Molecular structure of furan, determined by combined analyses of data obtained by electron diffraction, rotational spectroscopy and liquid crystal NMR spectroscopy

Journal ofMolecular Structure, 196 (1989) l-19 Elsevier Science Publishers B.V., Amsterdam - Printed

in The Netherlands

MOLECULAR STRUCTURE OF FURAN, DETERMINED BY COMBINED ANALYSES OF DATA OBTAINED BY ELECTRON DIFFRACTION, ROTATIONAL SPECTROSCOPY AND LIQUID CRYSTAL NMR SPECTROSCOPY

PHILLIP

B. LIESCHESKI

and DAVID W.H. RANKIN*

Department of Chemistry, University of Edinburgh, West Mains Road, Edinburgh EH9 355 (ct. Britain) (Received

13 July 1988)

ABSTRACT The molecular structure of furan has been determined by several structural analyses using various combinations of data from gas-phase electron diffraction, rotational spectroscopy and liquid crystal NMR spectroscopy. The benefits of using as many data from as many experimental techniques as possible are demonstrated. The best geometrical parameters (rz ) for furan assuming planarityandC,,symmetryare:rC(2)H=108.64(14),rC(3)H=108.62(16),rC=C=136.40(9), rC-0=136.41(7), rC-C=143.03(19) pm, LOC(2)H=117.35(14), LC(4)C(3)H=127.93(19), LCOC=106.74(7)“.

INTRODUCTION

Although the structure of furan in the gas phase has been well determined by microwave spectroscopy [ 1,2 1, the experimental results for the gas phase differed substantially from those reported for the crystalline phase [ 31. The most important parameters are the C-O and C=C distances, which are apparently almost equal in the gas phase, but differ by more than 4 pm in the crystal. Ab initio molecular orbital calculations at the 4-21G level [4] also suggest that the C-O bonds are nearly 5 pm longer than the C=C bonds, while this theoretical study also gives C-C bond lengths 2 pm greater than those found experimentally in both phases. As the basis set is increased, the parameters approach those found in the microwave studies, and there is no reason to suppose that there is any serious conflict between the experimental and theoretical results. The apparent discrepancy between gaseous and crystalline phase structures clearly requires resolution, and part of the purpose of this work was to find a *Author for correspondence.

0022-2860/89/$03.50

0 1989 Elsevier Science Publishers

B.V.

2

structure which was consistent with data obtained by several distinct techniques. Since we completed our refinements, a paper has been published claiming that the short C=C bond length obtained by X-ray diffraction is an experimental artefact, probably due to a combination of disorder in the crystal lattice and thermal motion [ 51. To resolve this apparent discrepancy the structure of furan was determined from a combination of experimental data obtained from electron diffraction (ED ), microwave spectroscopy (MW) and liquid-crystal NMR spectroscopy (LCNMR). This joint structural technique has been successfully applied to pyrazine [ 61, pyrimidine [ 61, thiophene [ 71 and o-dichlorobenzene [ 81. Information from ED/MW and LCNMR data tend to be complementary [ 6-81. LCNMR data easily locate hydrogen atoms, while the ED data are best at determining the positions of heavy atoms. For molecules containing fluorine or phosphorus, LCNMR and MW data are also complementary since these elements have only one naturally-occurring isotope, but l/2-spin nuclei. The combination of MW and ED data is a well established technique [ 91. Furan was also chosen to be another candidate for demonstrating the benefits of a joint (ED + MW -t-LCNMR) structural analysis. Furan contains only nine atoms, and as it has CZVsymmetry, determining its structure appears to be a simple problem. However this is not so. Firstly, the C-O and C=C bond distances are very similar, and the C and 0 atoms have similar scattering cross sections. As a result, the ED data cannot distinguish between these two different bond lengths. Secondly, there are two different C-H bond distances, which are once again indistinguishable by the ED data. Thirdly, its most-abundant, natural isotopomer is a near symmetric top which causes ambiguity in an analysis which only includes rotation constants from this isotopomer. Finally, the naturally-occurring isotopes for oxygen do not have l/2-spin nuclei, so LCNMR experiments on natural samples do not give any information on the location of the oxygen atom. Since furan is a deceptively difficult case, it is a good candidate for this work and was especially interesting to study. In this paper, the results for furan from several structural analyses using various combinations of data are presented. An analysis using only ED data and an analysis using only rotation constants from four non-deuteriated isotopomers were performed to illustrate the problems with using data from only one method. In the best joint analysis, the four sets of rotation constants, the ED data and the LCNMR data were combined to demonstrate the benefits of using several types of data in a structural determination. Since measured bond lengths tend to be dependent upon isotopes, parameters were incorporated into the geometric model to measure and compensate for these isotopic effects. The results from a joint analysis, which used rotation constants from only the near symmetric-top isotopomer, are also presented to show the potential hazards of working with an apparently overdetermined problem which in fact is actually

3

an underdetermined structure determined

system. Finally, our results are compared by microwave spectroscopy [ 21.

with the r,

EXPERIMENTAL

Furan (99+ % spectrophotometric grade) was purchased from the Aldrich Chemical Co. Ltd. and was used without further purification. Electron diffraction scattering intensity data were recorded on Kodak Electron Image plates using the Edinburgh gas electron diffraction machine [lo], operating at approximately 44 kV. The sample and nozzle were maintained at ambient temperature (300 K) during the runs. Three plates were exposed at each of the two camera distances, 286 and 128 mm, and plates for benzene were also run, to provide calibration of the electron wavelength and camera distances. The plates were traced using a Joyce Loebl Microdensitometer 6 at the SERC Laboratory, Daresbury, with a scanning program described previously [ 111. Calculations were performed using standard data-reduction [ 111 and least-squares refinement [ 121 programs. The weighting points used in setting up the off-diagonal weight matrices for the refinements are given in Table 1, with other experimental data. In all calculations involving ED data, the complex scattering factors of Schafer et al. [ 131 were used. Rotation constants for furan, furan-l’0, furan-2-13C and furan-3-13C were taken from Bak et al. [ 11, and are presented in Table 2. Constants for deuteriated species have not been used, even though these are available, and are needed for the determination of the full r, structure from microwave data. The changes in C-H bond lengths and possibly bond angles upon deuterium substitution may be quite large and neglect of these changes may introduce significant errors in hydrogen atom coordinates. The sizes of the changes can be computed from harmonic force fields, but this can only give estimates, and there is still considerable uncertainty. We prefer to depend on LCNMR data to provide information about hydrogen atom positions. More recent work [2,14] has given more precise rotation constants, which differ slightly from those reported earlier. However, revised constants for 13C and “O-substituted species are not given, and it has been pointed out that it TABLE 1 ED data analysis parameters Camera distance (mm)

(nm-‘) AS

%li”

SW1

SW2

128.32 285.55

4 2

80 20

100 40

304 122

Scale factor ki

%lax

Correlation parameter 4

Electron wavelength (pm)

356 144

0.3506 0.4730

0.752 (17) 0.762 (5)

5.668 5.669

4 TABLE 2 Rotation constants for furan and its isotopomers (MHz) Constants

&”

B,

Modelled B,”

Furan A B c

9446.96( 12) 9246.61(12) 4670.88(12)

9440.09 (20 ) 9239.17 (20) 4668.74( 15)

9439.88 9239.01 4669.18

Furan- j80 A B C

9447.66(12) 8841.72( 12) 4565.37( 12)

9440.87 (20) 8834.58 (20) 4563.32(15)

9440.66 8834.27 4563.70

Furan-2- ‘W A B C

9295.41(12) 9178.23(12) 4616.25(12)

9288.60(30) 9170.81(30) 4614.52(25)

9288.33 9170.46 4614.51

Furan-3- ‘T A B C

9403.73( 12) 9043.68(12) 4608.15 (12)

9396.88(30) 9036.39 (30) 4606.16(25)

9396.96 9036.69 4606.65

“From Bak et al. [ 11. %orrected for vibrational effects. ‘Based upon ED +4MW + LC results (see Table 8). is important to use rotation constants determined by uniform treatment of uniform sets of data, as systematic errors cancel [ 2 J. As substitution coordinates in the later paper [Z] are virtually identical to those given earlier [ 11, we have used only the original set of data. The direct dipolar couplings as measured in Merck Phase IV, a nematic liquid crystal solvent, at 301 K were taken from Diehl et al. [ 151. Unfortunately, some of the published direct couplings, denoted here as D (Old),were determined from indirect coupling constants, denoted as JCold), whose values were incorrect as a result of misassignment [ 161. The new values for these indirect coupling constants, denoted as J’“““‘, are compiled in Diehl et al. [ 161. Using these new values and the formula:

the new values for the observed direct dipolar couplings were determined. These new coupling values, denoted as Dexp, were further corrected for vibrational effects and used in the joint structural analyses. Their values are presented in Table 3.

5 TABLE 3 LCNMR direct dipolar couplings for furan (Hz) Couplings

D (ckua

Dews

Da”

Modelled D” d

QT.7

-271.8(l) -46.6(l) -38.4(2) -130.6(3) -599.3(3) -135.0(3) -30.4(5) -21.0(5) -103.0(4) -841.5(3) -67.2(5) -24.6(5)

-271.8(l) -46.6(l) -38.4(2) - 130.6(3) -600.2 (3) - 137.0(3) -28.5(5) -20.9(5) -102.9(4) -840.8(3) -67.3(5) -24.7(5)

-274.6(2) -47.0(l) -38.7(2) - 132.3(3) -659.1(7) - 138.8(3) -28.7(5) -21.0(5) - 104.7(4) -912.1(7) -68.2(5) -24.8(5)

- 274.6 -47.3 -39.1 - 131.4 -658.8 - 138.0 - 28.8 -21.8 - 104.5 -912.5 - 69.4 -25.4

D 6.8 D UT:; 02.6 D,,; D 2.8 D 2.9 D9.6 D:v D:,,s D:<.‘J

“From Diehl et al. [15]. bDexp=D(“‘d)+ (J(“‘d)-J(“ew) )/2; (see text). “Corrected for vibrational effects. dBased upon ED + 4MW + LC results (see Table 8).

Methods

Vibrational analysis

Since each method averages vibrational motion differently, the experimental data from each technique must be first treated for vibrational effects before the different structural information can be related to the common r, structure. The r, structure gives information on the distances between the average positions of atoms in the molecule. Normal mode analyses of furan were performed using the program GAMP [ 171, assuming CzVsymmetry for the force field determination and C, symmetry for the vibrational-rotational correction calculations for furan-2-13C and furan-3-13C. The force field for furan was obtained to give an optimal fit to the observed gas-phase vibrational frequencies for furan, furan-6,9- [‘H ] 2, furan-7,8- [*H ] 2 and furan- [*H ] 4 with less weight given to the C-*H stretch frequencies [ 181. The atom numbering and internal coordinates are shown in Fig. 1, while the definitions of the symmetry coordinates are given in Table 4. The force field matrices are presented in Table 5. For the ED structural analyses, the perpendicular amplitude correction coefficients K,, which are used to convert the ra distances determined directly from the ED data to the geometrically consistent r, distances, were calculated from this force field for a temperature of 300 K. Also the root-mean-square amplitudes of vibration were determined from the force field for the same temperature. In a structural analysis that included ED data, some vibrational amplitudes were fixed at these force-field (spectroscopic ) values. Others were allowed to refine separately or tied together in groups with their ratios set by the force-

6

Fig. 1. Atom numbering scheme and internal coordinate definitions for furan. y2 is the out-ofplane motion of C (2)) with the hydrogen atom defined first. r2 is the torsion about bond r,, defined bytheatomstringO(l)C(2)C(3)C(4). TABLE 4 Symmetry coordinates for furan C 2”

Definitions

S1= (I/&)

tr8+r71

& = r3 %= (l/JZ) [r,+r,l S,=(1/2) tP:5-P5+P;-P21 &= (l/2) [%+QI,--(yI- WJ2Ha,+%)l

B*

A2

B*

S,=

(l/&l

&= (I/&) &=(1/2)

[rs-ri.l [r4-r21 w-P4+P3-/%1

&=(1/2)

m-P5+P*-P;l

ST= (l/2)

[%-~Y,+%--oI,I

s,= w/2)

h= (I/&) [ry+rsl &= (I/&) tr,+r,l &=(1/2) [P&-P4+B;-Al

S2=

(l/&l

Sq= (l/d?)

[rg-r61 [r5-r11

[Y4-Y31 [74+721

&= WJ2)

[h-Y21

&= u/&2 s,= u/$4 s3= (l/2)

[Y4+Y:31 [7,-74+7,-7,1

sz= u/&4

tYs+Y*l

field values. The Ki values and refined amplitudes from the best joint structural analysis are presented in Table 6. The LCNMR data were corrected for vibrational effects according to the method of Sykora et al. [ 191. Using the force field described above, the direct couplings observed experimentally, Dexp, were converted to the vibrationallycorrected direct couplings, II”, which contain information on the r, distances. Their values are presented in Table 3. The rotation constants for each isotopomer were also corrected for vibra-

7

TABLE 5 Force field matrices for furan ( 100 newton m- 1)

5.4504 0.0 0.7462 0.0 -0.3732 0.0 0.0 0.0

5.4011 0.0 0.0 0.0 0.0 0.0 0.0

7.2365 1.7972 0.5316 0.5015 0.6152 -0.1025

1

2

3

7.7612 0.6668 0.3183 0.2874 1.0039 4

6.2377 - 0.0937 - 0.5328 0.0

0.4393 0.0 0.0

0.4734 0.0

2.0986

5

6

7

8

0.5001 0.0

1.8251

1 2 3 4 5 6 7

6

7

1 2 3 4 5 6 I 8

& 5.3159 0.0 0.0 0.0 0.0 0.0 0.0 1

5.4296 0.0 0.0 0.0 0.0 0.0

7.8448 0.3108 -0.6535 0.0268 0.0

5.9636 - 0.3868 0.0 0.7570

2

3

4

0.4075 0.0 0.0 5

‘4, 0.4235 - 0.0695 - 0.4656

0.3169 0.2770

1

2

1.4030

1 2 3

0.5614

1 2 3

3

B, 0.3703 0.0555 - 0.0999

0.3776 0.2052

1

2

3

tional effects using this force field. For furan and furan-l*O, CZVsymmetry was assumed in the vibrational-correction calculations, while C, symmetry was assumed for furan-2-13C and furan-3-13C. Under C, symmetry, the symmetry coordinates were regrouped and the F matrices were combined in block-diagonal form to reflect this symmetry reduction. Force constants that are isomorphic to those which couple modes from different symmetry species under CZVsymmetry were assumed to remain zero under the lower C, symmetry. The values for the force constants were not refined under this lower symmetry, but assumed to be the same as those from the homomorphic CaVforce field. The

8 TABLE 6 Interatomic pair information for furan (pm) Atom pair

i

r,

K,

Uib

1.8285 1.8053 0.2178 0.2040 0.1916 1.1483 1.0818 0.7664 0.7568 0.8517 0.5448 0.5321 0.8355 0.8075 0.5139 0.0833 0.0817 0.8778 0.5176 0.0673

7.9(7) 7.96 (tied to u,) 4.35(16) 4.59 (tied to u,) 4.49 (tied to u.?) 15.26 (spectros.) 15.29 (spectros.) 12.64 (spectros.) 11.56 (spectros.) 13.2(13) 12.2(10) 11.8 (tied to ull) 13.6 (tied to ulo) 13.5 (tied to ulO) 11.8 (tied to u,~) 5.14 (tied to uzo) 5.14 (tied to u2(,) 13.8 (tied to ulc,) 11.9 (tiedto u,,) 4.84(18)

1

H(6bCt2)

109.9(l)

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

H(7)-C(3) C(2)-C(3) C(3)-C(4) C(2)-0 H(6):H(7) H(7):H(8) H(6):H(9) H(6):H(8) H(6):C(3) H(6):C(5) H(6):C(4) H(7):C(2) H(7):C(4) H(7):C(5) C(2):C(4) C(2):C(5) H(6):O H(7):O C(3):O

109.8(2) 136.5(l) 143.1(2) 136.5(l) 273.4(4) 276.8(4) 414.6(2) 435.4(2) 224.4(2) 320.2(l) 331.1(2) 218.6(3) 226.6(2) 329.2(l) 223.4(l) 218.9(l) 209.8(l) 328.7(2) 224.1(l)

“Perpendicular amplitude corrections calculated for 300 K from force field. hVibrational amplitudes used or optimized in the ED + “MW + LC refinement.

agreement between the results from the ED + ‘MW + LC and ED + 4MW + LC joint structural analyses supports these assumptions. Strictly speaking, the vibrationally-corrected rotation constants give information about r: distances. At room temperature, the difference between the values for r, and r-z distances is negligible; however, for the case of furan, we decided to calculate the differences between rot(300 K) and rz distances for each atom pair using this force field and the formula: ra-rL=3a

(u+-ug)/2

where a is the Morse anharmonic oscillator term; u represents the corresponding vibrational amplitude, while T is 300 K. For bonded atom pairs, the value for a is taken to be 0.02 pm-l, while for the nonbonded pairs, it is assumed to be zero. Under the precision of this calculation, the corrections for all but three pairs were zero. The correction factors for the three heavy-atom bonded pairs were not zero, but still at least an order of magnitude smaller than their corresponding structural uncertainties determined from the best structural analysis. These insignificant corrections were still incorporated into the ED struc-

9

TABLE 7 ra to ri correction

factors for furan (pm)

i

Atom pair

r,-rz”

e.s.d. b

1 2 3 4 5

H(6)-C(2) H(7)-C(3) C(2)-C(3) C(3)-C(4) C(2)-0 Nonbonded

0.0000 0.0000 0.0027 0.0072 0.0075 0.0

0.14 0.16 0.09 0.19 0.07

“Calculated at 300 K from ED+4MW+LC (seeTable8).

force

field.

bEstimated

standard

deviations

determined

from

tural analyses for the sake of formality. Since the LCNMR data contain no couplings for these three heavy-atom pairs, there was no need to adjust any of the D” values. All structures reported for furan in this paper are r:. These correction factors are presented in Table 7. Because the force field is underdetermined, the vibrational correction factors would be expected to possess a certain amount of uncertainty. This uncertainty originating from the force field contributes significantly to the overall uncertainty of the vibrationally-corrected data. It has been observed by us that the in-plane modes (A, and B2) strongly affect the values for B,, while the out-of-plane modes (A, and B,) strongly influence the values for D”. In this work, the uncertainties in the vibrational correction factors were estimated by refining the force field to fit the vibrational frequencies under different conditions. The scatter in the values for the vibrational correction factors due to the slightly different force fields was used to estimate their uncertainties. The reported force field gave the best fit to the vibrational frequencies under the most reasonable conditions. The uncertainties in the vibrational correction terms are incorporated into the experimental values for B, and D” listed in Tables 2 and 3. Structural analysis In the structural analyses for furan, the molecule was assumed to be planar with CpVsymmetry. The very small inertial defects reported in the microwave study of Bak et al. [l] support the assumption of planarity. Under this assumption, the structure of furan can be completely defined by eight geometric parameters. In these analyses, two orientation parameters (S,, and S,,) for the LCNMR data, five amplitudes of vibration (u,, ug, ulO, u,, and uzO) for the ED data and two isotopic-effect parameters (6( “0) and 6( 13C)} for the MW data were also included when appropriate. These parameters were refined to fit the data by the least-squares refinement program, ED87, described previously [ 61. The ED data were weighted according to the scheme of Murata and Morino [ 201. Each one of the LCNMR direct couplings or rotation constants

10

was weighted by the reciprocal square of its total (observed+ force field) uncertainty. The first structural analysis that was performed used ED data, the LCNMR direct couplings and the rotation constants from two isotopomers, furan and furan-“0. It is denoted as ED-t ‘MW + LC (see Table 8). The normal-mode analyses and the vibrational correction factors were initially based upon the structure of Bak et al. [ 11. These correction factors were incorporated into the initial ED + ‘MW + LC refinement, and a new structure was determined. The normal-mode analyses and vibrational correction factor calculations were repeated using this new structure. These correction factors were then used in the second ED + ‘MW + LC refinement. This procedure was iterated until the resulting structure was self-consistent (2 cycles). In the ED +2MW +LC analysis, the eight geometric parameters were allowed to refine freely along with two orientation parameters and five amplitudes of vibration. Since rotation constants from two isotopomers with different oxygen isotopes were included as data in the structural analysis, an additional parameter to measure the isotopic effect on the C-O bond was also introduced into the model. This isotopic-effect parameter, denoted as 6( 180), is defined by the expression:

where r signifies bond length. The significant difference in the A rotation constants for furan and furan-180 can be explained by the isotopic dependence of the C-O bond length. The structural analysis denoted as ED + 4MW + LC was then performed on the combination of ED data, LCNMR couplings and rotation constants from the four non-deuterated isotopomers: furan, furan-180, furan-2-13C and furan3-‘“C. The vibrational force-field and vibrational correction factors were not optimized since the resulting structure agrees with the results from the ED + 2MW + LC analysis. In this analysis eight geometric parameters, two orientation parameters, five vibrational amplitudes and two isotopic-effect parameters were refined simultaneously. Since rotation constants of isotopomers containing 13C were included in this analysis, another isotopic-effect parameter, denoted as 6( 13C), was used and defined by: rC=13C=rC=C+6(13C) rC-13C=rC-C+d(13C) r’3C-0=rC-O+6(‘3C). The isotopic effects from 13C were assumed to be the same for and C-O bond lengths. The influence on the C-H bond lengths to be insignificant, since the stretching vibration of this bond is dent upon the mass of the hydrogen atom. Finally, the isotopic

the C-C, C=C was assumed largely depeneffect on dis-

P,

106.84(B)

106.74(7)

0.07327

0.07348

0.04828(20) -0.0098(35)

0.02301(13)

-O.O016(set)

0.04826 (39) -O.O094(set)

0.02293 (30) 0.04833 (47) -O.O094(set)

(set)

-O.O016(set)

-0.0094

0.06722

0.07593

0.04729 (32)

0.02292(11)

127.64( 18) 105.26 (42)

131.4(69)

128.2 (24) 106.68(17)

127.81(44) 106.90 (20)

127.90(37) 106.75(12)

0.02316(22)

143.22(33) 116.69(24)

105.7(7)

137.82(33)

143.67(73) 118.9(65)

143.45(110) 117.1(18)

142.24(73) 117.48(36)

143.01(40) 117.32(28)

108.13(21) 134.94(42)

108.12( 16)

ED+‘MW+LC

136.36(8) =rC=C

109.2 (6) =rC(2)-H

ED only

136.33(45) 136.28(33)

108.64(145) =rC(2)-H

4MW only

136.58(28) 136.64(23)

108.68 (39 )

108.40(39)

‘MW+LC

136.39(18) 136.42 (14)

108.67(29) 108.67(32)

.‘MW+LC

“Best structure attainable with present data. ‘Least-squares estimated standard deviation in parentheses.

Ro

12 6(P)

0.04819(20) -0.0094(34) -0.0016(25)

(pm)

0.02316(11)

9 SW

10 szz 11 S(0’“)

Orientation/isotopicparameters

117.44(15) 127.84(19)

117.35(14) 127.93( 19)

6 LOC(P)H (deg.) 7 iC(4)C(3)H 8 LCOC

136.56(g) 142.54(28)

136.40(g)

108.66( 16) 136.51(11)

108.62 (16)

136.41(7) 143.03(19)

108.48( 16)

108.64(14)b

ED+2MW+LC

4 rC0 5 rC-C

(pm)

ED+4MW+LC”

1 rC(2)H 2 rC(3)H 3 rC=C

Structural parameters

i

ryVstructures and other refinement parameters for furan

TABLE 8

12 TABLE 9 Least-squares

correlation Pab

Pl P2 PC? P4 P5 PS Pi P9 PI2

u:,

matrix” for furan P5

-54 -69 -59

P7

PS

P9

-66 -32 52

40 - -18 50

-30

72 -40

PlO

95 -48

83 -38 -58 47

-44 -72 -44

76 -36

-40

46

u1lJ n20

PS

14 32 58

“For the ED + 4 + MW + LC refinement, all elements are scaled by 100, and only off-diagonal elements with absolute values 2 30% are included. “p: structural/orientation/isotopic refinement parameters (see Table 8). ‘u: vibrational amplitude refinement parameters (see Table 6). dk: ED data scale factor refinement parameters (see Table 1) .

a

b

I 80

r

I--

1

160 /

320

240 I

r\\

(I

A,

s ("m-1)

l&O

hl-5

Fig. 2. Observed and final weighted difference molecular scattering to-plate distances of (a) 286 and (b) 128 mm.

intensities

for furan at nozzle-

tances between nonbonded atom pairs was assumed to be negligibly small, so the treatment of isotopic effects in the LCNMR data was not necessary. The last two assumptions are not too severe, since the measured isotopic effects for la0 and 13Cas determined by ED + 4MW + LC are also very small. This structure is the best attainable with the experimental data currently available. The parameters are listed in the first column of Table 8. In another analysis, using ED data alone, only six geometric parameters could be refined along with the five amplitudes of vibration. The two C-H bond lengths had to be assumed to be equal, while the C-O and C=C bond lengths

13

1

100 20CJ~3!0 400 :"p,;

700

Fig. 3. Observed and final weighted difference radial distribution curves, P (r ) /r, for furan. Before Fourier inversion the data were multiplied by s.exp[ -0.00002 s2/(Zo-fo) (Z,-fc)].

were also assumed to be equal. In the MW-only analysis, the four sets of rotation constants were used. Only seven geometric parameters could be refined. The orientation parameters and amplitudes of vibration did not apply in this case. The two C-H bond lengths were assumed equal, and the isotopic-effect parameters were set at values determined by the ED + 4MW + LC refinement. Analyses were also performed on combinations of MW and LCNMR data. In the analysis denoted as 4MW + LC, the four sets of rotation constants were combined with the LCNMR direct couplings, while in the analysis denoted as 2MW + LC, the LCNMR coupling were combined with the rotation constants for furan and furan-“0. In both, the eight geometric parameters and the two orientation parameters could be refined independently. The values for the isotopic-effect parameters were once again fixed at values set by the ED + 4MW + LC refinement. Results of all these refinements are included in Table 8. In Table 9 the least-squares correlation matrix for the ED + 4MW + LC refinement is presented. Figures 2 and 3 depict molecular intensity scattering and radial distribution curves based on the electron diffraction data. DISCUSSION

The first thing that is obvious from the ED-only analysis is the imprecise determination of the hydrogen positions. The two C-H bond lengths must be assumed equal, and still the angles involving hydrogen are only known with a precision (estimated standard deviation, e.s.d.) of + 7 degrees. The C=C and C-O bond distances are very similar, and because they are therefore strongly correlated, they cannot be refined separately. Also the C-C bond distance and the heavy-atom angle, L COC, are not well determined. From this, it appears that ED is definitely not the method of choice when studying molecules like furan. In the MW-only analysis, the situation is slightly better, although the two C-H bond distances must still be assumed to be equal. The precision of the

14

angles involving hydrogen has improved to -t 2 degrees, but the average C-H bond distance is less well determined than in the ED-only refinement. The C=C and C-O bond lengths can now be refined independently to obtain a precision of & 0.4 pm. In this analysis, only rotation constants from the non-deuteriated isotopomers could be used. When the rotation constants for furan-6,9- [‘HI2 were included in the structural analysis, a structure that did not agree with our other results or the r, structures reported in refs. 1 and 2, was obtained. One possible source of this discrepancy could be our force field, which was refined giving heavier weights to the C-H stretch frequencies than to the C-2H frequencies. It may thus be inadequate in treating the vibrational modes of deuteriated furan. Another possibility is that hydrogen/deuterium substitution is not a good method for determining hydrogen positions as a result of large isotope effects. This problem needs to be studied in more detail. In the MW + LC analyses all of the geometric parameters could be refined independently. The LCNMR data enable the positions of the hydrogen atoms to be determined more precisely than in the MW-only or ED-only analyses. The precisions of the C=C and C-O bond lengths have also improved for both analyses. The rotation constants from furan and furan-180 supply sufficient information in the 2MW + LC analysis to set the absolute size of the molecule and locate the oxygen atom, neither of which are given by the LCNMR couplings. Adding rotation constants for the other two 13C isotopomers into the 4MW + LC analysis further reduces the uncertainties in the determined geometric parameters, as expected. LCNMR-only and ED + LC analyses were not performed since neither would give information on the location of the oxygen atom. In the final joint analyses, data from all three techniques were combined. Even though ED is not the method of choice in the case of furan, it still has information to share. Also, to locate the oxygen atom, at least two sets of rotation constants had to be incorporated into the analysis, with one set being from furan-180. In both refinements, all geometric parameters along with the amplitudes and orientation parameters could be refined independently. In these refinements also, the appropriate isotopic-effect parameters were refined. Each bond length is determined with an e.s.d. of at most -t 0.2 pm, while the angles are known to better than + 0.2 degrees. Once again, the addition of the rotation constants from the two 13C isotopomers increases the precision of the determined structure. In addition, the ED R-factor (RG) is slightly reduced; however, it is still larger than that from the ED-only analysis. As a complete rS structure for furan, determined from MW data [l], has been reported [ 21, this is presented in Table 10 along with our best results from ED + 4MW + LC. The heavy-atom geometric parameters obtained in our work agree with the microwave results, and we observe the C-O and C=C bonds

15 TABLE 10 Comparison with earlier work Structural terms

rC(2)H (pm) rC(3)H rC=C rC-0 rc-C LOCH (deg.) LC(~)C(~)H L cot L occ L ccc

Authors’ results” 0 ra

Earlier MW resultsb

108.64(14) 108.62( 16) 136.40(g) 136.41(7) 143.03( 19) 117.35(14) 127.93 (19) 106.74(7) 110.49(7) 106.14(6)

107.48(2) 107.68(2) 136.10(3) 136.22(2) 143.01(5) 115.98(3) 127.83(2) 106.56(2) 110.65(2) 106.07 (2)

r,

“From ED + “MW + LC (see Table 8 ) . bFrom Mata et al. [ 2 1.

to have nearly equal lengths. We also observe that the two C-H bond lengths are very similar, but the absolute values do not agree: the values from our work for the C-H bond distances are about 1 pm longer. The value we obtained for the angle, LOCH, is about 1.5 degrees larger than that in the r, structure, but the values for the angle, L C (4)C (3)H, involving the other hydrogen atom agree well. We noticed a similar disagreement with the structure for thiophene [ 71. The positions of some hydrogen atoms as determined by this joint technique do not agree with results from earlier MW work. This discrepancy may be the result of comparing P, structures with ri structures, and it should be noted that in deriving the rs structure no account was taken of the effects of deuterium substitution on the bond lengths and angles. Our MW-only analysis, which yields a r”, structure, is unable to settle this question. Even though the average C-H bond length agrees more with our ED + 4MW + LC results than with their rs structure, its uncertainty is +- 1.5 pm. As more information is collected on a wider range of compounds, we hope to be able to explain this discrepancy. Finally, to demonstrate the potential pitfalls in a joint structural analysis, the results of a refinement using ED data, LCNMR couplings and rotation constants from only the most abundant isotopomer of furan are included in Table 8, labelled ED + ‘MW + LC. The eight geometric parameters along with the two orientation parameters and five amplitudes of vibration were allowed to refine simultaneously. A structure is determined which does not agree with any of the other results. The C=C and C-O bond lengths differ by 2.88 pm. In ED + ‘MW + LC, there are almost two hundred observations to be fitted by only fifteen refinement parameters. At first glance, this appears to be an overdetermined system; however, actually it is not. From the ED-only analysis,

16

it is obvious that information concerning the C=C and C-O bond lengths is highly correlated. Also there are no LCNMR couplings that involve the oxygen nucleus; thus the LCNMR data contain no information on the position of the oxygen atom. Finally the three rotation constants provide little information since furan is planar and a near symmetric-top. Even using all these data together, the position of the oxygen atom cannot be determined! This grossly incorrect structure nevertheless provides an acceptable fit to all three sets of experimental data. It is only when rotation data for a second isotopomer are included that a sensible solution can be found. Fortunately, this is an exceptionally difficult case, and this problem is not expected to recur frequently. CONCLUSION

These results from the structural analyses of furan have demonstrated the benefits of using as many data as possible from several experimental techniques. Even though the information from ED and LCNMR are complementary, their combination was still insufficient. The incorporation of rotation constants from several non-deuteriated isotopomers was required to complete the structure. The best structure we obtained, except for the positions of the hydrogen atoms, confirms the earlier MW structures. A major concern in this work is the assumption that LC-phase structures are comparable to gas-phase structures. The quality of the LCNMR data for furan has been questioned [ 161. However, we believe that the best method of comparing results from LCNMR data with data from ED and MW is by using this joint structural technique. By including ED data and rotation constants from as many isotopomers as possible in the analysis, the experimental couplings can be compared with the modelled couplings determined in the joint analysis. Thus which couplings cause the most disagreement can be determined. The problem with comparing a structure from a LCNMR-only analysis with a gas-phase structure is that the LCNMR-only analyses tend to be at best marginally determined. Small errors in the couplings plus large correlations between the structural and orientation parameters can lead to apparently distorted structures. The incorporation of extra information from ED and MW can help to reduce the parametric correlations. From our results, we believe that these LCNMR couplings for furan are adequate. Several workers are investigating and proposing methods of treating orientational deformation (one possible cause for disagreement between LC-phase structures and gas-phase structures). We feel that the vibrational correction of the LCNMR couplings is another serious problem. The vibrational treatment as proposed by Sykora et al. [ 191 is sound, but the force fields used in the method tend to be seriously underdetermined. To further aggravate the situation, the relative values for the vibrational corrections to the LCNMR couplings tend to be greater than those used for the other gas-phase data. The

17

vibrational correction factors for the rotation constants are less than one part per thousand; for the ED analysis, they are less than two percent, but for the LCNMR couplings, the correction factors can be as large as ten percent of the experimentally observed values. On closer examination of the furan data, it can be seen that the bonded C-H terms have the largest harmonic correction values, and the LCNMR couplings give the most information about these distances. Consequently, better force fields are needed for the correct vibrational treatment of the LCNMR data. We are investigating the possibility of using force fields calculated ab initio for this purpose. ACKNOWLEDGEMENT

We thank Dr. Stephen Cradock for his help in the use of the normal-mode analysis program, GAMP, and Dr. Heather E. Robertson for her help in collecting the electron diffraction data. One of the authors (P.B.L. ) must thank the National Science Foundation (NSF) for support under a North Atlantic Treaty Organization (NATO) Postdoctoral Fellowship awarded in 1987. We also thank the Science and Engineering Research Council (SERC) for financial support. APPENDIX

The consistency of the definitions for D” and rot In Sykora et al. [ 191, the theory for the vibrational treatment of the LCNMR direct coupling is presented. In this article, the (harmonic) vibrationally corrected direct coupling D”, which contains information about r, distance, is defined as: D”=D”+d” where D” is the value for the direct coupling under a rigid-bond model with equilibrium distance r, between the coupling nuclei, while da is the correction factor to this model for anharmonic vibration. No argument is given to justify this statement. To the best of the authors’ knowledge, no such supporting argument exists in the literature, not even one based upon the simple case for a linear molecule. A simple argument is presented below to demonstrate the consistency between r, and D”. Consider the case of a molecule with a pair of interacting nuclei lying along the z-axis of the molecular frame with at least three-fold symmetry. For this case, the internuclear r, distance is simply defined as: r,=r,+(dz) where r, is the equilibrium

distance

and (dz)

is the contribution

due to an-

18

harmonic vibration along the z-axis. Now the direct coupling nuclei in this molecule is expressed in terms of r, distance as:

Da= -k S,,

D" of the two

rG3

where k contains physical constants, such as the magnetogyric ratios for the coupling nuclei, while S,, is the orientation parameter as referenced to the zaxis of the molecular frame. Using the definition for rcu,one has: Da=-kS,,

(r,+(dz))-3

Using a binomial expansion of rg3 and the fact that (AZ) is generally small, one can show that the dominant terms of D" are:

Da= -k S,, r;3 +3k S,,

very

rF4 (AZ)

The first term is D",while the second term, according to Sykora et al. [ 191, is the anharmonic contribution d” for a pair of nuclei along a three-fold (or greater) symmetry z-axis. Therefore, one has:

D"=D"+d" thus the definition of D" is consistent with the definition of ra. In the above argument, the system is restricted to three-fold symmetry (or higher) in order to compare it with the special case given in Sykora et al. [ 191. However, this restriction is not necessary. With the orientation tensor being diagonal and the nuclei lying along or parallel to the z-axis, the expressions for r, and d” retain their same, simple forms, and the argument remains valid.

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