Buy article online - an online subscription or single-article purchase is required to access this article.
This paper demonstrates how numerical parameters usually used to assess the quality of a crystal structure solution (R, wR and S) may be misleading when studying a model refined against poor-quality data. Weakly diffracting crystals of tetrabutylammonium tetrabutylborate, a low-density organic salt comprising isoelectronic cations and anions, were measured using Cu and Mo Kα radiation. Along with the correct structural model, six erroneous structural models were constructed and refined against the same data. For both data sets it was found that models based on an incorrect unit-cell choice give lower values of R and wR than the correct one, thus apparently being in better agreement with measured data. Closer inspection of the measured data shows that this is in fact not the case.
Supporting information
For both compounds, data collection: CrysAlis CCD 170 (Oxford Diffraction Poland Sp., 2003); cell refinement: CrysAlis RED 170 (Oxford Diffraction Poland Sp., 2003); data reduction: CrysAlis RED 170 (Oxford Diffraction Poland Sp., 2003); program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997).
(ICu) Tetrabutylammonium Tetrabutylborate
top
Crystal data top
C16H36N·C16H36B | Dx = 0.846 Mg m−3 |
Mr = 481.72 | Cu Kα radiation, λ = 1.54184 Å |
Tetragonal, I41/a | Cell parameters from 231 reflections |
Hall symbol: -I 4ad | θ = 4.6–32.0° |
a = 18.9089 (6) Å | µ = 0.33 mm−1 |
c = 10.5803 (3) Å | T = 295 K |
V = 3782.9 (2) Å3 | Needle, colourless |
Z = 4 | 0.13 × 0.05 × 0.03 mm |
F(000) = 1104 | |
Data collection top
Oxford Diffraction Xcalibur Nova R
CCD diffractometer | Rint = 0.016 |
Graphite monochromator | θmax = 67.5°, θmin = 4.7° |
4159 measured reflections | h = −22→22 |
1665 independent reflections | k = −22→22 |
414 reflections with I > 2σ(I) | l = −12→12 |
Refinement top
Refinement on F2 | Primary atom site location: structure-invariant direct methods |
Least-squares matrix: full | Secondary atom site location: difference Fourier map |
R[F2 > 2σ(F2)] = 0.064 | Hydrogen site location: inferred from neighbouring sites |
wR(F2) = 0.265 | H-atom parameters constrained |
S = 0.75 | w = 1/[σ2(Fo2) + (0.1488P)2] where P = (Fo2 + 2Fc2)/3 |
1665 reflections | (Δ/σ)max < 0.001 |
79 parameters | Δρmax = 0.09 e Å−3 |
0 restraints | Δρmin = −0.10 e Å−3 |
Crystal data top
C16H36N·C16H36B | Z = 4 |
Mr = 481.72 | Cu Kα radiation |
Tetragonal, I41/a | µ = 0.33 mm−1 |
a = 18.9089 (6) Å | T = 295 K |
c = 10.5803 (3) Å | 0.13 × 0.05 × 0.03 mm |
V = 3782.9 (2) Å3 | |
Data collection top
Oxford Diffraction Xcalibur Nova R
CCD diffractometer | 414 reflections with I > 2σ(I) |
4159 measured reflections | Rint = 0.016 |
1665 independent reflections | |
Refinement top
R[F2 > 2σ(F2)] = 0.064 | 0 restraints |
wR(F2) = 0.265 | H-atom parameters constrained |
S = 0.75 | Δρmax = 0.09 e Å−3 |
1665 reflections | Δρmin = −0.10 e Å−3 |
79 parameters | |
Special details top
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 (Å2) top | x | y | z | Uiso*/Ueq | |
C5 | 0.97107 (14) | 0.69323 (15) | 0.28759 (18) | 0.1351 (11) | |
H5A | 0.9348 | 0.7143 | 0.2348 | 0.162* | |
H5B | 1.009 | 0.6778 | 0.2323 | 0.162* | |
C7 | 0.9082 (2) | 0.5785 (2) | 0.2609 (4) | 0.2189 (19) | |
H7A | 0.872 | 0.6034 | 0.2138 | 0.263* | |
H7B | 0.9446 | 0.5648 | 0.2011 | 0.263* | |
C4 | 0.7495 (2) | 0.3627 (3) | 0.0893 (6) | 0.285 (3) | |
H4A | 0.7326 | 0.3264 | 0.1451 | 0.428* | |
H4B | 0.7121 | 0.3769 | 0.0335 | 0.428* | |
H4C | 0.7649 | 0.4027 | 0.1381 | 0.428* | |
C8 | 0.8768 (3) | 0.5141 (3) | 0.3114 (5) | 0.298 (3) | |
H8A | 0.8681 | 0.4815 | 0.2437 | 0.446* | |
H8B | 0.833 | 0.5254 | 0.3525 | 0.446* | |
H8C | 0.9086 | 0.4931 | 0.3713 | 0.446* | |
B1 | 1 | 0.25 | 0.125 | 0.1115 (17) | |
N1 | 1 | 0.75 | 0.375 | 0.1276 (14) | |
C1 | 0.93493 (14) | 0.27842 (14) | 0.0358 (2) | 0.1326 (11) | |
H1A | 0.9533 | 0.3154 | −0.0187 | 0.159* | |
H1B | 0.9201 | 0.2397 | −0.0182 | 0.159* | |
C2 | 0.87032 (17) | 0.30693 (16) | 0.1020 (3) | 0.1548 (12) | |
H2A | 0.8848 | 0.3453 | 0.1571 | 0.186* | |
H2B | 0.8508 | 0.2699 | 0.1549 | 0.186* | |
C6 | 0.93998 (17) | 0.62889 (18) | 0.3515 (3) | 0.1688 (14) | |
H6A | 0.9769 | 0.605 | 0.3988 | 0.203* | |
H6B | 0.904 | 0.644 | 0.411 | 0.203* | |
C3 | 0.8111 (2) | 0.3345 (2) | 0.0123 (4) | 0.2045 (16) | |
H3A | 0.8297 | 0.3717 | −0.0411 | 0.245* | |
H3B | 0.7949 | 0.2963 | −0.0417 | 0.245* | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
C5 | 0.165 (2) | 0.164 (2) | 0.0767 (14) | −0.0121 (19) | 0.0014 (14) | −0.0131 (15) |
C7 | 0.235 (4) | 0.199 (4) | 0.223 (4) | −0.057 (3) | 0.000 (3) | −0.031 (4) |
C4 | 0.175 (4) | 0.299 (6) | 0.382 (7) | 0.054 (4) | 0.000 (4) | −0.048 (5) |
C8 | 0.323 (6) | 0.217 (5) | 0.353 (7) | −0.094 (4) | 0.064 (5) | −0.036 (5) |
B1 | 0.135 (3) | 0.135 (3) | 0.065 (3) | 0 | 0 | 0 |
N1 | 0.157 (2) | 0.157 (2) | 0.068 (2) | 0 | 0 | 0 |
C1 | 0.144 (2) | 0.163 (2) | 0.0906 (17) | 0.0136 (18) | 0.0119 (15) | −0.0015 (15) |
C2 | 0.159 (3) | 0.185 (3) | 0.121 (2) | 0.011 (2) | 0.000 (2) | −0.0107 (18) |
C6 | 0.182 (3) | 0.165 (3) | 0.159 (3) | −0.027 (2) | 0.016 (2) | 0.001 (2) |
C3 | 0.167 (3) | 0.213 (4) | 0.233 (4) | 0.017 (3) | 0.003 (3) | 0.003 (3) |
Geometric parameters (Å, º) top
C5—C6 | 1.511 (3) | C4—C3 | 1.518 (5) |
C5—N1 | 1.519 (2) | B1—C1 | 1.641 (2) |
C7—C8 | 1.456 (5) | C1—C2 | 1.508 (3) |
C7—C6 | 1.479 (4) | C2—C3 | 1.558 (4) |
| | | |
C6—C5—N1 | 115.9 (2) | C5—N1—C5v | 111.76 (10) |
C8—C7—C6 | 117.8 (4) | C5iv—N1—C5v | 111.76 (10) |
C1i—B1—C1 | 109.81 (16) | C5—N1—C5vi | 111.76 (10) |
C1i—B1—C1ii | 109.30 (8) | C5iv—N1—C5vi | 111.76 (10) |
C1—B1—C1ii | 109.30 (8) | C5v—N1—C5vi | 104.98 (19) |
C1i—B1—C1iii | 109.30 (8) | C2—C1—B1 | 117.23 (19) |
C1—B1—C1iii | 109.30 (8) | C1—C2—C3 | 114.8 (3) |
C1ii—B1—C1iii | 109.81 (16) | C7—C6—C5 | 112.8 (3) |
C5—N1—C5iv | 104.98 (19) | C4—C3—C2 | 110.0 (4) |
Symmetry codes: (i) −x+2, −y+1/2, z; (ii) y+3/4, −x+5/4, −z+1/4; (iii) −y+5/4, x−3/4, −z+1/4; (iv) −x+2, −y+3/2, z; (v) −y+7/4, x−1/4, −z+3/4; (vi) y+1/4, −x+7/4, −z+3/4. |
(IMo) Tetrabutylammonium Tetrabutylborate
top
Crystal data top
C16H36N·C16H36B | Dx = 0.838 Mg m−3 |
Mr = 481.72 | Mo Kα radiation, λ = 0.71073 Å |
Tetragonal, I41/a | Cell parameters from 145 reflections |
Hall symbol: -I 4ad | θ = 4.6–32.0° |
a = 18.958 (5) Å | µ = 0.05 mm−1 |
c = 10.624 (5) Å | T = 295 K |
V = 3818 (2) Å3 | Needle, colourless |
Z = 4 | 0.31 × 0.13 × 0.10 mm |
F(000) = 1104 | |
Data collection top
Oxford Diffraction Xcalibur CCD diffractometer | Rint = 0.172 |
Graphite monochromator | θmax = 27°, θmin = 4.1° |
ω scan | h = −23→24 |
12512 measured reflections | k = −24→24 |
2075 independent reflections | l = −13→13 |
408 reflections with I > 2σ(I) | |
Refinement top
Refinement on F2 | Primary atom site location: structure-invariant direct methods |
Least-squares matrix: full | Secondary atom site location: difference Fourier map |
R[F2 > 2σ(F2)] = 0.081 | Hydrogen site location: inferred from neighbouring sites |
wR(F2) = 0.255 | H-atom parameters constrained |
S = 0.74 | w = 1/[σ2(Fo2) + (0.1072P)2] where P = (Fo2 + 2Fc2)/3 |
2075 reflections | (Δ/σ)max < 0.001 |
79 parameters | Δρmax = 0.16 e Å−3 |
0 restraints | Δρmin = −0.12 e Å−3 |
Crystal data top
C16H36N·C16H36B | Z = 4 |
Mr = 481.72 | Mo Kα radiation |
Tetragonal, I41/a | µ = 0.05 mm−1 |
a = 18.958 (5) Å | T = 295 K |
c = 10.624 (5) Å | 0.31 × 0.13 × 0.10 mm |
V = 3818 (2) Å3 | |
Data collection top
Oxford Diffraction Xcalibur CCD diffractometer | 408 reflections with I > 2σ(I) |
12512 measured reflections | Rint = 0.172 |
2075 independent reflections | |
Refinement top
R[F2 > 2σ(F2)] = 0.081 | 0 restraints |
wR(F2) = 0.255 | H-atom parameters constrained |
S = 0.74 | Δρmax = 0.16 e Å−3 |
2075 reflections | Δρmin = −0.12 e Å−3 |
79 parameters | |
Special details top
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 (Å2) top | x | y | z | Uiso*/Ueq | |
N1 | 1 | 0.25 | 0.125 | 0.1053 (13) | |
C5 | 1.02892 (12) | 0.31500 (13) | 0.71514 (18) | 0.1075 (10) | |
H5A | 0.9906 | 0.3296 | 0.7697 | 0.129* | |
H5B | 1.066 | 0.2964 | 0.7686 | 0.129* | |
C1 | 1.02887 (13) | 0.30680 (15) | 0.21052 (17) | 0.1173 (10) | |
H1A | 1.0651 | 0.2859 | 0.2631 | 0.141* | |
H1B | 0.9912 | 0.3223 | 0.2657 | 0.141* | |
C6 | 1.05705 (15) | 0.37971 (17) | 0.6495 (3) | 0.1340 (11) | |
H6A | 1.0198 | 0.3988 | 0.597 | 0.161* | |
H6B | 1.0951 | 0.3652 | 0.5942 | 0.161* | |
B1 | 1 | 0.25 | 0.625 | 0.0946 (17) | |
C2 | 1.05991 (16) | 0.37135 (17) | 0.1468 (3) | 0.1461 (13) | |
H2A | 1.096 | 0.3567 | 0.0875 | 0.175* | |
H2B | 1.0232 | 0.3956 | 0.1001 | 0.175* | |
C7 | 1.0843 (2) | 0.43853 (19) | 0.7339 (4) | 0.1792 (15) | |
H7A | 1.0461 | 0.4544 | 0.7877 | 0.215* | |
H7B | 1.1211 | 0.4197 | 0.7877 | 0.215* | |
C3 | 1.0918 (2) | 0.4213 (2) | 0.2425 (4) | 0.2007 (18) | |
H3A | 1.0554 | 0.4351 | 0.3016 | 0.241* | |
H3B | 1.1279 | 0.3963 | 0.2893 | 0.241* | |
C8 | 1.1126 (2) | 0.4998 (2) | 0.6642 (5) | 0.261 (2) | |
H8A | 1.1519 | 0.485 | 0.6136 | 0.392* | |
H8B | 1.1279 | 0.5352 | 0.7229 | 0.392* | |
H8C | 1.0765 | 0.519 | 0.611 | 0.392* | |
C4 | 1.1231 (3) | 0.4852 (3) | 0.1881 (6) | 0.295 (3) | |
H4A | 1.1624 | 0.4724 | 0.1357 | 0.443* | |
H4B | 1.1391 | 0.5156 | 0.2545 | 0.443* | |
H4C | 1.0884 | 0.5094 | 0.1385 | 0.443* | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
N1 | 0.138 (2) | 0.138 (2) | 0.040 (2) | 0 | 0 | 0 |
C5 | 0.133 (2) | 0.1133 (19) | 0.0766 (16) | −0.0072 (15) | 0.0038 (14) | 0.0094 (15) |
C1 | 0.145 (2) | 0.144 (2) | 0.0622 (13) | −0.0142 (18) | −0.0064 (14) | −0.0113 (15) |
C6 | 0.162 (3) | 0.124 (3) | 0.116 (2) | −0.017 (2) | 0.0051 (18) | −0.0008 (19) |
B1 | 0.108 (3) | 0.108 (3) | 0.067 (3) | 0 | 0 | 0 |
C2 | 0.165 (3) | 0.136 (3) | 0.137 (3) | −0.019 (2) | 0.019 (2) | 0.006 (2) |
C7 | 0.195 (4) | 0.136 (3) | 0.206 (4) | −0.024 (3) | 0.010 (3) | 0.009 (3) |
C3 | 0.209 (4) | 0.174 (4) | 0.219 (4) | −0.053 (3) | 0.001 (3) | −0.039 (3) |
C8 | 0.294 (5) | 0.159 (4) | 0.330 (6) | −0.066 (4) | 0.035 (4) | −0.006 (4) |
C4 | 0.287 (6) | 0.180 (4) | 0.418 (8) | −0.081 (4) | 0.053 (5) | −0.034 (5) |
Geometric parameters (Å, º) top
N1—C1 | 1.512 (2) | C6—C7 | 1.521 (4) |
C5—C6 | 1.508 (3) | C2—C3 | 1.515 (4) |
C5—B1 | 1.654 (2) | C7—C8 | 1.479 (4) |
C1—C2 | 1.517 (3) | C3—C4 | 1.468 (5) |
| | | |
C1—N1—C1i | 111.18 (10) | C5iv—B1—C5ii | 109.59 (8) |
C1—N1—C1ii | 106.11 (19) | C5iv—B1—C5v | 109.24 (16) |
C1i—N1—C1ii | 111.18 (10) | C5ii—B1—C5v | 109.59 (8) |
C1—N1—C1iii | 111.18 (10) | C5iv—B1—C5 | 109.58 (8) |
C1i—N1—C1iii | 106.11 (19) | C5ii—B1—C5 | 109.24 (16) |
C1ii—N1—C1iii | 111.18 (10) | C5v—B1—C5 | 109.59 (8) |
C6—C5—B1 | 117.10 (18) | C3—C2—C1 | 111.0 (3) |
N1—C1—C2 | 116.53 (19) | C8—C7—C6 | 113.9 (4) |
C5—C6—C7 | 116.4 (3) | C4—C3—C2 | 114.4 (4) |
Symmetry codes: (i) −y+5/4, x−3/4, −z+1/4; (ii) −x+2, −y+1/2, z; (iii) y+3/4, −x+5/4, −z+1/4; (iv) −y+5/4, x−3/4, −z+5/4; (v) y+3/4, −x+5/4, −z+5/4. |
Experimental details
| (ICu) | (IMo) |
Crystal data |
Chemical formula | C16H36N·C16H36B | C16H36N·C16H36B |
Mr | 481.72 | 481.72 |
Crystal system, space group | Tetragonal, I41/a | Tetragonal, I41/a |
Temperature (K) | 295 | 295 |
a, c (Å) | 18.9089 (6), 10.5803 (3) | 18.958 (5), 10.624 (5) |
V (Å3) | 3782.9 (2) | 3818 (2) |
Z | 4 | 4 |
Radiation type | Cu Kα | Mo Kα |
µ (mm−1) | 0.33 | 0.05 |
Crystal size (mm) | 0.13 × 0.05 × 0.03 | 0.31 × 0.13 × 0.10 |
|
Data collection |
Diffractometer | Oxford Diffraction Xcalibur Nova R
CCD diffractometer | Oxford Diffraction Xcalibur CCD diffractometer |
Absorption correction | – | – |
No. of measured, independent and observed [I > 2σ(I)] reflections | 4159, 1665, 414 | 12512, 2075, 408 |
Rint | 0.016 | 0.172 |
(sin θ/λ)max (Å−1) | 0.599 | 0.639 |
|
Refinement |
R[F2 > 2σ(F2)], wR(F2), S | 0.064, 0.265, 0.75 | 0.081, 0.255, 0.74 |
No. of reflections | 1665 | 2075 |
No. of parameters | 79 | 79 |
H-atom treatment | H-atom parameters constrained | H-atom parameters constrained |
Δρmax, Δρmin (e Å−3) | 0.09, −0.10 | 0.16, −0.12 |
Subscribe to Acta Crystallographica Section A: Foundations and Advances
The full text of this article is available to subscribers to the journal.
If you have already registered and are using a computer listed in your registration details, please email
support@iucr.org for assistance.