Comparative refinement of correct and incorrect structural models of tetrabutylammonium tetra­butylborate – pitfalls arising from poor-quality data

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.

Computing details

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).

Figures

(ICu) Tetrabutylammonium Tetrabutylborate

Crystal data

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) Å^3	Needle, colourless
Z = 4	0.13 × 0.05 × 0.03 mm
F(000) = 1104

Data collection

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

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)] = 0.064	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.265	H-atom parameters constrained
S = 0.75	w = 1/[σ^2(Fo^2) + (0.1488P)^2] where P = (Fo^2 + 2Fc^2)/3
1665 reflections	(Δ/σ)max < 0.001
79 parameters	Δρmax = 0.09 e Å^−3
0 restraints	Δρmin = −0.10 e Å^−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.

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 (Ų)

	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 (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
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)

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—C5^v	111.76 (10)
C8—C7—C6	117.8 (4)	C5^iv—N1—C5^v	111.76 (10)
C1^i—B1—C1	109.81 (16)	C5—N1—C5^vi	111.76 (10)
C1^i—B1—C1^ii	109.30 (8)	C5^iv—N1—C5^vi	111.76 (10)
C1—B1—C1^ii	109.30 (8)	C5^v—N1—C5^vi	104.98 (19)
C1^i—B1—C1^iii	109.30 (8)	C2—C1—B1	117.23 (19)
C1—B1—C1^iii	109.30 (8)	C1—C2—C3	114.8 (3)
C1^ii—B1—C1^iii	109.81 (16)	C7—C6—C5	112.8 (3)
C5—N1—C5^iv	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

Crystal data

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) Å^3	Needle, colourless
Z = 4	0.31 × 0.13 × 0.10 mm
F(000) = 1104

Data collection

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

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)] = 0.081	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.255	H-atom parameters constrained
S = 0.74	w = 1/[σ^2(Fo^2) + (0.1072P)^2] where P = (Fo^2 + 2Fc^2)/3
2075 reflections	(Δ/σ)max < 0.001
79 parameters	Δρmax = 0.16 e Å^−3
0 restraints	Δρmin = −0.12 e Å^−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.

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 (Ų)

	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 (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
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)

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—C1^i	111.18 (10)	C5^iv—B1—C5^ii	109.59 (8)
C1—N1—C1^ii	106.11 (19)	C5^iv—B1—C5^v	109.24 (16)
C1^i—N1—C1^ii	111.18 (10)	C5^ii—B1—C5^v	109.59 (8)
C1—N1—C1^iii	111.18 (10)	C5^iv—B1—C5	109.58 (8)
C1^i—N1—C1^iii	106.11 (19)	C5^ii—B1—C5	109.24 (16)
C1^ii—N1—C1^iii	111.18 (10)	C5^v—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.