Magnesium sulfate hexahydrate at 120 K

The structure of [Mg(H₂O)₆]SO₄ was redetermined at 120 K, confirming the hydrogen-bond pattern found at room temperature [Zalkin et al. (1964). Acta Cryst. 17, 235-240] but showing the librational corrections of bond lengths to be unrealistic.

Computing details

Data collection: SMART (Bruker, 1999); cell refinement: SMART'; data reduction: SAINT (Bruker, 1999); program(s) used to solve structure: SHELXTL (Bruker, 1997); program(s) used to refine structure: SHELXTL; software used to prepare material for publication: SHELXTL.

magnesium sulfate hexahydrate

Crystal data

[Mg(H2O)6]SO4	F(000) = 960
Mr = 228.47	Dx = 1.765 Mg m^−3
Monoclinic, C2/c	Mo Kα radiation, λ = 0.71073 Å
a = 9.975 (2) Å	Cell parameters from 552 reflections
b = 7.186 (2) Å	θ = 11.9–25.7°
c = 24.267 (6) Å	µ = 0.48 mm^−1
β = 98.78 (1)°	T = 120 K
V = 1719.1 (7) Å^3	Block, colourless
Z = 8	0.75 × 0.40 × 0.35 mm

Data collection

SMART 1K CCD area-detector diffractometer	1689 independent reflections
Radiation source: fine-focus sealed tube	1604 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.020
Detector resolution: 8 pixels mm^-1	θmax = 26.9°, θmin = 1.7°
ω scans	h = −12→12
Absorption correction: multi-scan (SADABS; Sheldrick, 1998)	k = −8→8
Tmin = 0.679, Tmax = 0.837	l = −29→29
6251 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)] = 0.029	Hydrogen site location: difference Fourier map
wR(F^2) = 0.078	All H-atom parameters refined
S = 1.19	w = 1/[σ^2(Fo^2) + (0.0341P)^2 + 3.381P] where P = (Fo^2 + 2Fc^2)/3
1689 reflections	(Δ/σ)max = 0.001
159 parameters	Δρmax = 0.33 e Å^−3
0 restraints	Δρmin = −0.38 e Å^−3

Special details

Experimental. The data collection nominally covered full sphere of reciprocal space, by a combination of 4 sets of ω scans; each set at different φ and angle and each scan (10 sec exposure) covering 0.3° in ω. Crystal to detector distance 4.51 cm.

Geometry. All e.s.d.'s are estimated using the full covariance matrix.

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.

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

	x	y	z	Uiso*/Ueq
Mg1	0.5000	0.5000	0.0000	0.0127 (2)
Mg2	1.0000	0.93896 (12)	0.2500	0.0116 (2)
S	0.86905 (4)	0.44642 (6)	0.12308 (2)	0.01197 (14)
O1	0.77516 (13)	0.59334 (18)	0.13601 (5)	0.0151 (3)
O2	0.98840 (14)	0.44126 (19)	0.16642 (6)	0.0197 (3)
O3	0.91037 (14)	0.48866 (19)	0.06833 (6)	0.0161 (3)
O4	0.79963 (13)	0.26483 (18)	0.11916 (6)	0.0154 (3)
O5	0.58737 (15)	0.7159 (2)	0.04683 (6)	0.0175 (3)
H1	0.643 (3)	0.694 (4)	0.0748 (12)	0.028 (7)*
H2	0.549 (3)	0.802 (4)	0.0558 (11)	0.024 (7)*
O6	0.53553 (16)	0.3247 (2)	0.06722 (7)	0.0232 (3)
H3	0.501 (3)	0.227 (5)	0.0681 (12)	0.038 (8)*
H4	0.611 (3)	0.309 (4)	0.0868 (11)	0.026 (7)*
O7	0.31152 (15)	0.5521 (2)	0.02144 (7)	0.0213 (3)
H5	0.302 (3)	0.623 (4)	0.0456 (13)	0.030 (7)*
H6	0.243 (4)	0.532 (5)	0.0008 (17)	0.055 (10)*
O8	0.88639 (14)	1.1442 (2)	0.28192 (6)	0.0146 (3)
H7	0.841 (3)	1.106 (4)	0.3027 (11)	0.014 (6)*
H8	0.924 (3)	1.239 (4)	0.2957 (12)	0.036 (8)*
O9	0.88403 (16)	0.7415 (2)	0.28058 (6)	0.0171 (3)
H9	0.914 (3)	0.650 (5)	0.2958 (12)	0.034 (8)*
H10	0.810 (3)	0.720 (4)	0.2715 (12)	0.031 (8)*
O10	0.85847 (15)	0.9405 (2)	0.17928 (6)	0.0169 (3)
H11	0.838 (3)	0.845 (4)	0.1627 (12)	0.030 (7)*
H12	0.840 (3)	1.033 (4)	0.1592 (11)	0.022 (6)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Mg1	0.0118 (4)	0.0122 (4)	0.0135 (4)	−0.0001 (3)	−0.0001 (3)	−0.0007 (3)
Mg2	0.0113 (4)	0.0115 (4)	0.0116 (4)	0.000	0.0004 (3)	0.000
S	0.0123 (2)	0.0101 (2)	0.0126 (2)	0.00030 (16)	−0.00082 (17)	−0.00036 (16)
O1	0.0160 (7)	0.0134 (7)	0.0158 (7)	0.0027 (5)	0.0017 (5)	−0.0007 (5)
O2	0.0196 (7)	0.0144 (7)	0.0218 (8)	0.0013 (5)	−0.0076 (6)	−0.0014 (6)
O3	0.0175 (7)	0.0145 (7)	0.0169 (7)	0.0002 (5)	0.0045 (5)	0.0003 (5)
O4	0.0171 (7)	0.0114 (7)	0.0169 (7)	−0.0015 (5)	0.0003 (5)	0.0010 (5)
O5	0.0152 (7)	0.0162 (7)	0.0193 (8)	0.0029 (6)	−0.0030 (6)	−0.0046 (6)
O6	0.0188 (8)	0.0214 (8)	0.0258 (8)	−0.0080 (6)	−0.0079 (6)	0.0100 (6)
O7	0.0143 (7)	0.0275 (8)	0.0213 (8)	0.0016 (6)	0.0005 (6)	−0.0110 (7)
O8	0.0146 (7)	0.0135 (7)	0.0158 (7)	−0.0018 (5)	0.0031 (6)	−0.0021 (6)
O9	0.0137 (7)	0.0158 (7)	0.0209 (7)	−0.0011 (6)	−0.0003 (6)	0.0054 (6)
O10	0.0219 (7)	0.0126 (7)	0.0141 (7)	−0.0008 (6)	−0.0043 (6)	0.0009 (6)

Geometric parameters (Å, º)

Mg1—O5	2.0385 (15)	S—O1	1.4764 (14)
Mg1—O5^i	2.0385 (15)	S—O3	1.4814 (14)
Mg1—O6	2.0485 (15)	O5—H1	0.82 (3)
Mg1—O6^i	2.0485 (15)	O5—H2	0.78 (3)
Mg1—O7^i	2.0601 (15)	O6—H3	0.78 (3)
Mg1—O7	2.0601 (15)	O6—H4	0.83 (3)
Mg2—O9^ii	2.0409 (16)	O7—H5	0.79 (3)
Mg2—O9	2.0409 (16)	O7—H6	0.80 (4)
Mg2—O10^ii	2.0491 (14)	O8—H7	0.77 (3)
Mg2—O10	2.0491 (14)	O8—H8	0.82 (3)
Mg2—O8	2.0804 (16)	O9—H9	0.79 (3)
Mg2—O8^ii	2.0804 (16)	O9—H10	0.75 (3)
S—O2	1.4638 (14)	O10—H11	0.80 (3)
S—O4	1.4735 (14)	O10—H12	0.83 (3)
O5—Mg1—O5^i	180.00 (7)	O10^ii—Mg2—O8^ii	87.89 (6)
O5—Mg1—O6	90.96 (7)	O10—Mg2—O8^ii	91.67 (6)
O5^i—Mg1—O6	89.04 (7)	O8—Mg2—O8^ii	89.69 (9)
O5—Mg1—O6^i	89.04 (7)	O2—S—O4	110.28 (8)
O5^i—Mg1—O6^i	90.96 (7)	O2—S—O1	109.76 (8)
O6—Mg1—O6^i	180.00 (9)	O4—S—O1	109.87 (8)
O5—Mg1—O7^i	87.13 (6)	O2—S—O3	110.03 (9)
O5^i—Mg1—O7^i	92.87 (6)	O4—S—O3	108.42 (8)
O6—Mg1—O7^i	92.05 (7)	O1—S—O3	108.45 (8)
O6^i—Mg1—O7^i	87.95 (7)	Mg1—O5—H1	119 (2)
O5—Mg1—O7	92.87 (6)	Mg1—O5—H2	125 (2)
O5^i—Mg1—O7	87.13 (6)	H1—O5—H2	103 (3)
O6—Mg1—O7	87.95 (7)	Mg1—O6—H3	123 (2)
O6^i—Mg1—O7	92.05 (7)	Mg1—O6—H4	124.4 (19)
O7^i—Mg1—O7	180.00 (8)	H3—O6—H4	103 (3)
O9^ii—Mg2—O9	91.88 (9)	Mg1—O7—H5	121 (2)
O9^ii—Mg2—O10^ii	87.25 (7)	Mg1—O7—H6	123 (3)
O9—Mg2—O10^ii	93.18 (7)	H5—O7—H6	113 (3)
O9^ii—Mg2—O10	93.18 (7)	Mg2—O8—H7	113.3 (18)
O9—Mg2—O10	87.25 (7)	Mg2—O8—H8	120 (2)
O10^ii—Mg2—O10	179.38 (10)	H7—O8—H8	108 (3)
O9^ii—Mg2—O8	178.49 (7)	Mg2—O9—H9	124 (2)
O9—Mg2—O8	89.22 (6)	Mg2—O9—H10	128 (2)
O10^ii—Mg2—O8	91.67 (6)	H9—O9—H10	104 (3)
O10—Mg2—O8	87.89 (6)	Mg2—O10—H11	120 (2)
O9^ii—Mg2—O8^ii	89.22 (6)	Mg2—O10—H12	124.0 (18)
O9—Mg2—O8^ii	178.49 (7)	H11—O10—H12	112 (3)

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

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O5—H1···O1	0.82 (3)	1.97 (3)	2.780 (2)	169 (3)
O5—H2···O3^iii	0.78 (3)	1.98 (3)	2.741 (2)	165 (3)
O6—H3···O3^iv	0.78 (3)	1.94 (4)	2.720 (2)	178 (3)
O6—H4···O4	0.83 (3)	1.95 (3)	2.775 (2)	169 (3)
O7—H5···O4^iii	0.79 (3)	2.06 (3)	2.839 (2)	168 (3)
O7—H6···O3^i	0.80 (4)	2.09 (4)	2.874 (2)	165 (4)
O8—H7···O1^v	0.77 (3)	2.02 (3)	2.771 (2)	162 (3)
O8—H8···O2^vi	0.82 (3)	1.86 (3)	2.685 (2)	174 (3)
O9—H9···O2^ii	0.79 (3)	1.94 (3)	2.725 (2)	172 (3)
O9—H10···O8^vii	0.75 (3)	2.24 (3)	2.969 (2)	162 (3)
O10—H11···O1	0.80 (3)	1.99 (3)	2.784 (2)	168 (3)
O10—H12···O4^viii	0.83 (3)	1.94 (3)	2.765 (2)	174 (3)

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