The monoclinic and cubic phases of metaboric acid (precise redeterminations)

In monoclinic [beta]-HBO₂, endless [B₃O₃(OH)(H₂O)(O_2/2)] zigzag chains are linked via an extensive system of hydrogen bonds with stronger major [H...O between 1.67 (1) and 1.77 (1) Å] and weaker minor components [H...O between 2.48 (1) and 2.63 (1) Å]. The unique three-dimensional tetrahedral [BO_2/2O_2/2(H)] network structure of cubic [gamma]-­HBO₂ is stabilized by very short asymmetric hydrogen bonds [H...O2 1.48 (1) Å] with a donor-acceptor distance of 2.485 (1) Å and possesses small empty cages with a free diameter of ca 3.2 Å.

S1. Comment

Metaboric acid exists in three crystalline phases (Wells, 1984), which are prepared by dehydration of orthoboric acid and subsequent heat treatment. The monotropic phase transitions of HBO₂ are caused by polymerization and change from trigonal-planar BO₃ to increasing numbers of tetrahedral BO₄ units. Structural information available for the monoclinic β- and cubic γ-phases stem from the room-temperature single-crystal X-ray studies of Zachariasen (1963a,b) which were based on low numbers of reflections only (for today's standard). Nevertheless, reasonable positions of H atoms were obtained by inferring initial sites using geometrical criteria and subsequent refinements. In the course of our studies on borate clathrates we have carried out new structure refinements of both β- and γ-HBO₂ based on low-temperature single-crystal X-ray diffraction data which allowed the localization of all H atoms on difference Fourier maps. Our results are in close agreement with those of Zachariasen but of considerably higher precession and we can supplement his structure discussions regarding the hydrogen bonding schemes and the unique tetrahedral network structure of the γ-phase. These structural details may be of interest for example for studies on boron-oxide containing glasses and high-silica zeolites.

The basic structural units of both β- and γ-HBO₂ are six-membered B₃O₃-rings which are displayed in Fig. 1. In the β-phase the B2 and B3 atoms are both three-coordinated. To the B1 atom an H₂O molecule is bonded resulting in a distorted tetrahedral coordination. The B1 atom is slightly displaced [0.228 Å] from the otherwise nearly planar six-membered ring in the direction towards the water O5 atom. As is shown in Fig. 2, six-membered rings are linked via the O4 atoms into polymeric [B₃O₃(OH)(H₂O)(O_2/2)] zigzag chains of 2₁-symmetry {extended along [010]} which in turn are arranged in layers parallel (102). Chains are linked via intra-layer hydrogen bonds H3···O3 [1.77 (1) Å] between exocyclic O6–H3 hydroxyl groups and endocyclic O3 atoms and via inter-layer hydrogen bonds H1···O6 [1.70 (1) Å] and H2···O1 [1.67 (1) Å] donated by the water molecules to exocyclic hydroxyl O6 and endocyclic O1 atoms, respectively. In addition to these nearly linear hydrogen bonding systems of typical geometry, already discussed by Zachariasen (1963a), there are three further contacts [namely H2···O4 2.48 (1) Å, H2···O2 2.63 (1) Å and H3···O4 2.62 (1) Å] that, according to recently reported considerations on hydrogen bonds (Steiner & Saenger, 1992), may be taken as weaker minor components of multi-centre hydrogen-bonding systems (then, according to that H2···O1 and H3···O3 are the major components). This latter view finds some support by the bond-valence sum concept (Brown, 1992) when applying the graphical valence-distance correlation for H···O bonds of Brown & Altermatt (1985) to estimate O–H and H···O parameters. This method yields with (without) minor components the following valences for involved O atoms: 2.01 (1.96) for O2, 2.03 (1.92) for O4, 2.02 (2.13) for O5 and 2.00 (2.05) for O6 [valences for the remaining atoms: 2.03 for O1, 2.02 for O3, 3.07 for B1, 3.03 for B2, 3.02 for B3, 1.0 for all H].

In γ-HBO₂ the six-membered B₃O₃-ring of 3(C₃)-symmetry possesses a flat chair conformation [torsion angles ±39.92°], and the B atom is tetrahedrally coordinated. Fig. 3 shows the unique three-dimensional tetrahedral [BO_2/2O_2/2(H)] network structure. This is to our knowledge the only chemical representative which is topologically based on net 37 of O'Keeffe's (1992, 1995) compilation of uninodal 4-connected three-dimensional nets (maximum symmetry Pm3n; short Schläfli symbol is 3.4.8⁴). Considering only the tetrahedral nodes, there occurs one type of three-ring, one type of four-ring, one type of puckered oval eight-ring and one type of puckered circular eight-ring. Formally, the eight-rings define two types of channel systems each running parallel to [100] directions [on x,0,0 and x,1/2,0, respectively], and on the intersection of the oval channels [on 0,0,0] there exists a small [3₈8₆] cage of 23(T)-symmetry formed by six oval eight-rings and eight three-rings the latter being arranged with their centres on the corners of two interpenetrating tetrahedra of different sizes. Considering all atoms, the oval and circular channels are blocked by very strong, definitely asymmetric hydrogen bonds H···O2 [1.48 (1) Å] with a donor-acceptor distance of 2.485 (1) Å [geometrical parameters of short hydrogen bonds derived from neutron diffraction studies can be found by Joswig et al. (1982), and a review of very strong hydrogen bonds by Emsley (1980)]. Interestingly, according to the work of Schwarzmann & Christoph (1969) these strong hydrogen bonds exhibit an H—D isotope effect that results in a considerably larger cubic unit cell of the deuterated form (by 0.023 Å at room temperature) and renders the formation of γ-DBO₂ possible only after seeding and very long heating periods. The small empty cages of the γ-HBO₂-network have a free diameter of ca 3.2 Å (van der Waals radius for oxygen taken as 1.4 Å).

S2. Experimental

Orthoboric acid is placed in an open crucible and dehydrated at 373 K for 24 h to yield orthorhombic α-HBO₂, which is heated under closed conditions (Teflon-lined stainless steel autoclave) at 423 K for 24 h to yield crystalline β-HBO₂ (crystal size up to 3 mm). The β-phase is kept under closed conditions at 453 K for at least 7 d to give crystals of the γ-form (crystal size up to 0.5 mm). The conditions reported yield essentially pure-phase materials as checked by powder X-ray diffraction (Guinier diffractometer, Cuα₁ radiation).

S3. Refinement

Coordinates of the non-H atoms were taken from the literature (Zachariasen 1963a,b). All H atoms were located on difference Fourier maps, in the case of γ-HBO₂ after refinement of an extinction parameter.

Computing details

For both compounds, data collection: CAD-4 Software (Enraf-Nonius, 1989); cell refinement: SET4 in CAD-4 Software; data reduction: MolEN (Fair, 1990); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ORTEP-3 (Farrugia, 1997) and DIAMOND (Brandenburg & Berndt, 1999); software used to prepare material for publication: SHELXL97.

Figures

	Fig. 1. Six-membered B3O3-rings of β-HBO2 (left) and of γ-HBO2 (right). Displacement ellipsoids correspond to the 90% probability level. H atoms are represented as spheres of arbitrary radii (ORTEP-3; Farrugia, 1997). [Symmetry code: (i) y, z, x; (ii) z, x, y; (iii) -x + 1.5, -z + 1.5, y - 0.5].
	Fig. 2. Two parallel polymeric chains of one layer in β-HBO2 projected on (102). The two H2O-molecules seen between the two chains belong to chains in adjacent layers above and below. B atoms are shown as black spheres, O atoms as hatched spheres and H atoms as white spheres of arbitrary radii. Major (minor) components of hydrogen bonds are represented as thin (dashed) lines (DIAMOND; Brandenburg & Berndt, 1999).
	Fig. 3. Structure of γ-HBO2 as seen along [100] (DIAMOND; Brandenburg & Berndt, 1999).

(I) metaboric acid, β-phase

Crystal data

HBO2	F(000) = 264
Mr = 43.82	Dx = 2.069 Mg m^−3
Monoclinic, P21/c	Mo Kα radiation, λ = 0.71073 Å
a = 6.758 (1) Å	Cell parameters from 25 reflections
b = 8.844 (1) Å	θ = 12.0–23.7°
c = 7.075 (2) Å	µ = 0.21 mm^−1
β = 93.50 (1)°	T = 183 K
V = 422.1 (1) Å^3	Irregular polyhedron, colourless
Z = 12	0.45 × 0.30 × 0.30 mm

Data collection

Enraf-Nonius CAD4 diffractometer	θmax = 50.0°
ω–2θ scans	h = 0→14
4617 measured reflections	k = 0→19
4400 independent reflections	l = −15→15
3549 reflections with F > 4σ(F)	3 standard reflections every 200 reflections
Rint = 0.029	intensity decay: 1.5%

Refinement

Refinement on F^2	All H-atom parameters refined
R[F^2 > 2σ(F^2)] = 0.031	w = 1/[σ^2(Fo^2) + (0.0528P)^2 + 0.0061P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.087	(Δ/σ)max < 0.001
S = 1.08	Δρmax = 0.50 e Å^−3
4400 reflections	Δρmin = −0.57 e Å^−3
94 parameters

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.

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

	x	y	z	Uiso*/Ueq
B1	0.82973 (5)	−0.04305 (4)	0.23313 (6)	0.00774 (5)
B2	0.97799 (5)	0.21057 (4)	0.26215 (6)	0.00767 (5)
B3	0.67149 (6)	0.16278 (4)	0.40129 (6)	0.00801 (5)
O1	0.99486 (4)	0.06010 (3)	0.21706 (4)	0.00814 (4)
O2	0.81676 (4)	0.26220 (3)	0.35432 (4)	0.01051 (5)
O3	0.68233 (4)	0.01329 (3)	0.35631 (4)	0.00941 (4)
O4	0.87806 (4)	−0.19463 (3)	0.28819 (4)	0.00967 (4)
O5	0.72270 (4)	−0.04719 (3)	0.03131 (4)	0.00988 (4)
O6	0.51804 (4)	0.21638 (3)	0.49931 (5)	0.01135 (5)
H1	0.638 (2)	−0.1334 (15)	0.006 (2)	0.047 (4)*
H2	0.822 (2)	−0.0530 (16)	−0.0703 (19)	0.051 (4)*
H3	0.4367 (19)	0.1347 (13)	0.5269 (18)	0.039 (3)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
B1	0.00797 (11)	0.00388 (10)	0.01178 (12)	−0.00004 (8)	0.00394 (9)	−0.00032 (9)
B2	0.00788 (11)	0.00420 (10)	0.01121 (12)	−0.00041 (8)	0.00275 (9)	−0.00058 (9)
B3	0.00819 (11)	0.00480 (11)	0.01143 (13)	0.00057 (8)	0.00363 (9)	−0.00048 (9)
O1	0.00789 (8)	0.00376 (7)	0.01320 (9)	−0.00088 (6)	0.00417 (6)	−0.00123 (6)
O2	0.00953 (9)	0.00489 (8)	0.01783 (11)	−0.00085 (6)	0.00672 (8)	−0.00219 (7)
O3	0.00987 (8)	0.00441 (7)	0.01469 (10)	−0.00015 (6)	0.00682 (7)	−0.00105 (7)
O4	0.00966 (8)	0.00390 (7)	0.01601 (10)	0.00162 (6)	0.00549 (7)	0.00134 (7)
O5	0.01026 (9)	0.00778 (9)	0.01184 (9)	−0.00225 (7)	0.00267 (7)	−0.00057 (7)
O6	0.01098 (9)	0.00598 (8)	0.01801 (11)	0.00125 (7)	0.00834 (8)	−0.00018 (7)

Geometric parameters (Å, º)

B1—O4	1.4284 (5)	B3—O3	1.3628 (5)
B1—O1	1.4512 (5)	B3—O6	1.3671 (5)
B1—O3	1.4512 (5)	B3—O2	1.3738 (5)
B1—O5	1.5612 (6)	O5—H1	0.963 (14)
B2—O4^i	1.3485 (5)	O5—H2	1.013 (15)
B2—O1	1.3748 (4)	O6—H3	0.936 (12)
B2—O2	1.3812 (5)
O4—B1—O1	116.56 (3)	O3—B3—O2	121.00 (3)
O4—B1—O3	108.21 (3)	O6—B3—O2	118.44 (3)
O1—B1—O3	112.99 (3)	B2—O1—B1	121.01 (3)
O4—B1—O5	108.23 (3)	B3—O2—B2	119.91 (3)
O1—B1—O5	104.99 (3)	B3—O3—B1	121.46 (3)
O3—B1—O5	105.11 (3)	B2^ii—O4—B1	131.93 (3)
O4^i—B2—O1	117.98 (3)	B1—O5—H1	115.2 (8
O4^i—B2—O2	121.45 (3)	B1—O5—H2	111.2 (8)
O1—B2—O2	120.57 (3)	H1—O5—H2	103.7 (11)
O3—B3—O6	120.54 (3)	B3—O6—H3	108.2 (8)

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

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O5—H1···O6^iii	0.96 (1)	1.70 (1)	2.650 (1)	170.2 (8)
O5—H2···O1^iv	1.01 (1)	1.67 (1)	2.675 (1)	173.3 (8)
O5—H2···O4^v	1.01 (1)	2.48 (1)	3.081 (1)	117.1 (8)
O5—H2···O2^vi	1.01 (1)	2.63 (1)	2.902 (1)	95.4 (8)
O6—H3···O3^vii	0.94 (1)	1.77 (1)	2.678 (1)	163.6 (8)
O6—H3···O4^vii	0.94 (1)	2.62 (1)	3.155 (1)	117.0 (8)

Symmetry codes: (iii) −x+1, y−1/2, −z+1/2; (iv) −x+2, −y, −z; (v) x, −y−1/2, z−1/2; (vi) x, −y+1/2, z−1/2; (vii) −x+1, −y, −z+1.

(II) metaboric acid, γ-phase

Crystal data

HBO2	Mo Kα radiation, λ = 0.71073 Å
Mr = 43.82	Cell parameters from 25 reflections
Cubic, P43n	θ = 15.4–20.4°
a = 8.8811 (3) Å	µ = 0.25 mm^−1
V = 700.49 (4) Å^3	T = 183 K
Z = 24	Rhombic dodecahedron, colourless
F(000) = 528	0.3 mm (radius)
Dx = 2.493 Mg m^−3

Data collection

Enraf-Nonius CAD-4 diffractometer	θmax = 49.9°
ω–2θ scans	h = 0→19
3758 measured reflections	k = 0→19
686 independent reflections	l = 0→19
628 reflections with F > 4σ(F)	3 standard reflections every 200 reflections
Rint = 0.031	intensity decay: 1.3%

Refinement

Refinement on F^2	(Δ/σ)max < 0.001
R[F^2 > 2σ(F^2)] = 0.019	Δρmax = 0.29 e Å^−3
wR(F^2) = 0.045	Δρmin = −0.26 e Å^−3
S = 1.02	Extinction correction: SHELXL97 (Sheldrick, 1997), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
686 reflections	Extinction coefficient: 0.393 (13)
33 parameters	Absolute structure: Flack (1983)
All H-atom parameters refined	Absolute structure parameter: −1.4 (6)
w = 1/[σ^2(Fo^2) + (0.0197P)^2] where P = (Fo^2 + 2Fc^2)/3

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.

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

	x	y	z	Uiso*/Ueq
B	0.71733 (5)	0.80853 (5)	0.58110 (5)	0.00407 (7)
O1	0.82221 (4)	0.92596 (4)	0.64509 (4)	0.00427 (5)
O2	0.80015 (4)	0.66772 (3)	0.58016 (4)	0.00421 (5)
H	0.9275 (15)	0.8920 (16)	0.6707 (16)	0.035 (4)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
B	0.00421 (14)	0.00403 (14)	0.00397 (14)	0.00006 (11)	0.00022 (11)	−0.00001 (11)
O1	0.00374 (9)	0.00327 (10)	0.00580 (10)	0.00029 (7)	−0.00085 (7)	−0.00098 (8)
O2	0.00556 (10)	0.00352 (9)	0.00355 (9)	0.00102 (7)	0.00044 (8)	0.00027 (8)

Geometric parameters (Å, º)

B—O2^i	1.4428 (6)	B—O1	1.5094 (6)
B—O2	1.4508 (6)	O1—H	1.009 (13)
B—O1^ii	1.4803 (6)
O2^i—B—O2	112.75 (4)	O1^ii—B—O1	107.74 (4)
O2^i—B—O1^ii	108.08 (3)	B^iii—O1—B	126.97 (3)
O2—B—O1^ii	110.78 (4)	B^iv—O2—B	118.74 (4)
O2^i—B—O1	110.85 (3)	B^iii—O1—H	115.8 (8)
O2—B—O1	106.55 (3)	B—O1—H	116.8 (8)

Symmetry codes: (i) z, x, y; (ii) −x+3/2, −z+3/2, y−1/2; (iii) −x+3/2, z+1/2, −y+3/2; (iv) y, z, x.

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O1—H1···O2^v	1.01 (1)	1.48 (1)	2.485 (1)	176 (1)

Symmetry code: (v) z+1/2, −y+3/2, −x+3/2.