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Nuclear spin-spin coupling between fluorine and hydrogen in fluorobenzene
JOVRSAL
OP
MOLEC’I’LI\R
Nuclear
SPECTROSCOPY
2,
(1958)
%?&.%8
Spin-Spin Coupling between Fluorine Hydrogen in Fluorobenzene
Chemical Laboratory
of the
lTniver.sity of Copenhagen,
Copenhagen,
and
Denmark
J. ?\;. &IOOLERY Varian _4ssociates,
Palo
Alto,
California
AND
Deparfment
of Physics,
Stanford
University, Palo Alto, California
High resolution proton and fluorine nuclear magnetic resonance (nmr) spectra of fluorobenzene, 3D-, 2,4,6-Ds-, and 2,3,~,6-D*-fll~orob~nzene have been obtained and analyzed. Double irr~di&tion techniques were employed to eliminate the effects of t,he denterium nuclear spin. The secular eqnation for 4IMuorobenzene has been solved and the parameters adjusted for the best correspondence between the predicted and observed spectra. The nuclear spin couplings between t,he fluorine nucleus and the ortho, meta, and pttr:t protons :xe found to be, respectively, 9.4 f 0.2 cps, 5.8 f 0.2 cps, and 0.0 k 0.5 cps. These couplings are found too have the same sign as t.he proton-proton couplings in the fluorobenzene molecnle. This result is discussed and related t,o previous work on Auorobenzenes. INTRODUCTION 111 3 rerent publication on the nuclear spin-spin coupling in substituted beuzenes Baker (2) has st,ated that, “the ~u~~~~~~resonance spectrum of fluorobe~lze~le by its Rlultipli~it,y and intensity distrib~~tion shows that, t.he protons all couple equally t,o the fluorine. Equalit~y of coupling strikingly demonstrates the effect, of a-bond resonance, since the coupling is passed undiminished around the ring. In the corresponding proton spectrum :I spin-spin doublet is observed (coupling constant 6.6 cps). Since no internal chemical shift is evident in the prot,on spectrum, the hydrogens are ~hemi~~~Ily equivalent, and resonating structures bearing formal charges must be proport,ioI~ed to fulfiI1 this condition or be negligibie”. 525
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FIG. 1. High resolution fluorine nmr spectrum of fluorobenzene at 30 Mc/sec. Magnetic field increases linearly from left to right. Horizontal scale is calibrated in cycles/second. To most chemists this conclusion will be rather surprising. For example, fluorine attached to a benzene ring strongly directs bromine into the para position. The problem, therefore, highly deserves further investigation. Since the publication of Baker’s paper, increased stability in the strong applied magnetic field has been obtained, resulting in much higher resolving power of available nuclear magnetic resonance spectrometers. A glance at the proton and fluorine resonance spectra now obtainable shows, however, a richness of reproducible details which would require an interpretation based on a laborious solution of a complex secular equation. The fluorine spectrum is shown in Fig. 1. It was decided, therefore, to take advantage of the fact that substitution of hydrogen by deuterium greatly simplifies the spectra inasmuch as all couplings between the deuteron and other nuclei are about six times smaller than the corresponding proton couplings. In this respect deuterium substitution serves as a means of “blacking out” a certain number of protons. This makes the interpretation of the result much easier without, however, introducing any appreciable changes in the electron-distribution function of fluorobenzene which would result if one or more of the five hydrogen atoms had been substituted by fluorine, bromine, etc. EXPERIMENTAL The preparation of two of the deuterated species of fluorobenzene investigated here has been reported elsewhere (2). The 2,3,5 ,6-D4-fluorobenzene, not described earlier, was prepared at room temperature by bubbling anhydrous DC1 (from C$H&OCl and D20) through para-bromo-fluorobenzene (13.5g) to which 2g AlCh had been added. In this way the hydrogen was replaced by deuterium. The exchange procedure was controlled by observing the proton resonance spectra of small samples withdrawn from the flask at one-hour intervals. When the integrated intensity of the proton-resonance pattern had fallen to 5-10 % of its initial value, the exchange was interrupted. The tetradeutero-bromo-fluorobenzene was separated from AlCl, and some higher-boiling products by distillation in vucuo. After shaking with water for removal of DCl, drying over PzO5 and a second vacuum-distillation, 9g of 2,3,5,6-DJ-bromo-fluorobenzene was obtained. This quantity was added to a mixture of 20g CH&OOH, 50g H20, and 32g Zn-dust, contained in a 250-ml flask with reflux condenser. The mixture was kept at 100°C
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527
for 24 hours during which the bromine was quantitatively replaced by hydrogen without exchange of the deuterium atoms (3). The 2,3,5 ,6-D4-fluorobenzene was isolated by vacuum-distillation together with some water from which it was separated mechanically. After drying over P$& the sample was again distilled in NWUO at constant t#emperature, the pressure of each fraction taken being read. Due to a mishap during one of the operations the final yield was only 200 mg. This sample had, however, the same vapor-pressure as ordinary fluorobenzene. The quantity was sufficient for the nuc>lear magnetic resonance investigation. All features in the proton and fluorine spectra taken verified that its composit’ion was as postulated. The instrument used was a Varian Associates Model V-4300B High Resolution Nuclear Magnetic Resonance Spectrometer with fixed resonance frequencies of 30 M(*/sec and 40 Mcj’sec. In proton resonance experiments t,he applied magnetic, field intensity was then about 7050 and 9395 oersted, respectively, whilt iu fluorine resonance experimentjs it was 7500 and 10,000 oemted. ,1uxiliary apparatus was available which permitted st,rong irradiation at thcl deuterium resonance frequency, 4.605:3 M(*/sec, while the proton resonance* :tt 30 J\lc!sec was observed, and at bhe fluorine resonanc’e frequency, 37.630 IZIr I SW, while t,he proton resonance at, 10 M(a/sec was observed. This apparatus has been described elsewhere (.4j. Line separations in cycles/second were determined by the usuul audiofrequcnc*y sideband t)echnique. Since it was iut’ended to make all calculations with energies esprrssed in cyples/second, t)his method of measurement yielded the dnt:l in Louvrnieilt form. INTERPRETATION 2 ,.I ,:i ,Ci-Do-JEuorobenzenc.--This molecule has :L single proton para to the fluorine. The proton resonance consists of a number of complet,ely unresolved lines grouped around a pronounced maximum as shown in lcig. 2a. The deut,erons couple their spins to t,he prot,on t’oo weakly to permit’ resolution of the man? possible lines corresponding t,o t’he various deuteron spin orientat,ions. Howe\:er, if t,hc 1:-H coupling were appreciable, the pattern ought to display a doublet character. The fluorine resonanre spectrum shows the same general features. In order to determine the magnitude of the F-H para coupling it was necessary t’o resort t’o the t’echnique of “spin decoupling” in which the deut,erons were strongly irradiated at their resonance frequency while the prot,on spectrum was recorded. By this technique the effect of the proton-deuteron spin couplings was eliminated. The resulting spectrum, Fig. 2b, shows a very sharp line with a halfint#ensity width of approximately one cycle per second. Therefore, bhe para F-H spin-spin interaction is shown to be less than 0.5 cps. 2 ,/t ,A-DJYfluorobenzene.-This molecule has two hydrogen atoms in t,he posi-
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WILLIAMS
tion meta to the fluorine. The proton nmr spectrum showed two broad lines of equal intensity, Fig. 3a, with a peak separation of about 6 cps. The broadening is again due to interactions of each proton with the two nearest deuterium nuclei. In another experiment, the deuterons were again irradiated at their resonance frequency while the proton resonance was observed. Two equally intense, very sharp lines were observed with half-intensity width of 1.0 cps (Fig. 3b). The frequency separstion was 5.8 =t 0.2 cps. Thus the meta F-H coupling, J,rfIF, is is 5.8 & 0.2 cps. Interesting ~ddition~~l i~lformation was obtained by obser~ri~lg the fluorine resonance spectrum of this molecular species. ITnder high resol~~t.ioll 13 resolved lines were observed, shown in Fig. 4. Since t,he appearance of the spectrum suggests t,hat two of the lines each arise from coincidence of two lines in a simpler pattern, we are led to the following interpretation. The fluorine resonance is split by the protons into a triplet with intensities 1:2: 1 and a line separation of 5.8 cps. Each component of the triplet is further split into 5 lines with intensities 1: 2: 3: 2: 1 corresponding to equal interaction with tsvo nuclei of spin I. The measured coupling is 1.38 f 0.1 cps. Intensities of the 13 lines should occur in
FIG. 2. (a) Tracing of the proton resonance at 30 Mc/sec of 2,3,5,6-Da-fluorobenzene. (b) Tracing of the proton resonance at 30 Mc/sec observed while irradiating the deuterium strongly at 4.6053 Mc/sec.
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the ratio 1:2:3:2:3:4:6:4:3:2:3:2:1 which agrees well with Fig. 4. In addition toconfirming the result that the meta F-H coupling is 5.8 cps, the spectrum serves to establish the ortho F-H coupling. This is calculated from the ortho F-D coupling by multiplying by Y=/Y~ , which is 6.54. This gives a value of 9.0 f 0.7 cps to t#he ortho F-H coupling, designated JoHF. It wold be desirable to confirm this result directly and simply in either 3,4,5Ds-fluorobenzene or 3,5-Dz-fluorobenzene, but these compounds were not nvail-
x
FIG. 3. (a) Tracing of the proton resonance (b) Tracing of the proton resonance at 30 Mc/sec strongly at 4.6053 Mc/sec.
FIG. 4. Fluorine
resonance
at 30 Mc/sec of 2,4,6-Da-fluorobenzene. observed while irradiating the deuterium
at 30 Mc/sec
of 2,4,6-Ds-fluorobenzene.
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1
-15.2
WILLIAMS I 45.2
I 0.0
I -15.2
-15.2
AND
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1 0.0
I
0.0
45.2
I
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FIG. 5. (a) Calculated fluorine resonance spectrum of 4-D-fluorobenzene at 30 Mc/sec, based on exact treatment. (b) Observed fluorine resonance spectrum at 30 Mc/sec. (c) Predicted fluorine resonance spectrum with H-H couplings neglected. (d) Observed fluorine resonance spectrum at 40 Mc/sec.
able. However, the above result is confirmed by further evidence from the analyses of the complex spectra of 4-D-fluorobenzene and ordinary fluorobenzene. 4-D-JEuorobenzene.-The F” spectrum of this compound was observed at 30 and 40 Mc/sec, Figs. 5b and 5d. The 30 Mc/sec spectrum in particular shows a marked asymmetry, which is unusual for the spectrum of a single nucleus of a given species in a molecule. Fig. 5c shows the spectrum predicted for JOHF =
NUCLEhR
9.4 f
0.4l cps, JmHF = 5.8 f
SPIN-SPIN
531
COUPLING
0.2 cps, JpDF = JpHF = 0.0 ignoring
all H-H couplings. It is clear from a comparison of Figs. 5b, c, and d that coupling between the protons significantly affects the F” spect’rum. This adds three parameters to the problem: the chemical shift, 6, between the two groups of protons, and the ortho H-H and meta H-H couplings, designated JoHH and J,HH. When the exact solution was investigated it was found that the sense of the asymmetry depends upon t,he relative sign of the H-H couplings and the H-F couplings. Since this is important in determining the relative importance of various electronic interactions contributing to the coupling, considerable effort was expended to find the correct set of parameters to reproduce the spectrum. The exact treatment is based on t’he method of McConnell, McLean, and Reilly (S). Figure 5a shows the 30 MC/see spectrum calculated with the set of parameters which gives the best fit with the experimental data. These require J,HF J HF = 3 6 cps, which agrees with the choice of 9.4 cps for JoHF and 5.8 cps for for this system can be written J:,,,. The ’ Hamiltonian
x = - rfiH&
-
rn $IHiIZi
+ hJ,HFI,*
(11 + 12)
+ +
+
~JmHFL~(13+ I,) hJoHH(I,*13
1~14)
+ hJmHH&-I~+ 1~14)
D +
hJpHH(I,*14
+
bb),
where Hi is the local magnetic field at proton i. The sign convention for the J’s is chosen such that a positive coupling leads to a lower energy for antiparallel spins. In other systems JpHH has been found to be very small and is taken here to be zero. The zero order spin functions are divided into two representations: those which are symmetric to rotation about the F-D axis, and those which are antisymmetric. The functions are labeled by M, , the eigenvalue of IzF , and MH , the eigenvalue the eigenvalues are written with MF as a parameter, of I*fl. To avoid repetition, since only the sign of MF changes when the fluorine spin function changes. The zero order proton functions and their eigenvalues are given in Tables I and II for the set of states represented by insertion of one or the other of the two values, ++$ or -35, for .iiF . 1J,HF is increased to 9.4 cps from the value of 9.0 cps obtained by measurement of the D-F coupling in 2,4,6-Da-fluorobenzene since the lines corresponding to JoHF + J,m appear at f15.2 + 0.2 cps around the center of the pattern. The measurement of 5.8 cps for J,sF is considered much more reliable than the 9.0 cps for J, nF, hence the latter has been adjusted upward to give the correct sum.
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II t=
I
I
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COUPLING
-
+
-I-
II
II L.
I-
ti A..
1
-2
-
-
..!-
I
II
II
“n
N
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The F” spectrum divides into five groups of lines; those near the center, those near ~t7 cps, and those near f14 cps. These groups correspond to M, = 0, fl, and f2. The &lx= f2 lines are unaffected by the H-H coupling and are split zt (Jo”” + JmHF) from the center. The iP1, = fl lines have identical contributions from symmetric and a~~tisymmetric states. There is a quadratic secular equation to be solved, with JoHF - JmBF, 6, and JoHE as the parameters. At this stage of the calculation, JuHF - JmHF was believed to be 3.2 cps, and from this number the ratio of JoHH Lo 6 can be calculated. JoHH has been found typically to be approximately 8 cps in other work (t;, 7). This gives a preliminary value of 6.4 cps for 6 at 7050 gauss. In field independent units, S = 2.1 X lo-‘. The sign of 6 can be obtained from a proton spectrum taken at 40 Mc/sec while the fluorine was strongly irradiated at 37.630 MC/see, its resonance frequency in the same field. With the fluorine spin out of the picture, the strongest coupling is JoHH, observable as a splitting of approximately 9 cps in the spectrum. A value of 6 cannot be measured directly but can be calculated from a splitting in the spectrum which is equal to f (J,““)2 + 6’f ‘!’ - J, NH.A value of 6.85 cps at 40 Me/see, or 1.7 X lo--’ in field independent units is obtained, in fair agreement, with the value calculated above from the assumed value for JoHH. The lines at the lowest applied field values show triplet structure due to spin coupling to the deuterium, and therefore they must represent the protons meta to the fluorine. The local field at these meta protons is higher than that at the ortho protons, so that (H, - $X0)is positive. The M B= 12 lines are taken as unit intensity. Then the antisymmetric MH = 0 states lead to a line of relative intensity 2 at the exact center of the spectrum. The symmetric states lead to a quartic secular equation. This equation can be solved numerically for various values of the parameters JoKF - JaHFt 6, JoHHt and J, HH. For any given set of numbers, the sense of the asynlmetry in the spectrum is reversed if the sign of JoHF - JmHF is reversed with respect to JoHH and JmHH.Two “forbidden lines” are used to make the final assignment of signs. The final solution of the quartic equations for eigenvalues and eigenfunctions was performed on the IBM 650 eomputer at Stanford University. The data employed in the calculation represent an average of the data from a number of spectra, and consequently the calculated spectrum is not a perfect fit when compared with any individual spectrum. In both 30 and 40 Mc/sec spectra there appear weak lines near +3 cps and -6 cps. These are identified with the strongest of the forbidden lines in the calculated spectrum, and seem definitely to confirm the sense of the asymmetry. The numerical values finally used to obtain the best fit with the 30 Mc/sec spec- H,), Jo*= = trum were: JoHF - JmnF = +3.6 cps, 6 = +5.40 cps = -fir(H,
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535
+8.9 cps, and JmHH= f2.2 ~ps.~Xo solutions with JmHHhaving a sign opposite to JoHH fit the data. One should note that changing the sign of JoHF - JvLHF, .J;IH, and JnHH simultaneously leaves the spectrum unchanged, HOthat only a relative sign has been determined. The HE’ couplings have the same sign as the HH couplings. (n) Fluorobenzem-The F’” spectrum of ordinary fluorobenzene given in Fig. 1 does not closely resemble a 1: 5: 10: 10: 5: 1 sextet as previously reported (1, 8), although the intensity distribution in six regions of the spectrum is approximately described in this may. The oversimplification previously report’ed is the result of the poorer resolution and stability available at that time, and in the case of Gut,owsky et al., the use of a significantly lower field. In this molecule, the H-H csoupling tends to make the hydrogen nuclei equivalent, while the chemical shift tends to make them nonequivalent. When the interact’ions are comparable, the change in t’he appearance of the spectrum with field is faster than the linear drpendence of the chemical shift on field alone would indicate. Since the para H-F coupling is negligibly small, one predicts exactly the same F’” spect’rum for fluorobenzene as for the 4-D-fluorohenzene (Fig. 5b) if the H-H couplings are ignored. The fact that t’he spectra are obviously different points up the interest,ing result that a nucleus whose coupling to the fluorine is zero can still influence the fluorine spectrum. One can see this in a simpler case by calculating the spectrum which would be obtained from 2 ,G-Dz-fluorobenzcne, ignoring interactions with the deuterons. The 1;” spect,rum is predicted to have seven strong lines as opposed to three which would be predicted if the H-H coupling were neglected (or if the chemical shift between the meta and para prot’ons were very large compared to t,he ortho H-H coupling. In principle, the F” and H’ spectra of fluorobenzene could he calculated using the parameters obtained from the 4-D-fluorobenzcne. This wouldinvolve a secular equation of the sixth order and would result in lit’tle, if any, useful new information. DISCUSSION
The conclusive evidence that the proton-fluorine coupling is not equal at all positions around the ring leads one to investigate the problem of relating the observed values to the theory of spin-spin (1-I) coupling. Ramsey (9) developed the first complete theory of this interaction, followed by McConnell (IO), who has developed molecular orbital formulas, based on Ramsey’s calculation, which are valid for long range couplings. Couplings between nuclei of atoms which are not directly bonded to one another are designated as long-range couplings. Unfortunately, the detailed theory leads to the * JIZ is not necessarily equal to J34 . If they are unequal the conclusions not affected and the reported value of J,,,HH is the average of J~Q and Jsa .
given here are
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AND
WILLIAMS
conclusion that a number of interaction terms can contribute to a single coupling, and may even be of different sign. It follows, therefore, that information about the signs of the couplings will be very useful in understanding the relative values observed. Williams and Gutowsky (6, 11), and Gutowsky, Helm, Saika, and Williams (la), report the observation of the relative signs of the ortho, meta, and para H-P couplings, and numerical values of these couplings in a number of substituted fluorobenzenes. The ortho and meta couplings are found to be of the same sign in a number of cases, as is confirmed in the present work, and their values measured here fall within the range of values they observe. However, a para coupling of more than 2 cps is reported for five different substituted fluorobenzenes, two of which have signs opposite to that of the ortho coupling measured in the same molecule. The present work is a significant addition to the knowledge of the I* I couplings because it provides values for all of the couplings in unsubstituted fluorobenzene, and furthermore yields the relative sign of the H-P and H-H couplings. This last information gives strong evidence on the absolute signs of these couplings. Ramsey and Purcell (13) and McComlell (10) concur in the conclusion that for proton-proton couplings one interaction is dominant, and is the only one large enough to account for the observed magnitude of the couplings. This is a second-order term involving the Fermi (1/t) contact hyperfine interaction of an electron in an s-state with the nucleus. In Ramsey’s notation, this is JsHH. If the absolute sign of this term can be inferred theoretically, the results obtained here yield an absolute sign for the H-F couplings in fluorohenzene. McConnell (15) has stated that the proton-proton couplings are probably all positive. A positive sign corresponds t,o a lower energy for antiparallel spins. However, Alexander (18) has recently reported that proton-proton couplings of opposite sign are observed in I-butene. McConnell (17), using the Dirac vector model has calculated a negative coupling for protons on the same carbon. One must, therefore, argue carefully. If the simple MO picture (10) is correct, the proton-proton couplings are all positive. The vector model calculation applied to a chain of carbons, will predict an alternation of sign, since the negative coupling arises from a positive exchange integral between two orbitals centered on a carbon. In going around a ring, the odd or even number of carbons passed will lead to an alternation in the sign of the coupling. Furthermore, the coupling for protons on adjacent carbons will be positive. We thus have the prediction that the H-H couplings are all positive, or alternate in sign. Since we observe H-H ortho and meta couplings of the same sign, we are led to assign a positive sign. The same inference can be drawn from the work of Williams and Gutowsky (6, IS), which is based on the MO calculations of McConnell (10). They show that a positive contribution to the ortho and meta H-F couplings is needed to
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COUPLING
537
produce the sign reversal found in prior work between meta and para couplings. The only positive term larger than the one-electron negative terms is shown to he the contact term. But if it, is positive for the H-F couplings, it is positive for the H-H couplings also. We therefore conclude that the present information, together with that previously available, argues very strongly for positive H-H and H-F ortho and meta couplings. In order to obtain contact terms in t’he H-F couplings large enough to dominate the one electron negative terms, Williams and Gutowsky (18) find it necessary to assume that 3 % s character to the orbital centered on the fluorine which forms the g bond with the carbon. The disparity between the results of Gutowsky ri ~2. (12) and this work in the observed value of the para coupling is readily underst’ood. They measured the couplings in molecules in which substituents other t,han deuterium were used to block off various spin-pos&ions in order to obtain interpretable spectra. In SO doing, they could not avoid changing the electron dist’rihution in the moltwde and, hence, the coupling. This is apparent in the variation of the ortho H-1; wupling over the range 7.5 to 10.5 cps in various molecular species. The important negative terms which contribute to the clouplings are one-elect8roll terms which do not’ depend upon delocalized orhitals. These are very likely less affected by substituents than the .la-type term, which requires a clelocxlized “bond” between the two coupled nuclei. Since the para coupling is obser\-ed to h:Lx.C:I sign opposite to the ortho- coupling in poly-substituted fluorobenzenes, one presumes t,hat the negligibly small para c*oupling found in fluorohenzcne itself arises from a cancellation of almost equal one-electron t,erms and two-electron terms, and t’hat substitution interferes somewhat with the part of the nwlcar spin cwwlation which depends upon the two-elect,ron terms. To draw this wnelusion, however, one must know whether the .I, term is transmitt,ed in t,he o bonds of the molecule, or in t.he r elert,rons. McConnell (19) and Weissman (70) have shown that spin polarization can be tjr:tnsmitted from u to P electrons through at,omic exchange coupling. However, McConnell (21) has cxl~wlated that< the 7r electron contributions t’o JSHH are quite small. It is not iirww~rily t,rue that the distribution of JI, between u and T electron contributions is the same for H-F and H-H couplings. The estimat’es made of JaHF (18) give only the t,ot,al value of this term. h more detailed calculation of the interaction of the fluorine with the ring, or hyperfine coupling measurements of free radicals coutaining fluorine would be necessary to settle this question. The results of the present work do imply that in fluorobenzene itself t#he JcIHFterms for the para coupling are larger than in substituted fluorobenzenes. They do not allow in themselves a choice between u and ?r contributions to this term.
538
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We wish to acknowledge ter of Stanford University,
the assistance of Professor J. Herriot of the Computation who assisted with the machine computations.
ACENOWLEDGMENT
RECEIVED:
May
Cen-
6, 1958. REFERENCES
1. E. B. BAKER, J. Chem. Phys. 23, 984 (1955). 6. B. BAK, D. CHRISTENSEN, L. HANSEN-NYGAARD, AND E. TANNENBAUM, J. Chem. Phys. 26, 134 (1957). 3. B. BAR, J. Org. Chem. 21, 797 (1956). 4. A. L. BLOOM AND J. N. SHOOLERY, Phys. Rev. 97, 1261 (1955). 6. H. M. MCCONNELL, A. D. MCLEAN, AND C. A. REILLEY, J. Chem. Phys. 23,1152 (1955). 6’. G. A. WILLIAMS, thesis, University of Illinois, Sept. 1956. 7. VARIAN ASSOCIATES (unpublished results). 8. H. S. GUTOWSKY, L. H. MEYER, AND D. W. MCCALL, J. Chem. Phys. 23,982 (1955). 9. N. F. RAMSEY, Phys. Rev. 98, 303 (1953). 10. H. M. MCCONNELL, J. Chem. Phys. 24, 460 (1956). 11. H. S. GUTOWSKY AND G. A. WILLIAMS, J. Chem. Phys. 26, 1288 (1956). 12. H. S. GUTOWSKY, C. H. HOLM, A. SAIKA, AND G. A. WILLIAMS, J. Am. Chem. Sot. 79, 4596 (1957). 19. N. F. RAMSEY AND E. M. PURCELL, Phys. Rev. 86,143 (1952). 14. E. FERMI, 2. Physik 60, 320 (1930). lb. H. M. MCCONNELL, Ann. Rev. Phys. Chem. 8, 122 (1957). 16. S. ALEXANDER, J. Chem. Phys. 28,358 (1958). 17. H. M. MCCONNELL, J. Chem. Phys. 23, 2454 (1955). 18. G. A. WILLIAMS AND H. S. GUTOWSKY, J. Chem. Phys. 30 (1959). To be published. 19. H. M. MCCONNELL, J. Chem. Phys. 24, 764 (1956). RO. S. I. WEISSMAN, J. Chem. Phys. 26,890 (1956). df. H. M. MCCONNELL, J. Mol. Spectroscopy 1, 11 (1957).
OP
MOLEC’I’LI\R
Nuclear
SPECTROSCOPY
2,
(1958)
%?&.%8
Spin-Spin Coupling between Fluorine Hydrogen in Fluorobenzene
Chemical Laboratory
of the
lTniver.sity of Copenhagen,
Copenhagen,
and
Denmark
J. ?\;. &IOOLERY Varian _4ssociates,
Palo
Alto,
California
AND
Deparfment
of Physics,
Stanford
University, Palo Alto, California
High resolution proton and fluorine nuclear magnetic resonance (nmr) spectra of fluorobenzene, 3D-, 2,4,6-Ds-, and 2,3,~,6-D*-fll~orob~nzene have been obtained and analyzed. Double irr~di&tion techniques were employed to eliminate the effects of t,he denterium nuclear spin. The secular eqnation for 4IMuorobenzene has been solved and the parameters adjusted for the best correspondence between the predicted and observed spectra. The nuclear spin couplings between t,he fluorine nucleus and the ortho, meta, and pttr:t protons :xe found to be, respectively, 9.4 f 0.2 cps, 5.8 f 0.2 cps, and 0.0 k 0.5 cps. These couplings are found too have the same sign as t.he proton-proton couplings in the fluorobenzene molecnle. This result is discussed and related t,o previous work on Auorobenzenes. INTRODUCTION 111 3 rerent publication on the nuclear spin-spin coupling in substituted beuzenes Baker (2) has st,ated that, “the ~u~~~~~~resonance spectrum of fluorobe~lze~le by its Rlultipli~it,y and intensity distrib~~tion shows that, t.he protons all couple equally t,o the fluorine. Equalit~y of coupling strikingly demonstrates the effect, of a-bond resonance, since the coupling is passed undiminished around the ring. In the corresponding proton spectrum :I spin-spin doublet is observed (coupling constant 6.6 cps). Since no internal chemical shift is evident in the prot,on spectrum, the hydrogens are ~hemi~~~Ily equivalent, and resonating structures bearing formal charges must be proport,ioI~ed to fulfiI1 this condition or be negligibie”. 525
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d.0
+I52
FIG. 1. High resolution fluorine nmr spectrum of fluorobenzene at 30 Mc/sec. Magnetic field increases linearly from left to right. Horizontal scale is calibrated in cycles/second. To most chemists this conclusion will be rather surprising. For example, fluorine attached to a benzene ring strongly directs bromine into the para position. The problem, therefore, highly deserves further investigation. Since the publication of Baker’s paper, increased stability in the strong applied magnetic field has been obtained, resulting in much higher resolving power of available nuclear magnetic resonance spectrometers. A glance at the proton and fluorine resonance spectra now obtainable shows, however, a richness of reproducible details which would require an interpretation based on a laborious solution of a complex secular equation. The fluorine spectrum is shown in Fig. 1. It was decided, therefore, to take advantage of the fact that substitution of hydrogen by deuterium greatly simplifies the spectra inasmuch as all couplings between the deuteron and other nuclei are about six times smaller than the corresponding proton couplings. In this respect deuterium substitution serves as a means of “blacking out” a certain number of protons. This makes the interpretation of the result much easier without, however, introducing any appreciable changes in the electron-distribution function of fluorobenzene which would result if one or more of the five hydrogen atoms had been substituted by fluorine, bromine, etc. EXPERIMENTAL The preparation of two of the deuterated species of fluorobenzene investigated here has been reported elsewhere (2). The 2,3,5 ,6-D4-fluorobenzene, not described earlier, was prepared at room temperature by bubbling anhydrous DC1 (from C$H&OCl and D20) through para-bromo-fluorobenzene (13.5g) to which 2g AlCh had been added. In this way the hydrogen was replaced by deuterium. The exchange procedure was controlled by observing the proton resonance spectra of small samples withdrawn from the flask at one-hour intervals. When the integrated intensity of the proton-resonance pattern had fallen to 5-10 % of its initial value, the exchange was interrupted. The tetradeutero-bromo-fluorobenzene was separated from AlCl, and some higher-boiling products by distillation in vucuo. After shaking with water for removal of DCl, drying over PzO5 and a second vacuum-distillation, 9g of 2,3,5,6-DJ-bromo-fluorobenzene was obtained. This quantity was added to a mixture of 20g CH&OOH, 50g H20, and 32g Zn-dust, contained in a 250-ml flask with reflux condenser. The mixture was kept at 100°C
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COUPLING
527
for 24 hours during which the bromine was quantitatively replaced by hydrogen without exchange of the deuterium atoms (3). The 2,3,5 ,6-D4-fluorobenzene was isolated by vacuum-distillation together with some water from which it was separated mechanically. After drying over P$& the sample was again distilled in NWUO at constant t#emperature, the pressure of each fraction taken being read. Due to a mishap during one of the operations the final yield was only 200 mg. This sample had, however, the same vapor-pressure as ordinary fluorobenzene. The quantity was sufficient for the nuc>lear magnetic resonance investigation. All features in the proton and fluorine spectra taken verified that its composit’ion was as postulated. The instrument used was a Varian Associates Model V-4300B High Resolution Nuclear Magnetic Resonance Spectrometer with fixed resonance frequencies of 30 M(*/sec and 40 Mcj’sec. In proton resonance experiments t,he applied magnetic, field intensity was then about 7050 and 9395 oersted, respectively, whilt iu fluorine resonance experimentjs it was 7500 and 10,000 oemted. ,1uxiliary apparatus was available which permitted st,rong irradiation at thcl deuterium resonance frequency, 4.605:3 M(*/sec, while the proton resonance* :tt 30 J\lc!sec was observed, and at bhe fluorine resonanc’e frequency, 37.630 IZIr I SW, while t,he proton resonance at, 10 M(a/sec was observed. This apparatus has been described elsewhere (.4j. Line separations in cycles/second were determined by the usuul audiofrequcnc*y sideband t)echnique. Since it was iut’ended to make all calculations with energies esprrssed in cyples/second, t)his method of measurement yielded the dnt:l in Louvrnieilt form. INTERPRETATION 2 ,.I ,:i ,Ci-Do-JEuorobenzenc.--This molecule has :L single proton para to the fluorine. The proton resonance consists of a number of complet,ely unresolved lines grouped around a pronounced maximum as shown in lcig. 2a. The deut,erons couple their spins to t,he prot,on t’oo weakly to permit’ resolution of the man? possible lines corresponding t,o t’he various deuteron spin orientat,ions. Howe\:er, if t,hc 1:-H coupling were appreciable, the pattern ought to display a doublet character. The fluorine resonanre spectrum shows the same general features. In order to determine the magnitude of the F-H para coupling it was necessary t’o resort t’o the t’echnique of “spin decoupling” in which the deut,erons were strongly irradiated at their resonance frequency while the prot,on spectrum was recorded. By this technique the effect of the proton-deuteron spin couplings was eliminated. The resulting spectrum, Fig. 2b, shows a very sharp line with a halfint#ensity width of approximately one cycle per second. Therefore, bhe para F-H spin-spin interaction is shown to be less than 0.5 cps. 2 ,/t ,A-DJYfluorobenzene.-This molecule has two hydrogen atoms in t,he posi-
528
BAK,
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WILLIAMS
tion meta to the fluorine. The proton nmr spectrum showed two broad lines of equal intensity, Fig. 3a, with a peak separation of about 6 cps. The broadening is again due to interactions of each proton with the two nearest deuterium nuclei. In another experiment, the deuterons were again irradiated at their resonance frequency while the proton resonance was observed. Two equally intense, very sharp lines were observed with half-intensity width of 1.0 cps (Fig. 3b). The frequency separstion was 5.8 =t 0.2 cps. Thus the meta F-H coupling, J,rfIF, is is 5.8 & 0.2 cps. Interesting ~ddition~~l i~lformation was obtained by obser~ri~lg the fluorine resonance spectrum of this molecular species. ITnder high resol~~t.ioll 13 resolved lines were observed, shown in Fig. 4. Since t,he appearance of the spectrum suggests t,hat two of the lines each arise from coincidence of two lines in a simpler pattern, we are led to the following interpretation. The fluorine resonance is split by the protons into a triplet with intensities 1:2: 1 and a line separation of 5.8 cps. Each component of the triplet is further split into 5 lines with intensities 1: 2: 3: 2: 1 corresponding to equal interaction with tsvo nuclei of spin I. The measured coupling is 1.38 f 0.1 cps. Intensities of the 13 lines should occur in
FIG. 2. (a) Tracing of the proton resonance at 30 Mc/sec of 2,3,5,6-Da-fluorobenzene. (b) Tracing of the proton resonance at 30 Mc/sec observed while irradiating the deuterium strongly at 4.6053 Mc/sec.
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529
the ratio 1:2:3:2:3:4:6:4:3:2:3:2:1 which agrees well with Fig. 4. In addition toconfirming the result that the meta F-H coupling is 5.8 cps, the spectrum serves to establish the ortho F-H coupling. This is calculated from the ortho F-D coupling by multiplying by Y=/Y~ , which is 6.54. This gives a value of 9.0 f 0.7 cps to t#he ortho F-H coupling, designated JoHF. It wold be desirable to confirm this result directly and simply in either 3,4,5Ds-fluorobenzene or 3,5-Dz-fluorobenzene, but these compounds were not nvail-
x
FIG. 3. (a) Tracing of the proton resonance (b) Tracing of the proton resonance at 30 Mc/sec strongly at 4.6053 Mc/sec.
FIG. 4. Fluorine
resonance
at 30 Mc/sec of 2,4,6-Da-fluorobenzene. observed while irradiating the deuterium
at 30 Mc/sec
of 2,4,6-Ds-fluorobenzene.
530
BAK,
SHOOLERY,
I
1
-15.2
WILLIAMS I 45.2
I 0.0
I -15.2
-15.2
AND
I
II
1 0.0
I
0.0
45.2
I
45.2
FIG. 5. (a) Calculated fluorine resonance spectrum of 4-D-fluorobenzene at 30 Mc/sec, based on exact treatment. (b) Observed fluorine resonance spectrum at 30 Mc/sec. (c) Predicted fluorine resonance spectrum with H-H couplings neglected. (d) Observed fluorine resonance spectrum at 40 Mc/sec.
able. However, the above result is confirmed by further evidence from the analyses of the complex spectra of 4-D-fluorobenzene and ordinary fluorobenzene. 4-D-JEuorobenzene.-The F” spectrum of this compound was observed at 30 and 40 Mc/sec, Figs. 5b and 5d. The 30 Mc/sec spectrum in particular shows a marked asymmetry, which is unusual for the spectrum of a single nucleus of a given species in a molecule. Fig. 5c shows the spectrum predicted for JOHF =
NUCLEhR
9.4 f
0.4l cps, JmHF = 5.8 f
SPIN-SPIN
531
COUPLING
0.2 cps, JpDF = JpHF = 0.0 ignoring
all H-H couplings. It is clear from a comparison of Figs. 5b, c, and d that coupling between the protons significantly affects the F” spect’rum. This adds three parameters to the problem: the chemical shift, 6, between the two groups of protons, and the ortho H-H and meta H-H couplings, designated JoHH and J,HH. When the exact solution was investigated it was found that the sense of the asymmetry depends upon t,he relative sign of the H-H couplings and the H-F couplings. Since this is important in determining the relative importance of various electronic interactions contributing to the coupling, considerable effort was expended to find the correct set of parameters to reproduce the spectrum. The exact treatment is based on t’he method of McConnell, McLean, and Reilly (S). Figure 5a shows the 30 MC/see spectrum calculated with the set of parameters which gives the best fit with the experimental data. These require J,HF J HF = 3 6 cps, which agrees with the choice of 9.4 cps for JoHF and 5.8 cps for for this system can be written J:,,,. The ’ Hamiltonian
x = - rfiH&
-
rn $IHiIZi
+ hJ,HFI,*
(11 + 12)
+ +
+
~JmHFL~(13+ I,) hJoHH(I,*13
1~14)
+ hJmHH&-I~+ 1~14)
D +
hJpHH(I,*14
+
bb),
where Hi is the local magnetic field at proton i. The sign convention for the J’s is chosen such that a positive coupling leads to a lower energy for antiparallel spins. In other systems JpHH has been found to be very small and is taken here to be zero. The zero order spin functions are divided into two representations: those which are symmetric to rotation about the F-D axis, and those which are antisymmetric. The functions are labeled by M, , the eigenvalue of IzF , and MH , the eigenvalue the eigenvalues are written with MF as a parameter, of I*fl. To avoid repetition, since only the sign of MF changes when the fluorine spin function changes. The zero order proton functions and their eigenvalues are given in Tables I and II for the set of states represented by insertion of one or the other of the two values, ++$ or -35, for .iiF . 1J,HF is increased to 9.4 cps from the value of 9.0 cps obtained by measurement of the D-F coupling in 2,4,6-Da-fluorobenzene since the lines corresponding to JoHF + J,m appear at f15.2 + 0.2 cps around the center of the pattern. The measurement of 5.8 cps for J,sF is considered much more reliable than the 9.0 cps for J, nF, hence the latter has been adjusted upward to give the correct sum.
532
BAK,
SHOOLERY,
AND
II k
I
f
WILLIAMS
II t=
I
I
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SPIN-SPIN
533
COUPLING
-
+
-I-
II
II L.
I-
ti A..
1
-2
-
-
..!-
I
II
II
“n
N
534
BAK,
SHOOLERY,
AND
WILLIAMS
The F” spectrum divides into five groups of lines; those near the center, those near ~t7 cps, and those near f14 cps. These groups correspond to M, = 0, fl, and f2. The &lx= f2 lines are unaffected by the H-H coupling and are split zt (Jo”” + JmHF) from the center. The iP1, = fl lines have identical contributions from symmetric and a~~tisymmetric states. There is a quadratic secular equation to be solved, with JoHF - JmBF, 6, and JoHE as the parameters. At this stage of the calculation, JuHF - JmHF was believed to be 3.2 cps, and from this number the ratio of JoHH Lo 6 can be calculated. JoHH has been found typically to be approximately 8 cps in other work (t;, 7). This gives a preliminary value of 6.4 cps for 6 at 7050 gauss. In field independent units, S = 2.1 X lo-‘. The sign of 6 can be obtained from a proton spectrum taken at 40 Mc/sec while the fluorine was strongly irradiated at 37.630 MC/see, its resonance frequency in the same field. With the fluorine spin out of the picture, the strongest coupling is JoHH, observable as a splitting of approximately 9 cps in the spectrum. A value of 6 cannot be measured directly but can be calculated from a splitting in the spectrum which is equal to f (J,““)2 + 6’f ‘!’ - J, NH.A value of 6.85 cps at 40 Me/see, or 1.7 X lo--’ in field independent units is obtained, in fair agreement, with the value calculated above from the assumed value for JoHH. The lines at the lowest applied field values show triplet structure due to spin coupling to the deuterium, and therefore they must represent the protons meta to the fluorine. The local field at these meta protons is higher than that at the ortho protons, so that (H, - $X0)is positive. The M B= 12 lines are taken as unit intensity. Then the antisymmetric MH = 0 states lead to a line of relative intensity 2 at the exact center of the spectrum. The symmetric states lead to a quartic secular equation. This equation can be solved numerically for various values of the parameters JoKF - JaHFt 6, JoHHt and J, HH. For any given set of numbers, the sense of the asynlmetry in the spectrum is reversed if the sign of JoHF - JmHF is reversed with respect to JoHH and JmHH.Two “forbidden lines” are used to make the final assignment of signs. The final solution of the quartic equations for eigenvalues and eigenfunctions was performed on the IBM 650 eomputer at Stanford University. The data employed in the calculation represent an average of the data from a number of spectra, and consequently the calculated spectrum is not a perfect fit when compared with any individual spectrum. In both 30 and 40 Mc/sec spectra there appear weak lines near +3 cps and -6 cps. These are identified with the strongest of the forbidden lines in the calculated spectrum, and seem definitely to confirm the sense of the asymmetry. The numerical values finally used to obtain the best fit with the 30 Mc/sec spec- H,), Jo*= = trum were: JoHF - JmnF = +3.6 cps, 6 = +5.40 cps = -fir(H,
SCCLEAR
SPIN-SPIN
COUPLING
535
+8.9 cps, and JmHH= f2.2 ~ps.~Xo solutions with JmHHhaving a sign opposite to JoHH fit the data. One should note that changing the sign of JoHF - JvLHF, .J;IH, and JnHH simultaneously leaves the spectrum unchanged, HOthat only a relative sign has been determined. The HE’ couplings have the same sign as the HH couplings. (n) Fluorobenzem-The F’” spectrum of ordinary fluorobenzene given in Fig. 1 does not closely resemble a 1: 5: 10: 10: 5: 1 sextet as previously reported (1, 8), although the intensity distribution in six regions of the spectrum is approximately described in this may. The oversimplification previously report’ed is the result of the poorer resolution and stability available at that time, and in the case of Gut,owsky et al., the use of a significantly lower field. In this molecule, the H-H csoupling tends to make the hydrogen nuclei equivalent, while the chemical shift tends to make them nonequivalent. When the interact’ions are comparable, the change in t’he appearance of the spectrum with field is faster than the linear drpendence of the chemical shift on field alone would indicate. Since the para H-F coupling is negligibly small, one predicts exactly the same F’” spect’rum for fluorobenzene as for the 4-D-fluorohenzene (Fig. 5b) if the H-H couplings are ignored. The fact that t’he spectra are obviously different points up the interest,ing result that a nucleus whose coupling to the fluorine is zero can still influence the fluorine spectrum. One can see this in a simpler case by calculating the spectrum which would be obtained from 2 ,G-Dz-fluorobenzcne, ignoring interactions with the deuterons. The 1;” spect,rum is predicted to have seven strong lines as opposed to three which would be predicted if the H-H coupling were neglected (or if the chemical shift between the meta and para prot’ons were very large compared to t,he ortho H-H coupling. In principle, the F” and H’ spectra of fluorobenzene could he calculated using the parameters obtained from the 4-D-fluorobenzcne. This wouldinvolve a secular equation of the sixth order and would result in lit’tle, if any, useful new information. DISCUSSION
The conclusive evidence that the proton-fluorine coupling is not equal at all positions around the ring leads one to investigate the problem of relating the observed values to the theory of spin-spin (1-I) coupling. Ramsey (9) developed the first complete theory of this interaction, followed by McConnell (IO), who has developed molecular orbital formulas, based on Ramsey’s calculation, which are valid for long range couplings. Couplings between nuclei of atoms which are not directly bonded to one another are designated as long-range couplings. Unfortunately, the detailed theory leads to the * JIZ is not necessarily equal to J34 . If they are unequal the conclusions not affected and the reported value of J,,,HH is the average of J~Q and Jsa .
given here are
536
BAK,
SHOOLERY,
AND
WILLIAMS
conclusion that a number of interaction terms can contribute to a single coupling, and may even be of different sign. It follows, therefore, that information about the signs of the couplings will be very useful in understanding the relative values observed. Williams and Gutowsky (6, 11), and Gutowsky, Helm, Saika, and Williams (la), report the observation of the relative signs of the ortho, meta, and para H-P couplings, and numerical values of these couplings in a number of substituted fluorobenzenes. The ortho and meta couplings are found to be of the same sign in a number of cases, as is confirmed in the present work, and their values measured here fall within the range of values they observe. However, a para coupling of more than 2 cps is reported for five different substituted fluorobenzenes, two of which have signs opposite to that of the ortho coupling measured in the same molecule. The present work is a significant addition to the knowledge of the I* I couplings because it provides values for all of the couplings in unsubstituted fluorobenzene, and furthermore yields the relative sign of the H-P and H-H couplings. This last information gives strong evidence on the absolute signs of these couplings. Ramsey and Purcell (13) and McComlell (10) concur in the conclusion that for proton-proton couplings one interaction is dominant, and is the only one large enough to account for the observed magnitude of the couplings. This is a second-order term involving the Fermi (1/t) contact hyperfine interaction of an electron in an s-state with the nucleus. In Ramsey’s notation, this is JsHH. If the absolute sign of this term can be inferred theoretically, the results obtained here yield an absolute sign for the H-F couplings in fluorohenzene. McConnell (15) has stated that the proton-proton couplings are probably all positive. A positive sign corresponds t,o a lower energy for antiparallel spins. However, Alexander (18) has recently reported that proton-proton couplings of opposite sign are observed in I-butene. McConnell (17), using the Dirac vector model has calculated a negative coupling for protons on the same carbon. One must, therefore, argue carefully. If the simple MO picture (10) is correct, the proton-proton couplings are all positive. The vector model calculation applied to a chain of carbons, will predict an alternation of sign, since the negative coupling arises from a positive exchange integral between two orbitals centered on a carbon. In going around a ring, the odd or even number of carbons passed will lead to an alternation in the sign of the coupling. Furthermore, the coupling for protons on adjacent carbons will be positive. We thus have the prediction that the H-H couplings are all positive, or alternate in sign. Since we observe H-H ortho and meta couplings of the same sign, we are led to assign a positive sign. The same inference can be drawn from the work of Williams and Gutowsky (6, IS), which is based on the MO calculations of McConnell (10). They show that a positive contribution to the ortho and meta H-F couplings is needed to
NUCLEAR
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COUPLING
537
produce the sign reversal found in prior work between meta and para couplings. The only positive term larger than the one-electron negative terms is shown to he the contact term. But if it, is positive for the H-F couplings, it is positive for the H-H couplings also. We therefore conclude that the present information, together with that previously available, argues very strongly for positive H-H and H-F ortho and meta couplings. In order to obtain contact terms in t’he H-F couplings large enough to dominate the one electron negative terms, Williams and Gutowsky (18) find it necessary to assume that 3 % s character to the orbital centered on the fluorine which forms the g bond with the carbon. The disparity between the results of Gutowsky ri ~2. (12) and this work in the observed value of the para coupling is readily underst’ood. They measured the couplings in molecules in which substituents other t,han deuterium were used to block off various spin-pos&ions in order to obtain interpretable spectra. In SO doing, they could not avoid changing the electron dist’rihution in the moltwde and, hence, the coupling. This is apparent in the variation of the ortho H-1; wupling over the range 7.5 to 10.5 cps in various molecular species. The important negative terms which contribute to the clouplings are one-elect8roll terms which do not’ depend upon delocalized orhitals. These are very likely less affected by substituents than the .la-type term, which requires a clelocxlized “bond” between the two coupled nuclei. Since the para coupling is obser\-ed to h:Lx.C:I sign opposite to the ortho- coupling in poly-substituted fluorobenzenes, one presumes t,hat the negligibly small para c*oupling found in fluorohenzcne itself arises from a cancellation of almost equal one-electron t,erms and two-electron terms, and t’hat substitution interferes somewhat with the part of the nwlcar spin cwwlation which depends upon the two-elect,ron terms. To draw this wnelusion, however, one must know whether the .I, term is transmitt,ed in t,he o bonds of the molecule, or in t.he r elert,rons. McConnell (19) and Weissman (70) have shown that spin polarization can be tjr:tnsmitted from u to P electrons through at,omic exchange coupling. However, McConnell (21) has cxl~wlated that< the 7r electron contributions t’o JSHH are quite small. It is not iirww~rily t,rue that the distribution of JI, between u and T electron contributions is the same for H-F and H-H couplings. The estimat’es made of JaHF (18) give only the t,ot,al value of this term. h more detailed calculation of the interaction of the fluorine with the ring, or hyperfine coupling measurements of free radicals coutaining fluorine would be necessary to settle this question. The results of the present work do imply that in fluorobenzene itself t#he JcIHFterms for the para coupling are larger than in substituted fluorobenzenes. They do not allow in themselves a choice between u and ?r contributions to this term.
538
BAK, SHOOLERY, AND WILLIAMS
We wish to acknowledge ter of Stanford University,
the assistance of Professor J. Herriot of the Computation who assisted with the machine computations.
ACENOWLEDGMENT
RECEIVED:
May
Cen-
6, 1958. REFERENCES
1. E. B. BAKER, J. Chem. Phys. 23, 984 (1955). 6. B. BAK, D. CHRISTENSEN, L. HANSEN-NYGAARD, AND E. TANNENBAUM, J. Chem. Phys. 26, 134 (1957). 3. B. BAR, J. Org. Chem. 21, 797 (1956). 4. A. L. BLOOM AND J. N. SHOOLERY, Phys. Rev. 97, 1261 (1955). 6. H. M. MCCONNELL, A. D. MCLEAN, AND C. A. REILLEY, J. Chem. Phys. 23,1152 (1955). 6’. G. A. WILLIAMS, thesis, University of Illinois, Sept. 1956. 7. VARIAN ASSOCIATES (unpublished results). 8. H. S. GUTOWSKY, L. H. MEYER, AND D. W. MCCALL, J. Chem. Phys. 23,982 (1955). 9. N. F. RAMSEY, Phys. Rev. 98, 303 (1953). 10. H. M. MCCONNELL, J. Chem. Phys. 24, 460 (1956). 11. H. S. GUTOWSKY AND G. A. WILLIAMS, J. Chem. Phys. 26, 1288 (1956). 12. H. S. GUTOWSKY, C. H. HOLM, A. SAIKA, AND G. A. WILLIAMS, J. Am. Chem. Sot. 79, 4596 (1957). 19. N. F. RAMSEY AND E. M. PURCELL, Phys. Rev. 86,143 (1952). 14. E. FERMI, 2. Physik 60, 320 (1930). lb. H. M. MCCONNELL, Ann. Rev. Phys. Chem. 8, 122 (1957). 16. S. ALEXANDER, J. Chem. Phys. 28,358 (1958). 17. H. M. MCCONNELL, J. Chem. Phys. 23, 2454 (1955). 18. G. A. WILLIAMS AND H. S. GUTOWSKY, J. Chem. Phys. 30 (1959). To be published. 19. H. M. MCCONNELL, J. Chem. Phys. 24, 764 (1956). RO. S. I. WEISSMAN, J. Chem. Phys. 26,890 (1956). df. H. M. MCCONNELL, J. Mol. Spectroscopy 1, 11 (1957).