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Deuteron quadrupole coupling constants and relaxation times for the isomeric contiguously 13C 2H-labeled cyclohexenes
JOURNAL
OF
MAGNETIC
33,
RESONANCE
177-182
(1979)
Deuteron Quadrupole Coupling Constants and Relaxation Times for the Isomeric Contiguously 13C-‘H-Labeled Cyclohexenes JAN
B.
WOOTEN,
C. W.
Department
of Chemistry,
G. B.
JARVIS, AND
JOHN
Clemson Received
A. L.
SAVITSKY,
BEYERLEIN,
JACOBUS
University, May
Clemson,
South
Carolina
29631
13, 1978
The deuteron quadrupole coupling constants (Qo’s) have been determined for a mixture of isomeric monodeuterocyclohexenes (containing a low level of t3C enrichment in the CD bonds) from the *H NMR spectrum in nematic phase. The measured Qo’s are: 213.6+2.5, 179.9k2.9, and 178.8k3.0 kHz for the vinyl, ally], and homoallyl deuterium-substituted species, respectively. Employing these Qo values and spin-lattice relaxation times (Tr’s), it is concluded that reorientation of cyclohexene perpendicular to the molecular (pseudo)-plane is ca. twice as rapid as out-of-plane reorientation.
INTRODUCTION
The deuteron spin-lattice relaxation time, T,, is ideally suited for studying molecular reorientation since the contribution from the quadrupole mechanism to the relaxation dominates other possible contributions, e.g., dipole-dipole, spinrotation, etc. Consequently, the molecular correlation time, 7,, of a CD bond vector is simply related to Tl by the relation
PI in which the asymmetry of the electric field gradient about the CD bond is neglected. Calculating 7, from Eq. [l] and measured Tl values requires knowledge of the quadrupole coupling constant, Qn, which is known accurately for CD bonds in only a few highly symmetrical molecules. To expand the applicability of ‘H NMR to molecular reorientation studies, we have developed a technique for accurately measuring Qo which may be applied to any molecule regardless of symmetry (1,Z). The method requires determination of the 13CD dipolar and 2H quadrupolar splittings of the deuterated species in nematic phase. To avoid difficulties associated with reproducing the nematic phase conditions for separate 13C and 2H spectra, we have simultaneously obtained this information from a single deuteron spectrum. This technique necessitated a high level of r3C enrichment in the CD bond of interest such that the r3CD dipolar splitting would be observable. Extensive 13C enrichment often involves applying tedious (and always expensive) synthetic procedures to small quantities of highly enriched starting materials. Recently, 13C enrichment has been circumvented by utilizing an external 2H field stabilization lock and signal averaging for a sufficient period of time to obtain the 177
0022-2364/79/010177-06$2.00/0 Copyright 0 1979 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in Great Britain
178
WOOTEN
ET
AL.
requisite “CD dipolar splittings at natural 13C abundance (3). The field was locked on a sample of D20 contained in a sealed capillary adjacent to the sample insert, thus permitting the use of lo-mm sample tubes. The improved sensitivity and stability make it possible, in general, to measure 13CD dipolar couplings of any molecule with a low level of 13C enrichment by signal averaging. This produces a considerable reduction in cost and also obviates the need to work with extremely small quantities of materials in synthetic procedures. The purpose of this article is to report the application of this technique to determining simultaneously the quadrupolar coupling constants of the three nonequivalent deuterons in a mixture of isomeric monodeuterocyclohexenes with 17% 13C enrichment in the CD bond. The Qn values obtained for the vinyl, allyl, and homoallyl CD bonds and the corresponding T1 values are used to describe the molecular reorientation of cyclohexene. EXPERIMENTAL
The specifically substituted monodeuterocyclohexenes were prepared as follows: [ 1-r3C, 1-2H]cyclohexene was synthesized by modification of a procedure previously reported for the preparation of [1-r4C]cyclohexanone (4). [1-‘3C]Cyclohexanone was reduced with LiAlD4, and the [I-13C, l-2H]cyclohexanol thus prepared was dehydrated by a method reported previously (5). The isomeric n-13C, n-2Hcyclohexenes were formed by p-toluenesulfonic acid catalyzed rearrangement of [1-13C, l-2H]cyclohexene (at the boiling point) with subsequent distillation of the mixture of isomers ([l-13C, 1-2H]-, [3-13C, 3-*HI-, and [4-r3C, 4-2H]cyclohexene). Similarly, the deuterium-labeled analogs (lacking the 13C label) were prepared from [1-2HJcyclohexene. The 13.8-MHz 2H spectra were obtained with a Bruker HX-90 FT spectrometer equipped with an external deuterium lock. The field stabilization lock was accomplished via the deuterium resonance from a sealed capillary of D20 located immediately adjacent to the sample insert within the Bruker pretuned probe head. The nematic phase spectra were observed in samples containing 10 to 30 ~1 of cyclohexene in ca. 400 mg of Merck Nematic Phase IV (EM Laboratories, Elmsford, N.Y.). Typically, 25,000 scans were taken with a spectral width of 14,000 Hz, 2K data points in the real spectrum. The temperature was regulated to 302 f 0.5 K. The *H spin-lattice relaxation times were measured on a neat monodeuterocyclohexene mixture, using the standard inversion-recovery pulse sequence with a spectral width of 600 Hz and 4K transforms. A l-Hz line-broadening factor was applied before transformation. RESULTS
AND
DISCUSSION
The proton-decoupled *H spectrum of each cyclohexene isomer is a quadrupolar doublet with a large splitting, A, and a smaller splitting, VCD,of the 13C satellites, a result of 13CD dipolar coupling. The nematic phase spectrum of the mixture of vinyl, allyl, and homoallyl deuterium-substituted cyclohexenes is reproduced in Fig. 1. The quadrupolar splitting of each isomer is sufficiently different that each set of resonances is clearly resolved. Consequently, the Qn values for all three species can
DEUTERON
QUADRUPOLE
COUPLING
IN
CYCLOHEXENES
180
WOOTEN
ET
Al,.
be obtained by employing the data from a single spectrum in conjunction relation (6) A
6.180 QD=~ rCD
with the
PI
%D*kDi'
where rCD is the CD bond length and J cn is the isotropic indirect coupling constant. The direct dipolar coupling, &D, is related to VcD by the relation [31
vCD=12&D+-kDl.
The sign used before JCD in Eq. [2] depends on whether JcD has the same sign as or a sign opposite to that of DcD. It is easily determined from spectra obtained at several solute concentrations; the different concentrations result in various values of A and VCD.The proper sign for Eq. [2] is the sign of the intercept obtained from a linear plot Of A VS Vc,, (I, 2). The CD bond lengths, rco, were assumed to be equal to the CH bond lengths, rCH, calculated from the empirical linear relation rCH=1.1274-2.749~
10e4Jc~,
[41 which was obtained by fitting CH bond lengths of simple unsubstituted hydrocarbons (from microwave data) to experimental (indirect) coupling constants (JCH). This linear relationship is analogous to the one previously obtained by Muller and Pritchard for substituted benzenes (7). The uncertainty in CH bond length by this method is ca. 0.005 A, which is within the estimated error of the experimental . . determmatrons of Ton. Our estimates of r cn are expected to have no greater uncertainty. Calculated and experimental values of rcu for several hydrocarbons are presented in Table 1. The derived Qo values are presented in Table 2. The Qb value, 213.6* 2.5 kHz, for the vinyl CD bond is in good agreement with other values obtained for CD bonds in sp2-hybridized systems, e.g.,. for benzene, QD = 207 *2 kHz (3); pyridine, Q,(2) = 206 kHz, Qb(3) = 211 kHz, QD(4) = 196 kHz (8); and s-triazine, Qb = TABLE
1
CH BONDLENGTHSOFHYDROCARBONSCALCULATEDFROMEMPIRICAL RELATION[~] Hydrocarbon
JCH WY’
Ethane Ethylene Acetylene Benzene Cyclopentane Cyclopropane u J. B. Stothers, York, 1972. b L. E. Sutton Chemical Society,
kkdcalc)
125.0 156.2 248.7 159 128 161 “Carbon-13
(A)
1.093 1.084 1.059 1.084 1.092 1.083 NMR
1.093 1.086 1.059 1.084 1.09 1.08
Spectroscopy,”
(Ed.), “Interatomic Distances,” London, 1958, 1965.
Academic Spec.
Publs.
Press, 11,
18,
New The
DEUTERON
QUADRUPOLE
COUPLING TABLE
NMR
AND
MOLECULAR
PARAMETERS
IN
Vinyl
Qo &Hz)
213.6zk2.5 24.1 1.084
JCD (Hz) TCD (A)
Tl (set)
at 302
a Calculated
K from
1.56 JC-
181
2 FOR ISOMEKIC Deuteron
Parameter
CYCLOHEXENES
CYCLOHEXENES
position
Ally1
179.9* 2.9 19.2” 1.093
Homoallyl
178.8k3.0 19.2” 1.093
1.80
in cyclohexane.
208 kHz (9). The result is not in good agreement with the QD value (175 kHz) obtained for ethylene (10); this discrepancy is currently inexplicable. The ally1 and homoallyl deuterons, which are bonded to sp3-hybridized carbon, have QD values (179.9h2.9 and 178.8* 3.0 kHz, respectively) which differ somewhat from recent QD determinations of simple monosubstituted methyl derivatives, e.g., CDHZCIH, QD=163*3 kHz (1); CDHZCN, Qn= 156*3 kHz (I); and CDHZI, Qb = 163 f 3 kHz (2). They are, however, in better agreement with the value (191.48 f 0.77 kHz) obtained for monodeuteromethane (II). The lower values for the substituted derivatives suggest that an electronegative substituent may lower Qn whenever the deuteron is bonded to the carbon bearing the substituent. This conclusion is consistent with experimental results and theoretical calculations on monodeuteromethane, perdeuteromethyl fluoride, and deuterofluoroform (12). Equation [l] and the Qn and TI values were employed to calculate correlation times (7,) for the vinyl and ally1 deuterons. The ratio r,(allyl)/r,(vinyl) = 1.22 f 0.04 demands anisotropic reorientation for cyclohexene. Bauer et al. (13), in studies on aromatic compounds, have shown that in-plane reorientation (about the minor axis of the oblate ellipsoidal model) which displaces little solvent is faster than out-of-plane reorientations (about major axes of the ellipsoidal model) which displace larger volumes of solvent. The shape of cyclohexene (in any chair conformation) is similar to that of benzene; it is therefore reasonable to assume that the “out-of-plane” reorientations of cyclohexene, which displace comparable amounts of solvent, occur at comparable rates. Therefore, an ellipsoidal rotational diffusion model for the molecular reorientation (D, # D, = D,, where D, is the rotational diffusion coefficient for reorientation perpendicular to the pseudoplane and D, and D, are the rotational diffusion coefficients for reorientation out-of-plane) is reasonable. Using this model and diffusion axes assumed to be coextensive with the inertial axes for the energy-minimized cyclohexene geometry (calculated with the program STRAIN (Id)), theoretical correlation times were calculated from Woessner’s formula (15) for rigid, anisotropically reorienting molecules. If the theoretical rc for the ally1 CD bond is the average value calculated for the two nonequivalent orientations of this bond (pseudoaxial and pseudoequatorial), the theoretical ratio (rJallyl)/r,(vinyl)) can be brought into agreement with the experimental ratio with D,/DX = 1.9kO.2. This result is consistent with
182
WOOTEN
ET
AL.
results obtained for rigid planar molecules such as benzene (13, 16), pyridine (8), and s-triazine (9), for which it is observed that in-plane reorientation is more rapid than out-of plane reorientation. These calculations neglect internal reorientation about the bond axis connecting the ally1 and vinyl carbon atoms. This reorientation proceeds simultaneously with the internal reorientation about the axis connecting the ally1 and homoallyl carbon atoms, i.e., with ring inversion. Inclusion of contributions from internal reorientation would result in an even higher ratio DJD,, still consistent with conclusions regarding more rigid planar molecules (8,9, 13, 16). Results of earlier work on Internal reorientation (I 7) suggest that the rotational barrier between the two sp3-hybridized carbons (ally1 and homoallyl) is such that the internal reorientation contributions to relaxation are small compared to those resulting froin the overall reorientation of the molecule. Therefore, neglect of internal reorientation is assumed reasonable. The relaxation time for the homoallylic deuteron could not be measured accurately in the isomeric mixture of cylohexenes because of the low concentration of [4-13C, 4-‘Hlcyclohexene. However, the observed inversion times of the ally1 and homoallyl deuterons are approximately the same, indicating essentially equal T1 values. This result is consistent with the rotational diffusion model employed to calculate reorientational correlation times from Woessner’s theory (15). ACKNOWLEDGMENT
We express our gratitude to the National Science Foundation 07808) for support of this work.
(Grant CHE77-
REFERENCES 1.
J.B.WOOTEN,
A.L.BEYERLEIN,J.JACOBUS,
AND G.B.SAVITSKY,
J. Chem.Phys.65,2476
(1976).
2. J.B. WOOTEN,J.JACOBUS,G.B.SAVITSKY,
AND A.L.BEYERLEIN,
J. Chem.Phys.66,4226
(1977).
3. J.B. WOOTEN,G.B.SAVITSKY,
A. L.BEYERLEIN,
AND J.Jacosus,J.
Magn.
Reson.29,35
(1978).
4. 5. 8. 7. 8. 9. 10.
R.J.SPEER,M.L.HUMPHRIES,AND A.ROBERTS, J. Am. Chem.Soc.74,2443 (1952). H.WALDMANNANDF.PETRU, Chem.Ber. 83,287 (1950). P. DIEHL AND C. L. KHETRAPAL, NMR Basic Principles and Progress 1, 1 (1969). N.MULLERANDD.E.PRITCHARD,J. Chem.Phys. 31,768(1959). J.P. KINTZINGER AND J.M.LEHN, Mol.Phys.22,273 (1971). J.P. KINTZINGER AND J.M.LEHN, Mol.Phys.27,491 (1974). J.KOWALEWSKI,T.LINDBLOM,R.VESTIN,ANDT.DRAKENBERG, MoLPhys. 31,1669(1976). 11. S.C. WOFSY,J.S.MUENTER,ANDW.KLEMPERER, J. Chem.Phys.53,4005 (1970). 12. R. DITCHFIELD, in “Critical Evaluation of Chemical and Physical Structural Information" (D. R. Lide,Jr. and M. A. Paul, Ed.), pp. 577-578, National Academy of Sciences, Washington, D.C., 1974.
D.R.BAuER,G.R. ALMS,J.I.BRAUMAN,AND R.PEcoRA,J. Chem.Phys. 61,2255(1974). E.M.ENGLER,J.D.ANDOSE,ANDP.VR.SCHLEYER, J. Am. Chem.Soc.95,8005(1973); ANDOSE AND K. MISLOW, J. Am. Chem. Sot. %, 2168 (1974). 15. D. E. WOESSNER, J. Chem. Phys. 37,647 (1962). 16. K.T.GILLEN AND J.E.GRIFFITHS, Chem.Phys.Lett. 17,359 (1972). 17. T. K.CHEN, A.L.BEYERLEIN, AND G.B.SAVITSKY, J. Chem.Phys.63,3176(1975). 13. 14.
J.D.
OF
MAGNETIC
33,
RESONANCE
177-182
(1979)
Deuteron Quadrupole Coupling Constants and Relaxation Times for the Isomeric Contiguously 13C-‘H-Labeled Cyclohexenes JAN
B.
WOOTEN,
C. W.
Department
of Chemistry,
G. B.
JARVIS, AND
JOHN
Clemson Received
A. L.
SAVITSKY,
BEYERLEIN,
JACOBUS
University, May
Clemson,
South
Carolina
29631
13, 1978
The deuteron quadrupole coupling constants (Qo’s) have been determined for a mixture of isomeric monodeuterocyclohexenes (containing a low level of t3C enrichment in the CD bonds) from the *H NMR spectrum in nematic phase. The measured Qo’s are: 213.6+2.5, 179.9k2.9, and 178.8k3.0 kHz for the vinyl, ally], and homoallyl deuterium-substituted species, respectively. Employing these Qo values and spin-lattice relaxation times (Tr’s), it is concluded that reorientation of cyclohexene perpendicular to the molecular (pseudo)-plane is ca. twice as rapid as out-of-plane reorientation.
INTRODUCTION
The deuteron spin-lattice relaxation time, T,, is ideally suited for studying molecular reorientation since the contribution from the quadrupole mechanism to the relaxation dominates other possible contributions, e.g., dipole-dipole, spinrotation, etc. Consequently, the molecular correlation time, 7,, of a CD bond vector is simply related to Tl by the relation
PI in which the asymmetry of the electric field gradient about the CD bond is neglected. Calculating 7, from Eq. [l] and measured Tl values requires knowledge of the quadrupole coupling constant, Qn, which is known accurately for CD bonds in only a few highly symmetrical molecules. To expand the applicability of ‘H NMR to molecular reorientation studies, we have developed a technique for accurately measuring Qo which may be applied to any molecule regardless of symmetry (1,Z). The method requires determination of the 13CD dipolar and 2H quadrupolar splittings of the deuterated species in nematic phase. To avoid difficulties associated with reproducing the nematic phase conditions for separate 13C and 2H spectra, we have simultaneously obtained this information from a single deuteron spectrum. This technique necessitated a high level of r3C enrichment in the CD bond of interest such that the r3CD dipolar splitting would be observable. Extensive 13C enrichment often involves applying tedious (and always expensive) synthetic procedures to small quantities of highly enriched starting materials. Recently, 13C enrichment has been circumvented by utilizing an external 2H field stabilization lock and signal averaging for a sufficient period of time to obtain the 177
0022-2364/79/010177-06$2.00/0 Copyright 0 1979 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in Great Britain
178
WOOTEN
ET
AL.
requisite “CD dipolar splittings at natural 13C abundance (3). The field was locked on a sample of D20 contained in a sealed capillary adjacent to the sample insert, thus permitting the use of lo-mm sample tubes. The improved sensitivity and stability make it possible, in general, to measure 13CD dipolar couplings of any molecule with a low level of 13C enrichment by signal averaging. This produces a considerable reduction in cost and also obviates the need to work with extremely small quantities of materials in synthetic procedures. The purpose of this article is to report the application of this technique to determining simultaneously the quadrupolar coupling constants of the three nonequivalent deuterons in a mixture of isomeric monodeuterocyclohexenes with 17% 13C enrichment in the CD bond. The Qn values obtained for the vinyl, allyl, and homoallyl CD bonds and the corresponding T1 values are used to describe the molecular reorientation of cyclohexene. EXPERIMENTAL
The specifically substituted monodeuterocyclohexenes were prepared as follows: [ 1-r3C, 1-2H]cyclohexene was synthesized by modification of a procedure previously reported for the preparation of [1-r4C]cyclohexanone (4). [1-‘3C]Cyclohexanone was reduced with LiAlD4, and the [I-13C, l-2H]cyclohexanol thus prepared was dehydrated by a method reported previously (5). The isomeric n-13C, n-2Hcyclohexenes were formed by p-toluenesulfonic acid catalyzed rearrangement of [1-13C, l-2H]cyclohexene (at the boiling point) with subsequent distillation of the mixture of isomers ([l-13C, 1-2H]-, [3-13C, 3-*HI-, and [4-r3C, 4-2H]cyclohexene). Similarly, the deuterium-labeled analogs (lacking the 13C label) were prepared from [1-2HJcyclohexene. The 13.8-MHz 2H spectra were obtained with a Bruker HX-90 FT spectrometer equipped with an external deuterium lock. The field stabilization lock was accomplished via the deuterium resonance from a sealed capillary of D20 located immediately adjacent to the sample insert within the Bruker pretuned probe head. The nematic phase spectra were observed in samples containing 10 to 30 ~1 of cyclohexene in ca. 400 mg of Merck Nematic Phase IV (EM Laboratories, Elmsford, N.Y.). Typically, 25,000 scans were taken with a spectral width of 14,000 Hz, 2K data points in the real spectrum. The temperature was regulated to 302 f 0.5 K. The *H spin-lattice relaxation times were measured on a neat monodeuterocyclohexene mixture, using the standard inversion-recovery pulse sequence with a spectral width of 600 Hz and 4K transforms. A l-Hz line-broadening factor was applied before transformation. RESULTS
AND
DISCUSSION
The proton-decoupled *H spectrum of each cyclohexene isomer is a quadrupolar doublet with a large splitting, A, and a smaller splitting, VCD,of the 13C satellites, a result of 13CD dipolar coupling. The nematic phase spectrum of the mixture of vinyl, allyl, and homoallyl deuterium-substituted cyclohexenes is reproduced in Fig. 1. The quadrupolar splitting of each isomer is sufficiently different that each set of resonances is clearly resolved. Consequently, the Qn values for all three species can
DEUTERON
QUADRUPOLE
COUPLING
IN
CYCLOHEXENES
180
WOOTEN
ET
Al,.
be obtained by employing the data from a single spectrum in conjunction relation (6) A
6.180 QD=~ rCD
with the
PI
%D*kDi'
where rCD is the CD bond length and J cn is the isotropic indirect coupling constant. The direct dipolar coupling, &D, is related to VcD by the relation [31
vCD=12&D+-kDl.
The sign used before JCD in Eq. [2] depends on whether JcD has the same sign as or a sign opposite to that of DcD. It is easily determined from spectra obtained at several solute concentrations; the different concentrations result in various values of A and VCD.The proper sign for Eq. [2] is the sign of the intercept obtained from a linear plot Of A VS Vc,, (I, 2). The CD bond lengths, rco, were assumed to be equal to the CH bond lengths, rCH, calculated from the empirical linear relation rCH=1.1274-2.749~
10e4Jc~,
[41 which was obtained by fitting CH bond lengths of simple unsubstituted hydrocarbons (from microwave data) to experimental (indirect) coupling constants (JCH). This linear relationship is analogous to the one previously obtained by Muller and Pritchard for substituted benzenes (7). The uncertainty in CH bond length by this method is ca. 0.005 A, which is within the estimated error of the experimental . . determmatrons of Ton. Our estimates of r cn are expected to have no greater uncertainty. Calculated and experimental values of rcu for several hydrocarbons are presented in Table 1. The derived Qo values are presented in Table 2. The Qb value, 213.6* 2.5 kHz, for the vinyl CD bond is in good agreement with other values obtained for CD bonds in sp2-hybridized systems, e.g.,. for benzene, QD = 207 *2 kHz (3); pyridine, Q,(2) = 206 kHz, Qb(3) = 211 kHz, QD(4) = 196 kHz (8); and s-triazine, Qb = TABLE
1
CH BONDLENGTHSOFHYDROCARBONSCALCULATEDFROMEMPIRICAL RELATION[~] Hydrocarbon
JCH WY’
Ethane Ethylene Acetylene Benzene Cyclopentane Cyclopropane u J. B. Stothers, York, 1972. b L. E. Sutton Chemical Society,
kkdcalc)
125.0 156.2 248.7 159 128 161 “Carbon-13
(A)
1.093 1.084 1.059 1.084 1.092 1.083 NMR
1.093 1.086 1.059 1.084 1.09 1.08
Spectroscopy,”
(Ed.), “Interatomic Distances,” London, 1958, 1965.
Academic Spec.
Publs.
Press, 11,
18,
New The
DEUTERON
QUADRUPOLE
COUPLING TABLE
NMR
AND
MOLECULAR
PARAMETERS
IN
Vinyl
Qo &Hz)
213.6zk2.5 24.1 1.084
JCD (Hz) TCD (A)
Tl (set)
at 302
a Calculated
K from
1.56 JC-
181
2 FOR ISOMEKIC Deuteron
Parameter
CYCLOHEXENES
CYCLOHEXENES
position
Ally1
179.9* 2.9 19.2” 1.093
Homoallyl
178.8k3.0 19.2” 1.093
1.80
in cyclohexane.
208 kHz (9). The result is not in good agreement with the QD value (175 kHz) obtained for ethylene (10); this discrepancy is currently inexplicable. The ally1 and homoallyl deuterons, which are bonded to sp3-hybridized carbon, have QD values (179.9h2.9 and 178.8* 3.0 kHz, respectively) which differ somewhat from recent QD determinations of simple monosubstituted methyl derivatives, e.g., CDHZCIH, QD=163*3 kHz (1); CDHZCN, Qn= 156*3 kHz (I); and CDHZI, Qb = 163 f 3 kHz (2). They are, however, in better agreement with the value (191.48 f 0.77 kHz) obtained for monodeuteromethane (II). The lower values for the substituted derivatives suggest that an electronegative substituent may lower Qn whenever the deuteron is bonded to the carbon bearing the substituent. This conclusion is consistent with experimental results and theoretical calculations on monodeuteromethane, perdeuteromethyl fluoride, and deuterofluoroform (12). Equation [l] and the Qn and TI values were employed to calculate correlation times (7,) for the vinyl and ally1 deuterons. The ratio r,(allyl)/r,(vinyl) = 1.22 f 0.04 demands anisotropic reorientation for cyclohexene. Bauer et al. (13), in studies on aromatic compounds, have shown that in-plane reorientation (about the minor axis of the oblate ellipsoidal model) which displaces little solvent is faster than out-of-plane reorientations (about major axes of the ellipsoidal model) which displace larger volumes of solvent. The shape of cyclohexene (in any chair conformation) is similar to that of benzene; it is therefore reasonable to assume that the “out-of-plane” reorientations of cyclohexene, which displace comparable amounts of solvent, occur at comparable rates. Therefore, an ellipsoidal rotational diffusion model for the molecular reorientation (D, # D, = D,, where D, is the rotational diffusion coefficient for reorientation perpendicular to the pseudoplane and D, and D, are the rotational diffusion coefficients for reorientation out-of-plane) is reasonable. Using this model and diffusion axes assumed to be coextensive with the inertial axes for the energy-minimized cyclohexene geometry (calculated with the program STRAIN (Id)), theoretical correlation times were calculated from Woessner’s formula (15) for rigid, anisotropically reorienting molecules. If the theoretical rc for the ally1 CD bond is the average value calculated for the two nonequivalent orientations of this bond (pseudoaxial and pseudoequatorial), the theoretical ratio (rJallyl)/r,(vinyl)) can be brought into agreement with the experimental ratio with D,/DX = 1.9kO.2. This result is consistent with
182
WOOTEN
ET
AL.
results obtained for rigid planar molecules such as benzene (13, 16), pyridine (8), and s-triazine (9), for which it is observed that in-plane reorientation is more rapid than out-of plane reorientation. These calculations neglect internal reorientation about the bond axis connecting the ally1 and vinyl carbon atoms. This reorientation proceeds simultaneously with the internal reorientation about the axis connecting the ally1 and homoallyl carbon atoms, i.e., with ring inversion. Inclusion of contributions from internal reorientation would result in an even higher ratio DJD,, still consistent with conclusions regarding more rigid planar molecules (8,9, 13, 16). Results of earlier work on Internal reorientation (I 7) suggest that the rotational barrier between the two sp3-hybridized carbons (ally1 and homoallyl) is such that the internal reorientation contributions to relaxation are small compared to those resulting froin the overall reorientation of the molecule. Therefore, neglect of internal reorientation is assumed reasonable. The relaxation time for the homoallylic deuteron could not be measured accurately in the isomeric mixture of cylohexenes because of the low concentration of [4-13C, 4-‘Hlcyclohexene. However, the observed inversion times of the ally1 and homoallyl deuterons are approximately the same, indicating essentially equal T1 values. This result is consistent with the rotational diffusion model employed to calculate reorientational correlation times from Woessner’s theory (15). ACKNOWLEDGMENT
We express our gratitude to the National Science Foundation 07808) for support of this work.
(Grant CHE77-
REFERENCES 1.
J.B.WOOTEN,
A.L.BEYERLEIN,J.JACOBUS,
AND G.B.SAVITSKY,
J. Chem.Phys.65,2476
(1976).
2. J.B. WOOTEN,J.JACOBUS,G.B.SAVITSKY,
AND A.L.BEYERLEIN,
J. Chem.Phys.66,4226
(1977).
3. J.B. WOOTEN,G.B.SAVITSKY,
A. L.BEYERLEIN,
AND J.Jacosus,J.
Magn.
Reson.29,35
(1978).
4. 5. 8. 7. 8. 9. 10.
R.J.SPEER,M.L.HUMPHRIES,AND A.ROBERTS, J. Am. Chem.Soc.74,2443 (1952). H.WALDMANNANDF.PETRU, Chem.Ber. 83,287 (1950). P. DIEHL AND C. L. KHETRAPAL, NMR Basic Principles and Progress 1, 1 (1969). N.MULLERANDD.E.PRITCHARD,J. Chem.Phys. 31,768(1959). J.P. KINTZINGER AND J.M.LEHN, Mol.Phys.22,273 (1971). J.P. KINTZINGER AND J.M.LEHN, Mol.Phys.27,491 (1974). J.KOWALEWSKI,T.LINDBLOM,R.VESTIN,ANDT.DRAKENBERG, MoLPhys. 31,1669(1976). 11. S.C. WOFSY,J.S.MUENTER,ANDW.KLEMPERER, J. Chem.Phys.53,4005 (1970). 12. R. DITCHFIELD, in “Critical Evaluation of Chemical and Physical Structural Information" (D. R. Lide,Jr. and M. A. Paul, Ed.), pp. 577-578, National Academy of Sciences, Washington, D.C., 1974.
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