Electron spin resonance spectra of some isotopically substituted

RICHARD W. FESSENDEN

74

Electron Spin Resonance Spectra of Some Isotopically Substituted Hydrocarbon Radicals'

by Richard W. Fessenden Radiation Research Laboratories, Mellon Institute, Pittsburgh, Pennsylvania

(Received September 27, 1966)

Electron spin resonance spectra of the radicals 13CH3,WD3, 13CH3CHz,CH313CHz,WHz= CH, and CH3=l3CH have been observed in the liquid phase using the technique of in situ electron irradiation of hydrocarbons. The difference in the 13C splittings of CH3 (38.34 gauss) and CD3 (35.98 gauss) is interpreted in terms of the amplitude of the out-ofplane vibration. The conclusion drawn is that considerable lack of orbital following occurs. Hyperfine splittings are also reported for the normal and 13C-containing radicals CHzD and CHD2 in a krypton matrix and are used to check in more detail the effect of reduced mass upon both proton and 13Csplittings. The splitting at the CY position in ethyl radical (39.07 gauss) is very similar to that in methyl while the large (107.57 gauss) splitting in vinyl radical reflects the hybrid nature (6.5% s character) of the electron-containing orbital. Splittings a t the p positions in both radicals are small: 13.57 gauss for ethyl and 8.55 gauss for vinyl. The result for ethyl radical is in agreement with the simple molecular orbital treatment of the p-carbon splitting. Also reported is the value for ac at the CY position in cyclohexyl radical (41.3 gauss). The results for methyl, ethyl, and cyclohexyl radicals leave little doubt that in each case the three bonds around the radical carbon are coplanar. However, evidence from other work is drawn upon to suggest that perhaps substituted alkyl radicals such as CHZF, CHZOH, CH,CHOH, etc., may have a somewhat nonplanar configuration at the radical carbon.

Introduction It has long been recognized that carbon-13 hyperfine splittings can yield important information concerning the electronic and geometrical structure of hydrocarbon , ~ radicals. An early determination by Cole, et ~ l . of the 13C splitting in methyl radical (41 f 3 gauss) showed by the relative smallness of this value that the radical is planar, or nearly so, under the particular conditions (C&I matrix, 77°K). The usefulness of the 13C splitting is a result of the direct introduction, upon a departure from planarity, of s character into the orbital containing the unpaired electron together with the large potential splitting by carbon-13-of the order of 300 gauss for an electron in an sp3 hybrid orbitaL2 Evidence for the sensitivity of such hyperfine splittings to the detailed geometry is found in the difference of the 14N splittings in NH3+ and ND3f (isoelectronic with methyl radical). Cole attributed3 the 0.7-gauss or 4% difference to the change with reduced The Journal of Phusical Chemiatry

mass of the amplitude of the out-of-plane vibration. There are possible complications in that the spectra are of single crystals. The radicals are tumbling but not in an isotropic fashion so that only part of the anisotropic contributions are averaged out. Schrader and Karplus have presented4 a detailed treatment of the effect of this out-of-plane vibration upon the splitting by the central atom and have compared their findings with the carbon-13 splittings for CH3 and CD3 measured by us. Details of these experiments as well as splittings for the other two radicals, CH2Dand CHD2,are reported here. The 13Csplittings in these latter two radicals are used to check more fully the dependence of splitting upon reduced mass. (1) Supported, in part, by the U. S. Atomic Energy Commission. (2) T. Cole, H. 0. Pritchard, N. R. Davidson, and H. M. McConnell, Mol. Phya., 1, 406 (1958). (3) T.Cole, J . Chem. Phys., 35, 1169 (1961). (4) D. M.Schrader and M. Karplus, ibid., 40, 1593 (1964).

ISOTOPICALLY SUBSTITUTED HYDROCARBON RADICALS

75

For larger radicals the theory describing 13C splitt i n g ~is~ more complex but has been applied with moderate success to various conjugated radicals. A considerable problem exists,6 however, as how best to treat the splitting by carbon-13 in, for example, a methyl group directly attached to the ?r system. The carbon splittings in ethyl radical are very important, therefore, in helping to understand the theory for the more complex cases. From another point of view, continued interest in the possibility of alkyl radicals with other than planar configurations at the radical carbon' makes it important that 13Csplitting data exist for as many alkyl radicals as possible. Such data will help to determine the degree of agreement with theory and in turn help to establish whether or not radicals with nonplanar configurations do exist. The carbon-13 splittings reported here are a start in this direction. Although the carbon-13 splitting is t h e preferred indicator of radical configuration, these splittings are difficult to determine especially for the larger radicals. One might ask therefore about the behavior of the splitting by protons attached to the radical carbon as the three bonds around this carbon depart from coplanarity. Both an earlier calculation for methyl radical*and the more recent one2predict an increasingly negative proton splitting as the radical is bent. However, the observed departureg of the proton and deuteron splittings in cH3 and c D 3 from the ratio of the magnetic moments is in such a direction as to suggest a less negative splitting for a nonplanar radical. The observation of a small splitting at the a position in cyclopropyl radical (laal = 6.5 gauss) supports such a conclusion. This problem will be discussed further. The techniques developed in this laboratoryg for producing hydrocarbon radicals by steady-state radiolysis of liquid hydrocarbons were used to produce methyl, ethyl, and vinyl radicals in the liquid phase. While this method requires relatively large amounts of isotopically enriched material for the production of labeled methyl radicals, it was possible to produce ethyl and vinyl radicals from a minimal amount of ethylene-l-13C in ethane solution by utilizing, respectively, addition to the ethylene of hydrogen atoms and its enhanced decomposition by energy transfer from the ethane.1° It should be pointed out that spectra of 13C-containing radicals trapped in solids will, in general, be difficult to interpret because of the large anisotropy of the I3C hyperfine interaction. l1 There exist, however, certain radical-matrix combinations which allow sufficiently rapid tumbling of the radicals that isotropic spectra are obtained with line widths (-2 gauss) typical of those produced by intermolecular dipolar

broadening. Use of such systems has been made in obtaining 13C splittings in several cases starting with materials of naturally occurring isotopic composition. Solid cyclohexane between - 87" and the melting point (+So) gives an isotropic spectrum of cyclohexyl radical when irradiated.9*12Near the lower temperature limit the rate of diffusion is sufficiently slow that lines of the proper intensity for radicals containing 13C in the a position can be observed at each end of the spectrum. Similarly, it has been discovered13that methyl radicals produced in a krypton matrix at - 190" tumble rapidly and that sufficient signal is available with normal methane to see the 1% of 13C-containing radicals. By use of 13C-enrichedmethane, it was determined that the spectrum of 13CH3 radical produced in this matrix is changed very little from that in the liquid at comparable temperatures. This matrix method using unenriched (in 13C) CH2Dzwas used to obtain the spectra of 13Clabeled cH2D and cHD2. Very likely other systems will be found which will allow use of natural levels of carbon-13.

Experimental Section The irradiation setup, cavities, and X-band esr spectrometer were those used earlier. The liquid phase and krypton matrix experiments were performed as previously d e ~ c r i b e d . The ~ ~ ~ 13CH4 ~ sample was obtained from Isomet Corp. (57% 13C) and was diluted to a final percentage of 11.8% 13C with Phillips Research grade methane. The 13CD4was obtained from Kew England Nuclear Corp. (25% 13C, 99.5% 2H). Ethy1ene-l-l3C was obtained from Volk Radiochemical Co. (60% 13C) as was the CH2D2. Other materials were as previously reported.9*13

Results Methyl Radicals. Spectra of the radicals 13CH3and W D 3 were taken at -177" in the TE103 cavityg using approximately 6-ml liquid samples of the appropriate 13C-enriched methane. Recordings of the signals observed under typical irradiation conditions (-0.3 pa of 2.8-Mev electrons) are shown in Figures 1 and 2. The ( 5 ) M. Karplus and G. K. Fraenkel, J . Chem. Phys., 3 5 , 1312 (1961). (6) H.L.Strauss and G. K. Fraenkel, ibid., 3 5 , 1738 (1961). (7) F. D.Greene, C. Chu, and J. Walia, J . Am. Chem. SOC.,84, 2463

(1963). (8) M.Karplus, J . Chem. Phys., 30, 15 (1959). (9) R.W.Fessenden and R. H. Schuler, ibid., 3 9 , 2147 (1963). (10)R. W.Fessenden and R. H. Schuler, Discussions Faraday SOC., 36, 147 (1963). (11)(a) H.M. McConnell and R. W. Fessenden, J . Chem. Phys., 31, 1688 (1959); (b) T.Cole and C. Heller, ibid.,34, 1085 (1961). (12) S. Ogawa and R. W. Fessenden, ibid., 41, 994 (1964). (13) R. W. Fessenden and R. H. Schuler, ibid., 43, 2704 (1965).

Volume 7'1, Number 1 January 1967


76

"CH3

'3CH3

3 , 1 , 0,=38.34 -G

Figure 1. The esr spectrum observed a t -177" during the electron irradiation (0.3pa, 2.8 MeV) of liquid methane enriched to 11.8 at. % 13C. This is a second-derivative presentation and field increases to the right. Lines not accounted for by the drawings at the bottom are from the C Z Hradical. ~

I l l

Table I: Hyperfine Splittings of Isotopically Substituted Methyl Radicals" Radical

"CD3

I3CD3

LL

d 1 1 1 1 1 . 0,-35.98G

Figure 2. The esr spectrum during irradiation a t -177" of liquid CDd enriched to 25 at. yo W. Lines of the radicals W D 3 and 13CD3 are indicated at bottom.

aD

23.038 23.04 23,lO 23.10 23.21 23.19

...

...

... 3.531 3.54 3,552 3.55

38.34

t . .

enrichment is quite sufficient to allow identification and measurement of the positions of all of the lines from the carbon-13-containing radicals. No differences in width of the lines in the pairs differing only in the spin of the 13Cnucleus were observed. Unfortunately, therefore, the sign of the hyperfine constant cannot be determined as has been done for a number of radicals by the method of de Boer and Mackor.14 The absence of any effect is probably due to a combination of relatively broad line widths of methyl radical together with the low viscosity of the solvent liquid methane. The hyperfine constants of 12CH3,13CH3,12CD3, and WD3 radicals are given in Table I for the liquid phase experiments. In Table I1 the 13Csplittings are repeated and values of ac added for cH3 and CD, in a krypton Because of the small but quite matrix (at -188'). significant effect of the environment, it is nedessary to have measurements for all four radicals under similar conditions if an accurate intercomparison is to be made. In Figure 3 is shown the spectrum obtained from a 2.0-1. atmosphere of krypton containing an approximately 0.006-1. atmosphere of CHzDz in cavity IIIg a t approximately - 188'. During this experiment the electron-beam current was approximately 0.02 pa. Shown in Figure 4 is the high-field portion of the The Journal of Physical Chemistry

ac

aH

...

3,576 3.578

... 37.82

... 37.06

... 35.98

a I n gauss, signs not determined. Observed in liquid methane a t - 177". Observed in krypton matrix a t -188". Estimated accuracy ~ I ~ 0 . 0gauss. 1 Estimated accuracy f0.025 gauss.

Table 11: Observed and Calculated 13C Hyperfine Splittings" -Obsd-.

IZr Radical

Liquid

matrix

Calcdb

CH3 CHiD CHDz CD3

38.34 . . .c . . .c 35.98

38.53 37.82 37.06 36.18

38.53 37.82 37.04 36.18

a I? gauss, signs not determined. Calculated to fit the CHs and CD3 values from the matrix experiment. Not determined.

spectrum with the region outside the last line of the l2CH2D radical recorded a t a 200-fold increase in gain. The lines from the 13C-containing radicals are readily ~~

~

(14) E.de Boer and E. L.Mackor, J . Chem. Phys., 38, 1450 (1963).


-1

CHDt

d

2'5.2. G

I

L

Figure 3. Spectra of CHzD and CHDZradicals produced by irradiation of CH;D2 in a krypton matrix a t -188'. The small positive deflection just outside the negative excursion on each line is typical of that observed on nearly all methyl radical lines in this matrix. The two larger unaccounted-for peaks, twice an from the center, are probably from a small amount of CDa.

Figure 4. High-field portion of the spectrum of CHzD and CHDZin krypton. Right half taken a t a 200-fold increase in gain. At the bottom the lines of the normal species are indicated and the relationship with the lines of the W-containing radicals is shown. The off-scale line in the high-gain portion is the outer CHa line.

evident. The splittings measured in this spectrum are given in Table I. There are other lines in this outer region which become more evident upon longer irradiation. These are believed to be due to small amounts of various partially deuterated ethyl radicals as is shown by comparison with the spectrum of a sample containing only normal methane. Peculiarly, these lines do not continue to increase with increased dose but reach a steadystate level with their intensity approximately equal to that of the 13C-containingmethyl radicals. One other point regarding the radiation chemistry might be mentioned. Referring to the spectrum of Figure 3, the

77

central three lines of the cH2D spectrum and the tallest pair of lines in the cHD2 spectrum have equal statistical weight. The ratio of heights would, if the line widths are the same, represent the relative probability of losing either a deuterium or a hydrogen atom from CH2D2. A small second-order splitting of the central lines of CH2D helps to overemphasize the difference, but a similar comparison using various outer lines in the spectrum shows that the ratio is between 1.5 and 2 in favor of loss of H over D. This is in the same direction as the relative hydrogen yields from some irradiated normal and perdeuteriohydrocarbons.l5 Eth.yl and Vinyl Radicals. Earlier work with the system ethane-ethylenelO showed that at relatively low ethylene concentrations approximately half of the ethyl radicals came from the ethylene by hydrogen atom addition and that the ethylene decomposed (in part to vinyl radical) as if it were present at about 10 times its actual electron fraction. These results strongly suggested that an experiment involving a solution of 10% ethylene enriched at one position to 50-600/, I3C would provide observable lines for the radical species 13CH3CH2,CH313CH2,13CH2=CH, and CH2=l3CH. The spectrum obtained when an 8.2 mole yo solution of ethylene-lJ3C (60% 13C, 200-cc atmosphere) in ethane was irradiated with 0.045 pa of 2.8-3Iev electrons at -178' is shown in Figure 5 . The cavity designated as I11 in ref 9 was used. The spectra of the two types of 13C-labeled ethyl radicals are quite obvious and are indicated by the line drawing. The vinyl radical signal is somewhat weaker, but a larger percentage of the radicals contain carbon-13. Two of the lines for the radical labeled at the /3 position are observed in this portion of the spectrum as is indicated in Figure 5. Two more lines belonging to the radical with I3C at the a position are at fields higher than those shown in this scan. The four corresponding lines are visible on the low-field side as well as another line for the /3 species which becomes visible because of the asymmetry. Two other lines from the a-labeled radical which fall in the central portion of the spectrum are also visible. Upon slower field scan than that used for the spectrum of Figure 5, the lines of the labeled vinyl radicals have a signal-to-noise ratio of about 3. As with the methyl radical no line width or peak height differences are evident in any of these spectra so that no information regarding the signs of the carbon hyperfine constants is available. The 13C splittings for ethyl radical are laar/= 39.07 gauss and laS/ = 13.57 gauss with an rms deviation M.Burton, Discussions Faraday SOC.,12, 88 (1952),for CsDe and J. M.Yang and I. Marcus, J . Chem. Phgs., 43, 1585 (1965),for c-CaDm (15) See S. Gordon and

Volume 71,Number I

Januaru 1967


7s

----

I , - l_-_- ,

__-

---

CH3CHz

L

I

P

,

-

I

13CH3CH2

-a&)-

I - I L , - I - , -

I ---

_____-/.-----_-_

___-*-

I a&c)

--.___

I ka,(c)--

I

J

CHi3CHZ CH$H

'3Cti2CH

Figure 5. A portion of the esr spectrum observed during irradiation of ethane containing 8.2 mole % eth~lene-l-'~C(60% W).Spectra of the various ethyl and vinyl radicals are indicated at the bottom.

of a number of determinations from the same spectrum of 0.025 gauss. To within the experimental error, correct second-order shifts were observed. The assignment to a and p positions is based on the similarity of the larger value to the splitting in methyl radical as expected from the theory of Karplus and Fraenkel.5 Certain lines of the two types of labeled vinyl radicals could not be observed, as noted above, because of other strong lines a t the expected positions. I n all, six of the eight lines for the a-labeled radical could be measured and five of eight lines for the p-labeled species. I n order to use all available line positions for determining the carbon-splitting constants, the half-splittings from the various lines of the '2C-containing radicals to the corresponding lines in the 13C radical spectra were determined. These values, depending upon whether they represented high- or low-field displacement, were corrected for the second-order shift corresponding to the carbon splitting (about 0.9 gauss for the larger splitting). After this correction, the half-splittings agreed with an rms deviation of about 0.025 gauss. The hyperfine constants for vinyl radical are jaaI = 107.57 gauss and jaal = 5.55 gauss. The larger value is assigned to the radical labeled a t the a position because in this radical the electron is believed to be in a hybrid orbital with a direct carbon 2s contrib~tion.~ Based on equal line widths for all radicals, the labeled ethyl radical lines are expected to be 9.7y0 of the intensity of those of the 'ZC species (assuming 45% of the ethyl radicals come from the ethylenelO and that hydrogen atom addition is equally likely to either carbon of the labeled ethylene). The observed perThe Journal of Physical ChemGtry

centage is 9.2 with an error of about f1. The expected intensity for the lines of the labeled vinyl radicals is 38% that of the lines of the nonlabeled radicals while the observed value is around 25%. Probably some vinyl radical production is coming from unenriched ethylene produced in the radiolysis. Cyclohexyl Radical. The radiation of -6 cc of solid cyclohexane in cavity IIIgat -SOo produced spectra of cyclohexyl radical sufficiently intense that lines of approximately 0.5% intensity could be observed at a signal-to-noise ratio of approximately 3 outside the end lines of c - C ~ H I (see I Figure 6 ) . Although there is always the possibility that these lines are produced by some other minor species, the correct intensity and spacing to the end lines (including a 0.13-gauss secondorder shift), the appearance on one end of the weaker second-from-the-end line, and the lack of any other lines further out were together taken as sufficient proof that these lines are due to the W-containing species. The intensity ratio shows that the lines are from the radicals labeled at the a position. The splitting (41.3 gauss) is similar to the splittings a t the a positions of methyl and ethyl radicals. For certain of the purposes of this paper it is important only to demonstrate that the splitting is not large, as it would be for a nonplanar radical carbon. The absence of lines further out in the spectrum accomplishes this.

Discussion Methyl Radieals. The results for the methyl radicals will be discussed using the theory of Schrader and Karplu~.~ As mentioned in an earlier paper,la their


b R

79

of these radicals. For 6F3, at least, there can be little tendency for bent bonds because the value of ac is close to the maximum possible for a tetrahedral radical. First we will discuss the methyl radical using eq 2 with only the parabolic term in O2 included and show that the results of Schrader and Karplus for complete orbital following can indeed be calculated this way. The reduced mass, m,, for the out-of-plane vibration of a planar XYZZmolecule (Y is the central atom) in the special case where the XY and ZY bonds are of the same length and from equal angles with each other, can be written w nzr-’ = (2/mz) (l/mx) (9/my).16 The (transition) frequency is then

Figure 6. The spectrum of solid cyclohexane a t -80’ during irradiation. The outer portions are a t a 200-fold increase in gain and show lines attributed to cyclohexyl radicals containing 1aC a t the a position. Two unidentified lines (somewhat closer to the center) are also found in these high-gain portions.

+

v

-(-) 1 ICA

=

+

‘I2

2.rr 12m, calculated 13C hyperfine constant as a function of the angle of bend can (for complete orbital following) be expressed with very little error by

@(e)

= m(0)

+ 1190(2 tan28)

(1)

where 8 is the angle between the CH bonds and the plane of the three hydrogen atoms and 2 tan2 8 is the s character of the orbital containing the unpaired electron. With the replacement of 2 tan2 B by 2B2 (for small 8) this equation contains the first two terms of the general power series expansion a(e) = ao(o)

+

&e2

+ a4e4 + . . .

(2)

Because of the symmetry about the planar configuration, any actual behavior must be expressible in this form. For sufficiently small values of B only the first two terms will be needed. Comparison with eq 1 shows that to this approximation a2 should be taken as 2380. Complications such as incomplete orbital following will modify the coefficient a2 while a variation in following with angle will greatly modify the coefficients a4, etc. Since Schrader and Karplus showed4 that the extent of breakdown of the Born-Oppenheimer approximation is very small, determination of the splitting involves only finding the expectation value P. It should be noted that the basic features of the theory of the carbon-13 hyperfine splitting have been proven correct by the existence of radicals in which large I3C splittings are observed owing (presumably) to a large degree of bending and the consequent large s character to the orbital containing the unpaired electron. The clearest examples are CF3 (ac = 271 gauss),13 c H F 2 (ac = 1 4 9 gauss),l3 and vinyl radical (ac = 108 gauss, see below). Although some perturbation is expected upon fluorine substitution, it is highly likely that much of the increase is due to simple bending

where 1 is the bond length and the force constant leA refers to the coordinate A, the angle between the X Y bond and the plane containing Y and the two Z atoms. The angle B defined above is one-third of A near the planar configuration. For a quantum mechanical harmonic oscillator %’, the average of the square of displacement, is given by” -

E

x 2=

IC

For small displacements the average e’l over the oscillation is -

82 =

1-xz 912

Combining these we can write

where ml is the mass of the proton, is ml/m,, and vo = (l/2i~)(le~/1~m~)”~. Using the value of 447 cm-l given by Herzberg’* for ~ 2 ’ ’ of CD, and a CH bond length of 1.079 A, we have finally e2

= (0.536

x

io-2)cp’/*

Values of 9 calculated from this can be substituted into 24.5 and a0 18.9, respeceq 2 giving (in gauss) a0 itively, for ac of CH3 and cD3. For comparison, the increments above a0 calculated by Schrader and Karplus are 23.81 and 18.23. The close agreement of the two

+

(16) G.Hersberg, “Infrared and Raman Spectra,” D. Van Nostrand Co., Inc., Princeton, N. J., 1945,pp 179, 180. (17)H. Eyring, J. Walter, and J. Kimbal, “Quantum Chemistry,” J. Wilev and Sons, Inc., N~~ York, N. y.,194, 1) 39. (18) G.Hersberg, Proc. ROY. SOC. (London), ~ 2 6 2 , 291 (1961).

Volume 71, Number 1 January 1967


80

sets of values demonstrates the validity of our approximations. The difference between the values for the two radicals is about twice that observed and the absolute values are too large with reasonable values of ao. The conclusion, which follows from this, that complete orbital following is not consistent with the observed splittings, was reached by Schrader and Karpl~s.~ A different way of looking at the problem is to use the calculated values of 3 and the observed splittings for CH3 and CD3 to determine a. and a. The values so determined are a. = 28.27 and az = 997 using the data from the matrix experiments. The splittings found in the liquid phase experiments require a slightly adjusted value of no = 28.03. The simplest interpretation using the idea of incomplete orbital following is to say that the degree of following does not change with angle so that the value of p19 is (997/2380)”’ = 0.648. The data for CH2D and CHD2 can be used to check whether there is any evidence for a decrease in orbital following with increased bending as considered by Schrader and Karplus. As noted above, a change in p with angle will be evident through a term in 04. If such a term is important, there should be a departure of the observed values of ar: for CHzD and CHD2 from that predicted using the respective reduced masses and the a0 and a2 determined from the data for CH3 and CD3. The essentially perfect agreement shown in Table 11 gives no evidence for a large term in 04. Very recently, Andrews and PimentelZ0have detected infrared absorptions due to methyl radicals in an argon matrix. They conclude that the frequency of the out-of-plane vibration for CD3, for example, is 567 cm-l instead of 447 cm-I as used above. While this places some doubt upon the interpretation of Herzberg’s ultraviolet spectrum,’* the new value causes no change in our conclusion that a lack of orbital following is present. The value of a2 calculated from these new data is 1265 gauss and is still nearly a factor of 2 less than the expected 2380 gauss. An approach similar to that taken in treating the 13C splittings may be used in discussing the proton and deuteron splittings. Substitution of U H for ClH3 and CHD2 into equations of the form of (2) along with the appropriate values of 9 allows one to solve for a0 and az. The values found are a. = -24.46 gauss and a2 = 141.0 gauss with the sign of a. chosen to agree with theory. The predicted value for CHzD is shown in Table 111 and is within experimental error of the measured value. Also in Table 111 are the values for UD calculated from the U H value and the ratio of the magmoments.~h~ amountand direction of variation with reduced mass is in agreement with this calculation, The Journal of Physical Chemiatry

but there is still a deviation from the expected ratio of for the two radicals containing both H and D. The ratios of the observed splittings (UH/UD) are 6.541 for cH2D and 6.534 for CHD2. The departure from the expected value of 6.514 is about 0.3% and is 3 or more times the estimated experimental error based on scatter in the various spacings measured in these particular spectra. The splitting found for CD3 is also lower (by a similar amount) than that predicted in this same calculation. The departure from the theoretical ratio is not easily explained. It cannot be due to a “firsborder” effect of the out-of-plane vibration, as for small vibrational amplitudes there is in the first approximation still a threefold symmetry axis for any instantaneous configuration of the radical. 21 The singly occupied orbital will be directed along this axis and undergoes some rocking motion as the vibration occurs. Possible sources of the deviation of the ratio UH/UD from the theoretical are in-plane vibrations, a slight breakdown of the assumption of small vibrational amplitudes,22and matrix effects which somehow perturb the form of the out-of-plane vibration. The results for CHzD and CHDz give a limit to the degree of agreement which may be expected for calculations of the ratio a H / a D based only on the out-of-plane vibrational amplitude. In the calculation by Schrader and K a r p l u ~ using ,~ their first-choice values for the various integrals, an increasingly negative value for the hydrogen hyperfine constant was found as the radical was bent. No attempt was made to bring this feature into accord with the observed increase in the magnitude of the deuterium splitting in c D 3 over that expected by comparison with the splitting in CH,. It was noted,4 however, that there existed reasonable adjustments in the values of the integrals which could bring the ratio of splittings in CH3 and CD, into agreement with the experimental ratio without causing large perturbations in the calculated values of UH and ac. These adjustments were said to effect the change by modifying the direction of the variation of U H with angle at small departures from planarity. I n the results for the radicals given here it is clear that the parabolic form,

UH/UD

(19)As used by Schrader and Karplus,‘ p is a multiplicative parameter modifying 6. In all expressions 6 is replaced by PO. (20) W. L. S. Andrews and G. C. Pimentel, J. Chem. Phys., 44, 2527 (1966). (21) R.E.Moss [Mol.Phys., 10,339 (1966)]has treated the hydrogen splittings for CHa and CDa in a somewhat similar manner and has included the temperature dependence. He also predicts no deaarture of the ratio a d a D from 6.514 in this model. (22) A measure of the importance of such an effect is cos 0 2 which shows the fractional change in band length for motion perpendicular to the (instantaneous) planar form. This value is around 0.995,or a 0.5% change,


81

eq 2, works well and that much of the effect must come from the variation in zero-point vibrational amplitude. Because of the small change in UH with reduced mass, a moderate contribution from a4O4would not significantly affect the agreement between experiment and calculation for c H 2 D but would only modify the a0 and a2 coefficients. It is, therefore, necessary to look elsewhere for evidence concerning the behavior of U H for larger angles of bending. Geometry of Other Radicals. Except for the vinyl radical, which has available considerably different hybridizationj the only hydrocarbon radical which shows evidence of being significantly bent is the cyclopropyl radical where /arr(= 6.5 gauss. It is clear from this that a large decrease in U H with angle is possible, but the exact interpretation may be complicated by the strained ring. To investigate this small U H further, it should be determined if such a value for UH can be consistent with an equation of the form of (2). Because we have associated the variation in UH (as well as ac) with the bending and have concluded that there is a significant lack of orbital following in methyl radical, we need to increase the value of a2 to a2/p2 if we wish it to correspond to a radical in which the equilibrium geometry is nonplanar and little bond bending occurs. The value so calculated is (141) (2380/997) = 337 gauss. A radical with tetrahedral geometry (0 = 19.5’) would then be expected to have a hydrogen 337(0.34)2 = +14.8 gauss. splitting of -24.2 Clearly, the UH value of cyclopropyl radical is at least possible in this scheme. The CHF2 radical mentioned above is an apparent anomaly in that the 149-gauss carbon splitting indicates a rather large degree of bending while the hydrogen splitting is a quite normal 22.2 gauss. It was suggested earlierI3that this hyperfine constant might be positive rather than negative as in the usual case. A certain conclusion is that there is none of the behavior predicted by Schrader and Karplus as their expected value of UH for 0 = 12.7’ (from the 13C splitting) is -28 gauss. The radical CH2F with ac = 54.8 gauss13 does not allow any definitive conclusions regarding its possible departure from planarity as the increase over ac of methyl radical may be due to the substitution. This radical is, however, one of those which has been predicted by WalshZ3to be nonplanar, so other similar radicals should be considered. A radical most closely related to it is CHzOH which along with other a-alcohol radicals has somewhat unusual hyperfine splittings. Perhaps the unusual features of these spectra can be explained by a slight departure from planarity. The alcohol radicals are produced by abstraction of

hydrogen from the parent alcohol. This abstraction is effected either by the “OH radical” produced by H202 in a flow experiment (the technique of Tia+ Dixon and Normanz4) or by the OH radical produced in peroxide photolysis. 25 Because the resolution is better in the latter experiments, values for splittings from this work will be quoted whenever possible. Typical a-hydrogen splittings are 17.4 gauss in cHzOH and 15.4 gauss in CH3CHOH. The drop from the 23gauss value in methyl radical has been attributed to a loss of -0.25 of the spin density onto the hydroxyl oxygen. The CHI splitting in cH3CHOH of 22.2 gauss would seem to confirm this but the carbon splitting in c H 2 0 H (ac = 47.6 gauss)26 does not, because loss of spin density from the radical carbon would be expected to reduce the 13Csplitting from the methyl value rather than raise it. Comparison of the splittings in the radicals derived from allyl and benzyl alcohols also raises considerable doubt about such an explanation. In the photolysis experiment both cis and trans isomers of the radical CHZCH=CHOH (1-hydroxyallyl) are observed.25 Taking twice the average splitting on the 1- and 3-carbon less that on the 2-carbon gives 24.03 and 23.72 gauss, respectively, for Q of the “strong” and “weak” isomers. The value in allyl radical itself is 24.7 gauss. With the benzyl radical the reduction in splitting at the methylene position upon hydroxyl substitution is from 16.427to 14.97 The sum of the splittings by the ring protons in the radical C6HSCHOHis similarly reduced from 20.07 to 18.90 gauss. The very small change upon hydroxyl substitution in these conjugated radicals is very hard to explain when contrasted with the behavior in the saturated alcohols. An effect which may be related to the large difference between c H 3 and cHz0H is the relatively large perturbation of arrin the a-ethanol radical upon replacing CH3 by CF,. The values of a, are 15.4 gauss in CHIcHOHZ6and 18.16 gauss in CF&HOH.28 This change is rather large in view of the fact that the same substitution in ethyl radical itself changes arr by only half as much from 22.4 gauss in CH3cHZ9to 23.9 gauss in CF3CH~.29

+

+

(23) A. D. Walsh, J. Chem. SOC.,2306 (1953). (24) W. T. Dixon and R. 0. C. Norman, ibid., 3119 (1963). (25) R. Livingston and H. Zeldes, ibid., 44, 1245 (1966). (26) H. Fischer, private communication. In discussions with the author he also suggested that the slightly high carbon splittings in CHzF and CHzOH might indicate a slightly nonplanar structure. (27) H. Fischer, Z. Naturforsch., 20A, 488 (1965). (28) P. Smith, J. T. Pearson, and R. V. Tsina, Can. J . Chem., 44, 753 (1966). (29) R. W. Fessenden and R. H. Schuler, to be published.

V o l u m e 71,Number 1 January 1967

82


It is suggested that perhaps the explanation of these various facts may lie in a slightly nonplanar configuration areund the radical carbon of carbon of these radicals. Small changes such as substitution of CFs for CH3 might be expected to tip the energy balance enough to cause a relatively large change in configuration. The presence of the conjugated system in allyl and benzyl radicals would stabilize the planar form of the carbon a t the substitution site. Serious drawbacks to this proposal are the lack of a significant change in the proton splitting in CH2F (UH = 21.1 gauss) as well as no evidence that a 6-%gauss reduction in a H (a position) can be accompanied by only a modest increase in ac. The best that can be concluded, therefore, is that there is no consistent picture but that there are some rather strange facts to be explained, some part of which can no doubt be explained by specific effects of substitution and withdrawal of spin density onto the OH group in the alcohol radicals. Until a better understanding of the various aspects of this problem exists, the idea that substituted alkyl radicals may have a nonplanar configuration cannot be rejected lightly. Ethyl, V i n y l , and Cyclohexyl Radicals. In discussing the carbon-13 splittings in ethyl radical, the theory of Karplus and Fraenkel will be used. This theory is in the form5 3

a~

=;

(8'

3

+ CQcxiC)P~ + CQxicC~r" i=l

i=l

where the parameters Sc and QCX? describe the contribution from spin density on the carbon under consideration, these Q's taking into account the properties of the three bonds to the carbon, and the QX,cctaking into account the effect of spin density on adjacent atoms. The values given by Karplus and Fraenkel are (in gauss) Sc = -12.7, QCH' = 19.5, Qcc,' = 14.4, and &coC = -13.9 for carbon atoms with equivalent sp2 hybrid bonds and a C-C bond length of 1.38 A. For the ethyl radical the appropriate values are Qcc~' = 30.0 and QCW" = -20.9 gauss.6 From the value of 39.07 gauss a t the a position in ethyl radical it is seen that changing from a CH bond in methyl radical to a CC bond in ethyl has little over-all effect. The spin density on the methyl group (of the order of 0.08)9 is not expected to decrease ac greatly because of its small magnitude. It is clear, therefore, that Qcc~' is not much larger than QcHc. I n view of uncertainty in the magnitude of the effect produced by the spin density on the methyl group and the similarity of the splitting to the CH, value, it does not seem profitable to determine a Qcctc value. This is particularly The Journal of Physical Chemistry

true in view of the contribution to the 13C splitting by the out-of-plane vibration discussed in earlier sections. The P-carbon splitting is less than the Qcc~" value of -20.9 gauss so that the -0.08 spin density on the methyl group seems to contribute somewhat to the P splitting.30 The result that the /? splitting is relatively small is similar to that found for various methylsubstituted semiquinones where Strauss and Fraenkel'j concluded that the P-carbon splitting was proportional to the proton splitting of the methyl group with a constant of proportionality less than 1. It is clear, from their discussion of the large difference in the predictions of the valence bond and molecular orbital theories for the /?-carbon splitting in ethyl radical, that the 110 picture is much closer to the truth for this particular problem than the simple VB treatment. The /?-carbon-13 splitting in vinyl radical, though smaller, is of similar magnitude to that in ethyl radical. The difference is not too surprising in view of the different hybridization for this radical. The large aJ3C splitting of 107.57 gauss confirms the earlier conclusion that the unpaired electron is in a hybrid ~ r b i t a l . ~ Using 30 gauss as the value for a pure p orbital, the 77-gauss excess above this corresponds to approximately 6.5% s character. Such a hybrid corresponds to an HCH angle of 151' which is in the range suggested by Cochran, Adrian, and Bowers31 on the basis of the a- and /?-proton splittings. Since their calculated a-proton splitting is +5 gauss a t this angle, it is most likely that the observed coupling constant, lael = 13.4 gauss, is of positive sign. It should be pointed out that if, for the vinyl radical, one could observe the effect, upon both the a-hydrogen (deuterium) and the a-carbon-13 splittings, of substituting deuterium for hydrogen at the a position, the relative direction of the changes gives the relative signs of the hydrogen and carbon splittings. This will be true whenever the isotope effect can be ascribed to changes in the average bond angle and when a good theory exists for the direction of the change of hyperfine splitting with angle. For vinyl radical the small absolute value for a, shows that a, must become more positive (less negative) for increasing departures from a 180' HCC angle. The results f6r the cyclohexyl radical were included in this paper because this radical is specifically one of those for which a nonplanar configuration at the radical carbon has been postulated on chemical grounds.'

(30) We are assuming, in the absence of any experimental evidence, that the 8-13C splitting is negative as predicted by this theory. (31) E. L. Cochran, F. J. Adrian, and V. A. Bowers, J . Chem. Phya., 40, 213 (1964).


A 13Csplitting very similar to that of ethyl and methyl radicals is observed and is assigned to the a position. Even if there is some doubt as to the assignment of the observed lines to the 13C-containingcyclohexyl radical, any larger splitting would easily have been observed. This radical then must also have a configuration around the radical carbon close to planar. The clear results on this point for the three alkyl radicals considered here would seem to answer this question in a definitive fashion for all the more usual alkyl radicals if it were not for the various possible problems discussed above for substituted radicals. Until more *Tdata can be accumulated and until a better understanding of the behavior of a-proton s’plittings for nonplanar radicals is obtained, the situation is somewhat unclear. There is, however, no evidence from the spin resonance results to believe that alkyl radicals with normal values of aHat the a position are other than planar at the radical site. ~

~~~

Table III : Experimental and Calculated Proton and Deuteron SplittingsQsb -Obsd--

y C a l o d c -

Radical

aH

aD

CHa CHzD CHDz CD3

23.00 23.10 23.21

...

...

3.531 3.552 3.568

aH

23.00 23.10 23.21

...

aD

*.. 3.546 3.563 3.581

* Values are given for the a I n gauss, signs not determined. W-containing radicals in a krypton matrix. The shift in U H with reduced mass in going from W H a to WHa, etc., is calculated to be less than the experimental error. Calculated to fit a H of CHs and CHDZ. Values of UD calculated from U H and t,he ratio of the magnetic moments. Acknowledgment. The author gratefully acknowledges conversations with M. Karplus, who suggested that results for 13CD3 would be important. He is

83

also indebted to H. Fischer for permission to publish the latter’s 13C splitting for cH20H. The help of S. Ogawa with certain of the experiments is also appreciated.

Discussion M. W. HANNA (University of Colorado, Boulder). You quote calculations of Schrader and Karplus which indicate that the proton hyperfine coupling should become more negative as the radical becomes bent. Your experimental values indicate that these splittings may become more positive. Is the result of Schrader and Karplus dependent on parameters which might account for this discrepancy, or is a new theoretical approach or experimental interpretation necessary? R. W. FESSENDEN.Schrader and Karplus were able to get a positive-going proton splitting for a bent methyl radical by changing one of the less accurately known parameters. This same change also brought the calculated 13C splitting down and into better agreement with experiment. I do not wish to judge whether the value necessary to bring about this better agreement is likely or not.

M. C. R. SYMONS (University of Leicester, Leicester). With reference to the possible pyramidal configuration of RzCOH radicals, I would like to recall our postulate that the C-XO? group in organic nitro anions is slightly pyramidal. Solid-state studies have shown that as the spin density on NO2 increases, so the p/s ratio calculated from the 14Nhyperfine tensor decreases, and we suggest that this is due to an increase in the deviation from C-NO? planarity. M. T. ROGERS(Michigan State University, East Lansing). We have observed the esr spectrum of the methyl radical a t 77°K in irradiated sodium acetate trihydrate single crystals where one might possibly expect the average of the square of the displacement (3)to be smaller than in the liquid phase or the krypton matrix. The radicals appear to be reorienting about their threefold axes but the proton and 13C hyperfine splitting tensors were found. The isotropic proton splitting (22.3 f 0.5 gauss) and 13C splitting (37.7 f 0.5 gauss) both tend to be smaller than for the radicals in the liquid phase or krypton matrix. Unfortunately, the effects are small and our probable errors are rather large, partly because of the broader lines in the solid. However, if one takes the low 13C splitting as consistent with a somewhat smaller value of $, then our data associate a less negative value for the proton hyperfine splitting with a lower 82.

Volume Y l , Number 1 January 1967

Electron spin resonance spectra of some isotopically substituted

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