Nuclear
Spin
Relaxation in Methyl Groups
1783
Nuclear Spin Relaxation in Methyl Groups Governed by Three- and Sixfold Barriers Kenneth H. Ladner, Don K. Dailing, and David M. Grant* Department of Chemistry, University of Utah, Salt Lake City, Utah 84 1 12 (Received February 26, 1976) Publication costs assisted by the National Institutes of Health
The carbon-13 spin-lattice times, 2’1, and 13C-lH nuclear Overhauser enhancements were measured at 36 OC in a series of methyl-substituted aromatic compounds. The C-H dipolar relaxation time, T ~ Dwas , separated from the overall relaxation time, and then used to estimate the magnitude of the methyl rotational barriers. The results can be described by hindered rotation of the methyl group with the jumping rates and activation energies dependent upon the group arrangement.
Introduction Internal motion of methyl groups attached to an aromatic ring system has been investigated by a number of workers using a variety of techniques. While the majority of investigations relating relaxation times to systems dynamics have been carried out via proton magnetic resonance, several recent studies of methyl group rotation have focused on the determination of carbon-13 spin-lattice times ( Tl).1-4The theoretical treatment of the behavior of methyl groups undergoing hindered rotation with respect to molecules in a liquid has drawn keen interest in past investigations since the group forms an isolated three spin (-12CH3) or four spin system (-13CH3) which is quite amenable to i n t e r p r e t a t i ~ n . ~ - ~ Theory The principle mode of spin-lattice relaxation in most molecular systems is by spin-spin dipolar interactions. Simple theory predicts that the intrinsic dipolar relaxation rate, RlD(I,S), for two spins 1 and s is given bylo
where LY = 3/2 for like spins and a = 1for unlike spinsll and, of course, extreme narrowing is assumed. y~ and ys are the gyromagnetic ratios of nuclei I and S, respectively, rIs in the I-S distance, and Teff in the effective correlation time. The total dipolar relaxation of spin I due to coupling with all other spins, S, is given by N
RlD(1) =
S#I
(2)
RlD(I,S)
Where R~D(I,S) is given by eq 1and N is the number of spins. In this work it is assumed that all pair wise interactions are additive and that cross correlation effects may be neglected.12 In the case of a 13C nucleus relaxed by a lH, eq 1reduces to R~D(C,H) I 1 / T 1= ~ (2.25 X 1O1O se2)reff
(3) where a C-H distance of 1.08 A is assumed. If the internal rotation of a methyl group takes place by rotational diffusion about the symmetry axis of the methyl group, the effective correlation time is related to the rotational diffusion constant for internal rotation by13-15 1
=-
(-A +
)
B + (4) 4 6D 6D +Dint 6D +4Dint If the bonding at the methyl carbon is assumed to be tetrahedral then Teff
-
A = (3 cos2 0 1)2= 36/81 B = 12 sin2 8 cos2 0 = 96/81 C = 3 sin4 0 = 192181 where 0 is the angle between the methyl group reorientation axis and the methyl C-H vector. Equation 4 assumes that the methyl group is fixed to a hydrodynamic sphere whose motion is characterized by an overall diffusion constant D. The internal reorientation axis for Dint lies along the symmetry axis. In the model described by eq 4 it is also assumed that internal motion and overall motion are stochastically independent. In general Teff is a quite complicated function of the molecular geometry and intrinsic molecular dynamics. In this study, the dynamic implications of the dipolar relaxation in methyl groups will be probed assuming the overall diffusion to be isotropic. From Figure 1it is easily seen that information about the internal motion obtained from the spin-spin dipolar mechanism can only be obtained in the region u = 1to approximately u = 20 where u = (D Dint)/D. Within this region the dipolar relaxation rate can be used as a decreasingly sensitive probe to study the effects of steric interactions on the rotation of methyl groups. When the methyl group rotation becomes faster than the overall motion the effect of this motion averages out and no reliable information can be obtained in the value of u. This is a direct consequence of the fact that, in the extreme narrowing limit, RIDis most sensitive to the slowest motion governing reorientation of the interacting spins, except as the very rapid motion results in a static geometrical attenuation of the interaction. It should be noted, however, that if u becomes inordinately large (u 2 20) cross correlation effects can become important and it is then possible to extract “motional” information from multispin multiplet relaxation effects.12J6 An alternate first-order approximation of methyl group motion under hindered conditions starts with the hydrogen nuclei in three orientations, 120’ apart.5~15The methyl group is assumed to undergo instantaneous random jumps among these three orientations. The effective correlation time assuming this motional model is given by
+
(5) where D, 0, A, B, and C are as defined in eq 4, v is the internal methyl jump rate in s-l, and n = 3 for this threefold barrier model. In the case of a methyl group subject to a sixfold barrier The Journal of Physical Chemistry, Vol. 80, No. 16, IS76
K. H. Ladner, D. K. Dalling, and D. M. Grant
solubility of 7,12-dimethylbenz[a]anthracenethe signal-tonoise, SN, obtained was in the range 12-301. The SN obtained for the remaining compounds was in excess of 160:l.
I
2
,
8
,
5 a
10
20
,
I
,
so
Flgure 1. The dipolar rate, RID(cr) for a C-H interaction normalized by the value of u = 1 as a function of u = (D4- Qnt)/Dwhere 1 5 u Ia. When the internal rotation is much greater than the overall motion, u >> 1, and when the methyl group is locked with respect to the overall motion u = 1.
the methyl hydrogens assume six orientations, 60" apart and therefore n = 6. It is assumed that the overall rotation of the aromatic ring system is characterized by small step diffusion. Wilbur and Jonas,17 using the Chi test initially employed by Wallach and Huntress18 and applied in several c a ~ e s , l found ~ - ~ ~that small step diffusion was a reasonable model for toluene-d8 at low temperature and at higher pressure. Small deviations (factor of 2 or less) from this assumption because of the larger molecular weights of compounds used in this study should be of little consequence in the following section. The Chi test may also be used to estimate the validity of the 120° jump as a model for internal rotation. If the methyl group reorientation is impeded by a relatively high barrier, the time 1/v between jumps of 120° should be long compared to the time it takes a free rotor to reorientate through l2Oo,l5and
x=
/ [ ( 2 ~ / 3 ) ( I / k T ) l / ~>> ] 1
(6)
It has been shown that if x > 5 then the molecule is in the 120" jump regime. Upon substitution of the moment of inertia of a methyl group about its C3 axis ( I c H =~ 5.35 X g cm2) into eq 6 one finds that the jump rate must be smaller than 8.6 x 101ls-l in order to satisfy the Chi test. I t is further assumed that the effects of multispin dipolar cross correlation on the NOE enhancement factor are negligible. Werbelow and Grant24and B ~ c h n e have r ~ ~shown that cross correlation effects are relatively unimportant for methyl relaxation where Dint/D < 20. It is expected that such conditions are valid in the present studies. Experimental Section
All data were obtained on a Varian XL-100-15-FT NMR spectrometer a t a temperature of 36 f 1"C. Decoupling was accomplished using a specially constructed decoupler employing a Hewlett-Packard 1505 A frequency synthesizer and an EN1 Model 310 power amplifier.. 1-Methylnaphthalene, 1,4-dimethylnaphthalene,and 7,12-dimethylbenz[a]anthracenewere obtained from Aldrich Chemical Co. 1,8-Dimethylnaphthalene was prepared using the method of Vaughan et al.26Samples were degassed by four freeze-pumpthaw cycles on a vaccum line. Because of the low The Journal of Physical Chemistry, Vol. 80, No. IS, 1976
Results and Discussion The relaxation rates and nuclear Overhauser enhancements (7)of the ring and methyl carbons for this series of compounds are given in Table I. Using these values the 71' data are separated into T ~ dipolar D times and an effective time, Tlo, for all other relaxation p r o c e ~ s e s . ~The ~ - ~large ~ 7 values obtained for the various carbons demonstrates that the relaxation process is dipolar dominated. Values of D, Dint,and v calculated using eq 1and 2 are given in Table 11. 1-Methylnaphthalene (1-MN) and 1,4-dimethylnaphthalene (1,4-DMN) have similar parameters inasmuch as the methyl groups experience the same steric hindrance to rotation with respect to the peri proton of the ring system resulting in a threefold barrier. When both the C1 and CSpositions contain methyl groups (1,8-dimethylnaphthalene), it is reasonable to expect the increase found in the barrier to rotation because of the clo-se proximity of the two methyl groups. Activation energies for internal rotation have been measured for 1-MN34-36and 1,8-DMN34-37by proton spinlattice relaxation methods and these are also given in Table I1 confirming the general magnitudes found in this study. Table I1 also gives the methyl group jump and diffusion rates, and these are approximately the same for both 1-MN and 1,4-DMN. The methyl interaction with a peri proton prevents rapid rotation of the methyl group resulting in a reasonably large activation energy for 1-MN (2.4 kcal mol-l) as compared to, for example, the methyl group in toluene (0.014 kcal m ~ l - l ) In . ~the ~ case of 1,8-DMN the steric interactions are further increased resulting in a larger barrier to rotation and a decrease in the jump and diffusion rates. The jump rate, v, has been related to an activation energy for methyl group internal rotation using the simple relation~hip.l-~
where vo is the jump rate for zero barrier. A convenient measure of YO is the rate of rotation of a methyl fragment in the gas phase ( l z T I 1 ~ ~ Substitution )~'~. of this calculated vo and the values of v from Table I1 allows one to obtain VOfrom eq 7. These calculated activation energies are given in Table 11. For comparative purposes several activation energies for internal rotation obtained from proton spin-lattice relaxation methods are also given. The agreement between the values obtained from proton spin-lattice relaxation and those calculated from C-H dipolar relaxation is quite good when one considers the coarse approximations used in making the calculations and in modeling the system. Thus, a close relationship between activation energies for internal methyl group rotation and 13C spin-lattice relaxation rates is exhibited. Since the intramolecular dipolar relaxation mechanism is a sensitive probe to internal motion in the simple aromatic systems, the motional behavior of the two methyl groups in 7,12-dimethylbenz[a]anthracenewas also investigated. From Figure 2 it can be seen that the 7-methyl and 12-methyl groups experience quite different proton interactions. The 7-methyl group interacts with two peri protons, while the 12-methyl group interacts with a peri proton and the C1 ring proton. Because of low signal-to-noise (as discussed in the Experimental Section) and the expected deviation from overall isotropic diffusional motion of this molecule, a 15%error exists
Nuclear Spin Relaxation in Methyl Groups
1785
TABLE I: Spin-Lattice Relaxation Rates and Nuclear Overhauser Enhancement Factors Compound ~~~~
~
1-Methylnaphthalene 1,4-Dimethylnaphthalene 1,8-Dirnethylnaphthalene 7,12-Dimethylbenz [a]anthracene 7-methyl 12-methyl
0.2 0.4 0.2 0.5
0.2 0.4 0.2 0.5
2.0
1.9 2.0 2.0
0.2 0.3 0.3
2.0 2.0 2.0
0.15
2.0 2.0
0.15
Vdeq), kcal/mol
Vdlit.), kcal/mol
1.4
0.2 0.3
0.3 1.4
TABLE 11: Motional Parameters and Activation Energies for Internal Methyl Rotation Compound 1-Methylnaphthalene 1,4-Dimethylnaphthalene 1,8-Dimethylnaphthalene
H \.
-.
Dint(x 10-10),
5-1
5-1
1.5 0.9 2.0
7,12-Dimethylbenz[a]anthracene 7-methyl 12-methy1
* References 34-36.
D(X 1 0 - 9 ,
-0.8
u ( X 10-'0),
jumps 5-l
18.8 16.4 5.2
27.7
23.5 8.8
-234 -0.40
-441 -0.7
2.1 2.2
2.4a
2.8
3.0b 3.2"
4.4
Reference 37.
I
4.0-
TI D 3.0-
Flgure 2. Structure of 7,12-dimethylbenz[a]anthracene showing the distances of closest approach between the methyl protons and the adjacent ring protons. Only the ring protons pertinent to the discussion are shown.
2.0-
1.0
in the relaxation data. Figure 3 illustrates how these relatively large errors allow one to determine only lower and upper limits on the jump rates for the 7-methyl and 12-methyl groups. Using this approximate method one assigns a lower limit of 4.5 X 10l2jumps s-l to the 7-methyl group and an upper limit of 7.0 X lo9 jumps s-l to the 12-methyl group, as shown in Figure 3. The jump rate of the 7-methyl group is rather large, because of the sixfold symmetry of the two peri proton interactions. A highly sterically hindered group will reorientate rapidly if the unfavorable interactions are comparable for all rotameric conformers as in this sixfold barrier case. The 7methyl group spins rapidly because no rotameric conformer has significantly lower energy.39 Although the 12-methyl group also experiences two sterically unfavorable interactions the jump rate at it's upper limit is only 7.0 X lo9 s-l because now a strong threefold barrier dominates the sixfold term. Using ideal geometry and standard covalent radii to estimate geometrical parameters one calculates that the closest approach of the 7-methyl protons
-
I
TiDT(12-METHYL
I
0 8
I
I
I
I
9
10
It
12
I 13 14
LOG ( X I Figure 3. Dipolar relaxation time of methyl carbon as a function of log x, where x = 3/2u for the 12-methyl group and x = 3v for the 7-methyl group. The statistical range of the relaxation times of the 12-methyl D 6.5 s) are given carbon (TTD= 0.7 s) and the 7-methyl carbon ( T ~ = by the dashed lines.
to the peri protons is 1.4 8.On the other hand, the 12-methyl protons would only be separated from the C1 proton by 0.4 8 at the point of closest approach. Of course, these extremely low estimates cannot be correct and considerable deformation from ideal geometry must be expected. Qualitatively, however, it is this methyl-C1-proton interaction that essentially locks the rotation of the 12-methyl group as compared to the 7methyl group. Physically this suggests that internal reorientation of the 12-methyl group occurs in distinct jumps while The Journal of Physical Chemistry, Vol. 80, No. 16, 1976
1786
C. L. Kwan, M. Carmack, and J. K. Kochi
the 7-methyl group is approaching the rotation rate of a free rotor. This can be seen from Figure 3 and also from the previous discussion of the Chi text. Previous studies40 of the methyl TI'S in the several geometrical isomers of retinal revealed results analogous to those above. Sterically hindered gem- dimethylretinal exhibited the shortest values, while those involved in sixfold rotation barriers had the longest TI'S and methyls involved in threefold barriers were found to have intermediate rates of relaxation. Although only a qualitative analysis was made of the retinal methyl relaxation data, the detailed analysis of the compounds in this work, whose geometrical relationships are similar to those of the retinals, suggests the relevance of the findings in this work to an interpretation of the retinal study.
Acknowledgment. This investigation was supported by Grant No. 5-F32-CA-5131-02awarded by the National Cancer Institute, National Institutes of Health, and also under Grant No. GM08521 and RR057 supported by the National Institutes of Health. Helpful discussions with R. J. Pugmire and L. G. Werbelow are also acknowledged. References and Notes (1)T. D. Alger, D. M. Grant, and R. K. Harris, J. Phys. Chem., 76, 281 (1972). (2)J. R. Lyerla, Jr., and D.M. Grant, J. Phys. Chem., 76,3213 (1972). (3)K. F. Kuhimann and D. M. Grant, J. Chem. Phys., 55, 2998 (1971). (4) C. F. Schmidt, Jr., and S.I. Chan, J. Magn. Reson., 5 , 151 (1971). (5)P. S.Hubbard, J. Chem. Phys., 52,563 (1969). (6)A. Allerhand, J. Am. Chem. SOC.,95,8228 (1973). (7)W. Buchner, J. Magn. Reson., 12,79 (1973). (8)H. Versmold, J. Chem. Phys., 58, 5649 (1973). (9)L. G. Werbelow, J. Am. Chem. SOC.,95,5132 (1973).
(10)I. Solomon, Phys. Rev., 99,559 (1955). (11) A. Abragam, "The Principles of Nuclear Magnetism", University Press, Oxford, 1973,p 297. (12)L. G. Werbelow and D. M. Grant, J. Chem. Phys., 63, 544 (1975). (1 3) D. E. Woessner, J. Chem. Phys., 37, 647 (1962). (14)D.E. Woessner, J. Chem. Phys., 36, 1 (1962). (15)D.E. Woessner and B. S. Snowden, Jr., Adv. Mol. Relaxation Processes. 3, 181 (1972). (16)L. G. Werbelow, private communication. (17)D. J. Wilbur and J. Jonas, J. Chem. Phys., 62,2800 (1975). (18)D. Wallachand W. Huntress, J. Chem. Phys., 50, 1219 (1969). (19)W. M. M. J. Bovee and J. Smidt, Mol. Phys., 28, 1617 (1974). (20)K. T. Gillen and J. H. Noggle, J. Chem. Phys., 53, 801 (1970). (21)D. E. Woessner and B. S.Snowden, Adv. Mol. Relaxation Processes, 3, 181 (1972). (22)R. A. Assink and J. Jonas, J. Chem. Phys., 53, 1710 (1970). (23)W. T. Huntress, Adv. Magn. Reson., 4, l(1970). (24)L. G. Werbelow and D.M. Grant, J. Chem. Phys., 63, 4742 (1975). (25)W. Buchner, J. Magn. Resonance, 12,82 (1973);17,229 (1975). (26)W J. Mitchell, R. D.Topsom, and J. Vaughan, J. Chem. Soc., 2526 (1962). (27)K. F. Kuhlman, D. M. Grant, and R. K. Harris, J. Chem. Phys., 52,3439 (1970). (28)T. D.Alger and D. M. Grant, J. Phys. Chem., 75, 2538 (1971). (29)J. R. Lyerla, Jr., D. M. Grant, and R. K. Harris, J. Phys. Chem., 75, 585 (1971). (30)T. D. Alger, D.M. Grant, and J. R. Lyerla, Jr., J. Phys. Chem., 75,2539 (1971). (31)C. H. Wang, D. M. Grant, and J. R. Lyerla, Jr., J. Chem. Phys., 55, 4674 (1971). (32)J. R. Lyerla, Jr., D.M. Grant, and C. H. Wang, J. Chem. Phys., 55,4676 (1971). (33)T. D.Alger, S.W. Collins, and D.M. Grant, J. Chem. phys., 54,2820 (1971). (34)J. U. von Schutz, H. C. Wolf, and F. Noack, Magn. Reson. Relat. Phenom., Proc. Congr. AMPERE 16th, 1970, 644-647 (1971). (35)J. U. von Schutz and H. C. Wolf, 2.Naturforsch. A, 27(1),42 (1972). (36)J. U. von Schutz, W. Guttler, and H. C. Wolf, Z.Naturforsch.A, 28(1),69 (1973). (37)A. Saika, A. Kawamori, and R. Takagi, J. Magn. Reson., 7, 324 (1972). (38)H. D.Rudolph, A. Jaeschke, and P. wendling, Ber Bunsenges. phys. Chem., 70, 1172A(l968). (39)G. C. Levy, Acc. Chem. Res., 6, 161 (1973). (40)R. S.Becker, S.Berger, D. K. Dalling, D. M. Grant, and R. J. Pugmire, J. Am. Chem. SOC.,96,7006(1974).
Electron Spin Resonance Spectra of the Thiadiazolothiadiazole Radical Anion and Related Sulfur-Nitrogen Heterocycles C. L. Kwan, M. Carmack, and J. K. Kochl" Chemistry Department, lndiana University, Bloomington, lndiana 4740 1 (Received April 7, 1976)
The anion radical of the unique aromatic sulfur-nitrogen heterocycle, thiadiazolothiadiazole (TT), has been prepared by alkali metal reduction in ethereal solvent. The electron spin resonance parameters are compared with those calculated by McLachlan's perturbation method using two models for the sulfur atom, one including participation of the 3d orbitals and the other neglecting it. The 3d model affords good agreement with experimental results, although a similar distribution is obtained from the p orbital model. The same molecular orbital parameters can be used to predict hyperfine splittings in a series of aromatic anion radicals of related thiadiazolo analogues including benzothiadiazole, thiadiazolopyrazine, and thiadiazoloquinoxaline.
Introduction The replacement of the peripheral atoms of naphthalene with heteroatom equivalents consisting of sulfur and nitrogen is represented in thiadiazolothiadiazole.
The Journal of Physical Chemistry, Vol. 80, No. 16, 1976
This highly symmetrical heterocycle is a unique extension of naphthalene and tetraazanaphthalene, effected by replacing [-CH=CH-] groups with[-S-] in order to generate a planar aromatic system with no substituents. The close relationship between thiadiazolothiadiazole and naphthalene is shown by their similar physical properties,l and it raises the question of comparative molecular bonding in this interesting heteroaromatic system.
