J. fhys. Chem. 1980, 84, 1340-1344
1340
(15) (16) (17) (18) (19) (20) (21)
(22) (23)
(24) (25) (26) (27)
(28)
thermochemical: W. Finkelburg and J. J. Schumacher, J. fhys. Chem., Bodenstein Festband, 704 (1931), spectroscopic. M. A. A. Clyne and J. A. Coxon, Proc. R . Soc., London, Ser. A , 303, 207 (1968). See also ref 13. See also, J. L. Gole and E. F. Hayes, Int. J. Quantum Chem., Vol. HIS, 519-25 (1970). S. Rothenberg, P. Kollman, M. E. Schwartz, E. F. Hayes, and L. C. Allen, Int. J. Quantum Chem., 35, 715 (1970). C. C. J. Roothann, Rev. Mod. fhys., 32, 179 (1960). T. H. Dunning and P. J. Hay in “Methods of Electronic Structure Theory”, H. F. Schaefer 111, Ed., Plenum Press, New York, 1977. T. H. Dunning, J . Chem. fhys., 53, 2823 (1970). The general effects are twofold. First the X‘B, state of OClO is stabillzed relative to the ‘A1 and ‘8, states. All of the calculated OClO states are stabilized relative to the ClOO *A’ and ‘A” states; however, the quantitative shapes of all of the bending mode potentials remain virtually the same. Although we hope to continue with large-scale CI shdles in the near W e , at pesent we have considered excitations from only the highest five occupled valence orbltals. A. D. Walsh, J. Chem. Soc., 2260 (1953); R. S. Mulllken, Rev. Mod. Phys., 14, 204 (1942). Several possible quartet states were also generated through a variety of excitations invoking virtual orbitals for the x%, state. The energies of these states considerably exceed those of the doublet states dlscussed In the present manuscript. There is one possible low-lying quartet state which is inaccessible to our calculations lying slightly lower than the *Al state. Although this 48, state cannot be calculated, its bond length and bond angle are expected to change substantially relative to the ground state precluding its possible involvement in OCD Isomerization. R. J. Buenker and S. D. Peyerimhoff, Chem. Rev., 74, 127 (1974), and references therein. J. L. Goie and E. F. Hayes, J. Chem. Phys., 57, 360 (1972). M. J. Molina and F. S. Rowland, Nafure(London),249, 819 (1974). J. E. Lovelack, R. J. Maggs, and R. J. Wade, Nature(London),241, 194 (1973). The simple scheme presentedomlts posslble formation of OClO by CIO -I-O3 OClO 02. This reaction is believed to be quite slow (see ref 6b). K. E. Schuler, J. Chem. fhys., 21, 624 (1953). We specify the possible states but not the total number which one can obtaln of each
-
+
symmetry. (29) For 0 ‘ iAe-32; separation = 22.6 kcal, see L. Herzberg and G. Herzberg, Astrophys. J., 105, 353 (1947). For relative energies of ground-state?eactants: Doo(O,) = 118 kcallmol- Doo(CIO)= 55 kcallmol. (30) J. B. Coon and E. Ortiz, J. Mol. Spectrosc., 1, 81-94 (1957). (31) J. C. D. Brand, R. W. Redding, and A. W. Richardson, J . Mol. Spectrosc., 34, 399 (1970). (32) Even quantum changes in the b2 mode v3 are relatlvely prominent in the vibrational structure of the band system. Brand et al. (ref 31) exploredthe possibility that these bands “borrow” their Intensity from transitions involving the totally symmetrical modes. Relative intensities were calculated by using second-order corrected anharmonic vibrational wave functions. These calculations gave a good account of observed Intensities. (33) G. Herzbera and E. Teller. Z . phvs. Chem.. Abt. B. 21. 410 11933). (34) R. M. Badger, A. D. Wright, anb R. F. Whitlock, j . Chem.‘fhys:, 43. 4345 (19651. (35) This c o n c l kn-[long lifetime) is based in part upon the observations of Hunziker and Wendt (J. Chem. fhys., BO, 4622 (1974)). These authors estimated a llfetlme as long as several microseconds fo the ‘A’ state of HO . This must represent a strong lower bound for the lifetime of the state in CIOO, where the effect of the chlorine on the bonding is much weaker. (36) The program was written by Professor Bill Guinn, Universlty of Callfmla, Berkeley, CA. See Quantum Chemistry Program Exchange, QCPE Program 1761177, Department of Chemlstry, Iridlam University, Bloomlngton, IN. (37) R. H. Felton, private discussions. See also Wilson, Decius, and Cross, “Molecular Vibrations”, McGraw-Hill, New York, 1955, and Nakamoto, “Infrared Spectra of Inorganic and Coordlnation Compounds”, Wiley, New York, 1963. (38) These experiments are being done in collaboration with Professors L. Knight and A. Arrington of Furman University. (39) The s p e m may be characterized by vibronic coupling in the electronic ‘8, state which involves odd levels of the asymmetric stretch or vibronic interactlons connecting levels of the ‘A, and ‘B, states via the asymmetric stretch of the *A1state. These two cases will result in a variation of the intensity pattern as well as produce two posslble intensity patterns.
k‘
Molecular Motion in Brittle and Plastic Dodecamethylcyclohexasilane and Decamethylcyclopentasilane David W. Larsen,” Barbara A. Soltz, Chemistry Department, University of Missouri, St. Louis, Missouri 63 12 I
Frank E. Stary, Chemistry Department, Maryviiie Coi/ege, St. Louis, Missouri 63 14 1
and Robert West Chemistty Department, University of Wisconsin, Madison, Wisconsin 53706 (Received December 12, 1979)
A solid-state transition to a plastic-crystalline phase takes place at 350 K for [Si(CH,),], (1) and at 234 K for [Si(CH,),], (2). Molecular motion in the brittle and plastic phases of 1 and 2 was studied by using proton NMR relaxation data. Methyl reorientation and anisotropic molecular reorientation were observed in the brittle phases of both compounds. Anisotropic reorientation in 1 appears to occur simultaneously with inversion of the chair-form cyclohexasilane ring. The relative rates of methyl and molecular anisotropic reorientation in 2 could not be established from the NMR data. In the plastic phase, isotropic reorientation and translational diffusion were observed in both 1 and 2. The activation barriers are compared with those in hexamethyldisilane and anomalous features of the relaxation data are discussed.
Introduction Among the numerous linear and cyclic polysilanes now known,l the cyclic permethylpolysilanes are of particular interest.1cg2In a recent communication we reported that dodecamethylcyclohexasilane (1) shows plastic-crystalline behavior over a surprisingly large temperature range, from 350 K to the melting point of 526 K., In this paper we describe in more detail proton NMR studies of molecular 0022-3654/80/2084-1340$0 1.OO/O
motion in solid 1 and in the analogous five-membered-ring compound decamethylcyclopentasilane (2), which also shows plastic-crystalline behavior. Molecular motion in the solid state has previously been reported for hexamethyldi~ilane.~~~ Solids which form plastic crystals are generally globular in shape and may undergo a number of molecular motions, in both the plastic phase and the low-temperature (brittle) 0 1980 American Chemical Society
The Journal of Physical Chemistry, Vol. 84,
Molecular Motion In Brittle and Plastic Silanes
12
IO
8
6
4
2
10 3/T
Flgure 1. Relaxation times vs. reciprocal temperature for [Si(CH&] Tabulated data are given in Table 111.
phase? Anisotropic molecular reorientation about a symmetry axis is often observable in the brittle phase. Isotropic reorientation a t lower temperatures, and translational diffusion at higher temperatures, may take place in the plastic phase. Other internal motions, such as reorientation of methyl groups, may also be observed. We have measured proton NMR relaxation times' Tl (spin-lattice), TIP(rotating frame spin-lattice), T1D (dipolar), and second moments6 (M2)for 1 and 2 in both brittle and plastic phases. Analysis of these data allows the molecular motions for 1 and 2 to be characterized. The two compounds, though structurally related, show substantial differences; in their respective molecular motions.
Experimental Section (Me2Si)6(1) was prepared by condensation of Me2SiC12 with Na/K in the standard manner,9 then crystallized, sublimed, and thrice recrystallized from ethanol. The final product was >99,9% pure by high-performance LC. (Me2Si)6(2) was obtained from the mother liquors after crystallization of l9and was purified by repeated fractional sublimation. Final purity (by high-performance LC) was >99%. Phase-transition temperatures were determined by differential thermal analysis by using a Du Pont DTA apparatus. Compound 1 shows an endothermic phase and a melting endotherm at 526 K; transition at 350 Po 2 undergoes a similar endothermic transition at 234 K and melts at 454 K. NMR Measurements. Proton NMR relaxation times and second moments were measured as described previously" from 95 K to the melting point by using a Polaron (Watford, England) high-power pulsed NMR spectrometer operating at 60 MHz. A rotating field strength H1= 28 G was used in the rllpmeasurements, and H1= 60 G was used in all other measurements. Bloch decays were found to be Gaussian within experimental error for the polycrystalline samples used.
No. 11, 1980 1341
1342
The Journal of Physical Chemistry, Vol. 84, No. 11, 1980
Larsen et al.
0
-1 h
0
VI w
.c. w
E
r
0
c
Ej
-2
?d w
100
3
200
TEMPERATURE
(K)
Figure 4. Second moment vs. temperature for [Si(CH,),],. -3
-11
10
8
6
4
2
10~1~
Figure 3. Relaxation times vs. reciprocal temperature for [Si(CH3),I5. Tabulated data are given in Table 111.
fourth process, which is most likely translational diffusion. The various theoretical treatments of translation diffusion12-14 all predict for w17d >> 1 1
y2M2d
- = (constant)TlP wl27d
where w1 = yH,,y is the gyromagnetic ratio, M2d is the second moment modulated by diffusion, and 7d is the correlation time for diffusion. Thus, the activation barrier may be estimated from gradients of low-temperaturearms. From the TIDgradient, we estimate an activation barrier of 26 kcal/mol. In Figure 2, the brittle-to-plastic-phase transition lowers M2to 0.3 G2, which corresponds to i&(high) with respect to isotropic molecular reorientation. A further reduction in M2 to almost zero is observed above 400 K; this final line-width transition is associated with translational diffusion. At temperatures above this transition, the NMR spectrum is comparable to that of a liquid. Decamethylcyclopentasilane ( 2 ) . Compound 2 shows plastic-crystalline behavior over a temperature range of 220 K, even longer than for 1. The relaxation data for 2 are shown in Figure 3, and the second moment data are presented in Figure 4. The general features of the data for 2 are similar to those of 1, but with several differences. In the brittle phase of 2 (Figure 3), T1 exhibits a relaxation minimum which may be fitted by the BPP-type expression16J6
where y is the gyromagnetic ratio, Mzmodis the portion of M2 modulated by the motion, wo is the Larmor frequency, and 7, is the correlation time. The solid line in Figure 3
is calculated from eq 2 with MZmod = 6 G2 and 7, = (6.7 X exp(1.55 x 103/RT). Although TIpand T ~ may D be controlled by the same motion, the behavior is not accounted for by simple theory. In Figure 4, the M2plateau from 100 to 200 K corresponds to MZ(high) = 6.9 f 0.5 G2 with respect to this motion, the assignment of which is discussed below. Between 103/T 6 and the phase transition, both Tlp and Ti, are controlled by a second process, which may be anisotropic molecular reorientation by analogy to similar systems. The activation barrier for this motion is 2 kcal/mol. In Figure 4,it can be seen that no M2transition associated with the motion is observed due to the phase transition. In the plastic phase of 2, Tl appears to be controlled by isotropic molecular reorientation, and we estimate an activation barrier of 2.7 kcal/mol for the process. Tle is also controlled by this process between the phase transition and 103/T 3, and in addition, T1 x Tlp,which is predicted by simple theory. In Figure 4, the hf2(high) plateau = 0.3 G2 can be seen up to -300 K. Finally, the effects of translational diffusion can also be seen in T1, and T1? in Figure 3. The T1D gradient corresponds to an activation barrier of 17 kcal/mol. The final line narrowing is observed above -350 K.
-
-
Discussion The assignment of motions of the type of interest in this work is usually done by analysis of second-moment data. The structure is first assumed to be completely rigid and polycrystalline, and the “rigid lattice” second moment is calculated from the Van Vleck equation17 (3) where M2(rl)is in G2, n is the number of protons in the sample, and rjkis the distance between protons j and k in A. The sum is taken over all pairs in the sample. The values of rjkare obtained from X-ray crystallographic data where available, and the small contributions from 13Cand 29Siare omitted. The values of Mz in the presence of various assumed motions are then calculated by the use of reduction factors.lsJg These calculated Mz values are plateaus as confirthen compared with observed Mz(high) matory evidence. Following this procedure, assignment of the low-temperaturebrittle phase motions in both 1 and 2 to methyl reorientation is straightforward. X-ray crys-
Molecular Motlon in Brittle and Plastic Silanes tallographic dataz0which are available for 1were used to estimate21r.k in eq 3. M2 values obtained were M2(INTRA) = 25.8 G2,h ? ( I N T E R ) = 4 G2,giving Mz(,l)= 28.8 f 3 G2. Assuming rapid methyl reorientation and using reduction factors, we calculated M 2 ( M E ROT) to be 8.2 f 2 G2. In Figure 2, the M2 between 100 and 300 K exhibits a plateau, 6.8 f 0.5 G2, which is &(high) for the motion. Since &(ME ROT) = M2(high) within experimental error, this is confirmatory evidence that the motion is methyl reorientation. The problem with the above analysis is that it does not provide a unique assignment of the motion, and this problem is particularly severe with globular substances containing methyl groups. An anisotropic reorientation about an axis is often indistinguishable from methyl reorientation. For example, with 1 the structure is a chair form with a molecular C3axis. Molecular (or whole-body) reorientation about this axis assuming rigid methyl groups yields22M ~ ( M O L . R O T )= 7.8 f 2 G2,which is identical with M2(m ROT) urlthin the uncertainty of the calculation. Thus M2 data do not distinguish“ between these motions for 1. The assignment thus rests on the assumption that methyl reorientation (an internal motion) is more rapid than molecular reorientation (involving the whole body). Recent evidence from neutron-scattering studies of molecular solids which exhibit high-temperature plastic phases26indicates that, at least in a few instances, whole body reorientation occurs more rapidly than methyl reorientation in the low-temperature brittle phase. However, both the methyl and the molecular reorientations% cannot be rapid for 1 above 100 K, since M 2 ( M E + MOL ROT) = 3.6 1 G2, which does not agree with MZ(high)* For 1, the NMR data are most consistent with methyl reorientation being faster than molecular reorientation based on activation barriers. Barriers to methyl reorientation for solids of this type are generally observed3+J1 to be 1 3 kcal/mol. Thus, a barrier of 10 kcal/mol appears to be unreasonably large for methyl reorientation, and consequently the motion observable just below the phase transition probably involves anisotropic molecular reorientation. However, the M2 data are not consistent with this motion being a simple reorientation about the 3-fold molecular axis. MZ(m + MOL ROT) = 3.6 f 1G2was calculated above, and Figure 2 shows that &(hi h) C 1 G2 for this motion. The plateau is partially obscured by the phase transition. This discrepancy and the fact that the barrier for the motion is 10 kcal/mol indicate that additional motion is present. Most likely the ring inverts as the molecule reorients; if so, an effective 6-fold molecular axis would be created. A rough calculation indicates that simultaneous methyl motion, molecular reorientation, and ring inversion would reduce M2 to -1 G2. X-ray structural data are not available for 2. Evidence from a variety of studiesa on five-membered rings suggests that the stable conformation of 2 is puckered but that the structure is likely t c ~be essentially planar on average even a t low temperature because of “pseudorotation”.28 This motion will cause a reduction in the second moment. However, since bond angles and consequently the amplitude of the motion me unknown for 2, we have made crude estimates of second moments assuming a planar ring and a tetrahedral C-Si--C bond angle. Values obtained were M2(11 =)29 G2, M2(MJ3ROT) 8 G2, M 2 ( M E + MOL ROT) 7 2.4 G , and MZ(MOL ROT) = 4.5 G2. Under these assumptions, M2,,,) = 6.9 f 0.5 G2appears to agree only with methyl reorientation. The neglect of pseudorotation means that the above estimates are upper limits. It can be seen that the dominant factor in reducing the second moment is methyl reorientation, and the conclusion appears to be
The Journal of Physical Chemistry, Vol. 84, No. 7 7, 1980
1343
TABLE I: Calculated Second Moments for Motions in Cyclic Permethylated Polysilanes compd
motional state
calcd M,, GZ
[Si(CH,),],
rigid methyl reorient aniso mol reorient methyl + aniso mol reorient rigid methyl reorient aniso mol reorient methyl t aniso mol reorient
29.8 f 3 8.2 f 2
[ Si(CH,),],
’”
};:::1” 29’” 8a 4. 5’” 2.4’”
1
Crude estimates; see text.
TABLE 11: Activation Barriersa for Motions in Cyclic Permethylated Polysilanes
compd
methyl reorient
anisoisotropic tropic mol mol reorient reorient
trans1 diffusion
10 3 26 2 16 1.3 1.6b*c 2b 2.7 17 [Si(CH31 2 I I a kcal/mol. These two assignments are tentative; see s. text. The preexponential factor T~ = 6.7 X Values for other motions cannot be calculated since the minima for the motions are not observed.
qualitatively correct. The value of M~(MOL ROT) for 2 is substantially lower than that for 1. This is because whole-body reorientation for 2, in which the C-Si-C bond angle is assumed to be tetrahedral, places the Si-C bond axis at almost the “magic angle”, at which the reduction factor is Calculations done by using reliable structural data might provide a definite answer to this assignment for the low-temperaturemotion. In an attempt to further investigate this point, calculations were made Both on structural data for Si6(CH3)2Si(CH~2FeCp(CO),.29 the given proton positions and positions in which C-H bonds were adjusted to 1.09 A were used. However, both sets of calculations gave impossibly large results due to several proton pairs being extremely close. The calculated second momenta for 1 and 2 obtained as described above are summarized in Table I. The activation barriers for the various motions are summarized in Table 11. With either assignment for the low-temperature motions in 2, the barrier for methyl rotation for 2 is greater than that for 1. Whether the difference in steric hindrance is due to bond angles or bond length or both cannot be established in the absence of a structure for 2. Both barriers appear to be slightly below the reported barrier, 2.2 kcal/mol, for hexamethyldisilane (HMDS).4 The barrier to anisotropic reorientation in 2 is comparable to barriers for isotropic reorientation in 1, 2, and HMDS (1.5 kcal/mol),4 whereas the barrier to anisotropic reorientation in 1 is much larger as in HMDS (7.2 k ~ a l / m o l ) .Thus ~ in some structures, the intermolecular forces are such that internal motion is required (e.g., ring inversion in 1) in order for the molecule to reorient about its symmetry axis. This implies that the two motions are strongly coupled. In other structures (e.g., in 2) molecular reorientation occurs apparently independently of any other motion with the possible exception of pseudorotation, which is expected to be a motion of small amplitude compared to ring inversion. The barriers for translational diffusion for 1 and 2 are both greater than the barrier for HMDS (10.4 k ~ a l / m o l ) .Translational ~ diffusion reflects the intermolecular potentials, but no simple correlation exists between diffusion barriers and structural parameters.
1344
The Journal of Physical Chemistty, Vol. 84, No. 7 7, 7980
(2) L. Brough, K. Matsumura, and R. West, J. Am. Chem. Soc., in press. (3) D. W. Larsen, B.A. Sok, F. E. Staty, and R. West, Chem. Commun., 1093 (1978).
TABLE 111: Tabulated Relaxation Times f o r Cyclic Permethylated Polysilanes in t h e Plpstic Phase [Si(CHs)zl,
[Si(CH, 1 2 1 5
1031
T
103/
TI
TI, 1.2s
TIn
2.34 2.43 0.16m 2.47 5.9s 2.2s 2.50 2.5s 1.5m 2.53 5.3s 2.59 4.5s 2.62 4.5s 2.9m 2.67 4.1s 9.lm 2.81 3.0s 34m 2.85 2.6s 46m
T 2.60 2.78 2.80 2.88 2.89 2.99 3.02 3.08 3.13 3.18 3.24 3.31 3.36 3.41 3.61 3.65 3.86 4.07 4.08 4.10 4.14 4.1 5 4.20 4.29 4.37 4.41
TI
TI,
Tin
88m 0.43s 5.3s 4.8s
0.10m
0.28m 1.1s
4.5s 4. os 3.9s 3.7s 3.1s 3. Os
l.lm 2.0s 2.4s
2.2s 1.9s 1.5s 1.8s
2.2m 3.5m 5.8m 1Om 20m 43m 0.12s
1.2s 0.95s
0.80s 0.30s 0.90s
Larsen et al,
0.70s 0.25s 0.60s
(4) A. V. Chadwick, J. M. Chezeau, R. Folland, J. W. Forrest, and J. H. Strange, J . Chem. Soc., faraday Trans. 7, 71, 1610 (1975). (5) S. Albert, H. S. Gutowsky, and J. A. Ripmeester, J. Chem. Phys., 56, 1332 (1972). (6) See for example J. M. Chezeau, J. Defourcq, and J. H. Strange, Mol. Phys., 20, 305 (1971). (7) T. C. Farrar and E. D. Becker, “Pulse and Fourier Transform NMR”, Academic Press, New York, 1971. (8) A. Ahgam, “The Rsnclples of Nuclear Magnetism”, Ciarendon Press, Oxford, England, 1961, p 106. (9) R. West, L. Bough, and W. Wojnowskl, I m g . Synth., 19,265 (1979). (10) This transition is visually observable and has been noted earlier. See H. 0. v. Stolberg, Angew. Chem., Int. Ed. Engl., 2, 150 (1963). (1 1) D. W. Larsen and J. Y. Corey, J. Am. Chem. Soc., 99, 1740 (1977). (12) H. C. Torrey, Phys. Rev., 92, 962 (1953). (13) H. A. Resing and H. C. Torrey, Phys. Rev., 131, 1102 (1963). (14) D. Wolf, Phys. Rev. 8, 10, 2710 (1974);J. Magn. Reson., 17, 1 (1975); Phys. Rev. 6 ,15, 37 (1977). (15) N. Bloembergen, E. M. Purcell, and R. V. Pound, Phys. Rev., 73,
679 (1948). (16) Strictly speaking, this expression is valld only for the intramolecular (or hfrapup) reaientah conbhtion to reorlentah about an n-fdd axis, where n > 2. The Intermolecular (or Intergroup) contributions Involve terms in 7,/2 which have the effect of slightly shifting the
(17) (18) (19) (20)
minimum TI. Neglect of these terms does not appreciably affect activation barriers. J. H. Van Vleck, Phys. Rev., 74, 1168 (1948). J. 0. Powles and H. S. Gutowsky, J. Chem. phys., 21, 1704 (1953). G. W. Smith, J. Chem. Phys., 42, 4229 (1965). B. H. Carrel1and J. Donohue, Acta Crystatcgr., Sect. 8, 28, 1566
(1972). (21) X-ray crystallographlc structures In general do not locate protons
0.82s 0.46s 0.69s
Relaxation times for cyclic permethylated polysilanes in the plastic phase are summarized in Table III. One feature of the relaxation data in the brittle phases of both 1 and 2 is as yet unexplained theoretically. The hightemperature arms for both methyl reorientation Tl minima show Tl > T > TID. In 1, all three exhibit identical temperature Zependence, whereas in 2, the temperature dependence is more complicated. T1 # TIPin a hightemperature Tl arm does not result from any standard theory involving a single motion. However, if methyl reorientation occurs with some slower motion, e.g., a change in the C-Si-C bond angle, and if the slower motion is not coupled to the faster motion, then a weak Tlminimum can occur at high temperature (above the main minimum) and Tlp< Tl is predicted.a0 The behavior of 1 at 103/T 4 may be such a weak minimum, but the evidence is not compelling.
-
(22)
(23) (24) (25) (26)
accurately enough to provide completely reliable data for M, calthere is the added complication of an apparent culations. For l, disorder In the proton posltlons. The X-ray data were analyzed in terms of two different posltions for each proton. For this reason, certain interproton distances were estimated rather than calculated directly from X-ray results. The calculation is based on Slichter (ref 23), and one can show that for a rigid methyl group whose symmetry axis makes an angle a with the molecular reorientation axis, the reduction factor is 1/12[ 1 -I-2(9/4 cos2 a - l)’]. The major contribution to M2 Is the intrafroup methyl; methyl reorientation reduces this contribution to 5.6 G , and molecular reorientation reduces It to 5.1 G2. C. P. Slichter, “Prlnclples of Magnetic Resonance”, Harper and Row, New York, 1963, p 62. We note that, in principle, more accurately determined M, data combined with considerably more accurate structural data could distinguish between these two motions. A. J. Leadbetter, private communication. The second moment for protons involves terms in (1 3 cos2 where 6, is the angle between the Interprotonvector and the strong field (see ref 23). For two motlons, the spherical harmonic addition theorem yields ((1 - 3 cos2 e)) = (1 - 3 cos2 aM1 - 3 cos’ pX1 - 3 cos2 y)/4, where a is the angle between the mdecular axis and the strong field, fl is the angle between the molecular axis and the methyl axis, and y is the angle between the methyl axis and the interprotonvector. For axial me thy!^, y = 90°, @ = 6O, which gives a powder average reductlon factor 0.24, and for equitorlal methyls, y = 90°, = 66O, which gives a powder average reduction factor
-
Acknowledgment. This research was partially supported by the U S . Air Force Office of Scientific Research (NC)OAR, USAF Grant No. AF-AFOSR 78-3570.
0.016. (27) D. W. Larsen and B. A. Soltz, J. Phys. Chem., 81, 1956 (1977),
References and Notes
(28) J. E. Klpatrlck, K. S. Pitzer, and R. Spritzer, J. Am. Chem. SOC., 69, 2483 (1947). (29) T. Drahnak, R. West, and J. Calabrese, J . Organomet. Chem., in
(1) For revlews see: (a) H. Gllman and G. L. Schwebke, A&. & g m t . Chem., 1, 90 (1964); (b) M. Kumada and K. Tamao, IbM., 6, 19 (1968); (c) R. West and E. Carberry, Science, 189, 179 (1975).
and references contained therein.
press.
(30) D. W. Larsen and J. H. Strange, results to be submmed for publlcatbn.
