The proton magnetic resonance spectrum of enriched propene-2-C-13 oriented in a nematic phase

JOURNAL

OF MAGNETIC

RESONANCE

(1973)

l&314-325

The Proton Magnetic Resonance Spectrum of Enriched Propene-Z Oriented in a Nematic Phase” LAWRENCE Mellon

F. WILLIAMSI

Institute

of Science,

AND AKSEL A. BOTHNFXR-BY Pittsburgh:

Pennsylvania

15213

Received March 24, 1973 The PMR spectrum of propene-2-C-13 oriented in a nematic mesophase has been analyzed and the dipolar couplings have been interpreted in terms of internuclear distances and the order matrix, S, for several conformations of the methyl group. The CJL.axis of the methyl group is not appreciably tilted with respect to the carboncarbon single bond and prefers to orient parallel to the magnetic field. The NMR distances are compared with microwave data. Carbon-13-proton indirect couplings, obtained by spin-tickling in isotropic solution, are 151.923 Hz with the directly bonded proton, -1.038 Hz with the proton cis to the directly bonded hydrogen, -2.633 Hz with the other vinyl proton and -6.867 Hz with the methyl protons.

INTRODUCTION Most structure determinations using NMR have been for molecules whose magnetic atoms are protons arranged in a relatively rigid, symmetric fashion. Such systems generally yield simple spectra (depending on the degree of symmetry), have no aniso-

tropy in the indirect couplings and are free of complications due to internal motion. It has been only recently that attempts have been made to obtain geometric parameters for molecules whose dipolar couplings are averaged over multiple conformations (I). This work reports the NMR investigation of propene-2-C-13, where the methyl group conformation and the possibility of anisotropy in the carbon-13-proton J-values were of special interest. Microwave studies (2,3) have definitely established the planar symmetry of propene and indicate that the methyl group has a CJv axis which probably lies along the carbon-carbon single bond. However, the small hydrogen mass makes uncertain the position of out-of-plane protons, and in this case, use of nematic phase NMR may have a definite advantage. Theoretical calculations of the energies of two propene rotamers (4) (those in which a methyl group proton is either staggered or eclipsed with respect to the hydrogen on the carbon bonded to the methyl group (Fig. 1)) agree with the microwave result that the ground state is the staggered form, although both studies indicate appreciable populations for each conformer. * Abstracted in part from a thesis submitted in partial fulfillment of requirements for the Ph.D. degree at Carnegie-Mellon University, Pittsburgh, Pennsylvania, 15213. I’ Present address: Liquid Crystal Institute, Kent State University, Kent, Ohio 44242. 314 Copyright 0 1973 by Academic Press, Inc. All rights of reproduction Printed in Great Britain

in any form reserved.

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IN NEMATIC PHASE

315

Possibilities which merit attention are the staggered form, the eclipsed form, a weighted combination of both and a freely rotating methyl group. If planar symmetry and a C,, axis of the methyl group are assumed for propene, eight relative coordinates and three ordering parameters must be found from eleven distinct couplings and the system of equations is exactly determined. If the angle of the CJv axis with the carboncarbon single bond is fixed at 180”, i.e., a tilt angle of O”, the system of equations becomes overdetermined by one relationship. In cases where more than one rotamer was considered, it was necessary to assume that one S-matrix adequately described the average molecular orientation. This approximation will be discussed later.

FIG. 1. Staggered (a) and eclipsed (b) forms of propene showing numbering system and coordinate axes.

Calculations to predict the effect of molecular vibration on internuclear distances as measured by NMR have so far been unsuccessful (5), and are neglected here except to note that, for propene at 300”K, three rotational levels are expected to lie below the first vibrational mode (3). EXPERIMENTAL

Propene and 56.5 % enriched propene-2-C-13 were used as received from Matheson, Inc., and Merck and Co., Inc., respectively. Four samples, nematic and isotropic solutions of both propene and the isotropic mixture, were prepared by vacuum distillation into degassed solvents. The isotopic samples were roughly 5 ‘A by volume of propene in Ccl, to which TMS was added as an internal reference. The nematic phases were of equal propene concentration (ca. 10 % by volume) in Eastman Kodak’s “Nematic Mixture” and were thermally equilibrated in a water bath at magnet temperature (32°C).

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Nematic phase spectra were taken with a Varian Associates HA-100 spectrometer running unlocked in sideband mode. To prevent overlap of sideband and centreband signals it was necessary to replace the spectrometer’s internal oscillator with a General Radio Model 1160A variable frequency synthesizer operating at 6 kHz. The final spectra were recorded only when prominent peaks in the propene blank could be easily identified in the enriched sample. Isotropic and spin-tickled spectra were obtained with the MPC-HF 250 mHz superconducting spectrometer. Nematic spectra were recorded four times and isotropic spectra twice, with an average deviation in line positions of about 1.0 and 0.025 Hz, respectively. Nematic line widths at half height were approximately 5.0 Hz; the corresponding isotropic value was 0.25 Hz. RESULTS

isotropic Phase Spectrum The spectrum of the isotopically enriched mixture was separated into lines arising either from propene or propene-2-C-13 by subtracting the line positions of the nonenriched propene spectrum. When the lines arising from propene-2-C-13 were known, the signs of the JCH couplings were determined relative to each other and the proton couplings by observing the proton resonances while irradiating first the proton region and then the carbon-13 region. The isolated line positions were independently fit for the ‘two molecules with LAOCOON IIIr (6) adapted to a Univac 1108 computer. First guesses for JHH were obtained from a previous analysis of propcne (7). The isotropic spectrum of mixed propene is shown in Fig. 2. The peak at the extreme right is not found

FIG.

2(a).

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OF PROPENE-2-C-

13 IN NEMATlC

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317

b

FIG. 2. Experimental (upper traces) and calculated (lower traces) 2.50 MHz magnetic resonance spectrum of 56.5 ‘A enriched propene-2-C-13 in the isotropic phase. (a) Resonance band of proton 1; (b) resonance bands of protons 2 and 3 ; (c) resonance band of the methyl protons. See Fig. 1 for proton numbering.

318

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in the spectrum of propene, nor could it be assigned to the labeled molecule and is presumed to arise from an impurity. Results of the iterative fittings are shown in Table 1. With one exception, the signs and magnitudes of the indirect couplings are in good agreement with expected values. TABLE

1

SPECTRALPARAMETERSOF ISOTROPICPHASE PROPENE~*~ Parameter

WI= W2 W3 W&T, Jl,” J 13 J 1,rvle J 23 J 2,Me J 3J.e

C-12 Propene 1435.901 % 0.002d 1221.147 zk 0.002 1241.936 zt 0.002 424.192 10.089

f 0.002 Ik 0.003

16.983 i 0.003 6.47.5 2.171 -1.407 -1.776

zt & i A

0.002 0.003 0.002 0.002

J zc

J3c J c,rde rms Theoretical lines assigned Experimental frequencies assigned

0.020 Hz 180 54

Propene-2-C-13 1435.342 1220.711 1241.531 424.051 10.092 16.978 6.487 2.212

i + 5 zt i + i i

0.002 0.002 0.002 0.001 0.003 0.003 0.002 0.003

-1.396 zk0.002 -1.766 i 0.002 151.923 i 0.004 -1.038 f 0.004 -2.633 zk 0.004 -6.867 f 0.002 0.023 Hz 384

101

a See Fig. 1 for numbering. b All line positions obtained from PMR spectrum of enriched propene2-C-13. ’ Chemical shifts, Wi, are Hz from TMS, at 250 MHz. d Error estimates calculated by LAOCOON. e Couplings are given in Hz.

The coupling of carbon-13 to a directly bonded proton is accepted as positive and a survey of several compounds indicates a range of -4.0 to -7.6 Hz for the long range coupling of carbon-13 with the methyl protons (8). For a wide variety of substituted ethylenes, the two bond carbon-proton vinyl coupling, Jzc, is negative when the substituent is bonded to a carbon-13 cis to the proton (9). However, the sign of the remaining vinyl coupling, Jsc, with the proton tram to the substituent may have either sign, although it is usually positive (9, 20). In a study of the similar molecule, ally1 bromide, Feeney and Pauwels (II) obtained Jzc = +l.O i 0.3 and Jsc = +2.9 i 0.2. The magnitude of their results agree with those of this work, but are of opposite sign. All other couplings of ally1 bromide were reported to be of the same sign and magnitude as those found in this study. The isotope effect is plainly visible in the isotropic chemical shift values of the protons

PMR

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in propene-2-C-13. Substitution of a heavier isotope shifts the NMR signals of nearby nuclei to higher fields, implying an increase in shielding at those atoms, presumably because bonds to near neighbors are shortened and the zero-point vibrational amplitudes are smaller, resulting in a decreased polarizability of electrons near the site of isotopic substitution. As expected, the chemical shift for the hydrogen directly bonded to carbon-13 is the greatest (0.539 Hz), with lesser upfield shifts for the remaining vinyl protons (0.436 Hz for H, and 0.405 Hz for H3). The smallest change is experienced by the protons of the methyl group (0.141 Hz). As seen in Table 1, most differences between JHH values for propene and the corresponding couplings of propene-2-C-13 are greater than the sums of their expected errors as calculated by LAOCOON, although the largest difference, dJ,,, is only 0.04 Hz. It is possible that error bounds predicted by LAOCOON are too small in this case or that overlapping of lines from the two molecules, especially the resonances from protons 2 and 3, alters the line position measurements. Comparison with proton couplings obtained in the fit of the spectrum of nonenriched propene implies that the error limits of Table 1 should be increased by a factor of -4. Even with the increased expected errors AJz3 is too large. However, the error analysis of LAOCOON indicates that Jlz, Jlj, and Jz3 are coupled (as are J, ,Me, J2,Me, and J3,Me) and the sum J,, + J13 + Jz3 for all three fittings does agree to within the sum of the new error limits. Nematic Phase Spectrum

Nematic phase spectra for propene and enriched propene-2-C-13 are shown in Figs. 3 and 4. Separation of propene lines from those of propene-2-C-13 is more difficult for the anisotropic case because the resonance positions are highly temperature and concentration dependent. Here it was necessary to fit to the best straight line the prominent peaks of one spectrum to corresponding peaks in the other and use each propene frequency with the best-fit values to predict propene resonances in the mixed spectrum. Predicted and experimental frequencies usually agreed to within 5 Hz.l The propene spectrum was fit by calculating spectra for guessed S-values and the microwave geometry of Ref. (2)2 until calculated and experimental spectra were similar enough to refine the dipolar couplings iteratively using a dipolar version of LAOCOON WI. &I values obtained from the microwave coordinates and the refined chemical shifts and dipolar couplings of propene provided accurate first guess parameters for solving the spectrum of propene-2-C-13. Final values for the two spectra are listed in Table 2 where it can be seen that the chemical shifts and proton-proton couplings for the three cases are very similar. The large errors and very nearly equal values for propene and propene-2-C-13 in the isotopic mixture make it impossible to discern an isotope effect on either the chemical shifts or the ordering matrix. r The fitting function vi = avt + b allows for translation (by b) and expansion (a > 1) or contraction (a < 1) of the primed spectrum with respect to the unprimed. It should be noted that this method is only strictly applicable if the direct couplings are a function of one S-value; otherwise the two spectra must be very similar in appearance. In this case, with the exception of Dz3, corresponding DHn in the two spectra agreed to within 1%. 2 In this and following references to the microwave geometry, it is understood that the out-of-plane proton coordinates of the methyl group have been adjusted for CBUsymmetry.

328

WILLIAMS

AN!3

SOTHNER-BY

FIG. 3. 100 MHz proton magnetic resonance spectrum of propene oriented in a nematic phase at 32°C. (a) Experimental spectrum; (b) calculated spectrum.

-1695

FIG. 4. 100 MHz proton magnetic resonance spectrum of 56.5 7: enriched propene-2-C-13 in a nematic phase at 32°C.

2030

oriented

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OF PROPENE-2-C-13

IN NEMATIC

TABLE SPECTRAL

PARAMETERS

321

PHASE

2

OF NEMATIC

PHASE PROPEFIE@ 56.5 % C-l 3 Enriched

Parameter

Propene

WIC W2 K WtVle -%z 013 D1,ivte 023 D,,,,

-400.207 -314.928 -327.548 0 zt -617.544 59.777 -199.418 -7.547 -177.690 -428.766 866.928

D 3,ble

Di%,ble

sample f 0.309d + 0.317 f 0.082 0.054 f 0.141 rt 0.301 & 0.185 + 0.339 Y!=0.182 + 0.064 + 0.061

C-12

Molecule

-400.803 -314.075 -327.808

i 0.790 z!z 0.783 ziz 0.149 0 zt 0.099 -621.000 rt 0.149 59.974 i- 0.352 -199.954 i 0.177 -5.660 z!z 0.375 -179.482 + 0.173 -43 1.276 & 0.059 872.398 zk 0.056

DlC

Dx &C

&xe rms Theoretical Experimental

lines assigned frequencies

assigned

0.637 Hz 132 87

1.077 Hz 118 80

sample

C-13

Molecule

-401.108 -314.248 -327.608

k 0.149 rt 0.153 & 0.144 0 i 0.087 -620.617 3 0.126 59.270 i 0.121 -200.488 i 0.123 -5.014 i 0.227 -179.159 It 0.120 -431.490 i 0.130 872.177 i 0.094 808.281 + 0.344 -346.513 & 0.344 -32.532 rk 0.287 -175.115 It 0.157 1,187 Hz 178 113

a See Fig. 1 for numbering. b Jij values are assumed equal to those given in Table 1. e All chemical shifts, Wi, are referred to the methyl group. d Error estimates calculated by LAOCOON.

Structural Parameters of Propene-2-C-13

Structural parameters of propene-2-C-13 were found by a “variable metric” minimization (13) of the rms difference between unique observed and calculated dipolar couplings where

S‘,, (14) are the order parameters appropriate to planar symmetry and rij = (AXtj + A Y$ + AZtj)1’2

is the distance between atoms i and j. Atoms in the vinyl group have AZij = 0 and for methyl couplings Dij was modified to represent an averaged contribution from the three methyl protons. As discussed below, several molecular configurations were studied, and where the calculation involved rotamers, each conformation was averaged over three positions and weighted by its population. Trial guesses for the parameters were based on the microwave data of Ref. (L?),with the coordinates translated to place carbon-13 at the origin and rotated to align the CSGaxis along the --x direction. Before each iteration the S-values were best fit to the

322

WILLIAMS AND BOTHNER-BY

current geometry and the rms error was minimized with respect to nuclear coordinates only. All minima were confirmed by reminimization from a random step (5 % maximum) in the final parameters. The first configuration examined was that of Fig. l(a) where the Cxv axis was free to tilt. Surprisingly, the axis moved less than 3” and the minimum rms was I.37 Hz instead of zero. Minimization with the CZv axis tilt angle fixed at 0” produced a slightly higher rms (1.48 Hz), implying that the CJU axis is probably not tilted; therefore, al! following structural determinations were done with the methyl protons constrained to be equidistant from carbon-13 as well as from each other.

Mole

Fraction

of

Eclipsed

RoPmner

FIG. 5. Change in rms error for the best fit geometry for different mole fractions of staggered and eclipsed forms of propene (see Fig. 1). The minimum rms point was obtained after introducing the mole fraction as a parameter. The dashed line shows the error found for four or more equipopulated rotamers.

Optimization of the geometry of Fig. l(b) yielded a lower rms (0.68 Hz), which seems contrary to the theoretical and microwave results mentioned earlier. Better results were obtained, however, when the methyl group was postulated as freely rotating. Configurations having n equipopulated rotamers were optimized, where n = 2,3,4,6,X, IO, 1224. Fig. l(a) was considered rotamer 1 and the angular displacement of the methyl protons between rotamers was 120/n degrees. The system of equations remains overdetermined since the geometry of any rotamer can be found from that of rotamer 1. For fr 2 4 the minimum rms was 0.37 Hz and the best geometries were identical. An error of 0.29 Hz For n = 2, corresponding to 0.5 mole fraction of Fig. l(a) (X, = 0.5) with Fig. I(b), suggested that lower errors might be obtained for a system model composed of unequal populations of l(a) and l(b). Calculations for X, = 0.10, 0.15, . . .) 0.90 gave a smooth

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OF PROPENE-2-C-

13 IN NEMATIC

323

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curve of rms vs X, with a sharp minimum at 0.35 c X, c=0.40 and when X, was introduced as a parameter the rms error went to 0.014 Hz, where iteration was stopped, for X, - 0.37 (see Fig. 5). The NMR distances and ordering parameters for n > 4 equipopulated rotamers and. two unequally populated rotamers, both scaled to best fit the microwave distances, are presented in Table 3. The separately determined geometries are very consistent, with the rms error in the scaled distances being slightly lower for the n 2 4 case (0.026 ;r> than for the two rotamer, variable population case (0.032 A). TABLE NEMATIC PHASEDISTANCES’

Atom pair!’

AND ORDER PARAMETERSOF PROPENE-2-C-13

Microwave result (Ref. (2))

12 13 14 15 17 23 24 25 27 34 35 37 45 47

Two rotamers, variable population

2.431 3.072 3.100 2.580

1.090 1.861

1.758 2.147

rms error of fit to microwave data

S xx Two rotamers Four or more rotamers

2.455 3.093 3.104 2.565

1.114zk0.004

1.100 i 0.025 1.911 i 0.055

i k jr I + + rt

0.009 0.005 0.006 0.006 0.004 0.003 0.004

zt 0.058‘ i-o.043 & 0.029 ~-t 0.024

1.770 zt oc 2.128 i 0.001 0.0321 A

3.726& 4.135 zt 2.134 i 2.379 f 3.477 i 2.107 i 1.776+0" 2.128 i 0.026 8,

S-Values

Diagonal S-Values

s YY

0.04133 0.04176

Four or more equipopulated rotamers

2.466 + 0.010 3.096 I 0.007 3.109 rk 0.005 2.572zk 0.003 1.917 3.725 4.138 2.139 2.362 3.462 2.103

3.726 4.135 2.113 2.435 3.509 2.111

.-

3

-0.00259 -0.00314

s XY -0.03149 -0.03075

0.017 0.024 0.027 0.027 0.028 0.026 0.001

s xx 0.0563 0.0559

SYY -o.on5-0.0183

a Scaled to best fit the microwave data. b See Fig. 1 for numbering. c Held constant during iterative fitting of distances to dipolar couplings. DISCUSSION

The authors feel that vibrational effects and uncertainties in the dipolar make it impossible to distinguish whether a configuration of two unevenly rotamers, or one with a freely rotating methyl group, represented by four equally populated rotamers, best describes propene in a nematic solution. It to exclude the staggered form and, with less certainty, the eclipsed form propene conformers.

couplings populated (or more) is possible as unique

324

WILLIAMS

AND BOTHNER-BY

Quite reasonable results were obtained with the methyl group axis fixed and, in fact, the tilt angle changed only slightly in the case where it was permitted to vary. In all other instances the errors were sufficiently low that a change in the CSv axis would not have been geometrically significant. The use of a single S-matrix to describe the orientation of a molecule with rnu~ti~~~ conformations appears to be justified for propene. Corresponding order parameters calculated for Fig. l(a) and l(b) alone differ by small amounts and the S-values found for the overdetermined systems involving more than one rotamer all lie between those of the staggered and eclipsed forms (see Table 4). TABLE

4

S VALUES FOR SOME COWFIGURATIONS

s XX

Configuration

164 Wb) Cl'&) + l(b))/2 x, = 0.5 x, = 0.37b

Rotamers > 4

S YY

0.0426 0.0406 0.0416 0.0416 0.0413 0.0418

n See Fig. 1. b Variable population

OF PROPENE

-0.0043 -0.0012 -0.0028 -0.0031 -0.0026 -0.0031

SXY -0.0282 -0.0341 -0.0312 -0.0307 -0.0315 -0.0308

result.

Inspection of Table 3 shows that microwave and NMR parameters are close, impiying negligible anisotropy in the carbon-13-proton indirect couplings. However, several discrepancies are noteworthy. The nematic phase carbon-proton bond distance is larger than the microwave value which is based on substitution coordinates, r,, that commonly give shorter C-H bonds than either inertial coordinates, rO, or N measurements (1.5). The NMR distances dz3 and d34 differ between 2 and 3 % from those of Ref. (2), possibly because of vibrational effects, which may also account for the large difference between the nematic values of dzc and dsc. Vinyl compounds are known to have unequal geminal CH bond lengths (I6), but the difference is not usually so pronounced as found here. ACKNOWLEDGMENTS Part of this work was done with the support of NIH Grant RR 00292. The authors are grateful to Dr. Josef Dadok for assistance with the spin-tickling experiments. We would like to acknowledge valuable discussions with Dr. Alfred Saupe and Dr. Salvatore Castellano. REFERENCES 1. P. DIEHL, P. M. HENRICHS, AND W. NIEDERBERGER, PEDULLI, M. TIECCO, AND C. A. VERACINI, 1.

Mol. Phys. 20,139 (1971); L. LUNAZZI, 6. F. Chem. Sot., 6, 7.55 (1972); T. N. HUCKERRY;

Tetrahedron Letters 38, 3497 (1971). 2. D. R. LIDE, JR. AND D. CHRISTENSEN, J. Chem. 3. E. HIROTA, J. Chem. Phys. 45,1984 (1966). 4. B. TINLAND, J. Mol. Structures 6,152 (1970).

Phys. 35, 1374 (1961).

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5. W. BOVE~, C. W. HILBERS, AND C. A. MACLEAN, Mol. Phys. 17,75 (1969). 6. A. A. BOTH~\~ER-BY AND S. CASTELLANO, “Computer Programs for Chemistry” (Delos F. Detar: Ed.), Vol. 1, Chap. 3, Benjamin, New York, 1968. 7. A. A. BOTHNER-BY AND C. NAAR-COLIN, J. Amer. Chem. Sot. 83,231 (1961). 8. C. J. JAMESONAND M. C. DAMASCO, Mol. Phys. 18,491 (1970). 9. K. M. CRECELY, R. W. CRECELY, AND J. H. GOLDSTEIN, J. Mol. Spec. 37,252 (1971). 10. G. MIYAZIMI, Y. UTSUMI, AND K. TAKAHASHI, J. Phys. Chem. 73,137O (1969). 11. J. FEENEY AND P. J. S. PAUWELS, Mol. Phys. 14,209 (1967). 12. P. J. BLACK, K. D. LAWSON, AND T. 3. FLAUTT, J. Ctiem. Phys. 50,542 (1969). 13. W. C. DAVIDON, Argonne Natl. Lab. Report 5990, Rev. (1959). 14. A. SA~PE, Z. Ndtuvforsch. 20a, 572 (1965). 15. D. R. HERSCHBACH ohm V. W. LAURIE, J. Chem. Phys. 37, 1668 (1962); P. DIEHL AND 6. L. KXETRAPAL, “NMR, Basic Principles and Progress,” Vol. 1, Springer-Verlag, 1969. 16. R.ef. (2), Table VI.