The conformational equilibrium in [13C-1-methy~-cis-l,4-dimethylcyclohexane

HAROLD BOOTH AND JEREMY RAMSEY EVERETT' Department of Chemistry, University of Nottingham, Nottingham, England NG72RD

Received June 16, 1980

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . This paper is dedicated to Prof. Raymond U. Lemieux on the occasion of his 60th birthday

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HAROLD BOOTH and JEREMY RAMSEY EVERETT. Can. J. Chem. 58,2709(1980). The conformational equilibrium in [13C-l-methyl]-cis-l,4-dimethylcyclohexane has been assessed by (a) direct integration of

signals due toequatorial and axial methyl carbons in the 13C nmr spectrum at 172 K and (b) by measurement of the 13C chemical shifts of C-1 and C-4 in the spectrum at 300 K. It is concluded that a 13C isotope effect on the position of the degenerate equilibrium in cis-1,4-dimethylcyclohexaneis either nonexistent, oris too small to be detected by methodsofanalyses employed. The I3Cnmrdata incidental to the study (chemical shifts, coupling constants, spin-lattice relaxation times, nuclear Overhauser enhancements, and I-bond isotope shifts) are recorded for the title compound and its trans-isomer.

HAROLD BOOTH et JEREMY RAMSEY EVERETT. Can. J . Chem. 58,2709(1980). On a determine I'Cquilibre conformationnel du [13C methyl-11-dimethyl-1,4 cyclohexane cis par: (a) I'intCgration directe des

signaux des carbones de rnkthyles en positions axiale et Bquatoriale dans le spectre rmn du 13C B 172 K et (b) par la mesure des deplacements chimiques du I3C des carbones en position 1 et 4dans le spectre a 300 K. On a conclu que I'effet de I'isotope I3C sur la position de I'kquilibre degkneree du dimethyl-1,4 cyclohexane cis est inexistant ou trop faible pour 6tre dkcele par les mtthodes d'analyse utilisees. On a enregistre les donnees de la rmn du I3C inherentes a I'Ctude du compose Ctudie et de son isomere trans (deplacements chimiques, constantes de couplage, temps de relaxat~on spin-rkseau, effets Overhauser nucleaire et deplacements isotopiques de la liaison-1).

[Traduit par le journal]

Introduction examined cyclodecanone and measured the A number of recent papers (1, 2) have described m ~ ~ e m e n t s in I3C chemical shifts which accom-

isotope effects on equilibrium processes. using panied deuteration; effects were detected over chemical shift measurements, Baldry and ~ ~ b i ~ - distances of up to 6 bonds and were attributed to a son (1) were able to detect small changes in the direct, or intrinsic, isotope effect, rather than to position of chair-chair equilibria in cyclohexanes any perturbation of a conformational equilibrium when a CH, substituent was replaced by a CD, (4). Chertkov and Sergeyev (5) failed to detect substituent. Saunders et al. (2) using 1 3 ~ chemical (within 2%) any change in the conformational shifts, found it relatively easy to detect changes in equilibrium of cyclohexane when eleven hydrogen

the position of tautomeric equilibria of degenerate atoms were by deuterium atoms. flow- cations (e.g. 1 + 2) caused by replacement of CH, ever, the preference, in cyclohexanones, for axial by CD,, and of 3-CH, by 3433,. of considerable deuterium over axial hydrogen, has been demon-

interest was the change in the position of equilib- strated ORD measurements (6 7). rium 1 + 2 caused by replacement of 1 2 ~ ~ ~ by We considered it worthwhile to attempt to de- 13CH3, a change detected by the slight difference in termine the effect on the degenerate chair-chair chemical shift between C-1 and C-2. ~h~ ion 4, with equilibrium in cis-1,4-dimethylcyclohexane 5 * 6 the charge adjacent to 13C, was preferred to the ion 3. On the other hand, Wehrli et al. (3) recently

CH3 CH3 5 6

1 2 which would result from substitution of a 12CH, by a l3CH,. The occurrence of syn-axial nonbonded interactions in cyclohexanes is thought to be a major factor in determining conformational enthal- pies and, therefore, conformational equilibria.

3 4 Furthermore, the CH,/H syn-axial interactions may be considered to consist of both H/H and C/H

'Present address: Department of Chemistry, McGill Univer- interactions. The overall effect on the equilibrium 5 sity, Montreal, P.Q. + 6 due to the isotopic replacement may have two

0008-40421801232709-05$0 1 .OO/O 01980 National Research Council of CanadaIConseil national de recherches du Canada

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2710 CAN. J. CHEM. VOL. 58, 1980

contributions: a direct one due to the difference in interaction energy, at the same distance, between lZC/H and 13C/H interactions, and an indirect one, due to the different geometry induced in (7 * 8) by

the isotopic substitution. Neither effect is predicta- ble. With regard to the geometry of 7, compared to that of 5, it seems likely (cf. ref. 8) that both 13C-H and 13C-C bond lengths are less than the corre- sponding bond lengths for lZC. The relatively shorter 13C-H bond length in 7 should result in reduced syn-axial repulsive interactions of the HIH variety. On the other hand a shortening of the 13CH3-C bond causes a reduction in HIH and CH,/H distances, leading to increased repulsive interactions.

Results and Discussion The syntheses of cis-l,4-dimethylcyclohexane 7

+ 8 and trans- 1,4-dimethylcyclohexane 9, each enriched to the extent of 90.6% with 13C at one of the methyl carbons, employed well established methods which require no comment (see Experi- mental).

AN' -,,n

Two methods were used to measure the equilib- rium constant for 7 * 8. The first method involved the measurement of the relative areas of the well- separated signals due to equatorial methyl (1 '-CH,, 23.3 ppm) and axial methyl (1"-CH,, 17.4 ppm) carbons in the 13C nmr spectrum recorded at 173 K. This method is relatively inaccurate, whether in- strumental integration or the preferred method of hand planimetry is employed. Whilst the planime- ter is very accurate and capable of good reproduci- bility, the overall accuracy is limited by the uncer- tainty in choosing a straight line for the base of the signals. This uncertainty is obviously related to noise level and, therefore, to sample size and com- puter capability. The advantage of the method of relative areas is that it is direct and involves no assumptions, provided that the experimental parameters are chosen sensibly. In a multi-pulse Fourier transform 13C experiment, recorded with 'H decoupling, the relative signal areas are depen- dent on spin-lattice relaxation times and nuclear

Overhauser enhancements. Table 1 shows that the TI values of 172 K are little different for carbons of axial and equatorial methyl groups. Table 1 also includes the nuclear Overhauser enhancements for equatorial and axial carbons at 172 K; again the difference is insignificant. We conclude that the signal areas for equatorial and axial carbons reflect accurately the molecular proportions of 8 and 7 respectively. The relatively small nuclear Over- hauser enhancements (98-99%) for the methyl car- bons are noteworthy since they imply that only about 50% of the total spin-lattice relaxation is due to dipole-dipole interaction. Since samples were not degassed, there is the expected contribution to relaxation from dissolved oxygen. Nevertheless, it seems that there must be an appreciable contribu- tion from relaxation by spin rotation. From the low temperature area method, the equilibrium constant K (= 817) was determined to be 1.00. As a precau- tion, the same method was applied to the degener- ate system 5 $6. In this case the equilibrium con- stant was found to be 1.01 by instrumental integra- tion and 0.97 from hand planimetry, giving an aver- age of 0.99. We conclude that the 13C/12C isotope effect on the position of equilibrium 5 = 6 is nonexistent, or is too small to be detectable by the low temperature area method.

The second method used to measure the position of equilibrium in 7 C 8 involved chemical shift determinations and is, in principle, a more accurate method than the first. The basis of the method is the fact that the room-temperature averaged 13C chemical shifts of the methine carbons C-4" and C-4' is different from the room-temperature aver- aged chemical shifts of the methine carbons C-1" and C-1'. These averaged chemical shifts are, of course, identical in the degenerate equilibrium 5 6. The general theory is as follows. Let x and (1 - x) be the mole fractions of 7 and 8 respectively; let 6, and 6, be the observed, averaged chemical shifts of C-1 and C-4, respectively, at room temperature. If 6 and 641 are the chemical shifts of C- 1' and C-4', respectively, in 8, whilst 6111 and 64u are the corre- sponding shifts in 7, we may write

Let &e intrinsic 1-bond isotope shifts which ac- company the replacement of a lZCH3 by a 13CH3 be I, for ring carbon substituted by CH, (equatorial), and I, for ring carbon substituted by CH, (axial). Then

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BOOTH AND EVERETT. I.

TABLE 1. 13C relaxation times (TI), I3C['H] nuclear Overhauser enhance- ments, and the equilibrium constant for 7 = 8 (solvent CDCI,/CFCI,)

CH, axial CH, equatorial

TI (s) 1.07f 0.05" 1.00f 0.05" TI (s) 8.60+0.48b 8.60+0.48b

Nuclear Overhauser enhancement (%) 99" 98" Equilibrium constant 817 1.035 (instrumental integration)

1.028 (hand planimetry) 1.03 1 (average) 1 .OOC (corrected)

"172 K. b302 K. 'After correction for presence of 9.

It is assumed that intrinsic isotope shifts over 4- bonds are negligible (cf. ref. 8). From the above relationships, it can easily be shown that

[l] x = (64.. - 64.) + (64 - al) + Ie 2(tj4,, - li4,) + (Ie - la)

Now the observed signal for C-1 arises largely from molecules which are effectively doubly labelled (in 13C) at C-1 and the adjacent methyl carbon, and is therefore the low-field doublet part of an AB spin system (JAB = lJCC). The high-field doublet part of this system is a pair of satellites to the intense singlet due to the methyl carbon of singly labelled molecules. Analysis of the AB spectrum yields the chemical shift 6, and also the chemical shift of the methyl carbon in doubly labelled species. The ob- served signal for C-4 also arises largely from mole- cules containing a 13C-enriched methyl carbon at- tached to C-1, but since the coupling ,JCC is very small, this signal is a single line, the position of which yields 6, directly.

The 13C nmr spectrum of 7 G 8 recorded at temperatures below 195 K includes distinct reso- nances for CH3 (equatorial) in 8, CH3 (axial) in 7, C-1 ' (low-field half of AB quartet), C-4' (singlet), C-1" (low-field half of AB quartet), and C-4" (singlet). The chemical shifts 6,,, ti4,, 6,1,, and 64. are readily obtained from this spectrum. Thus all the parameters required for the calculation ofx through eq. [I] are available.

The most attractive feature of this method of assessing the position of equilibrium in 7 G 8 is that it involves the measurement of chemical shift dif- ferences in the spectrum of a single sample of a single compound. Most methods of determining conformational equilibria through measurement of chemical shifts utilize conformationally biased compounds as standards for chemical shift parameters. A basic weakness of such methods is that the validity of the models is always question- able; furthermore, chemical shift data are required from at least three compounds and are often re- corded in separate solutions. The present method,

although free from most of these objections, suffers from the drawback that the parameters 6,,, ?i4,, 6,,,, and 6q are derived from a low-temperature spec- trum whereas 6, and 6, come from a room- temperature spectrum.

Spectral data for [13C-l-methyl]-cis-1,4- dimethylcyclohexane are summarized in Table 2. Fourier transform spectra at 62.901 MHz employed 32 K data points over a spectral width of 2500 Hz, equivalent to digital resolution of 0.1526 Hz (0.002426 pprn), and corresponding to a possible error due to digitization of 3~0.0763 Hz (k0.001213 pprn). The spectrum at 180 K includes a "triplet" at 3 1.67 ppm, comprising a singlet due to C-2'',6" and a doublet (3JCC = 3.42 Hz) due to C-3'3' which is coupled to the equatorial methyl carbon. Since the combined signal due to C-2',6' and C-3",5" is an unresolved singlet at 29.20 ppm, it is evident that the 3-bond coupling between C-3",5" and the axial methyl carbon is less than 1.0 Hz. Table 2 indicates that the intrinsic 1-bond isotope effects for the sub- stituted ring carbons are -0.01 1510 pprn for I, and -0.01 1875 pprn for I,. The corresponding isotope effects for the methyl carbons are -0.0075833 pprn for equatorial methyl and -0.0002067 pprn for axial methyl.

The directions of these intrinsic isotope effects, to high field, are in agreement with the usual finding, that substitution of a nucleus by a heavier isotope produces greater shielding for all nuclei involved (9). Whereas I, and I, are identical, within experimental error, the isotope effects for the methyl carbons appear to show a dependence on the orientation of the methyl group. In the spectrum of 7 S 8 at 300 K the "triplet" observed at 31.13 pprn consists of a singlet due to C-2,6 (ZJcc = 0) and a doublet (3Jw = 2.29 Hz) due to C-33. The doub- let splitting represents the average of the 3Jcc val- ues for conformations 7 (< 1 Hz) and 8 (3.42 Hz), obtained from the spectrum at 180 K.

Before application of eq. [I], it was necessary to justify the assumption, implicit in [I], that the vari- ation in 13C chemical shifts with temperature is

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2712 CAN. J . CHEM. VOL. 58, 1980

TABLE 2. I3C chemical shiftsa at 62.901 MHz (6 values, ppm downfield from Me4Si) for carbons in [13C-l-methyl]- cis-l,4-dimethylcyclohexane 7 S 8

Chemical shift - - - -

Carbon 300Kb 180 K

DMcasured using 32K data polnts over 2500 Hz. a pursible error due to digit~zation of k0.001213 ppm.

bAveraged shifts observed, i.e. 6, = 6,s = 6,cetc. 'Doublet. 'Jcc 35.55 Hz. dDoublet. >Jcc2.29 Hz. CDoublet. 'JCc 34.64 Hz. '~oublet ; IJ , , 35.40 H;. OSinglet. 'Jcc 7 IHz. *Doublet, 'Jcc3.42 Hz.

approximately the same for cyclohexane carbon substituted by equatorial Me, as that substituted by axial Me. The temperature dependence of the 13C chemical shifts for cis-l-ethyl-4-methylcyclo- hexane 10 = 11 were recorded over a range of 36 K

below the slow exchange limit (10). The results confirm the work of Schneider and Freitag ( l l) , which demonstrated a linear deshielding, with in- creasing temperature, of ring carbons in cyclo- alkanes. In our case the plots of chemical shift against temperature indicated an approximately linear relationship for C-4 in both 10 and 11. In 10, C-4 was deshielded, with increasing temperature, by 3.18 x lop3 pprn K-I; the corresponding shiftltemperature gradient for C-4 in 11 was 3.63 x lo-) pprn K-I. If we assume that similar 13C shiftltemperature gradients hold for C-4' in 8 and C-4" in 7, then the discrepancy arising from the use of (Zi4" - Zi4,) at 180 K, rather than at 300 K, amounts to only 0.054 ppm. The entries in Table 2 yield the following chemical shift differences:

Application of these to eq. [I.] leads to a value for x of 0.4999424, i.e. 0.500, within experimental error. We conclude that any isotope effect (caused by replacement of 12CH3 by 13CH3) on the position of equilibrium in 5 = 6 is either nonexistent, or is too small to be detected by the technique employed.

The 13C nmr spectrum of the conformationally homogeneous [13C-l-methyl]-trans-l ,4-dimethyl- cyclohexane 9 was also measured and the relevant details appear in Table 3. As for the cis-isomer, chemical shifts for C- 1 '" and CH3- 1 '" were obtained by analysis of the AB spin system arising from doubly labelled molecules. Table 3 indicates that the intrinsic l-bond isotope effect for C-1"' is (Zi,.. - Zi4,,, =) -0.01603 pprn and for CH3-1"' is -0.00796 ppm. Encouragingly, these values are close to those determined for C- 1 and CH3- 1 ' in conforma- tion 8 of the cis-isomer 7 = 8.

The 13C-13C coupling constants of Tables 2 and 3 are of interest in suggesting a tentative correlation of J values with stereochemistry. Thus lJ(C-1', CH,) in 8 (i.e. equatorial methyl) is 35.40Hz, significantly greater than lJ(C-1", CH,) in 7 (i.e. axial methyl), which is 34.64 Hz. A larger effect, in the same sense, was noted by Barna and Robinson (12) for 4-tert-butyl-2-methylpiperidines and 4- tert-butyl-2-methylcyclohexanones, but was attri- buted to the proximity of nonbonding electrons or unsaturation. The coupling constant lJ(C-1 "', CH,) in trans-l,4-dimethylcyclohexane 9 is 35.89 Hz at 301 K and 35.64 Hz at 173 K, values which are close to the 36.0 (k0.3) Hz reported earlier for the comparable coupling in the major conformation of methylcyclohexane at 172 K (13). It is noteworthy that ,J(C-3, CH,) is 3.4-4.5 Hz for equatorial methyl, corresponding to a dihedral angle of 180°, whereas ,J(C-3, CH,) is 7 1 Hz for axial methyl, corresponding to a dihedral angle of 60". A

TABLE 3. 13C chemical shiftsa at 25.15 MHz (6 values, pprn downfield from Me4Si) and 301 Kfor carbons in [,13C-l-methyl]-trans-1,4-

d~methylcyclohexane 9

Carbon Shift

1 '" 32.961 lob 2"',6'" 35.85105 3"',5"' 35 34862'

4 "' 32.97713 CH3-I"' 22.83280b CH3-4"' 22.84076

'Measured using 16K data points over 1OOO Hz, a possible errordue to di itization of k0.00243 ppm.

9~oub le t , 'Jcc 35.89 Hz (35.64 Hz at 17: K).

Doublet, l J ~ ~ 4 . 5 2 Hz.

Zi4" - Zi4, = 6.760815 pprn Zi4- ti1= 0.011510ppm

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BOOTH AND EVERETT. I. 2713

Karplus-type correlation of vicinal coupling (,Jcc) with dihedral angle is now well established (14,15). Of greater interest is the significant difference be- tween ,J(C-3"', CH,) in 9 (4.5 Hz) and ,J(C-3', CH,) in 8 (3.4 Hz). (The former compares well with the value of 4.3 Hz recorded for methylcyclohexane, ref. 13.) One or both of two factors may contribute to an explanation of the difference: the remote axial methyl in 8 causes a slight flattening of the ring, relative to the effect of equatorial methyl (16-20), leading to a loss of coplanarity of the coupling pathway CH3-C1-C2-C3. At the same time the change of the 4-methyl substituent from an equato- rial orientation in 9 to an axial orientation in 8 may affect ,JCc because the electronegativity effect of methyl will depend on orientation (21).

Experimental 13C spectra were recorded for solutions in CFC1,-CDCI, (9: 1

vlv) at 25.15 MHz on a JEOL JNM-PS-100 spectrometer inter- faced to a Nicolet 1085 20 K computer, and at 62.90 MHz on a Bruker WM-250 spectrometer. General instructions for the pre- paration of 1,4-dialkylcyclohexanes have been given elsewhere (22).

[13C-l-Methyl]-1 ,4-dimethylcyclohexane 4-Methylcyclohexanone (1.442 g, 0.0129 mol) was reacted

with the Grignard reagent formed from magnesium turnings (0.34 g, 0.014 mol) and ["C] iodomethane(2.0g, 0.014 mol, 91.0 13C at.%). [l-Me-13C]-l,4-Dimethylcyclohexanol (2.48 g, > 100%) was isolated as a pale yellow oil still containing some ether. The alcohol was dehydrated using 4-methylbenzene- sulfonic acid (0.3838 g) to give [l-Me-13C]-l,4-dimethylcyclo- hex-1-ene (0.9574g, 0.0862 mol) as a colourless oil. The alkene (neat) was hydrogenated over PtOz (0.1026 g) to yield a mixture of cis- and trans-[] -Me-13C]-1 ,4-dimethylcyclohexane (0.5432g, 0.00481 mol) as a colourless oil (M+: 113.1298, C,13ClHl, requires 113.1282). The mixture was completely separated using a 12 ft x 2 in. aluminium column packed with 30% SE-30coated on a support of acid-washed siliconized 60-80 mesh Chromosorb W. At a column temperature of 65°C and a flow rate of 30cm3 min-I, the trans- and cis-isomers had reten- tion times of 45.6 min and 57.0 min respectively. In the lH nmr spectrum (CDCI,), the methyl proton of the trans-isomer, at 6 0.86 ppm, gave a doublet of doublets with separations of 122.5 Hz (lJCH) and 5.5 Hz (3JHH). The methyl protons of the

cis-isomer, at 6 0.94 ppm, gave a doublet of doublets with separations of 122 Hz ('Jc,) and 6.2 Hz (?IHH).

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(1971). 17. J. D. REMIJNSE. H. VAN BEKKUM. and B. W. WEPSTER.

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