1758
The Journal of Physical Chemistry, Vol, 83, No. 13, 7979
D. W . Larsen and
F. E. Stary
Molecular Motion in Enantiomers and Racemic Compounds. Mandelic Acid, Dimethyl Tartrate, and Menthol David W. Larsen" Department of Chemistry, University of Missouri-St.
Louis, St. Louis, Missouri 63 12 1
and Frank E. Stary Department of Chemistry, Maryville College, St. Louis, Missouri 63 14 1 (Received April 13, 1978; Revised Manuscript Received November 27, 1978)
A pulsed NMR study of three optically active organic compounds is reported. Relaxation times, T1 and TID, and second moments were measured as a function of temperature from -95 K to the melting point. The solids were studied as pure enantiomers and as racemic compounds. Mandelic acid (I) exhibited 180" phenyl flips, characterized by EA = 15 kcal/mol (Id) and 8 kcal/mol (Idl). Dimethyl tartrate (11) exhibited methyl reorientation exp(2.0 x 103/RT) s for both I11 and IIdl. Small differences between 111 characterized by T C = (8.5 x and IIdl TIDvalues were observed near the methyl reorientation T1 minimum. In addition, IIdl exhibited a second unassigned process with E A = 7 kcal/mol, just below the melting point. A second process also occurs in III, but at a slower rate than that of IIdl. Menthol (111) exhibited methyl reorientation characterized by T~ = (1.8 X exp(2.3 X 103/RT) s for both IIIl and IIIdl. Introduction The characterization of organic solids consisting of pairs of optical isomers has been studied1 by means of the phase I I 1 rule and by use of binary phase diagrams. For cases in H-C-OH O H OH which racemization is absent, the variety of observed IC 0 2 H I1 binary phase diagrams can be classified2 by three basic types: mixtures, racemic compounds, and solid solutions. 1 A mixture consists of pure d and pure 1 crystals and it exhibits a eutectic a t the racemic composition. For a C H 3 \ C / CI H 3 racemic compound, the d-l pairwise interaction is presumably dominant, whereas, for a solid solution, d-d, 1-1, and d-1 interactions are all comparable. It is of interest to consider molecular motion in pure solid enantiomers and in the corresponding racemic solid CH3 as determined from pulsed NMR relaxation measureI11 ments. If a racemic mixture is formed, there should be recrystallization of commercially available compounds from only very minor differences in molecular motion between aqueous solution. Observed melting points were 131 "C the enantiomer and the racemic mixture; these small (d enantiomer) and 118 "C (racemate). Dimethyl tartrate differences are probably not detectable in NMR mea(11) samples were prepared by sublimation of commercially surements. If a solid solution is formed, one expects available compounds. Observed melting points were 48 substantial differences in molecular motion between the "C (1 enantiomer) and 90 "C (racemate). Menthol (111) enantiomer and the racemic solid solution. These have been observed experimentally in the case of ~ a m p h o r . ~ , ~ samples were prepared from commercially available compounds without further purification. Observed melting The pure enantiomer exhibits relaxation data that are points were 42 "C ( 1 enantiomer) and 33 "C (racemate). interpretable by well-established t h e ~ r y . ~The - ~ solid Polycrystalline samples were prepared and placed into solution exhibits relaxation data for the methyl reorienglass tubes for study. tation that are attributable to a distribution of correlation NMR Measurements. Proton NMR measurements were times,8 which presumably result from "nonuniform enmade using a Polaron (Watford, England) high power (2.5 vironments seen by the various methyl units". These latter kW) pulsed NMR spectrometer operating a t 60 MHz. data are not interpretable by the same well-established Values of the spin-lattice (TI) and the dipolar (TID)retheory. In the case of formation of a racemic compound, laxation timessJO were measured as described previousone expects substantial differences between relaxation data ly.l1-l3 Values of the second moment (M,) of the NMR for pure enantiomers and corresponding racemates. In line were also measured, as described previ~usly,ll-~~ from addition the data should be interpretable by use of known analysis of the Bloch decay, which was found to be theory for both solids. Gaussian within experimental uncertainty for all polyIt is thus of interest to determine the extent to which crystalline samples. The samples were studied over the differences in molecular motion between enantiomer and temperature range 95 K to the melting point of the sample. racemic compound can be observed by use of pulsed NMR All NMR parameters were found to be reversible with relaxation data. We have chosen three systems, dimethyl respect to temperature change; no effects of annealing or tartrate, mandelic acid, and menthol, for study. These hysteresis could be detected once thermal equilibrium was substances all form racemic compounds with large difestablished in the sample. ferences between melting points of the enantiomer and Phase Diagrams. The phase diagram for I has been racemate. reported.14J5 Phase diagrams for I1 and 111 were deterExperimental Section mined from melting point and DTA data. I1 exhibits a "eutectic" at approximately 5% d1:95% I , and I11 exhibits Samples. Mandelic acid (I) samples were prepared by 0022-3654/79/2083-1758$01.00/00 1979 American Chemical Society
The Journal of Physical Chemistry, Vol. 83, No. 13, 1979
Molecular Motion in Enantiomers and Racemic Compounds
I
I
I
I
I
I
10
9
8
7
6
5
: I
I
4
3
0
TABLE I: Summary of Parameters for Motions compd Id
2
Y
2-
1n
W u
Lo
5 +
0-
z
E
b-
3
E
-1-
” s
-2 -
Id1 111, IIdl IIdl 1111, IIIdl
EA 9
kcal/mol
15
ro,s
GZ
>3a
-10-15
(GI)
8 2.0 7 2.3
M , (mod),
motion Ph flip
8.5 X 10‘l4
3a 4.0b
Ph flip Me reorient
lo-’*
5.5c
Me reorient
1.8 X
a Obtained directly from Figure 3. Obtained by use Obtained by use of eq 2, of eq 2, as shown in Figure 4. as shown in Figure 5 .
of I ( I d ) are presented in Figure 1, and data for the dl racemate of I ( I d l ) are presented in Figure 2. Second moment data are presented in Figure 3. These data indicate that the molecular motion exhibited by Id is quite different from that exhibited by Idl. In Figure 1, T1 appears to be independent of temperature, whereas T1D exhibits the low temperature arm of a relaxation minimum for 103/T< 4.5. From the gradient of TID,we calculate EA = 15 kcal/mol for the process. For 103/T > 4.5, TID may be controlled by a second, much lower activation barrier process.16 Second moment data for Id in Figure 3 indicate that there is a line width transition above 280 K. This transition is associated with the 15 kcal/mol process in Figure 1. The transition results in a decrease of 1 3 G2in M 2 from 8 G2to 5 5 G2. In Figure 2, Tl for Idl exhibits the low temperature arm of a relaxation minimum for 103/T< 6. From the gradient, we estimate EA = 7.2 kcal/mol for the process. For 103/T > 6, T1 appears to be independent of temperature. Ti, exhibits a well-defined minimum centered at 103/T= 5.6. From the low temperature gradient, we estimate EA= 8.0 kcal/mol for the process. Both Tl and TIDminima in Figure 2 may be attributed to the same motion, and the line width transition for Id1 in Figure 3 between 160 and 260 K may also be attributed to this motion. It can be seen that the line width transition results in a decrease in M2 of about 3 G2 for Idl. If one assumes an Arrhenius expression for the correlation times to fit the experimental data, values of ro may be estimated17for the two systems:
-
-3 -
-4
300
Flgure 3. Second moments vs. temperature for d - and dl-mandelic acid. Solid lines are drawn arbitrarily through the data points.
Flgure 1. Relaxation times vs. reciprocal temperature for d-mandelic acid. Solid lines are drawn arbitrarily through the data points.
w
200 TEMPERATURE (K)
10~1~
TI
100
1759
10
9
8
7
6
5
4
3
2
10~1~ Flgure 2. Relaxation times vs. reciprocal temperature for dl-mandelic acid. Solid lines are drawn arbitrarily through the data points.
a “eutectic” at approximately 50% dl:50% 1. All three systems exhibit phase diagrams characteristic of d l compound formation. Experimental Results Mandelic Acid. Relaxation data for the d enantiomer
7,
=
To
exP(EA/RT)
(1)
The experimental parameters are shown in Table I . Dimethyl Tartrate. Relaxation data for the 1 enantiomer (111) and the dl racemate (IIdl) are presented in Figure 4. It can be seen that T1 data are identical within experimental error for the two systems, except for lo3/T = 3-3.5. The T1 minimum due to molecular motion may be fitted11J8 by use of eq 1 and
1760
The Journal of Physical Chemistry, Vol. 83, No. 13, 1979
D. W. Larsen and F. E. Stary L
1
P
h
0
Y V
Y W
E .a-
+ 5 -1
-7 \
I
s
,.#’
4
u CL W 0
-1
,,G‘ -2
0‘ /.
\
&.-,’/ d /’/
/ /’ /
/
P ,’
-.-’ -0-
TID
-3
a”,$
,I/’
0
dl
0 0
1
9
dl
on
1
-4 111C
1110
0 .
8
7
6
5
4
3
10~1~ Figure 4. Relaxation times vs. reciprocal temperature for I- and &dimethyl tartrate. Solid line is calculated by use of eq 2. Dashed lines are drawn arbitrarily through the data points. r
where y is the gyromagnetic ratio and MZmdis the portion of M2 modulated by the motion. The calculated line is shown in Figure 4 and parameters used in the calculation are shown in Table I. It can be seen that the fit is satisfactory. The motion is undoubtedly random reorientation of the methyl groups about their C3axes. It can be seen in Figure 4 that TID data for 111 and IIdl show slight differences at low temperature (lo3/ T > 9) and show larger differences at high temperature (103/T< 5). The T1D difference at low temperature might be due to an additional relaxation process for IIdl; however, no effects due to a second process can be seen in Tl or in the M2data. The M2 data for 111 and IIdl are constant within experimental error over the entire temperature range 95-300 K. Furthermore, the M2value is the same (7.0 G2) for both I11 and IIdl. These observations suggest that an additional low temperature relaxation process for IIdl is not the cause of the difference in low temperature T1D data. Alternately, the difference could be due to a slightly different modellg for the motion in the two compounds. The behavior of TI, for 111and IIdl at high temperature is attributable to the onset of a second motional process in both compounds. The decrease in T I Dwith increasing temperature corresponds to a portion of the low temperature arm of a relaxation minimum. The motion is more rapid for IIdl than for IIl, and is characterized by an activation energy of -7 kcal/mol for IIdl. The parameters are summarized in Table I. The slight decrease in Tl with increasing temperature for 103/T< 3.5 may also be attributed to this second motion. Menthol. Relaxation data for the 1 enantiomer (IIIl) and the db racemate (IIIdl) are presented in Figure 5 , and M2 data are presented in Figure 6. It can be seen in Figures 5 and 6 that there is no difference beyond experimental
9
3
7
6
5
4
3
10~1~ Figure 5. Relaxation times vs. reciprocal temperature for I- and &menthol. Solid line is calculated by use of eq 2. Dashed lines are drawn arbitrarily through the data points.
uncertainty in values for IIIl and for IIIdl except that both Tl and T ~ values D are approximately twice as long for IIIl as for IIIdl a t room temperature (103/T 3.4). This small difference may be due to contribution from a second motion, but such a small difference is difficult to interpret. Tl exhibits a well-defined relaxation minimum which may be fitted by eq 1 and 2 as shown in Figure 5. The behavior of TID indicates that it is also controlled by the same motion, which is undoubtedly methyl reorientation. A portion of the line width transition associated with methyl reorientation can be seen in Figure 6. The parameters associated with this motion are shown in Table I.
-
Discussion The assignment of motions can be assisted by analysis of second moment data. One first calculates a rigid lattice second moment value from the Van Vleck equationz6(eq 3) in which n is the number of protons in the sample, rij (3) is the separation between protons i and j in A, and the sum is taken over all proton pairs ij in the sample. Values of rijare obtained from crystallographic data. The calculated MZcrl) values are then corrected for molecular motion by use of reduction factors,17 and finally calculated and observed M2values are compared. The crystal structure for Idl has been reported,27and, from it, we calculatez8M2intra= 3.4 G2 and Mzinkr = 6 f 2 G2, which results in M2(rl)= 9.4 f 2 G2. This agrees within the uncertainty with the low temperature M2 value for Idl, and thus the structure may be considered to be rigid below 140 K. Since the low temperature plateaus in Figure 3 are identical for both Id and Idl, Id is probably rigid below -260 K. The transition lowers M2 by -3 Gz for both Id1 and Id, and we now attempt to assign the motion. The crystal structure for Idl indicates that each enantiomer is paired with its opposite enantiomer by two hydrogen bonds, with a two-dimensional planar structure
Molecular Motion in Enantiomers and Racemic Compounds i
i
01
I
Od' "
100
200
300
The Journal of Physical Chemistty, Vol. 83, No. 13, 1979
1761
tected for 111. In addition, for 111, since the methyl reorientation minimum can be fitted by a single expression of the type shown by eq 2, there is thus no detectable difference among the three methyl groups in the menthol molecule. It is surprising that the isopropyl methyls are indistinguishable from the ring methyl. For 11, slow motions appear to be observable just below the melting point, with a substantial difference between I11 and IIdl. Finally, there appears to be no correlation between melting point and degree of molecular motion. For mandelic acid, Id1 melts below Id, and Id1 exhibits a greater degree of molecular motion (phenyl flips). For dimethyl tartrate, I11 melts below IIdl, yet IIdl exhibits a greater degree of molecular motion. For menthol, IIIdl melts below 1111,yet there is little or no difference in the molecular motion.
TEMPERATURE (K)
Flgure 6, Second moments vs. temperature for I- and dl-menthol. A solid line is drawn arbitrarily through the data points.
built up by two additional hydrogen bonds for each enantiomer. The phenyl groups are perpendicular to the planes, with phenyl groups stacked alternately, one from each plane. This suggests that a likely motion is one involving 180' flips of the phenyl groups. In addition, inspection of the contributions to the second moment indicates that almost the entire M2 arises from contributions from phenyl protons. The third factor in favor of phenyl motion is the relatively large observed activation barrier, 8 kcal/mol. If one assumes random 180" flips of the phenyls, is reduced to 2.3 G2 and we estimate MPinter is reduced to 3 G2,which results in M2(Ph flip) = 5.3 f 2 G2. This is in agreement with the observed M 2 plateau in Figure 3 for Id1 above -250 K. The crystal structure for Id has not been published to our knowledge. However, it is clear that the pure enantiomer cannot form the same hydrogen-bonded structure as is observed for Idl, in which, for a hydrogen-bonded pair, one phenyl lies above the plane and the other lies below. The NMR results suggest that the motion in Id is also 180' flips of phenyl groups, but with a much larger activation barrier. Presumably, the relatively open structure for Idl, which allows for facile phenyl flips, is not found in Id. The barriers for phenyl flips can be compared with the observed barrier for 180" flips which is observed25in solid benzene just below the melting point. The observed barrier is 16 kcal/mol, which is about the same as that for Id. The second motion observed for Id, with E A I1kcal/ mol, has no M2 transition associated with it, and thus its assignment cannot be tested by the above procedure. Also, in the absence of a crystallographic structure for this particular molecule, it is pointless to postulate a motion. The observed barriers to methyl reorientation in I1 and I11 are what one might reasonably expect based on similar stru~tures.l'-~~ That no difference in E A between 1 and dl forms in I1 and I11 should be observed is not surprising since the barriers are not particularly sensitive to subtle structural changes. The motion with EA = 7 kcal/mol in IIdl is difficult to assign for the same reason discussed above, the absence of an M2 transition. However, in this case, a reorientation about the long axis of the tartrate structure is a reasonable candidate for the motion.29 In summary, we conclude that pure enantiomers appear to exhibit different molecular motions than those exhibited by the racemic compounds. Certain structural features, as in I, can give rise to very large differences in motion between pure enantiomer and racemic compound. In the case of methyl reorientation, smaller but definite differences exist for 11, and no observable difference was de-
Acknowledgment. We thank Dr. Chickos and Dr. Garin for supplying samples used in the study and for helpful discussions. We also thank McDonnell Douglas Astronautics Co. for the use of a storage oscilloscope and for running the DTA analyses.
References and Notes H. W. 8. Roozeboom, Z.Phys. Chem., 28, 484 (1899). R. M. Secor, Chem. Rev., 63, 297 (1963). J. E. Anderson and W. P. Siichter, J. Chem. Phys., 41, 1922 (1964). G. P. Jones, D. C. Douglas, and W. D. McCaii, Rev. Sci. Instrum., 36, 1460 (1965). (5) N. Bioembergen, E. M. Purceii, and R. V. Pound, Phys. Rev., 73, 679 (1948). (6) R. Kubo and K. Tomita, J . Phys. SOC.Jpn., 9, 888 (1954). (7) E. 0. Stejskai, D. W. Woessner, T. C. Farrar, and H. S. Gutowsky, J . Chem. Phys., 31, 55 (1959). (8) T. M. Connor, Trans. Faraday SOC., 60, 1574 (1964). (9) T. C. Farrar and E. D. Becker, "Pulse and Fourier Transform NMR", Academic Press, New York, 1971 IO) J. Jeener and P. Broekaert, Phys. Rev., 157, 232 (1967). 11) D. W. Larsen and J. Y. Corey, J. Am. Chem. Soc., 99, 1740 (1977). 12) D. W. Larsen and T. A. Smentkowski, J. &g. Reson., 28, 171 (1977). 13) D. W. Larsen, J. Y. Corey, T. A. Smentkowski, and F. E. Stary, J . Organornet. Chem., 135, 161 (1977). 14) Y. Fujita, Y. Baba, A. Kagemoto, and R. Fujishiro, Nippon Kagaku Kaishi, 1563 (1972). 15) C. Fouquey and M. Leciercq, Tetrahedron, 26, 5637 (1970). 16) The fact that T , is independent of temperature indicates that spin-lattice relaxation for I d may be controlled by paramagnetic impurities in the solid. This suggests that, at iow temperature, TI, wiii also approach temperature independence due to paramagnetic impurities. Thus, assuming that there is a low temperature motion contributing to T,I one obtains from the gradient, E, N 1 kcaVmoi, but with a large uncertainty, for the motion. (17) The approach used to interpret the experimental data is presented in ref 11 and 12. (18) Strictly speaking, eq 2 is applicable only to an isotropic motion; however, its use facilitates the obtaining of activation parameters T~ and E,. Values of M, obtained by use of eq 2 are in general not in agreement with those obtained from direct measurement of M, transitions. (19) The behavior of T,, in the high temperature limit ( ~
