Anisotropy of indirect couplings and accurate molecular structures of 1,2- and 1,3-difluorobenzenes by combined analysis of gas electron diffraction, rotational spectroscopy and liquid crystal NMR data

Journal of Molecular Structure 984 (2010) 102–110

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Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc

Anisotropy of indirect couplings and accurate molecular structures of 1,2- and 1,3-difluorobenzenes by combined analysis of gas electron diffraction, rotational spectroscopy and liquid crystal NMR data Ewan M. Brown, Derek A. Wann, David W.H. Rankin ⇑ School of Chemistry, University of Edinburgh, West Mains Road, Edinburgh EH9 3JJ, UK

a r t i c l e

i n f o

Article history: Received 17 August 2010 Received in revised form 10 September 2010 Accepted 10 September 2010 Available online 17 September 2010 Keywords: Molecular structure Electron diffraction Liquid crystal NMR Anisotropy of indirect couplings Difluorobenzene

a b s t r a c t In the combined analysis of gas-phase electron-diffraction scattering data, rotation constants and dipolar coupling constants from NMR experiments in liquid crystal solvents, not only are high-accuracy molecular structures of 1,2- and 1,3-difluorobenzene obtained, but the anisotropic components of some of the CF and FF indirect couplings have been deduced directly from the experimental data. The benefits of combined analyses of data from several different experimental techniques, and factors influencing the accuracy of structures determined in this way, are discussed. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction The three isomeric difluorobenzenes are ideally suited for structure determination by the combined analyses of gas electron diffraction (GED) data, dipolar NMR couplings measured in liquid-crystal solvents (LCNMR), and rotational data (1,2- and 1,3-isomers only). The difficulty of determining their structures by ED alone is heightened, compared to those of other substituted aromatics, by the fact that their carbon-fluorine bond lengths are similar to the carboncarbon bond lengths. This effectively reduces the number of distinct features in their radial-distribution curves and leads to a high degree of correlation between refining parameters in the analyses. The existence of only one stable isotope of fluorine makes determination of coordinates of all atoms from rotation constants by isotopic substitution almost impossible, and the 1,4 compound does not have a permanent dipole moment. In contrast, the molecules are ideally suited to LCNMR analysis, having six 100%-abundant spin-1/2 nuclei. If 13C satellites can be assigned then it is possible to determine direct coupling constants for all HH, FF, HF, CF and CH nuclear pairs. It is therefore possible, in principle, to determine a complete, although unscaled, structure using LCNMR data alone. However, there is evidence of anisotropy of some of the indirect coupling constants between FF and CF nuclear pairs. This would normally suggest that it ⇑ Corresponding author. E-mail address: [email protected] (D.W.H. Rankin). 0022-2860/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2010.09.013

would be wise to exclude these values from the analysis, so complete structures would not be obtained. These molecules therefore call for analysis of all the available data. Simultaneous analysis of structural data obtained by several techniques often yields a complete and accurate structure, whereas data from one technique alone would give an incomplete and/or less accurate set of parameters. Although there is a method, SARACEN, that utilises both experimental and theoretical data [1–3], purely experimental analyses are preferable for suitable molecules. Gas electron-diffraction data and rotation constants are routinely combined, and we have also been able to use dipolar couplings obtained by LCNMR. The latter combination has been particularly successful for aromatic rings, for which the absence of low-frequency vibrational modes has been a significant beneficial factor [4–6]. In a combined analysis, by providing information about the structure from electron-diffraction data and rotation constants, not all the LCNMR data are needed to define the structure. There is therefore the potential to extract the anisotropic components of the indirect couplings between the heavier nuclei, for which the direct couplings are effectively derived from the structure. A systematic study of chlorinated benzenes [6–13] was undertaken primarily to assess the validity of combining gas-phase and solution-phase data, and it has been demonstrated that the accuracy of these combined analyses matches their impressive precision [14], so it is shown that at least for these molecules interactions between solvents and solutes do not distort the structures significantly. The

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structures of these chlorobenzenes also showed the effects of multiple substitution. Replacement of hydrogen by chlorine results in shortening of the ring C–C bonds adjacent to the substituent, widening of the ring angle at the substituent site, and a smaller narrowing of the two neighbouring ring angles. These effects are largely additive on multiple substitution, but there are also further distortions, mainly attributable to steric interactions between adjacent substituents. Fluorine causes greater distortions than chlorine, because the magnitudes of substitution effects depend mainly on the electronegativity of the substituent [15], but steric effects arising from fluorine substituents on adjacent carbon atoms are less significant than those for chlorine [16]. We have studied the three isomers of difluorobenzene. Combined analysis of electron-diffraction data and dipolar coupling constants for 1,4-difluorobenzene have already been published [17]. In that case, the absence of a dipole moment precluded the measurement of rotation constants by microwave spectroscopy. In this present paper we present the results of combined analyses of electron diffraction, microwave and liquid-crystal NMR data for 1,2- and 1,3-difluorobenzene. Sufficient experimental data, including LCNMR data in several solvents [18,19] and rotation constants for several isotopomers [20], are available to allow us to refine the anisotropies of some of the indirect 13C19F and the 19F19F coupling constants, as well as yielding extremely accurate structures. This approach, using data from several experimental methods, is significantly different from that used to analyse data obtained by LCNMR. Allowance for the distortions of the solute caused by the aligning solvent is possible, but requires good data for solutions in several distinct solvents [21]. In our work, uncertainties associated with the measured dipolar couplings are larger, because allowance is also made for possible errors in the vibrational corrections, but by including data from other techniques in the leastsquares refinements, correlations between parameters are reduced. This results in a structure that is consistent with all the data, and usually allows all geometrical parameters to be refined, resulting in small esds.

spectrum was the identification of a first-order sub-spectrum involving the four most intense lines [marked 1, 2 ,3 and 4 in Fig. 1a]. Experimenting with trial values for the orientation parameters showed that the separation of lines 1 and 2 (or lines 3 and 4) is exactly equal to 3DFF. The coupling constant DFF can therefore be measured directly from the spectrum; its value is ±404.89 Hz. Furthermore, because the vector between the two fluorine atoms lies parallel to the y axis of the coordinate system used, the value of DFF is dependent on only one orientation parameter (Syy). By determining DFF, the value of Syy is also determined (for the assumed internuclear separation). Knowing the approximate value of Syy it becomes a simple matter to vary Szz until enough of the lines in the calculated and experimental spectra can be matched to allow refinement of the spectral parameters. It must be remembered that there are still two possible solutions to the spectral assignment, depending on the sign of DFF. Fortunately, during the refinement of the direct coupling constants it became apparent that DFF is negative; the couplings obtained with it negative reproduced the experimental spectrum with an r.m.s. deviation of just 0.31 Hz, whereas with a positive value the r.m.s. deviation was 2.7 Hz. Fig. 1a shows the final calculated spectrum, derived from refined direct coupling constants, and a representation of the experimental spectrum. In the final refinement a total of 76 lines were assigned; only lines arising from two or more overlapping peaks were left unassigned. Once the 19F spectrum had been analysed, assignment of the 1H spectrum was relatively simple. Both spectra were recorded using the same sample at the same temperature and so, to a good approximation, the orientation parameters are the same for each spectrum. All that remained was to refine the calculated direct couplings to fit the experimental spectrum. In the final refinement a total of 87 lines were assigned and the r.m.s. deviation was 0.37 Hz. Once more, the only lines that were not assigned were those arising from overlapping peaks. The calculated and experimental line positions and intensities are shown in Fig. 1b. The final values obtained for the direct coupling constants that were used in the structure refinements are listed in Table S1.

2. Results and discussion

2.2. Force fields and vibrational corrections

2.1. Analysis of LCNMR spectra

In order to undertake the refinements of the structures, estimates of amplitudes of vibration were required, as well as other vibrational terms that are needed to relate the various kinds of experimental data to a common structural base, rh0 [24]. To obtain these quantities, it was necessary to derive a force field. In earlier NMR studies of difluorobenzenes [18,19,25] force fields for chlorobenzenes were modified and used to calculate vibrational corrections. The estimated errors of the vibrationally corrected dipolar couplings, used to weight the observations in the structural analysis, were assumed to be identical to those of the uncorrected couplings, i.e. the force field and correction terms derived from it were tacitly assumed to be absolutely perfect. As the uncertainties of observed couplings are sometimes very small, such an assumption can lead to vibrationally corrected dipolar couplings being seriously overweighted in the refinements. Our approach has been to compute a force field using experimentally determined vibrational frequencies [26] in conjunction with the MM3 [27] force field. This method was chosen because the force field is based on experimental data for a very large number of molecules. An ab initio force field could equally well be used, but in this work the entire analysis is based on experimental data. The program ASYM [28] then provided the amplitudes of vibration, which were used as starting values for the GED refinement, and the parallel and perpendicular vibrational corrections, also needed in the analysis of electron-diffraction data. The force field also provides the terms needed to correct rotation constants and dipolar coupling constants. A small modification

Originally we set out to record all the necessary data for this project, but it became clear that literature data would be sufficient. The 1H and 19F NMR spectra of 1,2-difluorobenzene in the liquid crystal solvent E7, recorded at room temperature, had by then been recorded. These spectra were analysed, although eventually only the data from the 19F spectrum were included in the structure refinements. The large number of lines, due to the presence of six spin-1/2 nuclei, made the analysis of these spectra far from trivial. The analysis was carried out using two programs developed in Edinburgh, based on the well-known spectrum analysis program, LEQUOR [22]. LCSIM uses approximate coordinates and trial orientation parameters to simulate spectra, and visual comparison with the experimental spectrum allows a start to be made on assigning resonances. The second program, SLIQUOR, then refines spectral parameters (chemical shifts and direct and indirect coupling constants), and as the quality of the fit improves, more resonances can be included. In the present case, starting chemical shifts and indirect coupling constants were taken from the published data of Ernst et al. [23]. The 19F spectrum was analysed first, because it is relatively simple. A systematic search for approximate values of the orientation parameters was carried out with limited success; although many of the more intense lines in the spectrum could be identified, it was impossible to assign any of the smaller lines unambiguously. It transpired that the key to the assignment of this

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(a) 19F spectrum

(1)

(2)

(3)

(4) Calculated

Frequency/Hz -2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

2500

Experimental

(b) 1H spectrum

Calculated

Frequency/Hz 14

16

18

20

22

24

26

28

30

32

34

36

38

40

42

44

46

*10

48

50 52

54

56

58

60

62 64

66

68

70

72

74 76

2

Experimental

Fig. 1. Simulated experimental line positions and intensities in the NMR spectra of 1,2-difluorobenzene in E7.

to ASYM (now included as standard) was necessary so that the covariance matrices, used to correct the dipolar couplings from D0 to Da, could be calculated. These matrices depend on the terms hDxDyi, hDxDzi and hDyDzi, where Dx, Dy and Dz are the components of the instantaneous excursion of the internuclear vector from the equilibrium position. In this way data from the three techniques, GED, LCNMR and MW spectroscopy, were reduced to a common basis. The refinements, whether based on GED data alone, or also incorporating rotation constants and/or dipolar couplings, were thus of type rh0. It was not possible to refine rh1 structures, because the vibrational correction terms allowing for

curvilinear motions cannot at present be calculated for dipolar coupling constants. However, for a reasonably rigid planar molecule this is not a serious limitation. Vibrationally corrected coupling constants, Da, are given in Tables S1 and S2 for 1,2- and 1,3-difluorobenzene, respectively, with uncertainties derived from both the spectral analysis and the vibrational correction terms. Our calculated corrections to dipolar coupling constants are not identical to those used in earlier work [18,19]. We have shown that uncertainties of terms calculated in this way are roughly proportional to their magnitudes, and that 10% of the magnitude, with a lower limit of 0.1 Hz, is a

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reasonable estimate [17]. Allowing for these realistic uncertainties results in the weights given to the dipolar couplings in our analyses being lower than those used in the earlier work. Some of the apparent variations in the structures of molecules in different liquidcrystalline solvents probably result from fitting of over-precise data exactly. This is a severe problem when the number of independent observations does not greatly exceed the number of refined structural and orientation parameters, resulting in strong correlations between the refining geometrical parameters. Moreover, because observed dipolar coupling constants are also often very highly correlated, the number of independent observations may be less than the total number of observations. Combining gas electron diffraction (or any other relevant data) with the dipolar coupling constants reduces these correlations, giving a more robust experimental data set. 2.3. Molecular model for 1,2-difluorobenzene For all structural analyses it was assumed that 1,2-difluorobenzene has C2v symmetry. Its geometry was defined by 11 independent structural parameters (see Table 1). Four defined the ring C–C bond lengths, one the C–F and two the C–H bond lengths. With all the ring distances defined, only one angle parameter was required for the ring, and three more angles described the deviations of C–F and C– H bonds from their respective extrapolated bisectors of their adjacent ring CCC angles. In each of these last three cases a positive deviation reflects displacement of the fluorine or hydrogen atoms to-

wards the nearest neighbouring fluorine atom. See Fig. 2a for the atom numbering. Initial values of these parameters were 139 pm for all C–C bond lengths, 134 pm for C–F and 108.5 pm for both C–H bond lengths. All angles were initially assumed to be 120°. Calculated parallel and perpendicular amplitudes of vibration were used for each of the 36 distinct internuclear distances within the molecule. 2.4. Structure refinement for 1,2-difluorobenzene First refinements were based on only GED data, and soon converged, with RG at 6.5%. At this stage, none of the three C–C difference parameters would refine with reasonable standard deviations, and so all were fixed at zero. The average C–H distance was refined but no other parameters relating to hydrogen could be. The ring showed little deviation from regular hexagonal geometry, although the deviation angle for the fluorine substituent was significant at 0.7(2)°. The refinement was then switched from the ra to the rh0 basis, which brought RG down to 6.2% after a few cycles of refinement. At this stage all of the amplitudes of vibration (other than those for HH pairs) were refined, either individually, or in groups with ratios fixed as calculated. The final structure obtained using ED data alone (for which RG = 5.9%) is included in Table 1. Rotation constants of the principal isotopic species were introduced as extra data, first with high uncertainties (i.e. low weights), gradually reducing their uncertainties until they matched the combined values from the experiments and the vibrational corrections.

Table 1 Refined parameters (rh0) from the combined GED, MW, and LCNMR analysis for 1,2-difluorobenzene.a

a b c

Geometric parameters

GED

GED + MW

GED + MW + LCNMR

Independent p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11

[rC(1)–C(2) + rC(2)–C(3) + rC(3)–C(4) + rC(4)–C(5)]/4 [rC(1)–C(2)]–[rC(2)–C(3) + rC(3)–C(4) + rC(4)–C(5)]/3 [rC(2)–C(3)]–[rC(3)–C(4) + rC(4)–C(5)]/2 [rC(3)–C(4)]–[rC(4)–C(5)] rC–F [rC(3)–H(9) + rC(4)–H(10)]/2 [rC(3)–H(9)–rC(4)–H(10)] \C–F deviationb \C(1)–C(2)–C(3) \C(3)–H(9) deviationb \C(4)–H(10) deviationb

138.9(2) 0.0(fixed) 0.0(fixed) 0.0(fixed) 133.7(4) 107.2(7) 0.0(fixed) 0.7(2) 120.1(2) 0.0(fixed) 0.0(fixed)

138.9(2) 0.0(9) 0.6(9) 0.0(fixed) 134.3(4) 107.8(5) 0.0(fixed) 0.4(3) 120.3(2) 0.0(fixed) 0.0(fixed)

139.34(10) 0.6(4) 2.2(4) 1.8(5) 134.4(3) 108.1(2) 0.3(4) 0.6(1) 120.7(1) 0.6(1) 0.7(1)

Dependent d1 d2 d3 d4 d5 d6 d7 d8

rC(1)–C(2) rC(2)–C(3) rC(3)–C(4) rC(4)–C(5) rC(3)–H(9) rC(4)–H(10) \C(2)–C(3)–C(4) \C(3)–C(4)–C(5)

138.9(2) 138.9(2) 138.9(2) 138.9(2) 107.2(7) 107.2(7) 119.9(4) 120.1(2)

138.9(7) 138.5(8) 139.1(3) 139.1(3) 107.8(5) 107.8(5) 119.7(3) 120.0(2)

138.9(3) 138.0(3) 139.3(3) 141.1(3) 108.0(3) 108.2(3) 119.4(2) 119.9(1)

Orientation parametersc p12 Syy ZLI 1167 1H p13 Szz ZLI 1167 1H p14 Syy ZLI 1167 19F p15 Szz ZLI 1167 19F p16 Syy ZLI 1132 1H p17 Szz ZLI 1132 1H p18 Syy ZLI 1132 19F p19 Szz ZLI 1132 19F p20 Syy E7 19F p21 Szz E7 19F

– – – – – – – – – –

– – – – – – – – – –

0.04054(9) 0.05997(12) 0.03653(9) 0.05370(11) 0.07219(16) 0.10322(20) 0.07339(17) 0.10464(19) 0.07393(17) 0.13365(23)

Anisotropic indirect couplingsb p22 F(7)F(8) p23 C(2)F(8) p24 C(3)F(8)

– – –

– – –

28.6(119) 79.3(715) 11.2(60)

Distances (r) are in pm and angles (\) are in degrees. Values in parentheses are the standard deviations of the last digits. For definition see text. For descriptions of solvents see text.

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E.M. Brown et al. / Journal of Molecular Structure 984 (2010) 102–110 Table 2 Rotation constants/MHz used in the structural analysis of 1,2-difluorobenzene.

a

Fig. 2. The molecular structures of (a) 1,2-difluorobenzene, and (b) 1,3-difluorobenzene, showing the atom numbering. In each case the y axis is parallel to the line passing through the two fluorine atoms, and the z axis is the C2 symmetry axis.

Constant

Observeda

Corrected

Calculated

Uncertainty

Difference

B principal C principal B 13C(1) C 13C(1) B 13C(3) C 13C(3) B 13C(4) C 13C(4)

2227.89 1323.86 2226.01 1321.57 2222.37 1315.24 2191.05 1309.20

2227.58 1323.72 2225.70 1321.43 2222.06 1315.10 2190.74 1309.07

2227.62 1323.72 2225.66 1321.37 2222.01 1315.16 2190.79 1309.08

0.160 0.068 0.160 0.068 0.160 0.068 0.160 0.068

0.04 0.00 0.04 0.06 0.05 0.06 0.05 0.01

Observed rotation constants are taken from Ref. [20].

LCNMR data allowed the simultaneous refinement of all 21 structural and orientational parameters in addition to eight amplitudes of vibration or groups of tied amplitudes. Although the fit to the rotation constants remained good and RG rose only slightly, to 6.4%, many of the calculated direct coupling constants differed from the observed values by as much as five standard deviations. These discrepancies cannot be attributed solely to underestimation of the errors due to the vibrational corrections as they also occur for a number of couplings for which the vibrational corrections are extremely small. As was noted in our earlier study of 1,4-difluorobenzene [17], these apparent discrepancies could be attributed to anisotropic components of one or more of the indirect coupling constants involving these atoms. The model used for refinement was then amended to include factors that allow for the anisotropy of these CF and FF indirect (J) couplings. It was assumed that each observed coupling constant was the sum of the direct, dipolar coupling, Dij, and a contribution from the anisotropy of the indirect coupling, J aniso , given by J aniso  Sij , where Sij is the orientation parameter for ij ij the ij vector. Three terms, representing anisotropy of the indirect coupling between atom pairs 2–8, 3–8 and 7–8, were then included in the refinement. With these additional refining parameters the fit of calculated and measured coupling constants was much better and the RG factor dropped to 5.1%. The experimental data did not include information that would allow refinement of further anisotropic components of indirect coupling constants. The final refinement is based on GED data at two nozzleto-camera distances, eight rotation constants and a total of 81 direct coupling constants. Table S3 shows interatomic distances and amplitudes of vibration from the final refinement, Table S4 lists the least-squares correlation matrix calculated during the final refinement, and the atomic coordinates are given in Table S5. The corresponding molecular–intensity scattering and radial-distribution curves are shown in Fig. S1 and Fig. 3a, respectively. 2.5. Molecular model for 1,3-difluorobenzene

Even these two extra data were sufficient to reduce the estimated standard deviations of some of the parameters significantly. The rotation constants for the three 13C isotopomers were then introduced, and no problems were experienced in fitting all the experimental rotation constants to within their respective uncertainties (see Table 2). The introduction of the rotation-constant data also allowed refinement of two of the C–C difference parameters (albeit with fairly large standard deviations), although rC(3)– C(4)  rC(4)–C(5) (p4) could still not be refined. No additional parameter relating to hydrogen-atom positions could be refined, either. The final structure obtained using GED data and rotation constants (RG = 5.9%) is also shown in Table 1. Dipolar coupling constants recorded in three different solvents (ZLI 1132, ZLI 1167 and E7) were then included in the refinement. Two independent orientation parameters, Syy and Szz, were allowed to refine for each experiment in each solvent. Inclusion of the

Although it is of the same symmetry as 1,2-difluorobenzene (C2v), the structure of 1,3-difluorobenzene is slightly better suited to determination by GED, as it has only three distinct C–C distances. Altogether 11 geometrical parameters were required, three bond lengths for the ring and four for the peripheral atoms, two ring angles, and two angles locating two fluorine and two hydrogen atoms. Full details are given in Table 3; see Fig. 2b for the atom numbering. Initial values were chosen assuming a regular hexagonal structure, and vibrational amplitudes were calculated for the 38 distinct internuclear distances within the molecule. 2.6. Structure refinement for 1,3-difluorobenzene The refinement procedure was similar to that used for 1,2difluorobenzene, starting with GED data only and introducing rota-

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tering intensity curves are shown in Fig. S2, and the radial-distribution curves in Fig. 3b. 3. Conclusions 3.1. Combined analysis These studies serve to highlight some important points about the technique of combined analysis. In the first instance, it is clear that the use of GED data alone was insufficient to determine either of the structures completely. In general, the diffraction data supplied information on the ring geometry and the positions of the fluorine atoms, but C–C bond-length difference parameters could not be refined well or at all. The addition of rotation constants allowed some of these difference parameters to be refined but still little could be said about the positions of the hydrogen atoms. Only on introducing the dipolar coupling constants could any of the C– C–H angles be refined successfully. Moreover, the results were generally improved when two or more sets of direct coupling constants were included. This helped to reduce the effects of random errors in the LCNMR data (see below). The case of 1,3-difluorobenzene, in particular, shows how powerful the technique of combined analysis can be. In the GED analysis, only six of the 11 structural parameters could be refined whereas in the final combined analysis all 11 structural parameters, as well as 10 orientation parameters and the anisotropies of two indirect couplings, were successfully refined.

Fig. 3. Experimental GED radial-distribution curve and final theoretical-minusexperimental difference curve, P(r)/r, for (a) 1,2-difluorobenzene, and (b) 1,3difluorobenzene. Before Fourier inversion the data were multiplied by sexp(0.00002s2)/(ZC  fC)(ZF  fF).

tion constants and then dipolar coupling constants as the refinement progressed. With GED data alone, an rh0 structure was refined, with RG at 6.4%. The difference parameter rC(1)– C(2)  rC(3)–C(4) (p3) and the parameters determining the hydrogen-atom positions could not be refined at this stage. Eight independent rotation constants (see Table 4) then were included, which allowed refinement of the mean C–H bond length, although the remaining C–C bond-length difference parameter could not be refined. The main effect was an improvement in the determination of the ring angles and the C–C–F angle. The RG factor (6.6%) was slightly higher than with the GED data alone. Parameter values from all refinements can be found in Table 3. The LCNMR data obtained from solvent ZLI 1132 were then included. In general, the fit to these coupling constants was better than the fit in the case of 1,2-difluorobenzene. Notable exceptions were the C–F and F–F coupling constants, which were several standard deviations from their observed values, suggesting that indirect couplings between heavier nuclei have a significant anisotropic component (Janiso) that is inseparable from the direct coupling constant. Coupling constants recorded using the solvent ZLI 1167 were also added, allowing the simultaneous refinement of all 11 structural parameters as well as 10 orientation parameters and eight groups of amplitudes of vibration. Two terms representing anisotropy of the indirect coupling for atom pairs 7–9 and 3–9 were also included, giving a final RG factor of 6.9%. Other anisotropy terms could not be refined. The results of the combined structural analysis can be found in Table 3. A full list of interatomic distances and amplitudes of vibration is given in Table S6, the least-squares correlation matrix calculated during the final refinement is shown in Table S7, and the atomic coordinates in Table S8. The corresponding molecular scat-

3.2. Structures The structures obtained for the difluorobenzenes are largely consistent with expectations arising from previous studies [7– 9,29]. In particular the effects of fluorine substitution on the internal ring angles are easily predicted; the ipso angle opens out while the adjacent angles are reduced by approximately half the amount. The remaining ring angles are also affected but to a lesser degree. This is a well-determined and widely studied effect [30,31] and applies to a whole range of electron-withdrawing substituents. In the case of the difluorobenzenes, the distortion of the ring geometry from a regular hexagon can be considered as a superposition of the effects arising from the two individual fluorine atoms. In 1,2-difluorobenzene these effects are in competition, so angle C(1)–C(2)–C(3) is increased by the ipso fluorine but is decreased by the ortho fluorine, although to a lesser degree. For this reason, the ring geometry of 1,2-difluorobenzene is remarkably close to that of a regular hexagon, with the largest deviation of an internal angle being just 0.7(1)°. The distortions in 1,3-difluorobenzene are very different because the effects of the two fluorine atoms are combined constructively. This produces some significant angular distortions within the ring, particularly at C(2), with the angle C(1)–C(2)– C(3) refining to 117.8(3)° in the final combined analysis. In contrast, the fluorine atoms in 1,4-difluorobenzene are sufficiently far apart to have essentially independent effects on the ring angles. The ring angles are therefore similar to the ipso and ortho angles observed in fluorobenzene [29]. In general, the increase of the ring angle at a carbon atom substituted with an electron-withdrawing group is associated with shortening of the two adjacent bonds. This has been rationalised in terms of hybridisation effects [31], in which there is an increase in the p character of the sp2-hybrid orbital of the substituted carbon that points towards the substituent. This effectively leads to a decrease in the p character of the remaining sp2 orbitals and hence to shortening of the C–C bonds. Similar effects are observed for the bond lengths in the difluorobenzenes. In general, the bonds adjacent to the fluorine-substi-

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Table 3 Refined parameters (rh0) from the combined GED, MW, and LCNMR analysis for 1,3-difluorobenzene.a. Geometric parameters

a b c

GED + MW

GED + MW + LCNMR

Independent p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11

[rC(1)–C(2) + rC(3)–C(4) + rC(4)–C(5)]/3 [rC(1)–C(2) + rC(3)–C(4)]/2–[rC(4)–C(5)] [rC(1)–C(2)]–[rC(3)–C(4)] rCF [rC(2)–H(8) + rC(4)–H(10) + rC(5)–H(11)]/2 [rC(4)–H(10) + rC(5)–H(11)]/2–rC(2)–H(8) [rC(4)–H(10)–rC(5)–H(11)] \C(1)–C(2)–C(3) \C(2)–C(3)–C(4) \C(2)–C(3)–F(9) \C(3)–C(4)–H(10)

139.0(2) 2.2(11) – 134.1(5) – – – 118.0(7) 121.9(2) 117.6(6) –

139.1(2) 1.4(8) – 133.8(4) 108.3(5) – – 118.1(6) 122.0(2) 118.6(2) –

139.13(13) 0.1(4) 6.9(4) 133.4(4) 108.0(3) 0.4(4) 2.9(6) 117.8(3) 121.7(3) 118.3(2) 119.1(2)

Dependent d1 d2 d3 d4 d5 d6 d7

rC(1)–C(2) rC(3)–C(4) rC(4)–C(5) rC(2)–H(8) rC(4)–H(10) rC(5)–H(11) \C(3)–C(4)–C(5)

138.3(3) 138.3(3) 140.5(9) 108.5(fixed) 108.5(fixed) 108.5(fixed) 119.8(7)

138.6(2) 138.6(2) 140.0(7) 108.3(5) 108.3(5) 108.3(5) 118.9(4)

139.5(3) 138.8(3) 139.2(3) 108.3(4) 108.1(4) 107.8(5) 119.1(3)

Orientation parametersc p12 p13 p14 p15 p16 p17 p18 p19 p20 p21

Syy ZLI 1132 1H Szz ZLI 1132 1H Syy ZLI 1132 19F Szz ZLI 1132 19F Syy ZLI 1167 1H (Exp 1) Szz ZLI 1167 1H (Exp 1) Syy ZLI 1167 1H (Exp 2) Szz ZLI 1167 1H (Exp 2) Syy ZLI 1167 19F Szz ZLI 1167 19F

– – – – – – – – – –

– – – – – – – – – –

0.09354(22) 0.06773(21) 0.09374(29) 0.06766(21) 0.05773(16) 0.04239(16) 0.06947(18) 0.05312(18) 0.06971(15) 0.05315(18)

Anisotropic indirect couplingsb p22 p23

F(7)F(9) C(3)F(9)

– –

– –

24.9(12) 30.4(595)

Distances (r) are in pm and angles (\) are in degrees. For definition see text. For descriptions of solvents see text.

Table 4 Rotation constants/MHz used in the structural analysis of 1,3-difluorobenzene.

a

GED

Constant

Observeda

Corrected

Calculated

Uncertainty

Difference

B principal C principal B 13C(1) C 13C(1) C 13C(2) B 13C(4) C 13C(4) C 13C(5)

1760.53 1197.35 1752.14 1193.29 1194.68 1751.52 1189.63 1188.09

1760.14 1197.22 1751.74 1193.16 1194.55 1751.12 1189.50 1187.96

1760.11 1197.27 1751.45 1193.07 1194.59 1751.17 1189.57 1187.97

0.200 0.065 0.200 0.065 0.200 0.065 0.200 0.065

0.03 0.05 0.29 0.09 0.04 0.05 0.07 0.01

Observed rotation constants are taken from Ref. [20].

tuted carbon atom are shortened by between 1 and 2 pm. However, care should be taken when assessing these results as the bond-length differences are not all well determined. A notable exception to this rule is the C(1)–C(2) bond in 1,2-difluorobenzene. Being adjacent to both fluorine substituents, it might be expected that this bond would be extremely short. In fact it turns out to be the longer than the C(2)–C(3) bond, which is only adjacent to one fluorine substituent. This could be rationalised in terms of steric repulsion between the fluorine atoms, but this explanation is inconsistent with the observation that the fluorine atoms are bent towards each other, by 0.6(1)°. It seems likely, therefore, that the lengthening of this bond is due to electronic, rather than steric, factors. The electron-withdrawing effect of the fluorine atoms leaves the carbon atoms with a slight positive charge, so they experience electrostatic repulsion, thereby counteracting the bond-shortening

effect described above. It is satisfying to note that a similar effect is observed in 1,2-dichlorobenzene [7]. The use of combined analysis, in particular the inclusion of LCNMR data, allows more subtle structural effects to be studied. For example, in all three difluorobenzenes the C–H bonds adjacent to the fluorine substituents are bent towards the fluorine atom by between 0.5 and 1°. The consistency of this result is a good indication of the accuracy of the technique. In the case of 1,3-difluorobenzene, the direction of the bond C(2)–H(8) is fixed by the symmetry of the molecule and instead it is the C–F bonds that are displaced towards this hydrogen atom, by 1.0(2)°. Unfortunately, the C–H bond lengths are not determined with sufficient accuracy to show how they are affected by fluorine substitution in the ring. Ab initio calculations have suggested that C–H bond lengths are likely to change by only a few tenths of a pm [32]. 3.3. Uncertainties The use of MM3 to calculate vibrational corrections for data to be used in combined analyses has proved successful, and higher levels of theory would give at least equally reliable values. In particular, the relatively large uncertainties associated with the corrections to rotation constants do not prevent useful structural information from being obtained. The calculation of corrections to direct dipolar coupling constants is also satisfactory, especially in view of the consistency of the results regarding the C–H angle deviations. In general, assuming an uncertainty of 10% in the correction term results in data that are consistent with a single struc-

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ture. However, extra caution must always be taken when employing DCF or DFF coupling constants. The likelihood of significant anisotropy of the associated indirect coupling constants should be taken into account, either by excluding such couplings from the refinement, perhaps by increasing their uncertainties, or, as in the present examples, using sufficient data to be able to estimate some or all of the Janiso terms. In some cases calculated direct coupling constants do not agree with the observed values. In particular, some of the coupling constants of the directly bonded C–H atom pairs differ by three or four standard deviations. This can perhaps be attributed to underestimation of the uncertainties of the vibrational corrections. However, discrepancies are also found for a number of coupling constants for which the correction term is very small. In such cases, the uncertainty in the original observation becomes dominant. If such a coupling does not fit well in the combined analysis then it is possible that this uncertainty has been underestimated. These uncertainties are usually produced by the programs used in the analysis of the LCNMR spectra. However, these programs do not take into account such factors as uncertainties in the line positions from the NMR experiment or uncertainties in the indirect coupling constants (whether due to a significant anisotropic contribution or to solvent- or temperature-dependency of J). The possibility of misassignment of one or more lines is also ignored. This is very unlikely to be a problem in a case such as this. During the combined analysis, the molecular geometry is refined on the rh0 basis, which should be consistent with the LCNMR data. However, when calculating the theoretical molecular scattering intensities the rh0 distances are first transformed to rg distances using perpendicular amplitudes, calculated during the vibrational analysis. At present no account is taken of the uncertainties of the calculated perpendicular amplitudes, such as those arising from the use of rectilinear rather than curvilinear normal coordinates, and so this presents another possible source for discrepancies in the calculated direct couplings. Finally, it should not be forgotten that the sample in the LCNMR experiment is in a different phase to the samples in the GED and MW experiments. The possibility of structural variations between the molecules in these phases should not be ruled out. Although the molecules and solvents used in this work were chosen to minimise the possibility of such distortions (i.e. they are unlikely to have any significant intermolecular interactions, that would cause major deformations of the solute molecules), it cannot be assumed that the LCNMR data and gas-phase data are completely compatible. However, the fact that the couplings fit as well as they do would suggest that any such differences must be small, and the use of LCNMR data in the combined analysis is thereby justified.

lar coupling constants was also determined from spectra of a solution (0.4 M) in liquid crystal E7, recorded at room temperature (293 K) with a Bruker WH360 spectrometer. The 19F and 1H spectra were recorded for the same samples under identical conditions, so order parameters were taken to be the same for both data sets. Dipolar coupling constants were consistent, so the validity of this assumption was confirmed. All coupling constants are listed in Table S1 alongside their values after being corrected for the effects of vibrations, as described below. The atom numbering is given in Fig. 2a. Dipolar coupling constants for 1,3-difluorobenzene, recorded for solutions in the liquid-crystalline solvents ZLI 1167 and ZLI 1132, were also taken from the literature [19]. Their values are listed in Table S2, before and after correction for vibrational effects. The atom numbering is shown in Fig. 2b. For both 1,2- and 1,3-difluorobenzene various literature rotation constants [20] were corrected for the effects of vibrations so that they could be used as extra data in the refinements. The weights given to the experimental data during the leastsquares refinement are important. For the GED data, an off-diagonal weight matrix is used with elements defined as

wii ¼ ðsi  smin Þ=ðsw1  smin Þ smin 6 si 6 sw1 wii ¼ 1 sw1 6 si 6 sw2 wii ¼ ðsmax  si Þ=ðsmax  sw2 Þ sw2 6 si 6 smax wij ¼ 0 i – j  1 wij ¼ 0:5ðwii þ wjj Þqk

i¼j1

where sw1 and sw2 are weighting points for the distance k and are chosen by inspection, and q is the correlation parameter. For the LCNMR data and rotation constants, the weight matrix is extended with diagonal terms only. These diagonal weighting terms are inversely proportional to the squared uncertainties of the observations and are scaled to the standard deviation of the fit of the GED data points. Acknowledgements We thank the EPSRC for funding D.A.W. (EP/F037317), and its predecessor SERC for funding E.M.B. EPSRC had no direct role in the design of the study, nor in collection, analysis or interpretation of data, writing of this report, or the decision to submit the manuscript for publication. We also acknowledge Drs. Paul Brain and Andrew Turner for their help preparing the electron-diffraction analysis programs and thank Dr. Lise Hedberg for adapting the ASYM program. Appendix A. Supplementary material

4. Experimental Samples of 1,2- and 1,3-difluorobenzene (purity 99%) were purchased from Aldrich and used without further purification. GED data were recorded at camera distances of 286 and 128 mm on Kodak Electron Image plates using the Edinburgh apparatus [33] operating at 44.5 kV, and obtained in digital form using a Joyce Loebl MDM6 microdensitometer at the EPSRC Daresbury Laboratory [34]. During experiments the sample and nozzle were maintained at 293 K. Data for benzene were also recorded, to provide calibration of the electron wavelength and camera distances. Other experimental data are listed in Table S9. Data reduction and leastsquares refinements were performed using ed@ed version 2.4 [35], and the scattering factors of Ross et al. [36]. For 1,2-difluorobenzene, dipolar coupling constants, measured in the liquid-crystalline solvents ZLI 1167 and ZLI 1132, were taken from the literature [18], and a complete set of HH, HF and FF dipo-

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