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The crystal structures of the title compounds were determined with net intensities I derived via the background–peak–background procedure. Least-squares optimizations reveal differences between the low-order (0 < s < 0.7 Å−1) and high-order (0.7 < s < 1.0 Å−1) structure models. The scale factors indicate discrepancies of up to 10% between the low-order and high-order reflection intensities. This observation is compound independent. It reflects the scan-angle-induced truncation error, because the applied scan angle (0.8 + 2.0 tan θ)° underestimates the wavelength dispersion in the monochromated X-ray beam. The observed crystal structures show pseudo-I-centred sublattices for three of its non-H atoms in the asymmetric unit. Our selection of observed intensities (I > 3σ) stresses that pseudo-symmetry. Model refinements on individual data sets with (h + k + l) = 2n and (h + k + l) = 2n + 1 illustrate the lack of model robustness caused by that pseudo-symmetry. To obtain a better balanced data set and thus a more robust structure we decided to exploit background modelling. We described the background intensities B(\displaystyle\mathrel{\mathop H^{\rightharpoonup}}) with an 11th degree polynomial in θ. This function predicts the local background b at each position \displaystyle\mathrel{\mathop H^{\rightharpoonup}} and defines the counting statistical distribution P(B), in which b serves as average and variance. The observation R defines P(R). This leads to P(I) = P(R)/P(B) and thus I = Rb and σ2(I) = I so that the error σ(I) is background independent. Within this framework we reanalysed the structure of the copper(II) derivative. Background modelling resulted in a structure model with an improved internal consistency. At the same time the unweighted R value based on all observations decreased from 10.6 to 8.4%. A redetermination of the structure at 120 K concluded the analysis.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768101004050/lc0029sup1.cif
Contains datablocks Cu120K, Cu294K, Mn

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108768101004050/lc0029Cu294Ksup2.hkl
Contains datablock Cu294K

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108768101004050/lc0029Cu120Ksup3.hkl
Contains datablock Cu120K

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108768101004050/lc0029Mnsup4.hkl
Contains datablock Mn

CCDC references: 170324; 170325; 170326

Computing details top

For all compounds, data collection: CAD4_(Enraf-Nonius,_1994); cell refinement: CAD4 (Enraf-Nonius, 1994); data reduction: process_MolEN_(Fair,_1990); program(s) used to solve structure: Patterson and Fourier; program(s) used to refine structure: LSFM MolEN (Fair, 1990); molecular graphics: PLATON (Spek, 2000); software used to prepare material for publication: BTABLE PTABLE CIF IN MolEN (Fair, 1990).

Figures top
[Figure 1] Fig. 1.  
(Cu294K) Copper(II) bis(hydrogenmalonate) dihydrate top
Crystal data top
C6H10CuO10F(000) = 310
Mr = 305.68Dx = 2.02 Mg m3
Monoclinic, P21/nMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ynCell parameters from 25 reflections
a = 7.0655 (7) Åθ = 10.0–23.0°
b = 7.5017 (8) ŵ = 2.22 mm1
c = 9.676 (1) ÅT = 294 K
β = 100.88 (2)°Prism, blue
V = 503.6 (2) Å30.20 × 0.20 × 0.20 mm
Z = 2
Data collection top
Enraf Nonius CAD4
diffractometer
4117 reflections with > 0.0σ(I)
Radiation source: xray tubeRint = 0
Graphite monochromatorθmax = 45.0°, θmin = 1.5°
ω/2θ scansh = 014
Absorption correction: psi scan
North et al. (1968)
k = 014
Tmin = 0.90, Tmax = 1.0l = 1919
4333 measured reflections3 standard reflections every 120 min
4117 independent reflections intensity decay: none
Refinement top
Refinement on F0 constraints
Least-squares matrix: fullAll H-atom parameters refined
R[F2 > 2σ(F2)] = 0.083Weighting scheme based on measured s.u.'s
wR(F2) = 0.064(Δ/σ)max = 0.05
S = 4.11Δρmax = 1.09 e Å3
4117 reflectionsΔρmin = 1.84 e Å3
99 parametersAbsolute structure: 'weight 4Fo2/(σ2(Fo2) + 0.0001 Fo4)'
0 restraints
Crystal data top
C6H10CuO10V = 503.6 (2) Å3
Mr = 305.68Z = 2
Monoclinic, P21/nMo Kα radiation
a = 7.0655 (7) ŵ = 2.22 mm1
b = 7.5017 (8) ÅT = 294 K
c = 9.676 (1) Å0.20 × 0.20 × 0.20 mm
β = 100.88 (2)°
Data collection top
Enraf Nonius CAD4
diffractometer
4117 reflections with > 0.0σ(I)
Absorption correction: psi scan
North et al. (1968)
Rint = 0
Tmin = 0.90, Tmax = 1.03 standard reflections every 120 min
4333 measured reflections intensity decay: none
4117 independent reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0830 restraints
wR(F2) = 0.064All H-atom parameters refined
S = 4.11Δρmax = 1.09 e Å3
4117 reflectionsΔρmin = 1.84 e Å3
99 parametersAbsolute structure: 'weight 4Fo2/(σ2(Fo2) + 0.0001 Fo4)'
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Cu11.00000.00001.00000.01851 (9)
O10.7338 (2)0.4889 (2)0.9444 (2)0.0322 (6)
O20.9134 (2)0.2475 (1)1.0133 (1)0.0233 (4)
O30.4451 (2)0.0606 (2)0.7995 (2)0.0279 (5)
O40.7488 (2)0.0810 (1)0.9062 (1)0.0221 (4)
Ow1.0838 (2)0.0884 (2)0.7723 (1)0.0264 (5)
C10.7609 (2)0.3142 (2)0.9471 (1)0.0176 (4)
C30.5996 (2)0.0093 (2)0.8578 (2)0.0183 (5)
C20.5960 (2)0.2097 (2)0.8651 (2)0.0270 (7)
H1w1.087 (3)0.180 (3)0.762 (2)0.049 (7)*
H2_10.588 (5)0.224 (4)0.777 (3)0.10 (1)*
H2w1.198 (4)0.054 (3)0.778 (3)0.048 (7)*
H2_20.480 (6)0.229 (5)0.914 (4)0.13 (1)*
H1_10.83720.57981.00370.0909*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Cu10.01515 (8)0.01567 (9)0.0267 (1)0.00193 (7)0.00413 (8)0.00311 (8)
O10.0277 (6)0.0240 (5)0.0503 (8)0.0029 (4)0.0054 (6)0.0073 (5)
O20.0201 (4)0.0188 (4)0.0335 (5)0.0035 (4)0.0070 (4)0.0057 (4)
O30.0172 (4)0.0213 (4)0.0591 (8)0.0011 (4)0.0054 (5)0.0079 (5)
O40.0173 (4)0.0188 (4)0.0333 (5)0.0018 (4)0.0036 (4)0.0033 (4)
Ow0.0221 (4)0.0230 (5)0.0361 (5)0.0000 (4)0.0041 (4)0.0015 (4)
C10.0169 (4)0.0179 (5)0.0181 (4)0.0010 (4)0.0015 (4)0.0006 (4)
C30.0148 (4)0.0178 (5)0.0234 (5)0.0008 (4)0.0008 (4)0.0018 (4)
C20.0253 (6)0.0175 (5)0.0444 (8)0.0011 (5)0.0134 (6)0.0016 (6)
Geometric parameters (Å, º) top
Cu1—O21.967 (1)Ow—H1w0.70 (2)
Cu1—O41.933 (1)Ow—H2w0.84 (3)
O1—C11.324 (2)C1—C21.501 (2)
O1—H1_11.082 (1)C3—C21.505 (2)
O2—C11.249 (2)C2—H2_10.85 (3)
O3—C31.246 (2)C2—H2_21.03 (4)
O4—C31.267 (2)
O2—Cu1—O493.34 (5)O4—C3—C2122.5 (1)
C1—O1—H1_1122.2 (1)C1—C2—C3121.9 (1)
H1w—Ow—H2w104 (2)C1—C2—H2_1111 (2)
O1—C1—O2120.9 (1)C1—C2—H2_2106 (1)
O1—C1—C2114.3 (1)C3—C2—H2_194 (1)
O2—C1—C2124.8 (1)C3—C2—H2_2100 (1)
O3—C3—O4122.6 (1)H2_1—C2—H2_2122 (3)
O3—C3—C2114.9 (1)
(Cu120K) Copper(II) Hydrogenmalonate Dihydrate top
Crystal data top
C6H10CuO10F(000) = 310
Mr = 305.68Dx = 2.07 Mg m3
Monoclinic, P21/nMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ynCell parameters from 25 reflections
a = 7.019 (2) Åθ = 10.1–23.0°
b = 7.472 (2) ŵ = 2.28 mm1
c = 9.498 (2) ÅT = 120 K
β = 99.94 (2)°Prism, blue
V = 490.7 (4) Å30.40 × 0.20 × 0.20 mm
Z = 2
Data collection top
Enraf Nonius CAD4
diffractometer
2972 reflections with > 3.0σ(I)
Radiation source: xray tubeRint = 0
Graphite monochromatorθmax = 44.9°, θmin = 1.5°
ω/2θ scansh = 014
Absorption correction: psi scan
North et al. (1968)
k = 014
Tmin = 0.800, Tmax = 1.000l = 1919
4248 measured reflections3 standard reflections every 120 min
4248 independent reflections intensity decay: none
Refinement top
Refinement on F0 constraints
Least-squares matrix: fullAll H-atom parameters refined
R[F2 > 2σ(F2)] = 0.048Weighting scheme based on measured s.u.'s
wR(F2) = 0.052(Δ/σ)max = 0.033
S = 3.06Δρmax = 1.92 e Å3
2972 reflectionsΔρmin = 2.32 e Å3
99 parametersAbsolute structure: 'weight 4Fo2/(σ2(Fo2) + 0.0001Fo4)'
0 restraints
Crystal data top
C6H10CuO10V = 490.7 (4) Å3
Mr = 305.68Z = 2
Monoclinic, P21/nMo Kα radiation
a = 7.019 (2) ŵ = 2.28 mm1
b = 7.472 (2) ÅT = 120 K
c = 9.498 (2) Å0.40 × 0.20 × 0.20 mm
β = 99.94 (2)°
Data collection top
Enraf Nonius CAD4
diffractometer
2972 reflections with > 3.0σ(I)
Absorption correction: psi scan
North et al. (1968)
Rint = 0
Tmin = 0.800, Tmax = 1.0003 standard reflections every 120 min
4248 measured reflections intensity decay: none
4248 independent reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0480 restraints
wR(F2) = 0.052All H-atom parameters refined
S = 3.06Δρmax = 1.92 e Å3
2972 reflectionsΔρmin = 2.32 e Å3
99 parametersAbsolute structure: 'weight 4Fo2/(σ2(Fo2) + 0.0001Fo4)'
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Cu11.00000.00001.00000.00621 (8)
O10.7352 (2)0.4921 (2)0.9414 (2)0.0157 (5)
O20.9139 (2)0.2498 (2)1.0125 (1)0.0097 (4)
O30.4442 (2)0.0620 (2)0.7989 (2)0.0111 (5)
O40.7487 (2)0.0815 (2)0.9050 (1)0.0091 (4)
Ow1.0847 (2)0.0874 (2)0.7724 (1)0.0108 (4)
C10.7604 (2)0.3165 (2)0.9466 (2)0.0078 (5)
C30.5985 (2)0.0092 (2)0.8581 (2)0.0083 (5)
C20.5922 (2)0.2107 (2)0.8688 (2)0.0105 (6)
H1w1.080 (4)0.197 (4)0.763 (3)0.036 (9)*
H2_10.564 (4)0.255 (4)0.774 (3)0.025 (7)*
H2w1.182 (5)0.043 (4)0.765 (4)0.034 (9)*
H2_20.484 (4)0.233 (4)0.923 (3)0.025 (7)*
H1_10.842 (4)0.569 (4)0.989 (3)0.010 (6)*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Cu10.00626 (7)0.00340 (8)0.01128 (9)0.0007 (1)0.00264 (7)0.0009 (1)
O10.0157 (5)0.0102 (5)0.0239 (6)0.0008 (5)0.0028 (4)0.0025 (6)
O20.0095 (4)0.0065 (4)0.0149 (5)0.0018 (4)0.0037 (4)0.0015 (4)
O30.0075 (4)0.0069 (4)0.0269 (6)0.0006 (4)0.0037 (4)0.0040 (5)
O40.0079 (4)0.0061 (4)0.0158 (5)0.0010 (4)0.0025 (4)0.0010 (4)
Ow0.0096 (4)0.0076 (4)0.0172 (5)0.0005 (4)0.0003 (4)0.0003 (4)
C10.0088 (5)0.0058 (5)0.0094 (5)0.0003 (4)0.0001 (4)0.0003 (5)
C30.0084 (4)0.0066 (5)0.0103 (5)0.0010 (6)0.0004 (4)0.0007 (6)
C20.0112 (6)0.0052 (5)0.0197 (7)0.0006 (5)0.0053 (5)0.0007 (5)
Geometric parameters (Å, º) top
O1—C11.324 (2)C1—C21.505 (2)
O1—H1_10.99 (2)C3—O31.249 (2)
O2—Cu11.972 (1)C3—O41.268 (2)
O2—C11.252 (2)C3—C21.511 (2)
O3—C31.249 (2)C2—C11.505 (2)
O4—Cu11.936 (1)C2—C31.511 (2)
O4—C31.268 (2)C2—H2_10.95 (3)
Ow—H1w0.82 (3)C2—H2_21.00 (3)
Ow—H2w0.77 (3)Cu1—O21.972 (1)
C1—O11.324 (2)Cu1—O41.936 (1)
C1—O21.252 (2)Cu1—Ow2.428 (1)
C1—O1—H1_1118 (1)C1—C2—H2_1107 (1)
H1w—Ow—H2w116 (3)C1—C2—H2_2104 (1)
O1—C1—O2120.7 (1)C3—C2—H2_1106 (1)
O1—C1—C2114.4 (1)C3—C2—H2_2103 (1)
O2—C1—C2124.9 (1)H2_1—C2—H2_2112 (2)
O3—C3—O4122.3 (2)O2—Cu1—O493.55 (5)
O3—C3—C2114.9 (1)O2—Cu1—Ow85.64 (5)
O4—C3—C2122.8 (1)O4—Cu1—Ow90.75 (5)
C1—C2—C3121.8 (1)
(Mn) Manganese(II) Bis(hydrogenmalonate) Dihydrate top
Crystal data top
C6H10MnO10F(000) = 302
Mr = 297.08Dx = 2.00 Mg m3
Monoclinic, P21/nMo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ynCell parameters from 25 reflections
a = 7.0909 (7) Åθ = 12.0–28.0°
b = 7.3518 (7) ŵ = 1.39 mm1
c = 9.577 (1) ÅT = 294 K
β = 99.73 (2)°Prism, pink
V = 492.1 (2) Å30.1 × 0.1 × 0.1 mm
Z = 2
Data collection top
Enraf Nonius CAD4
diffractometer
2085 reflections with > 3.0σ(I)
Radiation source: xray tubeRint = 0
Graphite monochromatorθmax = 49.9°, θmin = 1.5°
ω/2θ scansh = 015
Absorption correction: psi scan
North et al. (1968)
k = 015
Tmin = 0.94, Tmax = 0.999l = 2020
5395 measured reflections3 standard reflections every 120 min
5395 independent reflections intensity decay: none
Refinement top
Refinement on F0 constraints
Least-squares matrix: fullAll H-atom parameters refined
R[F2 > 2σ(F2)] = 0.060Weighting scheme based on measured s.u.'s
wR(F2) = 0.051(Δ/σ)max = 0.018
S = 3.06Δρmax = 1.66 e Å3
2085 reflectionsΔρmin = 1.92 e Å3
99 parametersAbsolute structure: 'weight 4Fo2/(σ2(Fo2) + 0.0001 Fo4)'
0 restraints
Crystal data top
C6H10MnO10V = 492.1 (2) Å3
Mr = 297.08Z = 2
Monoclinic, P21/nMo Kα radiation
a = 7.0909 (7) ŵ = 1.39 mm1
b = 7.3518 (7) ÅT = 294 K
c = 9.577 (1) Å0.1 × 0.1 × 0.1 mm
β = 99.73 (2)°
Data collection top
Enraf Nonius CAD4
diffractometer
2085 reflections with > 3.0σ(I)
Absorption correction: psi scan
North et al. (1968)
Rint = 0
Tmin = 0.94, Tmax = 0.9993 standard reflections every 120 min
5395 measured reflections intensity decay: none
5395 independent reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0600 restraints
wR(F2) = 0.051All H-atom parameters refined
S = 3.06Δρmax = 1.66 e Å3
2085 reflectionsΔρmin = 1.92 e Å3
99 parametersAbsolute structure: 'weight 4Fo2/(σ2(Fo2) + 0.0001 Fo4)'
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Mn11.00000.00001.00000.0132 (1)
O10.7244 (3)0.5026 (3)0.9372 (2)0.041 (1)
O20.8972 (2)0.2574 (3)1.0157 (2)0.0276 (8)
O30.4367 (2)0.0615 (3)0.7944 (2)0.0292 (8)
O40.7410 (2)0.0797 (3)0.8926 (2)0.0256 (8)
Ow1.0897 (2)0.0889 (2)0.8033 (2)0.0268 (8)
C10.7477 (3)0.3238 (3)0.9466 (3)0.0214 (9)
C30.5909 (3)0.0112 (3)0.8533 (2)0.0211 (9)
C20.5813 (3)0.2144 (3)0.8719 (3)0.026 (1)
H1w1.061 (7)0.204 (9)0.740 (5)0.16 (2)*
H210.540 (4)0.277 (5)0.783 (3)0.049 (9)*
H2w1.207 (5)0.044 (5)0.784 (4)0.06 (1)*
H220.451 (5)0.241 (6)0.897 (4)0.09 (1)*
H110.873 (6)0.589 (6)0.985 (4)0.12 (1)*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Mn10.0110 (1)0.0099 (1)0.0209 (2)0.0009 (2)0.0024 (1)0.0002 (2)
O10.044 (1)0.0274 (9)0.059 (1)0.001 (1)0.0039 (9)0.003 (1)
O20.0270 (8)0.0206 (8)0.0376 (9)0.0045 (7)0.0082 (7)0.0034 (8)
O30.0179 (7)0.0269 (8)0.052 (1)0.0024 (7)0.0029 (7)0.0098 (8)
O40.0207 (7)0.0207 (8)0.0392 (9)0.0015 (7)0.0002 (7)0.0027 (8)
Ow0.0228 (7)0.0245 (8)0.0344 (9)0.0006 (7)0.0038 (7)0.0028 (8)
C10.0206 (9)0.019 (1)0.025 (1)0.0015 (9)0.0029 (8)0.0012 (9)
C30.0194 (8)0.0200 (9)0.0240 (9)0.001 (1)0.0023 (7)0.001 (1)
C20.022 (1)0.019 (1)0.041 (1)0.0003 (9)0.005 (1)0.002 (1)
Geometric parameters (Å, º) top
Mn1—O22.042 (2)O4—C31.260 (3)
Mn1—O42.033 (2)Ow—H1w1.04 (6)
Mn1—Ow2.188 (2)Ow—H2w0.94 (3)
O1—C11.327 (3)C1—C21.505 (3)
O1—H111.25 (4)C3—C21.507 (4)
O2—C11.250 (3)C2—H210.97 (3)
O3—C31.261 (3)C2—H221.01 (4)
O2—Mn1—O490.07 (7)O3—C3—C2114.8 (2)
O2—Mn1—Ow86.90 (7)O4—C3—C2122.9 (2)
O4—Mn1—Ow91.13 (7)C1—C2—C3122.6 (2)
C1—O1—H11113 (2)C1—C2—H21105 (1)
H1w—Ow—H2w105 (3)C1—C2—H22117 (2)
O1—C1—O2120.5 (2)C3—C2—H21112 (1)
O1—C1—C2114.7 (2)C3—C2—H22106 (2)
O2—C1—C2124.7 (2)H21—C2—H2287 (2)
O3—C3—O4122.3 (2)

Experimental details

(Cu294K)(Cu120K)(Mn)
Crystal data
Chemical formulaC6H10CuO10C6H10CuO10C6H10MnO10
Mr305.68305.68297.08
Crystal system, space groupMonoclinic, P21/nMonoclinic, P21/nMonoclinic, P21/n
Temperature (K)294120294
a, b, c (Å)7.0655 (7), 7.5017 (8), 9.676 (1)7.019 (2), 7.472 (2), 9.498 (2)7.0909 (7), 7.3518 (7), 9.577 (1)
β (°) 100.88 (2) 99.94 (2) 99.73 (2)
V3)503.6 (2)490.7 (4)492.1 (2)
Z222
Radiation typeMo KαMo KαMo Kα
µ (mm1)2.222.281.39
Crystal size (mm)0.20 × 0.20 × 0.200.40 × 0.20 × 0.200.1 × 0.1 × 0.1
Data collection
DiffractometerEnraf Nonius CAD4
diffractometer
Enraf Nonius CAD4
diffractometer
Enraf Nonius CAD4
diffractometer
Absorption correctionPsi scan
North et al. (1968)
Psi scan
North et al. (1968)
Psi scan
North et al. (1968)
Tmin, Tmax0.90, 1.00.800, 1.0000.94, 0.999
No. of measured, independent and
observed reflections
4333, 4117, 4117 [ > 0.0σ(I)]4248, 4248, 2972 [ > 3.0σ(I)]5395, 5395, 2085 [ > 3.0σ(I)]
Rint000
(sin θ/λ)max1)0.9940.9941.077
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.083, 0.064, 4.11 0.048, 0.052, 3.06 0.060, 0.051, 3.06
No. of reflections411729722085
No. of parameters999999
H-atom treatmentAll H-atom parameters refinedAll H-atom parameters refinedAll H-atom parameters refined
Δρmax, Δρmin (e Å3)1.09, 1.841.92, 2.321.66, 1.92
Absolute structure'weight 4Fo2/(σ2(Fo2) + 0.0001 Fo4)''weight 4Fo2/(σ2(Fo2) + 0.0001Fo4)''weight 4Fo2/(σ2(Fo2) + 0.0001 Fo4)'

Computer programs: CAD4_(Enraf-Nonius,_1994), CAD4 (Enraf-Nonius, 1994), process_MolEN_(Fair,_1990), Patterson and Fourier, LSFM MolEN (Fair, 1990), PLATON (Spek, 2000), BTABLE PTABLE CIF IN MolEN (Fair, 1990).

 

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