An investigation of H-atom positions in sulfuric acid crystal structures

Hirsch, T.K.; Ojamäe, L.

doi:10.1107/S0108768104000540

An investigation of H-atom positions in sulfuric acid crystal structures

Hydrogen conformations in crystalline H₂SO₄·8H₂O and H₂SO₄·6.5H₂O have been studied using a system developed by Hirsch [(2003), Z. Anorg. Allg. Chem. 629, 666-672]. New H-atom coordinates, as estimated from DFT calculations, are given for these structures.

Keywords: theoretical calculations; H-atom coordinates; sulfuric acid crystal structures.

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Supporting information

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768104000540/na5005sup1.cif
Contains datablocks global, I, II, III, IV

Computing details top

For all compounds, program(s) used to refine structure: (Jana2000; Petricek and Dusek, 2000); software used to prepare material for publication: (Jana2000; Petricek and Dusek, 2000).

Figures top

(I) top

Crystal data top

SO₄·2(H5O₂)·4(H2O)	β = 116.2165°
M_r = 242.20	V = 1195.7 (13) Å³
Monoclinic, Cc	Z = 4
a = 10.560 (4) Å	D_x = 0 Mg m⁻³
b = 10.560 (4) Å	Mo Kα radiation, λ = 0.71073 Å
c = 11.952 (11) Å	× × mm

Data collection top

h = ?→?	l = ?→?
k = ?→?

Refinement top

Crystal data top

SO₄·2(H5O₂)·4(H2O)	β = 116.2165°
M_r = 242.20	V = 1195.7 (13) Å³
Monoclinic, Cc	Z = 4
a = 10.560 (4) Å	Mo Kα radiation
b = 10.560 (4) Å	× × mm
c = 11.952 (11) Å

Data collection top

Refinement top

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

	x	y	z	U_iso*/U_eq
S1a	0	0.125	0	0.01950 (6)
O1a	0.07426 (9)	0.14626 (9)	−0.07806 (8)	0.0287 (3)
O1b	0.01777 (9)	0.23829 (9)	0.07806 (8)	0.0287 (3)
O1c	−0.15232 (9)	0.10374 (9)	−0.07806 (8)	0.0287 (3)
O1d	0.06029 (9)	0.01171 (9)	0.07806 (8)	0.0287 (3)
O2a	0.32917 (8)	−0.00558 (7)	0.26498 (8)	0.0256 (3)
O2b	0.23693 (8)	0.57168 (7)	0.23502 (8)	0.0256 (3)
O2c	0.43581 (8)	0.75558 (7)	0.26498 (8)	0.0256 (3)
O2d	−0.00190 (8)	0.67832 (7)	0.23502 (8)	0.0256 (3)
O3a	0.27905 (10)	0.01940 (10)	0.46276 (8)	0.0283 (3)
O3b	0.16302 (10)	0.42267 (10)	0.03724 (8)	0.0283 (3)
O3c	0.18371 (10)	0.23060 (10)	0.46276 (8)	0.0283 (3)
O3d	0.37422 (10)	0.32733 (10)	0.03724 (8)	0.0283 (3)
H2aA	0.3916	0.0593	0.2541	0.00287 (3)*
H2aB	0.2339	0.0025	0.1934	0.00287 (3)*
H2bA	0.2807	0.5121	0.3064	0.00287 (3)*
H2bB	0.3073	0.6396	0.2461	0.00287 (3)*
H2cA	0.3957	0.8420	0.2621	0.00287 (3)*
H2cB	0.4613	0.7497	0.1942	0.00287 (3)*
H2dA	0.0277	0.7387	0.3061	0.00287 (3)*
H2dB	0.0858	0.6396	0.2377	0.00287 (3)*
H3aA	0.2308	0.1251	0.4621	0.00287 (3)*
H3aB	0.2049	−0.0466	0.4491	0.00287 (3)*
H3aC	0.3059	0.0113	0.3915	0.00287 (3)*
H3bA	0.1903	0.4856	0.1081	0.00287 (3)*
H3bB	0.1039	0.3553	0.0507	0.00287 (3)*
H3bC	0.2693	0.3745	0.0376	0.00287 (3)*
H3cA	0.2450	0.2960	0.4494	0.00287 (3)*
H3cB	0.0857	0.2401	0.3915	0.00287 (3)*
H3dA	0.4466	0.3951	0.0506	0.00287 (3)*
H3dB	0.4192	0.2651	0.1087	0.00287 (3)*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
S1a	0.01888 (6)	0.01800 (7)	0.02250 (10)	0.00000 (6)	0.00994 (4)	0
O1a	0.0389 (4)	0.0239 (4)	0.0333 (4)	0.0074 (3)	0.0251 (4)	0.0054 (4)
O1b	0.0301 (4)	0.0290 (4)	0.0333 (4)	0.0101 (3)	0.0196 (4)	0.0115 (4)
O1c	0.0207 (4)	0.0239 (4)	0.0333 (4)	0.0026 (3)	0.0044 (4)	−0.0054 (4)
O1d	0.0215 (4)	0.0290 (4)	0.0333 (4)	−0.0001 (3)	0.0098 (4)	−0.0115 (4)
O2a	0.0239 (3)	0.0261 (3)	0.0269 (4)	−0.0001 (3)	0.0112 (3)	−0.0016 (2)
O2b	0.0250 (3)	0.0239 (3)	0.0269 (4)	0.0002 (3)	0.0105 (3)	−0.0007 (2)
O2c	0.0250 (3)	0.0261 (3)	0.0269 (4)	0.0012 (3)	0.0125 (3)	0.0016 (2)
O2d	0.0275 (3)	0.0239 (3)	0.0269 (4)	0.0009 (3)	0.0133 (3)	0.0007 (2)
O3a	0.0302 (4)	0.0282 (4)	0.0305 (4)	0.0028 (3)	0.0171 (3)	−0.0013 (3)
O3b	0.0275 (4)	0.0261 (4)	0.0305 (4)	0.0051 (3)	0.0123 (3)	0.0040 (3)
O3c	0.0238 (4)	0.0282 (4)	0.0305 (4)	0.0040 (3)	0.0099 (3)	0.0013 (3)
O3d	0.0297 (4)	0.0261 (4)	0.0305 (4)	0.0016 (3)	0.0147 (3)	−0.0040 (3)

(II) top

Crystal data top

SO₄·2(H3O)·6(H2O)	β = 116.2165°
M_r = 242.20	V = 1195.7 (13) Å³
Monoclinic, Cc	Z = 4
a = 10.560 (4) Å	D_x = 0 Mg m⁻³
b = 10.560 (4) Å	Mo Kα radiation, λ = 0.71073 Å
c = 11.952 (11) Å	× × mm

Data collection top

h = ?→?	l = ?→?
k = ?→?

Refinement top

Crystal data top

SO₄·2(H3O)·6(H2O)	β = 116.2165°
M_r = 242.20	V = 1195.7 (13) Å³
Monoclinic, Cc	Z = 4
a = 10.560 (4) Å	Mo Kα radiation
b = 10.560 (4) Å	× × mm
c = 11.952 (11) Å

Data collection top

Refinement top

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

	x	y	z	U_iso*/U_eq
S1a	0	0.125	0	0.01950 (6)
O1a	0.07426 (9)	0.14626 (9)	−0.07806 (8)	0.0287 (3)
O1b	0.01777 (9)	0.23829 (9)	0.07806 (8)	0.0287 (3)
O1c	−0.15232 (9)	0.10374 (9)	−0.07806 (8)	0.0287 (3)
O1d	0.06029 (9)	0.01171 (9)	0.07806 (8)	0.0287 (3)
O2a	0.32917 (8)	−0.00558 (7)	0.26498 (8)	0.0256 (3)
O2b	0.23693 (8)	0.57168 (7)	0.23502 (8)	0.0256 (3)
O2c	0.43581 (8)	0.75558 (7)	0.26498 (8)	0.0256 (3)
O2d	−0.00190 (8)	0.67832 (7)	0.23502 (8)	0.0256 (3)
O3a	0.27905 (10)	0.01940 (10)	0.46276 (8)	0.0283 (3)
O3b	0.16302 (10)	0.42267 (10)	0.03724 (8)	0.0283 (3)
O3c	0.18371 (10)	0.23060 (10)	0.46276 (8)	0.0283 (3)
O3d	0.37422 (10)	0.32733 (10)	0.03724 (8)	0.0283 (3)
H1bA	−0.01978	0.24230	0.15023	0.00287 (3)*
H2aA	0.39129	0.05780	0.25234	0.00287 (3)*
H2aB	0.23539	0.00041	0.19246	0.00287 (3)*
H2bA	0.28128	0.51290	0.30652	0.00287 (3)*
H2bB	0.30694	0.64010	0.2459	0.00287 (3)*
H2cA	0.39706	0.84231	0.26393	0.00287 (3)*
H2cC	0.52964	0.74651	0.34593	0.00287 (3)*
H2dA	0.02895	0.73821	0.30610	0.00287 (3)*
H2dB	0.08523	0.63929	0.23653	0.00287 (3)*
H3aB	0.20998	−0.04815	0.45060	0.00287 (3)*
H3aC	0.30612	0.01027	0.39306	0.00287 (3)*
H3bA	0.18907	0.48754	0.10611	0.00287 (3)*
H3bB	0.10093	0.36101	0.04964	0.00287 (3)*
H3cA	0.24094	0.29332	0.44518	0.00287 (3)*
H3cC	0.22351	0.14289	0.46276	0.00287 (3)*
H3dA	0.44670	0.39468	0.04957	0.00287 (3)*
H3dB	0.41978	0.26390	0.10877	0.00287 (3)*
H3dC	0.27662	0.37076	0.03774	0.00287 (3)*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
S1a	0.01888 (6)	0.01800 (7)	0.02250 (10)	0.00000 (6)	0.00994 (4)	0
O1a	0.0389 (4)	0.0239 (4)	0.0333 (4)	0.0074 (3)	0.0251 (4)	0.0054 (4)
O1b	0.0301 (4)	0.0290 (4)	0.0333 (4)	0.0101 (3)	0.0196 (4)	0.0115 (4)
O1c	0.0207 (4)	0.0239 (4)	0.0333 (4)	0.0026 (3)	0.0044 (4)	−0.0054 (4)
O1d	0.0215 (4)	0.0290 (4)	0.0333 (4)	−0.0001 (3)	0.0098 (4)	−0.0115 (4)
O2a	0.0239 (3)	0.0261 (3)	0.0269 (4)	−0.0001 (3)	0.0112 (3)	−0.0016 (2)
O2b	0.0250 (3)	0.0239 (3)	0.0269 (4)	0.0002 (3)	0.0105 (3)	−0.0007 (2)
O2c	0.0250 (3)	0.0261 (3)	0.0269 (4)	0.0012 (3)	0.0125 (3)	0.0016 (2)
O2d	0.0275 (3)	0.0239 (3)	0.0269 (4)	0.0009 (3)	0.0133 (3)	0.0007 (2)
O3a	0.0302 (4)	0.0282 (4)	0.0305 (4)	0.0028 (3)	0.0171 (3)	−0.0013 (3)
O3b	0.0275 (4)	0.0261 (4)	0.0305 (4)	0.0051 (3)	0.0123 (3)	0.0040 (3)
O3c	0.0238 (4)	0.0282 (4)	0.0305 (4)	0.0040 (3)	0.0099 (3)	0.0013 (3)
O3d	0.0297 (4)	0.0261 (4)	0.0305 (4)	0.0016 (3)	0.0147 (3)	−0.0040 (3)

(III) top

Crystal data top

SO₄·2(H₃O)·4.5(H₂O)	β = 121.4202°
M_r = 215.17	V = 928.2 (3) Å³
Monoclinic, Im	Z = 4
a = 6.8182 (10) Å	D_x = 0 Mg m⁻³
b = 26.876 (5) Å	Mo Kα radiation, λ = 0.71073 Å
c = 5.936 (1) Å	× × mm

Data collection top

h = ?→?	l = ?→?
k = ?→?

Refinement top

Crystal data top

SO₄·2(H₃O)·4.5(H₂O)	β = 121.4202°
M_r = 215.17	V = 928.2 (3) Å³
Monoclinic, Im	Z = 4
a = 6.8182 (10) Å	Mo Kα radiation
b = 26.876 (5) Å	× × mm
c = 5.936 (1) Å

Data collection top

Refinement top

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

	x	y	z	U_iso*/U_eq
S1	0.25	0.128980 (10)	0.25	0.01402 (12)
O1	0.3693 (2)	0.08064 (3)	0.2808 (3)	0.0199 (4)
O2	0.30450 (10)	0.16239 (3)	0.0904 (2)	0.0203 (4)
O3	0.0003 (2)	0.12035 (4)	0.1106 (3)	0.0242 (4)
O4	0.3335 (2)	0.15105 (3)	0.5113 (3)	0.0257 (5)
O5	0.9815 (2)	0.21805 (3)	0.7249 (3)	0.0244 (5)
O6	0.2426 (2)	0.25058 (3)	0.3903 (3)	0.0215 (4)
O7	0.7533 (2)	0.18307 (3)	0.2393 (3)	0.0204 (4)
O8	0.6801 (3)	0	0.8882 (4)	0.0289 (7)
O9	0.4760 (3)	0.07605 (4)	0.8838 (4)	0.0356 (7)
O10	0.1200 (2)	0	0.2700 (3)	0.0224 (4)
O11	0.0289 (3)	0	0.6534 (4)	0.0283 (7)
O12	0.8391 (2)	0.08076 (4)	0.6232 (3)	0.0257 (5)
H5a	1.10323	0.19500	0.85573	0*
H5b	0.89289	0.20320	0.54228	0*
H5c	0.87635	0.23183	0.79696	0*
H6a	0.24468	0.27263	0.52434	0*
H6b	0.28698	0.21706	0.46408	0*
H7a	0.83011	0.15553	0.20714	0*
H7b	0.59578	0.17300	0.18247	0*
H8a	0.84657	0.00000	1.02936	0*
H8b	0.59622	0.03227	0.88523	0*
H9a	0.42051	0.07825	1.00462	0*
H9c	0.41886	0.10402	0.75989	0*
H10a	0.20689	0.02945	0.27175	0*
H11a	−0.05600	0.03285	0.64306	0*
H11b	0.07600	0.00000	0.52035	0*
H12b	0.88410	0.09628	0.79306	0*
H12c	0.67175	0.08195	0.50978	0*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
S1	0.01460 (10)	0.01240 (10)	0.0163 (2)	0.00010 (10)	0.00893 (13)	−0.00120 (13)
O1	0.0204 (4)	0.0137 (3)	0.0274 (7)	0.0025 (3)	0.0138 (4)	0.0003 (4)
O2	0.0196 (4)	0.0200 (4)	0.0235 (7)	0.0018 (3)	0.0128 (4)	0.0050 (4)
O3	0.0149 (4)	0.0287 (4)	0.0317 (6)	−0.0011 (4)	0.0140 (4)	0.0037 (5)
O4	0.0389 (5)	0.0187 (4)	0.0191 (8)	−0.0011 (4)	0.0149 (6)	−0.0035 (4)
O5	0.0246 (4)	0.0239 (4)	0.0243 (8)	−0.0038 (4)	0.0124 (5)	−0.0059 (5)
O6	0.0231 (4)	0.0181 (4)	0.0223 (7)	−0.0004 (3)	0.0113 (4)	−0.0035 (4)
O7	0.0189 (4)	0.0179 (3)	0.0285 (7)	−0.0022 (3)	0.0152 (4)	−0.0036 (4)
O8	0.0310 (6)	0.0248 (6)	0.0387 (11)	0	0.0235 (7)	0
O9	0.0555 (8)	0.0300 (5)	0.0414 (9)	−0.0208 (5)	0.0393 (8)	−0.0153 (6)
O10	0.0258 (5)	0.0119 (5)	0.0378 (6)	0	0.0225 (4)	0
O11	0.0289 (6)	0.0277 (6)	0.0353 (11)	0	0.0216 (7)	0
O12	0.0219 (4)	0.0269 (4)	0.0267 (8)	−0.0004 (3)	0.0115 (5)	0.0026 (5)

(IV) top

Crystal data top

SO₄·2(H₃O)·4.5(H₂O)	β = 121.4202°
M_r = 215.17	V = 928.2 (3) Å³
Monoclinic, Im	Z = 4
a = 6.8182 (10) Å	D_x = 0 Mg m⁻³
b = 26.876 (5) Å	Mo Kα radiation, λ = 0.71073 Å
c = 5.936 (1) Å	× × mm

Data collection top

h = ?→?	l = ?→?
k = ?→?

Refinement top

Crystal data top

SO₄·2(H₃O)·4.5(H₂O)	β = 121.4202°
M_r = 215.17	V = 928.2 (3) Å³
Monoclinic, Im	Z = 4
a = 6.8182 (10) Å	Mo Kα radiation
b = 26.876 (5) Å	× × mm
c = 5.936 (1) Å

Data collection top

Refinement top

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

	x	y	z	U_iso*/U_eq
S1	0.25	0.128980 (10)	0.25	0.01402 (12)
O1	0.3693 (2)	0.08064 (3)	0.2808 (3)	0.0199 (4)
O2	0.30450 (10)	0.16239 (3)	0.0904 (2)	0.0203 (4)
O3	0.0003 (2)	0.12035 (4)	0.1106 (3)	0.0242 (4)
O4	0.3335 (2)	0.15105 (3)	0.5113 (3)	0.0257 (5)
O5	0.9815 (2)	0.21805 (3)	0.7249 (3)	0.0244 (5)
O6	0.2426 (2)	0.25058 (3)	0.3903 (3)	0.0215 (4)
O7	0.7533 (2)	0.18307 (3)	0.2393 (3)	0.0204 (4)
O8	0.6801 (3)	0	0.8882 (4)	0.0289 (7)
O9	0.4760 (3)	0.07605 (4)	0.8838 (4)	0.0356 (7)
O10	0.1200 (2)	0	0.2700 (3)	0.0224 (4)
O11	0.0289 (3)	0	0.6534 (4)	0.0283 (7)
O12	0.8391 (2)	0.08076 (4)	0.6232 (3)	0.0257 (5)
H2a	0.48124	0.17063	0.16035	0*
H5a	1.11572	0.20169	0.86029	0*
H5c	0.89049	0.23065	0.80004	0*
H6a	0.24013	0.27323	0.51827	0*
H6b	0.29115	0.21882	0.47900	0*
H7a	0.83619	0.15547	0.22193	0*
H7c	0.84422	0.19584	0.42743	0*
H8a	0.84628	0.00000	1.03031	0*
H8b	0.59598	0.03229	0.88403	0*
H9a	0.41987	0.07781	1.00378	0*
H9c	0.42327	0.10451	0.76322	0*
H10a	0.20647	0.02940	0.27134	0*
H11a	−0.05650	0.03273	0.64420	0*
H11b	0.07634	−0.00002	0.52108	0*
H12b	0.88280	0.09818	0.78781	0*
H12c	0.67265	0.08261	0.50683	0*

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
S1	0.01460 (10)	0.01240 (10)	0.0163 (2)	0.00010 (10)	0.00893 (13)	−0.00120 (13)
O1	0.0204 (4)	0.0137 (3)	0.0274 (7)	0.0025 (3)	0.0138 (4)	0.0003 (4)
O2	0.0196 (4)	0.0200 (4)	0.0235 (7)	0.0018 (3)	0.0128 (4)	0.0050 (4)
O3	0.0149 (4)	0.0287 (4)	0.0317 (6)	−0.0011 (4)	0.0140 (4)	0.0037 (5)
O4	0.0389 (5)	0.0187 (4)	0.0191 (8)	−0.0011 (4)	0.0149 (6)	−0.0035 (4)
O5	0.0246 (4)	0.0239 (4)	0.0243 (8)	−0.0038 (4)	0.0124 (5)	−0.0059 (5)
O6	0.0231 (4)	0.0181 (4)	0.0223 (7)	−0.0004 (3)	0.0113 (4)	−0.0035 (4)
O7	0.0189 (4)	0.0179 (3)	0.0285 (7)	−0.0022 (3)	0.0152 (4)	−0.0036 (4)
O8	0.0310 (6)	0.0248 (6)	0.0387 (11)	0	0.0235 (7)	0
O9	0.0555 (8)	0.0300 (5)	0.0414 (9)	−0.0208 (5)	0.0393 (8)	−0.0153 (6)
O10	0.0258 (5)	0.0119 (5)	0.0378 (6)	0	0.0225 (4)	0
O11	0.0289 (6)	0.0277 (6)	0.0353 (11)	0	0.0216 (7)	0
O12	0.0219 (4)	0.0269 (4)	0.0267 (8)	−0.0004 (3)	0.0115 (5)	0.0026 (5)

Experimental details

	(I)	(II)	(III)	(IV)
Crystal data
Chemical formula	SO₄·2(H5O₂)·4(H2O)	SO₄·2(H3O)·6(H2O)	SO₄·2(H₃O)·4.5(H₂O)	SO₄·2(H₃O)·4.5(H₂O)
M_r	242.20	242.20	215.17	215.17
Crystal system, space group	Monoclinic, Cc	Monoclinic, Cc	Monoclinic, Im	Monoclinic, Im
Temperature (K)	?	?	?	?
a, b, c (Å)	10.560 (4), 10.560 (4), 11.952 (11)	10.560 (4), 10.560 (4), 11.952 (11)	6.8182 (10), 26.876 (5), 5.936 (1)	6.8182 (10), 26.876 (5), 5.936 (1)
β (°)	116.2165	116.2165	121.4202	121.4202
V (Å³)	1195.7 (13)	1195.7 (13)	928.2 (3)	928.2 (3)
Z	4	4	4	4
Radiation type	Mo Kα	Mo Kα	Mo Kα	Mo Kα
µ (mm⁻¹)	?	?	?	?
Crystal size (mm)	× ×	× ×	× ×	× ×

Data collection
Diffractometer	?	?	?	?
Absorption correction	–	–	–	–
No. of measured, independent and observed (?) reflections	?, ?, ?	?, ?, ?	?, ?, ?	?, ?, ?
R_int	?	?	?	?

Refinement
R[F² > 2σ(F²)], wR(F²), S	?, ?, ?	?, ?, ?	?, ?, ?	?, ?, ?
No. of reflections	?	?	?	?
No. of parameters	?	?	?	?
No. of restraints	?	?	?	?
Δρ_max, Δρ_min (e Å⁻³)	?, ?	?, ?	?, ?	?, ?

Computer programs: (Jana2000; Petricek and Dusek, 2000).

Format		BIBTeX
		EndNote
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Format		BIBTeX
		EndNote
		RefMan
		Refer
		Medline
		CIF
		SGML
		Text
		Plain Text

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