3970
B. WARE,K. WILLIAMSON, AND J. P. DEVLIN
An Infrared Study of Internal-Rotational Barriers in Solid 7~ Complexes
of Methylbenzenes. I. Hexamethylbenzene-Tetracyanoethylene by Bennie Ware, Ken Williamson, and J. Paul Devlin Department of Chemistry, Oklahoma State thiversity, Stillwater, Oklahoma
74074 (Received February 6 , 1968)
The temperature dependence of the splitting of the infrared doublet produced by the in-plane rock and out-of plane wag of the methyl groups in crystalline hexamethylbenzene (HMB), as observed in oriented crystals, leads to an estimate of the barrier to internal rotation of these groups in good agreement with the published values deduced from inelastic neutron-scattering and nmr data. This agreement has prompted a study of the effect of charge transfer on this barrier in the crystalline complexes of HMB with tetracyanoethylene. The barrier was found to be reduced in both the 2: 1 and 1: 1 complexes, with a -30% reduction in the 2: 1 case most striking. This result suggests the presence of competing effects of charge-transfer and intermolecular steric forces, both factors being somewhat more important in the 1:1 than the 2 : l case.
I. Introduction The barrier to methyl group rotation in solid hexamethylbenzene (HMB) has been the subject of study by various techniques in recent Quantitative results have been obtained by Rush and Taylor using inelastic neutron scattering, by which method they have estimated a torsional frequency of 120 cm-I and a barrier of 1.07 f 0.09 kcal for T > l15"K.3 Allen and Cowking have deduced a somewhat larger value (1.6 kcal) from nmr measurement~.~Leech, et al., have noted that variations in infrared-band contours are consistent with onset of methyl group rotations below 200°K but failed to deduce any quantitative values for the relevant parametem2 Using oriented single crystals and polarized infrared radiation, we have found that the most temperature-sensitive infrared-band complex, that produced by methyl group wagging, is composed of two bands, one polarized in-plane and the second polarized perpendicularly to the benzene plane. These components are well split at 90°K but slowly shift toward one another until at 300°K they are nearly coincident. By assuming that the decrease in the magnitude of this splitting is the result of the onset of rotation, an estimate of the barrier to internal rotation may be made. Since this method was found to yield a barrier height in reasonable agreement with the published values, 3 , 6 we have extended the method to obtain approximate barrier heights for HMB in the 2 : 1 and 1:1 solid-state complexes with tetracyanoethylene (TCNE). It was hoped that the new data would reflect changes in barrier height that could be correlated with the effect of charge transfer on molecular electronic structures.
11. Experimental Section The key to the experimental study is an ability to grow HRIB and its complexes with TCNE in highly oriented needlelike crystals attached to an infrared The Journal of Phasical Chemistry
transparent substrate so that infrared-active in-plane and out-of-plane modes may be observed alternately using polarized radiation.6 Sample orientation is accomplished by depositing onto the substrate immersed in an ether solution. A polished rectangular crystal of NaCl is positioned upright in a 100-ml beaker containing approximately 2 mmol of sample in 50 ml of dry ether. Evaporation of the ether results in deposition of parallel crystals with molecular planes oriented perpendicularly to the substrate surface. However, molecular stacking f-or the complexes, depicted in Figure la, differs from that for the pure HMB (Figure lb) in the orientation of the molecular planes with respect to the needle axis. The orientation for pure Hl\/IB is precisely that which RIann and Thompson observed upon crystallizing liquid HMB between quartz plates.' The deposited crystals and substrate were mounted in a standard low-temperature infrared cell and were The spectral range from 1350 to cooled to -90°K. 1500 cm-l, which contains the methyl group wagging band complex, was then scanned repeatedly at 10" intervals as the sample was slowly warmed to room temperature, at which point the sample was rotated 90" and the procedure repeated. Though an AgCl beam polarizer was available, we obtained improved spectra by making use of the instrument polarization only, which is about 80% effective in this range. I n addition to the studies of the oriented crystals of HMB and its complexes, the band complex for the (1) E. R. Andrews, J. Chem. Phys., 18, 607 (1950). (2) R. C. Leech, D. B. Powell, and N. Shepard, Spectrochim. Acta, 22, l(1965). (3) J. J. Rush and T. I. Taylor, J . Chem. Phys., 44, 2749 (1966). (4) J. J. Rush, ibid., 47, 3936 (1967). (5) P. F. Allen and A. Cowking, ibid., 47, 4286 (1967). (6) B. Hall and J. P. Devlin, J. Phys. Chern., 71, 465 (1967). (7) J. Mann and H. W. Thompson, Proc. Roy. SOC., A211, 168 (1953).
397 1
AN INFRARED STUDY OF INTERNAL-ROTATION BARRIERS
.',
MERE
-
--\
AXIS
I
0 -_-
/--
*20.C
,,
00 '00 I
Figure 1. Stacking of molecules relative to the crystal needle axis in the solid state of (a) the HMB-TCNE complex and (b) the pure HMB. The view is perpendicular to the substrate surface.
I
1500
methyl wagging modes for HMB, mesitylene (symmetrical trimethylbenzene, TMB), and durene were observed using random polycrystalline films in the temperature range 90-300°K. Also, the spectrum of a KBr pellet of the durene-TCNE complex was checked against that of the pure durene for this temperature range. All spectra were measured using a Beckman IR-7 spectrometer.
1400
Figure 2 depicts the effect of temperature on the components of the 1450-cm-1 band complex for HMB as observed for the 1 : l complex with TCNE. These spectral changes are reversible and completely typical of those obtained for both HMB complexes as well as pure HMB except for the presence of additional splittings in the pure HMB spectrum which are absent above phrase transition a t -115°K. Note that as the temperature increases, the 1436-cm-1 out-of-plane component shifts slowly toward 1450 cm-l, while the higher frequency in-plane mode a t 1460 cm-I shifts to meet it. The temperature dependence of A, the difference between the two peak frequencies, is shown for the various cases in Figure 3. Though A decreases markedly, in no case does it reach zero at room temperature, contrary to what has been concluded using disoriented samples.2 The spectra for the randomly oriented HMB, durene, and T M B samples presented in Figure 4 contrast the temperature dependence of the 1450-cm-1 splitting as observed for the latter two cases with that for HMB. Whereas the splitting vanishes a t -200°K for pure HMB, the T M B components are still well defined a t 300"K, and A is largely unchanged from its 130°K value. Likewise, the only major change for durene accompanies a solid-phase transition, but the sharpness of the durene bands relative to those of TMB is undoubtedly significant. The experimental plot of A vs. T for HMB and its complexes has a form reminiscent of the variation of the Boltzmann factor with temperature. Since the vibrational modes which determine A, methyl group
I 1400
Cm'
Figure 2. Temperature dependence of the components of the 1450-crnb1band system for the 1 :1 HMB-TCNE complex: ., perpendicular (to ring) polarization, -, parallel polarization.
.. ..
111. Results for HMB, HMB-TCNE, and 2 HMB-
TCNE
I
1400 lsoo
600
32
L
28f
4
80
1
TRANSTION
+PHASE
I
120
I
160
I
200
I
I
240
280
T('K) Figure 3. Plot of A os. T for pure HMB (-), HMB-TCNE (- -), and 2HMB-TCNE .): X, HMB; #, HMB-TCNE; 0,2HMB-TCNE.
--
(a
-
rock, and methyl group wag involve primarily motions within the methyl group and since temperature dependence of the contour of the band complex under consideration has previously been related to onset of free rotation,2 we have analyzed our A curves (Figure 3) in terms of the probability of methyl group reorientation modes as determined by barrier height and temperaVolume 7.9, Number 18 November 1968
3972
B. WARE,K. WILLIAMSON, AND J. P. DEVLIN
CY'
Figure 4. Temperature dependence of the 1450-cm-1 band complex for thin polycrystalline films of HMB, TMB, and durene and a KBr pellet of the durene-TCNE complex. Note that a phase transition negates any comparison of the durene splittings a t 130 and 200°K.
fact that there are fewer rotors per benzene ring greatly reduces the statistical probability of reorientational modes in durene. Thus at 300°K this probability is insufficient to greatly affect the 1450-cm-' splitting. Of course it is possible that, as for TMB, the A value is insensitive to CH3 reorientational motion, but the proximity of the CH3 groups plus the temperature dependence for A in the durene-TCNE complex (Figure 4) argue against this insensitivity. Viewed in this manner, the TMB and durene data support rather than detract from the idea of relating the A temperature dependence observed for HMB and its TCNE complexes to the probability of reorientational motions. Thus, assuming a 1.07 kcal threefold rotational barrier for methyl group rotation, as reported from the neutron-scattering study, the probability of reorientating methyl groups as a function of temperature was estimated statistically. More specifically, we used a truncated partition function of the form8
Q ture. Such an approach may appear inconsistent with the T M B data (Figure 4)) since it has been fairly well established that the rotational barrier is considerably lower in TMB than HMB, so that one might expect a stronger A temperature dependence for T M B than HMB. This expectation vanishes when one recognizes that the relative potential energy for in-plane and outof-plane wagging of methyl groups, as reflected in the splitting of the 1450-cm-' band, should be insensitive to methyl group rotation in TMB but not in HMB. The methyl groups experience only weak steric forces in TMB, whereas adjacent CH3 groups "bump" together in the HMB wagging modes. Thus it is understandable that effective elimination of the methyl group structure by rapid reorientational motions could reduce the vibrational potential energy difference for the in-plane and out-of-plane coordinates of HMB. As observed, this would be reflected in a coalescence of the two 1450-cm-' components as the probability of reorientational modes increases with temperature. A corollary would seem to be that the 1450-cm-' splitting in HMB arises largely from methyl group interactions, whereas the same splitting for TMB, although of a comparable magnitude, must result primarily from the directional characteristics of the methyl group-ring interactions. The splitting for TMB is preserved a t high temperatures, since CHa group rotation has a secondary effect on interactions with the ring. It is interesting that the marked broadness of the T M B 1450-cm-' band, even at 130°K (Figure 4), is consistent with an exceptional degree of methyl group motion as expected from the low potential barrier. The insensitivity of the A value to temperature for durene (Figure 4) probably has a different origin. The barrier to rotation in durene has been indicated to be somewhat larger than for HMB.4 This fact plus the The Journal of Physical Chemistry
= m=mo
= Qr
2e-
+
iE/lcT
mtBhlkT i=O
(1)
Qv
for each methyl rotor, with terms for three torsional energy states spaced by 0.33 kcal (120 cm-') below the barrier top an+ five quasi-free-rotation energy states above the barrier. The torsional states are threefold degenerate, while the rotation, which has been approximated using a rotor with fixed axis, may be in either the left- or right-hand sense. By defining PAas the probability of a given rotor being above the barrier (ie., PA= Qr/QV) so that PB= 1 - PAis the probability that a rotor is in a torsional state, one obtains
+
+
PIA= ~ P A P B~~~ P A ' P B ~ 2oPA3PB3 15PA4PB2 6 P A 6 P ~$. P A 6 (2) as the probability that at least one rotor per HMB molecule is quasi-free. This model completely ignores coupling between the methyl rotors but can be viewed as the limiting case of weak coupling. However, had weak coupling been included in the model, the first rotational state would not be characterized by the rotation of a single rotor but by a mode wherein all six H;\4B rotors, being coupled, experience some freedom of rotation. The statistical analysis is simplified by ignoring coupling, a procedure adopted since there are no data available to permit introduction of coupling in a quantitative manner. Throughout this study two energy manifolds which differed only in the spacing of the quasi-free-rotation states and their position (energy) relative to the torsional states were used to express eq 1. One manifold was obtained by deducing the quantum number (mo)for the
+
+
(8) This partition function is based on an energy manifold suggested by K. S. Pitzer, "Quantum Chemistry," Prentice-Hall, Inc., Englewood Cliffs, N. J., 1953, p 243.
3973
AN INFRARED STUDY OF INTERNAL-ROTATION BARRIERS first reorientating state by equating mo2Bhto the barrier energy and solving for mo. This gave mo = 8, so that in this case, which led to probabilities labeled P1~(1), the first summation in eq 1 ranged from 8 to 12. Also the energies in the first summation were expressed relative to the potential minimum rather than to the i = 0 torsional state. An alternate manifold was determined by following Pitzer* more closely so that mo was obtained from the assumed equality mo2
= [(barrier energy)/2]/Bh
so that for a 1.07-kcal barrier mowas taken as 6, and the energies in eq 1 were all expressed relative to the i = 0 torsional state. This manifold thus gave the probability P l A ( 2 ) , the temperature dependence of which is compared with that of Pl~(1) and A for pure Hn4B in Figure 5. The correspondence between the plots of P l A ( 1 ) and A, as judged from their general shape and the position of the inflection points (dA/dT),i, and (dP/dT),,,, is satisfactory (-220 vs. 203°K)) whereas the inflection point in the P l A ( 2 ) curve appears at a significantly lower temperature (180°K). Since the inflection points for the P l ~ ( 1 )and A curves in Figure 5 could be brought into coincidence with a slight increase in the assumed barrier height, a causal relationship between the dependence of P 1 A and A on T is suggested. Moreover, the P l A ( 2 ) and A curves become compatible when a barrier of 1.53 kcal is used in eq 1. Since this is slightly less than the barrier deduced from nmr data,s it is apparent that the experimental A us. T curve for pure HMB, whether interpreted in terms of PlA(1) orPlA(2),points to a rotational barrier within the 1.07-1.60-lccal range established by neutron-scattering and nmr measurements. Although PlA(2) is possibly more soundly based theoretically so that our analysis tends to favor the nmr value for the barrier height, we have compared P 1 ~ (with l ) A in the 90-300°K range for the 2: 1 and 1: 1 complexes of HMB with TCNE with an estimate of the change in the barrier to methyl group rotation in these complexes as the main objective. Since, as Figure 3 indicates, the inflection point in the A us. T curve for the 1: 1complex occurs at -210"K, the indicated barrier height is only slightly less than for the pure solid HMB. On the other hand, the entire curve for the 2: 1 complex (Figure 3) is obviously displaced to lower temperatures, and, to match the inflection temperature of -170"K, the barrier height used in evaluating PIA(^) was reduced to 0.83 kcal. Thus, relative to pure HMB, the barrier to methyl group rotation is apparently reduced in both the 2: 1 and 1: 1 complexes with the effect much more pronounced in the 2: 1 case.
IV. Discussion A decrease in barrier height as a result of charge trans-
\
1
10 I0
140 I
220 I
180 1
,
260 I
300 1
TCK)
Figure 5 . Comparison of the temperature dependence of A, P l ~ ( l )and , P I A ( 2 ) for pure HMB in the range of 10030O0K: ----,A; --, PlA(1); ' ' ', PlA(2).
fer from the HMB donor is not surprising, since this action would logically reduce any methyl carbon-bensene ring double bonding. However, since this donor action is more extensive in the 1: 1 than 2 : 1 complex, charge-transfer action alone should lead to a lower barrier in the 1: 1than in the 2: 1complex. Since this is not observed, it is obvious that some other factor is dominant and, therefore, our results cannot possibly give a quantitative measure of the influence of charge transfer on barrier height. It appears that to understand the relationship between the internal-rotation barrier heights determined for pure HMB and its complexes with TCNE one must consider lattice structures and intermolecular interactions as well as the per cent of electron transfer. The lattices are all characterized by stacking of planar molecules with dominant intermolecular forces between molecules within a tack.^,^ However, the interplanar distances in 1: 1 complexes are known to be significantly shorter than for pure organic aromatic crystal^,^ and, since the 1: 1 crystals are more stable than the 2: 1, it is very likely that the spacing in the 2: 1 crystal is intermediate to that of pure HMB and the 1:1 crystal. Thus it is easy to imagine that relatively weak inter-
s. C. Wallwork, Acta Crystallogr., 8 , 787 (1955); (b) S. C. Wallwork, J . Chem. SOC.,14, 494 (1961). (9) (a) T. T. Harding and
Volume 72, Number 1% November 1068
3974 molecular forces in the 2 : 1 complex permit the effect of charge transfer to be revealed as a significant reduction in the rotational barrier height, whereas the stronger intermolecular forces in the 1: 1 complex effectively counteract any charge-transfer effect. This is a qualitative view, but one potentially important fact is suggested. Intermolecular forces are important in determining internal-rotation barrier heights in crystals and should not be neglected. This observation is consistent with the -0.3-kcal change in barrier height for the 111-11 solid-phase transition in HMB.336 I n any case the principal indications from this study are that the barrier to internal rotation of the methyl groups in HMB is reduced from the pure HMB crystal value by as much as 300join the 2 : 1complexwith TCNE, primarily because of charge transfer, while shorter intermolecular distances, accompanied by stronger intermolecular steric forces, result in cancellation of the major portion of the effect of charge transfer in the 1: 1 complex. The model that leads to these deductions involves several assumptions and simplifications, but there seems to be little doubt that the variation of the parameter A is in some manner related to excitation of the methyl group torsional motions. Perhaps the most unattractive aspect of the uncoupled-rotor model is the necessity to relate the variation in A to free rotation of a single methyl group per HMB molecule. As mentioned, the rotors are in fact coupled so that the concept of a single freely rotating group does not apply. That is, one rotor cannot rotate without perturbing the orientations of all six rotors so that the rotational energy is passed rapidly around the ring. It should be noted that in addition to arguments already made there are other infrared data which support the general approach that has been described.
The Journal of Physical Chemistry
B. WARE,E(. WILLIAMSON, AND J. P. DEVLIN For example, cursory results for the complex HMBchloranil indicate a rotational barrier slightly greater than for the 1:1 HMB-TCNE case. This is consistent with X-ray results which indicate the importance of steric forces involving the bulky chlorine atoms.9 Also, the infrared data for durene (Figure 4) though not quantitative, point to a substantially greater rotational barrier for pure durene than for HMB. As previously noted, this is compatible with the 2 kcal (or greater) barrier that has been reported for durene.'O Perhaps more pertinent is the apparently considerable reduction in the barrier height in the durene-TCNE complex, as indicated by the strong dependence of A on T apparent in Figure 4. This is not surprising, since durene is structured to accept TCNE as a neighbor with less steric interaction than in the 1: 1 HRIIB-TCNE complex. Thus the charge-transfer effect on the barrier may not be canceled by intermolecular interactions. Finally, it is obvious that our results for the 2: 1 and 1 : 1 complexes of HMB with TCNE permit an estimate of the torsional frequencies for these crystals. For the 1: 1 case the predicted value is lower than but within 10 cm-l of the value (120 cm-l) for pure HMB, while a value of -105 cm-l is predicted for the 2 : l complex. A check on this value for the 2: 1 complex would be a critical test of the model used throughout this study. Acknowledgment. The support of this research by the National Science Foundation under Grant GP-6689 is gratefully acknowledged. We are also indebted to the journal referees of this paper for many helpful comments and suggestions. (10) J. J. Rush, Bull. Amer. Phys. Soc., 10, 492 (1965).
