Redetermination of hydro­nium perchlorate at 193 and 293 K

A sample of hydro­nium perchlorate, H₃O⁺·ClO₄^-, crystallized from ethanol at ambient temperature, was found to be orthorhombic (space group Pnma) at both 193 and 293 K, with no phase transition observed in this temperature range. This contrasts with the earlier observation [Nordman (1962). Acta Cryst. 15, 18-23] of a monoclinic phase (space group P2₁/n) at 193 K for crystals grown at that temperature from perchloric acid. The hydro­nium and perchlorate ions lie across a mirror plane but it is not possible to define at either temperature a simple description of the H-atom positions due to the three-dimensional tumbling of the hydro­nium cation.

S1. Comment

The formation of the hydronium ion in water has been frequently postulated to explain the abnormal mobility of protons through water. Evidence of their existence in crystals has been obtained by X-ray diffraction methods (Volmer, 1925; Luzatti, 1953); for example, the X-ray diffraction pattern of perchloric acid monohydrate is very similar to that of ammonium perchlorate, implying that the perchloric acid monohydrate is, in fact, hydronium perchlorate. This question was investigated by both NMR spectroscopy (Richards & Smith, 1951) and Raman spectroscopy (Taylor & Vidale, 1956), which provided early evidence for the occurrence of the hydronium ion. The early NMR data suggested that the hydronium ion was nearly planar, but subsequent X-ray diffraction studies on a wide variety of salts containing the hydronium ion gave H—O—H angles with an average value of 109.3 (5)° (Lundgren & Williams, 1973).

Richards & Smith (1951) found that the hydronium ions in the perchlorate salt undergo re-orientation at high temperature in the solid state, and a phase transition was observed at 243 K (Taylor & Vidale, 1956). The orientational disorder is also supported by a room-temperature X-ray diffraction analysis (Lee & Carpenter, 1959), in which the hydronium ions are rotating or disordered among several orientations, although no direct evidence for the location of the H atoms appeared in electron-density projections and no further attempt was made to locate them. In the low-temperature X-ray study reported by Nordman (1962), it was found that at 193 K, hydronium perchlorate crystallized from perchloric acid in the monoclinic space group P2₁/n, while Lee & Carpenter (1959) suggested a transition above 243 K to a space group of higher symmetry, viz. orthorhombic Pnma with a = 9.065 (8), b = 5.569 (4) and c = 7.339 (4) Å.

In the present study, we have redetermined the crystal structure of hydronium perchlorate at both 193 K and room temperature (293 K) (Fig. 1) using a sample crystallized at ambient temperature from ethanol solution. We observed no temperature-dependent phase transition even though we recycled the sample several times through the temperature range 193–293 K; the orthorhombic space group Pnma was consistently observed at both 193 and 293 K.

In this orthorhombic phase, perchlorate atoms Cl1, O1 and O2, and hydronium atom O1W lie on the mirror plane at y = 1/4 (Fig. 2). The geometry of the perchlorate anion is effectively constant, within experimental error, over the temperature range 193–293 K (Tables 1 and 2).

Detailed scrutiny of an extensive series of difference map sections in different planes adjacent to the O1W atom show that the electron density associated with the three H atoms forms a fairly uniform and nearly spherical shell (approximately of radius of 1 Å) around the water O atom. This implies that the hydronium cation is actually tumbling with nearly spherical symmetry at both 193 and 293 K. This tumbling of the hydronium cation is consistent with the rather long (>2.94 Å) contact distances between O1W and the surrounding O atoms of the anions (Table 3 and Fig. 2). Even at 193 K, the O1W···O distances may not be short enough for the formation of hydrogen bonds strong enough to tether the cations firmly to the anions; thus, the hydronium cations may still be tumbling with nearly spherical symmetry. In view of these findings, it is not possible to say anything about the shape and dimensions of the hydronium cation or anything about the details of the hydrogen bonding at both 193 and 293 K. This study concurs with the 293 K study of the orthorhombic phase (Lee & Carpenter, 1959) and confirms the disordered nature of the hydronium cation. By contrast, in the monoclinic phase there are three O···O contact distances between a given cation and three neighbouring anions lying in the range 2.63 (1)–2.71 (1) Å, and the H atoms were explicitly located in fully ordered sites, leading to the identification of three cation–anion O—H···O hydrogen bonds (Nordman, 1962).

The persistence at 193 K of the orthorhombic phase is in contrast to the observation by Nordman (1962) of a monoclinic phase below 243 K, and two possible interpretations suggest themselves. The sample employed here may be much purer than that used by Nordman and thus may lack the specific trace impurities required to initiate the phase transformation. Alternatively, the monoclinic phase may, in fact, be a disappearing polymorph (Bernstein & Henck, 1998).

S2. Experimental

The sample of hydronium perchlorate used was an adventitious by-product from the attempted synthesis of a copper(II) macrocyclic complex by the [2 + 2]-cyclocondensation between sodium 2,6-diformyl-4-methylphenolate (0.1863 g, 1 mmol) and 1,4-phenylenediamine (0.1081 g, 1 mmol) in ethanol (30 ml) via the sodium template method (Gou & Fenton, 1994). A yellow solid was obtained (0.195 g, 0.38 mmol) and was then transmetallated with Cu(ClO₄)₂·6H₂O (0.292 g, 0.76 mmol) in ethanol (25 ml). The solution was refluxed under nitrogen for 1 h. The resulting hot clear solution was filtered and left to cool in air. After several days, colourless crystals of hydronium perchlorate were deposited.

S3. Refinement

Examination of an extensive series of difference electron density plots in different planes adjacent to atom O1W showed that the three H atoms form a fairly uniform nearly spherical shell (of approximate radius 1 Å) of electron density around the hydronium O atom, at both temperatures. Since this implies that the hydronium cation is tumbling in three dimensions with nearly spherical symmetry at 193 K and 293 K, the H atoms were not included in the refinements. The indicated temperature of 193 K for the sample was measured with the low-temperature attachment that came with the Bruker 1 K CCD diffractometer. The measured temperature was at the nozzle of the cold N₂ stream and accordingly to Bruker's specification, the temperature at the sample would be at most 2–3 K higher.

Computing details

For both compounds, data collection: SMART (Siemens, 1996); cell refinement: SAINT (Siemens, 1996); data reduction: SAINT; program(s) used to solve structure: SHELXTL (Sheldrick, 1997); program(s) used to refine structure: SHELXTL; molecular graphics: SHELXTL; software used to prepare material for publication: SHELXTL.

Figures

	Fig. 1. The independent components of orthorhombic hydronium perchlorate at 193 K, showing 50% probability displacement ellipsoids and the atom-numbering scheme. H atoms have been omitted (see text). [Symmetry code: (i) x, 1/2 − y, z.]
	Fig. 2. A view of the O···O contacts around the hydronium atom O1W at 193 K. Symmetry codes are as given in Table 3.

(I) hydronium perchlorate

Crystal data

H3O^+·ClO4^−	F(000) = 240
Mr = 118.47	Dx = 2.006 Mg m^−3
Orthorhombic, Pnma	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ac 2n	Cell parameters from 1600 reflections
a = 9.1517 (9) Å	θ = 3.5–28.3°
b = 5.7886 (6) Å	µ = 0.86 mm^−1
c = 7.4034 (8) Å	T = 193 K
V = 392.20 (7) Å^3	Block, colorless
Z = 4	0.28 × 0.24 × 0.14 mm

Data collection

Siemens SMART CCD area-detector diffractometer	532 independent reflections
Radiation source: fine-focus sealed tube	490 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.018
Detector resolution: 8.33 pixels mm^-1	θmax = 28.2°, θmin = 3.5°
ω scans	h = −9→12
Absorption correction: multi-scan (SADABS; Sheldrick, 1996)	k = −7→7
Tmin = 0.795, Tmax = 0.889	l = −9→8
2301 measured reflections

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.045	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.117	H-atom parameters not defined
S = 1.11	w = 1/[σ^2(Fo^2) + (0.0501P)^2 + 1.0711P] where P = (Fo^2 + 2Fc^2)/3
532 reflections	(Δ/σ)max < 0.001
34 parameters	Δρmax = 0.53 e Å^−3
0 restraints	Δρmin = −0.47 e Å^−3

Special details

Experimental. The data collection covered over a hemisphere of reciprocal space by a combination of three sets of exposures; each set had a different ϕ angle (0, 88 and 180°) for the crystal and each exposure of 10 s covered 0.3° in ω. The crystal-to-detector distance was 5 cm and the detector swing angle was −35°. Crystal decay was monitored by repeating fifty initial frames at the end of data collection and analysing the intensity of duplicate reflections, and was found to be negligible.

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 (Ų)

	x	y	z	Uiso*/Ueq
Cl1	0.42999 (8)	0.2500	0.19125 (11)	0.0167 (3)
O1	0.3097 (3)	0.2500	0.0657 (4)	0.0279 (7)
O2	0.5667 (3)	0.2500	0.0972 (5)	0.0366 (8)
O3	0.4197 (2)	0.0470 (3)	0.3043 (2)	0.0253 (5)
O1W	0.3200 (3)	0.2500	0.6653 (4)	0.0315 (7)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Cl1	0.0142 (4)	0.0193 (4)	0.0165 (4)	0.000	0.0009 (3)	0.000
O1	0.0276 (15)	0.0336 (16)	0.0226 (13)	0.000	−0.0108 (12)	0.000
O2	0.0225 (15)	0.048 (2)	0.0395 (17)	0.000	0.0151 (13)	0.000
O3	0.0275 (10)	0.0207 (10)	0.0276 (10)	0.0007 (7)	−0.0022 (8)	0.0065 (7)
O1W	0.0260 (14)	0.0358 (17)	0.0327 (15)	0.000	0.0014 (12)	0.000

Geometric parameters (Å, º)

Cl1—O2	1.431 (3)	Cl1—O3^i	1.446 (2)
Cl1—O1	1.441 (3)	Cl1—O3	1.446 (2)
O1—Cl1—O2	110.72 (19)	O2—Cl1—O3	109.77 (11)
O2—Cl1—O3^i	109.77 (11)	O3—Cl1—O1	108.91 (10)
O1—Cl1—O3^i	108.91 (10)	O3^i—Cl1—O3	108.73 (17)

Symmetry code: (i) x, −y+1/2, z.

(II) hydronium perchlorate

Crystal data

H3O^+·ClO4^−	F(000) = 240
Mr = 118.47	Dx = 1.963 Mg m^−3
Orthorhombic, Pnma	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ac 2n	Cell parameters from 1439 reflections
a = 9.2343 (15) Å	θ = 3.5–28.3°
b = 5.8178 (9) Å	µ = 0.84 mm^−1
c = 7.4606 (12) Å	T = 293 K
V = 400.81 (11) Å^3	Block, colorless
Z = 4	0.28 × 0.24 × 0.14 mm

Data collection

Siemens SMART CCD area-detector diffractometer	545 independent reflections
Radiation source: fine-focus sealed tube	483 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.019
Detector resolution: 8.33 pixels mm^-1	θmax = 28.3°, θmin = 3.5°
ω scans	h = −12→10
Absorption correction: multi-scan (SADABS; Sheldrick, 1996)	k = −7→7
Tmin = 0.799, Tmax = 0.891	l = −8→9
2348 measured reflections

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.047	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.130	H-atom parameters not defined
S = 1.16	w = 1/[σ^2(Fo^2) + (0.0596P)^2 + 0.6383P] where P = (Fo^2 + 2Fc^2)/3
545 reflections	(Δ/σ)max < 0.001
34 parameters	Δρmax = 0.47 e Å^−3
0 restraints	Δρmin = −0.37 e Å^−3

Special details

Experimental. The data collection covered over a hemisphere of reciprocal space by a combination of three sets of exposures; each set had a different ϕ angle (0, 88 and 180°) for the crystal and each exposure of 10 s covered 0.3° in ω. The crystal-to-detector distance was 5 cm and the detector swing angle was −35°. Crystal decay was monitored by repeating fifty initial frames at the end of data collection and analysing the intensity of duplicate reflections, and was found to be negligible.

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 (Ų)

	x	y	z	Uiso*/Ueq
Cl1	0.43197 (9)	0.2500	0.19179 (11)	0.0262 (3)
O1	0.3147 (4)	0.2500	0.0651 (4)	0.0456 (8)
O2	0.5686 (4)	0.2500	0.1019 (5)	0.0575 (11)
O3	0.4202 (2)	0.0486 (4)	0.3035 (3)	0.0400 (6)
O1W	0.3192 (4)	0.2500	0.6655 (4)	0.0440 (8)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Cl1	0.0245 (5)	0.0289 (5)	0.0252 (5)	0.000	0.0016 (3)	0.000
O1	0.0487 (19)	0.053 (2)	0.0352 (16)	0.000	−0.0180 (15)	0.000
O2	0.0367 (18)	0.072 (3)	0.063 (2)	0.000	0.0243 (16)	0.000
O3	0.0456 (12)	0.0324 (12)	0.0420 (11)	0.0006 (9)	−0.0033 (9)	0.0097 (9)
O1W	0.0381 (17)	0.0493 (19)	0.0447 (17)	0.000	0.0018 (14)	0.000

Geometric parameters (Å, º)

Cl1—O2	1.429 (3)	Cl1—O3^i	1.442 (2)
Cl1—O1	1.437 (3)	Cl1—O3	1.442 (2)
O1—Cl1—O2	110.9 (2)	O2—Cl1—O3	109.77 (13)
O2—Cl1—O3^i	109.77 (13)	O3—Cl1—O1	108.85 (12)
O1—Cl1—O3^i	108.85 (12)	O3^i—Cl1—O3	108.68 (18)

Symmetry code: (i) x, −y+1/2, z.