Simultaneous variation of multipole parameters and Gram-Charlier coefficients in a charge-density study of tetrafluoroterephthalonitrile based on X-ray and neutron data

Difficulties encountered in modelling the scattering of fluorine in organic compounds have been investigated through refinements of accurate X-ray and neutron diffraction data measured on tetrafluoroterephthalonitrile, TFT, at 122.4 K. Multipole refinements led to a highly contracted octopole on fluorine. The subsequent analysis revealed that fluorine does not possess a valence octopole but exhibits anharmonic thermal motion that can be modelled by the octopole multipole parameters. The scattering contribution from the octopole shows the same cubic dependence in the scattering vector as the Gram-Charlier expansion of the nuclear displacements to third order. The analysis also showed that refinement of third-order Gram-Charlier coefficients on fluorine requires data to at least 0.93 Å^-1 resolution in . The X-ray data extending to 1.27 Å^-1 were of sufficient resolution to include third-order Gram-Charlier coefficients for N, F and the cyano C atoms in the refinement, whereas the neutron data only enabled refinement of the third-order Gram-Charlier coefficients for nitrogen. The refinements of the neutron and X-ray diffraction data yielded identical atomic displacement parameters for all the atoms. Though inclusion of anharmonic motion for N and F atoms provides the best model, it does not affect the crystal electron density, and all intramolecular bond critical points have identical features. Application of the anharmonic model, however, leads to small differences in the intermolecular interactions, which is illustrated by the electrostatic potential adjacent to the N atom. The characteristics of the C-F bond were elucidated by the topological analysis of the crystal electron density, which also supported the proposed quinonoid structure of the benzene ring.

Computing details

Data collection: Enraf-Nonius Express for X1, X2. Cell refinement: Rafd9 for NEUT1, NEUT2; Enraf-Nonius Express for X1, X2. Data reduction: Racer for NEUT1, NEUT2; DREADD (Blessing, 1987) for X1, X2. For all compounds, program(s) used to refine structure: VALRAY (Stewart, 1998).

Figures

(NEUT1) tetrafluoroterephthalonitrile

Crystal data

C8F4N2	Dx = 1.850 Mg m^−3
Mr = 200.10	Neutron radiation, λ = 0.8395 Å
Orthorhombic, Cmca	Cell parameters from 25 reflections
a = 7.6944 (19) Å	θ = 20.0–21.4°
b = 9.7457 (16) Å	µ = 0.00156 mm^−1
c = 9.5827 (15) Å	T = 122 K
V = 718.6 (2) Å^3	Block, light-yellow
Z = 4	3.1 × 2.3 × 1.2 mm
The cell parameters are taken from the X-ray diffraction experiment. The parameters obtained using neutron diffraction are a=7.6988(3)AA, b=9.7421(3)AA, c=9.5806(1)AA.

Data collection

Four-circle HUBER diffractometer	1523 independent reflections
Radiation source: reactor	1298 reflections with I > 2σ(I)
Cu 220 transmission geometry monochromator	Rint = 0.049
%T Coupled ${\w}–x\q$–scans with scan width between 1.2 and 4.5$^{^χirc}$ and $1^λeq x^λeq 2$.	^θmax = 56.2°,^θmin = 4.7°
Absorption correction: integration DATAP (Coppens, 1970)	h = ^−15^→15
Tmin = 0.996, Tmax = 0.999	k = ^−4^→18
3222 measured reflections	l = ^−8^→18

Refinement

Refinement on F^2	38 parameters
Least-squares matrix: full	0 restraints
wR(F^2) = 0.055	Weighting scheme based on measured s.u.'s w = 1/[σ^2(Fo^2)]
S = 2.73	(Δ/σ)max = 0.0001
2994 reflections	Extinction correction: B-C type 1 Lorentzian isotropic

Special details

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.

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

	x	y	z	Uiso*/Ueq
F	0.30534 (4)	0.38510 (4)	0.07916 (4)	0.0186 (1)
N	0.00000	0.15956 (3)	0.22933 (3)	0.0235 (1)
C1	0.00000	0.38049 (3)	0.08080 (3)	0.0109 (1)
C2	0.15604 (3)	0.44102 (2)	0.04018 (2)	0.0115 (1)
C3	0.00000	0.25841 (4)	0.16326 (4)	0.0146 (1)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
F	0.01341 (10)	0.01997 (12)	0.02241 (13)	0.00398 (9)	−0.00234 (9)	0.00352 (11)
N	0.03675 (16)	0.01473 (10)	0.01899 (12)	0.000000	0.000000	0.00702 (9)
C1	0.01293 (11)	0.00915 (10)	0.01066 (10)	0.000000	0.000000	0.00084 (8)
C2	0.01107 (7)	0.01093 (7)	0.01243 (8)	0.00096 (6)	−0.00046 (6)	0.00089 (6)
C3	0.02067 (13)	0.01087 (11)	0.01231 (11)	0.000000	0.000000	0.00236 (9)

(NEUT2) tetrafluoroterephthalonitrile

Crystal data

C8F4N2	Dx = 1.850 Mg m^−3
Mr = 200.10	Neutron radiation, λ = 0.8395 Å
Orthorhombic, Cmca	Cell parameters from 25 reflections
a = 7.6944 (19) Å	θ = 20.0–21.4°
b = 9.7457 (16) Å	µ = 0.00156 mm^−1
c = 9.5827 (15) Å	T = 122 K
V = 718.6 (2) Å^3	Block, light-yellow
Z = 4	3.1 × 2.3 × 1.2 mm
The cell parameters are taken from the X-ray diffraction experiment. The parameters obtained using neutron diffraction are a=7.6988(3)AA, b=9.7421(3)AA, c=9.5806(1)AA.

Data collection

Four-circle HUBER diffractometer	1523 independent reflections
Radiation source: reactor	1298 reflections with I > 2σ(I)
Cu 220 transmission geometry monochromator	Rint = 0.049
%T Coupled ${\w}–x\q$–scans with scan width between 1.2 and 4.5$^{^χirc}$ and $1^λeq x^λeq 2$.	^θmax = 56.2°,^θmin = 4.7°
Absorption correction: integration DATAP (Coppens, 1970)	h = ^−15^→15
Tmin = 0.996, Tmax = 0.999	k = ^−4^→18
3222 measured reflections	l = ^−8^→18

Refinement

Refinement on F^2	44 parameters
Least-squares matrix: full	0 restraints
wR(F^2) = 0.054	Weighting scheme based on measured s.u.'s w = 1/[σ^2(Fo^2)]
S = 2.70	(Δ/σ)max < 0.001
2994 reflections	Extinction correction: B-C type 1 Lorentzian isotropic

Special details

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. NOTICE: The model includes Gram-Charlier parameters to describe anharmonic motion of the N atom.

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

	x	y	z	Uiso*/Ueq
F	0.30534 (4)	0.38509 (4)	0.07916 (4)	0.0186 (1)
N	0.00000	0.15949 (6)	0.22883 (6)	0.0235 (1)
C1	0.00000	0.38049 (3)	0.08080 (3)	0.0109 (1)
C2	0.15604 (3)	0.44102 (2)	0.04018 (2)	0.0115 (1)
C3	0.00000	0.25840 (4)	0.16324 (4)	0.0146 (1)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
F	0.01341 (10)	0.01999 (12)	0.02239 (13)	0.00399 (9)	−0.00233 (9)	0.00353 (11)
N	0.03684 (15)	0.01471 (10)	0.01898 (12)	0.000000	0.000000	0.00702 (9)
C1	0.01290 (11)	0.00916 (10)	0.01066 (10)	0.000000	0.000000	0.00088 (8)
C2	0.01106 (7)	0.01094 (7)	0.01242 (7)	0.00095 (6)	−0.00046 (6)	0.00089 (6)
C3	0.02065 (13)	0.01089 (11)	0.01229 (11)	0.000000	0.000000	0.00236 (9)

(X1) tetrafluoroterephthalonitrile

Crystal data

C8F4N2	Dx = 1.850 Mg m^−3
Mr = 200.10	Mo Kα radiation, λ = 0.71073 Å
Orthorhombic, Cmca	Cell parameters from 25 reflections
a = 7.6944 (19) Å	θ = 20.0–21.4°
b = 9.7457 (16) Å	µ = 0.18 mm^−1
c = 9.5827 (15) Å	T = 122 K
V = 718.6 (2) Å^3	Block, light-yellow
Z = 4	0.30 × 0.24 × 0.22 mm
F(000) = 392

Data collection

Enraf-Nonius CAD4 diffractometer	2371 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	Rint = 0.013
Graphite monochromator	θmax = 64.9°, θmin = 4.0°
ω–2θ scans	h = −19→19
33259 measured reflections	k = −24→24
3239 independent reflections	l = −24→24

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
wR(F^2) = 0.024	Weighting scheme based on measured s.u.'s w = 1/[σ^2(Fo^2)]
S = 0.69	(Δ/σ)max < 0.001
3239 reflections	Δρmax = 0.19 e Å^−3
100 parameters	Δρmin = −0.17 e Å^−3
0 restraints	Extinction correction: B-C type 1 Lorentzian isotropic

Special details

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. NOTICE: The model is a multipole model varying the multipole parameters as described in the manuscript.

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

	x	y	z	Uiso*/Ueq
F	0.305690 (13)	0.384960 (11)	0.079230 (12)	0.0191 (1)
N	0.00000	0.159490 (14)	0.229560 (15)	0.0240 (1)
C1	0.00000	0.380430 (9)	0.080850 (10)	0.0120 (1)
C2	0.156090 (9)	0.440980 (6)	0.040210 (7)	0.0126 (1)
C3	0.00000	0.258490 (11)	0.163290 (11)	0.0157 (1)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
F	0.01421 (3)	0.02048 (3)	0.02271 (4)	0.00422 (2)	−0.00238 (3)	0.00334 (3)
N	0.03747 (7)	0.01518 (4)	0.01932 (4)	0.000000	0.000000	0.00719 (3)
C1	0.01425 (3)	0.01019 (3)	0.01168 (3)	0.000000	0.000000	0.00095 (2)
C2	0.01243 (2)	0.01196 (2)	0.01351 (2)	0.001028 (18)	−0.000533 (19)	0.001041 (15)
C3	0.02244 (4)	0.01145 (3)	0.01313 (3)	0.000000	0.000000	0.00266 (3)

(X2) tetrafluoroterephthalonitrile

Crystal data

C8F4N2	Dx = 1.850 Mg m^−3
Mr = 200.10	Mo Kα radiation, λ = 0.71073 Å
Orthorhombic, Cmca	Cell parameters from 25 reflections
a = 7.6944 (19) Å	θ = 20.0–21.4°
b = 9.7457 (16) Å	µ = 0.18 mm^−1
c = 9.5827 (15) Å	T = 122 K
V = 718.6 (2) Å^3	Block, light-yellow
Z = 4	0.30 × 0.24 × 0.22 mm
F(000) = 392

Data collection

Enraf-Nonius CAD4 diffractometer	2371 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	Rint = 0.013
Graphite monochromator	θmax = 64.9°, θmin = 4.0°
ω–2θ scans	h = −19→19
33259 measured reflections	k = −24→24
3239 independent reflections	l = −24→24

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	Weighting scheme based on measured s.u.'s w = 1/[σ^2(Fo^2)]
wR(F^2) = 0.021	(Δ/σ)max < 0.001
S = 0.61	Δρmax = 0.15 e Å^−3
3239 reflections	Δρmin = −0.16 e Å^−3
122 parameters	Extinction correction: B-C type 1 Lorentzian isotropic

Special details

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. NOTICE: The model is a multipole model varying the multipole parameters as described in the manuscript. The model includes furthermore, Gram-Charlier parameters to describe anharmonic motion of the atoms N, F, and C3.

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

	x	y	z	Uiso*/Ueq
F	0.30605 (4)	0.38496 (4)	0.07948 (4)	0.0191 (1)
N	0.00000	0.15913 (4)	0.22916 (4)	0.0240 (1)
C1	0.00000	0.380440 (8)	0.080860 (8)	0.0120 (1)
C2	0.156100 (8)	0.440980 (6)	0.040210 (6)	0.0126 (1)
C3	0.00000	0.25839 (3)	0.16312 (3)	0.0157 (1)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
F	0.01420 (2)	0.02047 (3)	0.02273 (3)	0.00421 (2)	−0.00239 (2)	0.00334 (3)
N	0.03757 (7)	0.01517 (3)	0.01930 (4)	0.000000	0.000000	0.00723 (3)
C1	0.01420 (3)	0.01021 (2)	0.01172 (3)	0.00000	0.000000	0.00095 (2)
C2	0.012435 (19)	0.011994 (18)	0.013505 (19)	0.001003 (16)	−0.000529 (17)	0.001041 (13)
C3	0.02243 (4)	0.01145 (3)	0.01312 (3)	0.000000	0.000000	0.00267 (2)