. B54, 921–924.
  • Oxford Diffraction (2006). CrysAlis RED and CrysAlis CCD Oxford Diffraction Ltd, Abingdon, England.
  • Rudman, R., Lippman, R. & Eilerman, D. (1979). American Crystallographic Association Abstracts, Winter Meeting, Honolulu, HI, Vol. 6, No. 2, p. 73.
  • Rudman, R., Lippman, R., Sake Gowda, D. S. & Eilerman, D. (1983). Acta Cryst. C39, 1267–1271.
  • Shakked, Z., Viswamitra, M. A. & Kennard, O. (1980). Biochemistry, 19, 2567–2571. [PubMed]
  • Sheldrick, G. M. (2008). Acta Cryst. A64, 112–122. [PubMed]
  • Tusvik, P. H., Mostad, A., Dalhus, B. & Rosenqvist, E. (1999). Acta Cryst. C55, 1113–1115.

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