INFLUENCE OF INTEERNAL MOTION ON CARBON-13
RELAXATION
argon matrix isotopic v 3 frequencies is in excellent agreement with the 116.8 & 0.5"microwave valueOz0 Hence, reliable angles can be calculated from va matrix frequencies. Clearly, the precision of these crilcula,tions depends upon accurate frequency measurem ent and isotopic arrharmonicities being nearly the same. It is also helpful to have data for both terminal and central atom isotopic substitutions.
Conclusions The vibrational fundamentals of ozone in argon m&rices are in very good agreement with gas-phase values The intense infrared mode v3 is two wave numbers lower in the matrix phase; the bending mode v2 occurs 2--3 cm-l higher. The intense Raman active fundamental va agrees within one wave number with gas-phase values. It i s interesting to note the extraordinary infrared intensity of v3 and weakness of v l
Influence
of'
3213
of ozone and the complete reversal of this intensity relationship in the Raman spectrum. The technique of laser-Raman matrix isolation spectroscopy is useful for obtaining Raman spectra of relatively small amounts of sample molecules. For photolytically unstable molecules such as ozone, the matrix cage apparently retards photodecomposition such that excellent Raman spectra of the trapped molecule can be obtained.
Acknowledgments. The authors gratefully acknowledge financial support for this research by the National Science Foundation under Grant No. GP-28582 and a Governor's Fellowship for R . 6.8., Jr. We acknowledge helpful discussions with Dr. Alfred Arkell on ozone Bynthesis. (20) R.H . Hughes, J. Chem. Phys., 24, 131 (1956)
nternal Motion on the Carbon-13 Relaxation
Times of Methyl Carbons y James R. Lyerla, Jr., and David M. Grant* Department of Chemistry, University of Utah, Salt Lake City, Utah 84118 (Received May 1 , 1978) PuEslication costs assisted by the National Instit Utes of Health
lac-
The carbon-13 spin-lattice relaxation times, T I , and { 'H ] nuclear Overhauser enhancements have been determined at 38' for 14.1 and 23.5 kG fields for various methyl carbons subject to internal reorientational motion. The contributions of the C-H dipolar and spin-rotation mechanisms to T1have been separated from the overall relaxation rate. The influence of methyl internal rotation on the C-H dipolar and spin-rotation relaxation rates has been discussed and C-H dipolar rates have been used to estimate the magnitude of methyl rotational barriers.
Introduction The use of nuclear magnetic relaxation times as a means of investigating molecular dynamics in liquid systems has been well established.lV2 Although the precise details of the microdynamic behavior of the liquid are not readily available from these relaxation data,3 the results do allow semiquantitative evaluation of the molecular motion. While the majority of reports relating relaxation times to a system's dynamics have been carried o u t cia proton magnetic resonance, several recent studies have focused on the determination of carbon-13 spin-lattice relaxation times ( T I ). 4 - 1 2 I n particular, work from this has concentrated on simple molecular systems with the purpose of elucidating the relaxation mechanisms governing 13C
relaxation. By separating the C-H dipolar part from the overall 13C relaxation rate, these workers have (1) N. Bloembergen, E. M. Purcell, and R . V. Pound, Phys. Rev., 73, 679 (1948). (2) J. S. Waugh in "Molecular Relaxation Processes," Academic Press, London, 1966. (3) W. T.Huntress, Jr., 1.Phys. Chem., 73, 103 (1969). (4) K. T. Gillen, M. Schwartz, and J. H . Noggle, Mol. Phys., 20, 899 (1971). (5) D. Doddrell and A. Allerhand, J. Amer. Chem. Hoc., 93, 1558 (1971). (6) H . Jaeckle, U. Haeberlen, and D. Schweitzer, J. Magn. Resonance, 4, 198 (1971). (7) K. F. Kuhlmann, D. M. Grant, and B. K. Harris, J. Chem. Phys., 52, 3439 (1970). (8) T. D. Alger, S. W. Collins, and D. M . Grant, ibid., 54, 2820 (1971).
The Journal of Physical Chemistry, Vol. 76, N o . 28,is73
3214
JAMES R. LYERLA, JR,,AND DAVIDM. GRANT I
Tabhe I: h (14 kG),
XI (23 kG),
see
aec
6.4 f 0.4 17.3 f 0.8 11.5 f 0.8 11.6zk 1 . 1
6.7 f 0.3 17.3 f 1.0 11.5 =k 0.9 12.9 =!= 0.5
Moleculu
(CHa)80 ("CHa)&O '3CHaCC4 ( '3CHa)aCCl WHaCOQCH3~ c&coO'*C~~a a This value of ferent technique.
in agreement with that reported Results taken from ref 12.
~ C is B
VCH
1 . 6 8 f 0.07 0.73 f 0.06a 1.60 f 0.12 1.70 f 0.13
(7
ho,
ma
#ec
1.69f0.10 0.78 f 0.05" 1.62 f 0.09 1.82zk0.15
7.8 f 0.6 45.3 f 3.4 14.3 f 1.4 13.7 f 1.6 5 1 A f 8.0 37.6 =k 4.2
4 2 . 9 3 ~3.1 2 8 . 1 f 2.1 5 9 . l f 6.0 104 f 12.5 2 4 . 6 f 3.7 33.1 f 3 . 7
0.7) by G. LaMar [J.Amer. Chem. Soc., 93, 1040 (1971)] using a dif-
discussed the correlation times obtained in terms of motional features of these liquid systems. 9-12 Herein are reported lBCproton-decoupled spin-lattice relaxation times and nuclear Overhauser enhancements (?\TOE) for the methyl carbons of molecules in which the methyl group is restricted in its internal reorientation. From this information the rotational barriers may be determined. *O-I1
Experimental Section The compounds under study (methyl sulfoxide, acetone, tert-butyl chloride, and methylchloroform) were spectral quality and used without further purification. Samples were degassed using standard freeze-pumpthaw cycles bef0s.e being sealed. TI and NOE values were determined on a Varian AFS-60 spectrometer operating at 14..I kG equipped with noise-modulated proton decoupling. In order to investigate any field dependence of the relaxation rate, TI and NOE values were also determined on a Varian XL-100-15 spectrometer operating a t 23.5 kG and also equipped with noisemodulated proton decoupling. Operating temperature of the AFS-60 probe under the experimental conditions was 38 f 2' and the XL-100-15, equipped with variable-temperature controller, was adjusted to have the same probe temperature. NOE determinations and relaxation measurements made via adiabatic fast passage techniques have been previously d e ~ c r i b e d . ~ - ~
Results Reported in Table I are the
hd,
W H (23 kG)
(14 kG)
lacT1 values and 13C-
treated quantitatively in accordance with the approach of Kuhlmann, Grant, and Harris: i.e.
Tid
The Journal of .Physical Chemistry, Val. 76, No. 28, lQY2
YHTI/~?'c~GH
(2)
where in the extreme narrowing limit yH and y~ are the respective magnetogyric ratios of the proton and carbon. The relaxation times corresponding to the C-H dipolar mechanism is given by Tld, and TI, characterizes the time for all other mechanisms which in the cases studied here appear to be dominated by the spinrotation term. Tld and TI, have been evaluated and are reported in Table I. Also included are the Tld and TI, values for the methyl and methoxy carbons of methyl acetate as determined elsewhere.l2 As both of these carbons are subject to energy barriers to internal motion, they are pertinent to the subsequent discussion.
Discussion A . Dipolar Relaxation. Assuming that intermolecular C-H dipolar interactions are negligible, the value of Tld characterizes the time scale for the C-H intramolecular dipolar interactionb9 Neglect>of the intermolecular contributions is an excellent approximation in considering the relaxation of carbons with directly attached protons owing to the Y C R - ~ distance depen~'~ treatdence of the dipolar ~ o u p l i n g . ~ Formalistic ment of the C-H intramolecular dipolar interaction for a methyl carbon yields
{ 'H ] NOE enhancement factors,O ~ C H ,of the various
methyl carbons. The data represent an average of at least three determinations of each parameter. The close agreement of both parameters at the two different fields indicates negligible contributions from field-dependent mechanisms to the 13C relaxation process. The average values of TI and VCH at the two fields were used in the analysis which follows. While T1 and NOE values individually provide some qualitative information, their combination allows separation of the relaxation mechanisms into the dipole-dipole and all other processes and these separate contributions may then be
=
(3) where
Teff
is an effective correlation time for molecular
(9) J. R. Lyerla, Jr., D. M. Grant, and R. K. Harris, J. Phys. Chem., 75, 585 (1971). (10) K. F. Kublmann and D. M. Grant, J . Chem. Phys., 5 5 , 2998
(1971). (11) T. 76, 281 (12) T. (1971). (13) A.
D. Alger, D. M. Grant, and R. K. Harris, J-, Phys. Chem., (1972). D. Alger, D. M. Grant, and J. R. Lyerla, Jr., ibid., 75, 2539 J. Jones, D. M. Grant, and K . F. Kuhlmann, J . Amer. Chem.
SOC.,91, 5013 (1969).
INFLUBNCIE OF h"ERNAL
MOTIONON
CARBON-13
RELAXATION
reorientation. Wide the Teff parameter is readily calculated once T l d is known, separation of axial reorientation times from Teff requires an assumed model of molecular reorientation in the liquid. The model usually assumed ie that of a sphere undergoing small-step anguula,r d i f f u ~ i o n . ' ~ ,However, ~~ more recent treatments by Woessner10pX7 and 0thers~1'~ have accounted for the motional anistropy of most molecular systems by considering small-step diffusion of a rigid ellipsoid. Furthermore, Woessner' has considered the effects of internal motion upon the TI of a nucleus attached to a molecule of ellipsoidal shape. One model of me thy./ internal reorientation is that of a methyl top undergoing random jumping among its three equivalent p 0 s i t i 0 n s . ~ ~ The ~ ~ lac ~ relaxation rate arining from the C- dipolar interaction for such a methyl carbon attached to a molecule whose symmetry or greater is given in the Woessner construct by is
3215
Table 11: Calculated Values of Methyl Internal Rotational Barriers from 1*C Dipolar Relaxation Rates
Molecule
(CHahSO (CHahCO (CH,)CCh (CHs)sCC1 (CHs)COOCFIs CHICOO(CHs)
R X
D X 10-11,
10-11,
886-1
sec-1
0.350 1.6b 1.3c 1.40 1.4' 1.4'
4.0 29.9 1.2 0.5
49.4 21.0
VO
VO
(eq B),
(lit),e
kod/mol
kcal/mol
2.21 0,92 2.9 3.5 0.67 1I
3.07,'2.87
[email protected] 2.91 4.3h 0.48 1.19'
a Value calculated using microviscosity calculations on density and viscosity data from H. L. Schlafer and W . Schaffernicht, Angew. Chem., 72, 618 (1960). 5 From microviscosity calculations using data from E. Hatscheck, "The Viscosity of Liquids," Van Nostrand, New York, N. Y., 1928, and also from ''0 nmr relaxation results: E. V. Goldammer and €1. G. Hertz, J. Phys. Chem., 74, 3734 (1970). c Values from interpretation of dielectric relaxation results of S. Mallikarjun and N. E. Hill, Trans. Faraday Soc., 61, 1389 (1965). Microviscosity calculations from data of W. J. Jones and 5.T. Bouden, Phil. Mag., 36, 705 (1945). Values represent gas-phase data and uniess otherwise noted derive from W. Gordy and R. L. Cook in "Technique of Organic Chemistry," Vol. IX, A. Weissbmger, Ed., Interscience, New York, N. Y., 1970, p 477. a.Dreialer and G. Dendl, 2. Naturforsch. A , 20, 1431 (1965). 0 J . 0 . Bwalen This is and C. C. Costain, J. Chem. Phys., 31, 1562 (1959) the value for teri-butyl fluoride to be compared with the value reported here for tert-butyl chloride. This is the value for OCH, in formic acid to be compared with the value reported here for acetic acid. 2 This value is probably too low due to the larger value of R which results from the rather small D value, and the error in the estimate i s probsbly greater than in the remaining entries. f
where D I is the rotational diffusion constant perpendicular to the symmetry axis, a the ratio of the parallel to perpendicular diffusion parameters, the geometric constants A , B , and C are defined in ref 19, and R is 8/2 the total jumping rate of the methyl from any of its three equivalent positions. Provided T M ,D I , and (P are available, eq 4 can be used to compute R; however, D I and cr are not known for most molecules and indeed for CZvor lower symmetries an additional diffusion parameter must also be known to account for the nonequivalence in. reorientational rates about all three principal axes. Nevertheless, estimates of R can be made provided certain simplifying assumptions are allowed. If the molecules are assumed to undergo isotropic reorientation (Le., u = 1)then eq 4 reduces to
+ where D is now the overall isotropic diffusion rate. Values of D can be estimated from microviscosity theory21 using temperature dependent density and viscosity data or from dielectric relaxation times. Values of D at'c approximately 38" have been calculated for the molecules under consideration and are given in Table 11. Based on these D values and the TI^ times given in Table I, R values are then computed using e q 5 and are reported in Table 11. It is acknowledged that eq 4 and 5 neglect coupling between the
overall molecular motion and the internal process and also ignores the intermolecular effects on the internal vibrational modes. The values of R can be related to methyl internal rotational barrier using a conventional relationship"S1'" of the form
where Ro is 3//z the rate of reorientation for zero barrier and VOis the potential barrier in cal/mol. A convenient measure of Rois the rate of rotation of a methyl >"~ by fragment in the gas phase ( ~ T / I I X ~multiplied the "2 degeneracy factor. Using this calculated Ro (1.3 X 10'8 sec-l) and the value of R from eq 5 , one (14) W. T. Huntress, Jr., Advan. Magn. Resonance, 4, 1 (1970). (15) N. Bloembergen, E. M. Purcell, and R. V. Pound, Phys. Rev., 73, 679 (1948). (16) D. E. Woessner, J . Chem. Phys., 37, 647 (1963). (17) D. E. Woessner, B. S. Snowden, Jr., and E. T . Strom, Mol. Phys., 14, 265 (1968). (18) T. T. Bopp, J . Chem. Phys., 47, 3621 (1967). (19) D. E. Woeasner, B. S.Snowden, Jr., and G . a.?/leyer, ibid., 50, 719(1969). (20) N. Bloembergen, Phys. Rev.,104, 1542 (1956). (21) K. T.Gillen and J . H. Koggle, J. Chem. P h y ~ . 53, , 801 (1970).
The Journul of Physical Chemistry, Vol. 78, N o . 88, 1978
32168
JAMESR. LYERLA,JR., AND DAVID&/I. GRANT
may obtain Vo from eq 6. These calculated barriers is necessary to consider only the effects of internal are also reported in Table' 11. For comparative purmotion on the TI, relaxation times. A lower barrier poses some gas-phase microwave values of the barriers to methyl rotational motion will yield a comparatively are also given. The agreement between the microlonger spin-rotation correlation time and greater anguwave values and those determined from Tld measurelar velocities thereby increasing the importance of the ments is generally quite good in view of the several spin-rotation mechanism. Hence the lower the barrier to internal reorientation, the more efficient, the spinapprloximations used in making the calculations. This result indicates a close relationship between methyl rotation process and the smaller the value of TI,. Exrotational barriers and 13C spin-lattice relaxation amination of the T I , data in Table 1 and the corretimes. sponding barrier in Table I1 calculated from the Tld values show exact correspondence to this anticipated In all cases but that of DMSO, the D values from trend. Furthermore, where the barrier is high, the T I , microviscosity and dielectric data are quite similar, relaxation time i s inefficient compared to Tld. This thus the majority of differences in the 1/Tld rates qualitative discussion stresses the significance of inshould arise from internal rotational effects on T e f f . ternal motion upon both the magnitude of relaxation The effect of internal motion is to shorten Teff resulting times and the relative importance of various relaxation in a less efficient C-€3 dipolar process and a larger value mechanisms. for Tld. Indeed, acetone and the two carbons of interOne further result also supports the relative imest in methyl acetate have longer TI^ values while the portance of the spin-ro tation mechanism in low-barrier values in tert-HuC1 and CH&Cl3 with their higher barmethyls. A very low nuclear Overhauser enhancement riers are much reduced and their dI'! values are largely factor was found in nitromethane (TCH = 0.10), in which determined by the overall rotational motion. The the internal methyl barrier is only 6 cal/mol. Here Tnd in DMSO is also consistent with this model as its the methyl governed by a sixfold barrier is for all more efficient dipolar process relative to tert-BuC1 and practical purposes a free rotor. Thus, the spin-rotaCH3CC13 arises in its slower overall reorientation rate. tion interaction should dominate the relaxation process Thus, these results provide evidence of a relationship TCH value for CHaNO, indicates. as the between Tld times for methyl carbons and the respecThe above results demonstrate the degree to which t,jve methyl antwnal barriers. Furthermore, the aprotational barriers influence the relative efficiencies of plicability of the method t o liquids when most other the C-H dipolar and spin-rotational relaxation promethods are restricted t o gases, further emphasizes cesses in small molecules. Furthermore, this study the importance of this technique. indicates the significance of separating the contribu23. Xpin-lboiation Mechanism. On the basis of of the various relaxation mechanisms to T1in distions previous studiesz2exhibiting negligible chlorine effects cussing molecular dynamics and illustrates how quanon carbon relaxation and as no field dependence of the i s possible in the case of Ihe dipolar titative treatment TI results are dircernihle, the relaxation rate repredata. As spin-rotation interaction constants become rented by t h e T I ,times is ascribed t o the spin-rotation available similar information can be obtahed from the mechanism. This relaxation mechanism has not respin-rotation data, which a t this point can be treated ceived the same attention as devoted to the dipolar only qualitatively. process because of t h e paucity of data on spin-rotation interaction constants. The spin-rotation interaction Acknowledgment. This research was supported by arises from the coupling between the nuclear magnetic the Kational Institutes of Health under. Grant No. moment vector and the magnetic field associated with GA1-08521. the angular momentum of the molecular s y ~ t e m . ~ ~ - - ~ ~ (22) J. R. Lyerla, Jr., D. M. Grant, and R. D. Bertrand, J . Phys. The coupling depends on the magnitude of the field Chem., 75, 3936 (1971). generated and on a correlation time that governs the (23) C. Deverell, Mol. Phys., 18, 319 (1970) decay of the molecular angular momentum. (24) D. K. Green and J. G. Powles, Proc. Phys. Soc., London, 85, 87 (1965). As in the case of acfffor the dipolar process, -rBrmust (25) C. H.Wang, D. M. Grant, and J. R. Lyerla, J r . , J . Chem. ~ h y s . , be regarded as some composite average decay time but 55, 4674 (1971). is affected by internal motion in a manner which is (26) J. R. Lyerla, Jr., D. M. Grant, and C. H. Wang, ibid., 55, opposite from t h a t of Teff. To a first approximation it 4676 (1971).
l'he Journal of Physkal Chemistry, Vol. 76, No. 88, 1978
