NOTES
unresolved extra-hyperfine structure (Figure 3). The spectrum extended over about 120 gauss with about 90 gauss between the apparent centers of the outer lines of the basic triplet. The center line also showed some structure suggestive of the superposition of a doublet on a singlet. The reaction of poly-44sopropylstyrene with deuteiium atoms produced a highly distorted line with a shape suggesting the superposition of a doublet with about 40 gauss splitting superimposed on a singlet about 15 gauss wide and shifted slightly downfield from the center of the doublet (Figure 4). The foregoing material is summarized in Table I.
Discussion The fact that, for each of the alkyl aromatics studied, the spectrum produced by hydrogen atom reaction differed from the spectrum produced by deuterium atom reaction suggests that addition to form cyclohexadienyl radicals was the dominant mode of reaction, rather than hydrogen or deuterium atom abstraction from a side chain.
3095
argument is possible for the 3-methyl hydrogens, however, and they should be closely analogous in reactivity to the hydrogen atom of the methyl group of toluene. Thus these data presented here constitute additional evidence that hydrogen atoms add to the aromatic ring of simple alkyl aromatics rather than abstracting from the alkyl side chain. Acknowledgments. We wish to thank Dr. Leo A. Wall of the National Bureau of Standards, Washington, D. C., for a gift of 4-isopropylstyrene polymer. (10) R. B. Ingalls and D. Kivelson, J . Chem. Phys., 38, 1907 (1963).
Nuclear Magnetic Resonance Study of Rotational Isomerism in
meso-2,3-Dibromobutane1 by K. K. Deb The Robert Robinson Laboratories, Licerpool 7 , England (Receiaed March 8, 1567)
Abstraction of atoms from any polymer by hydrogen or deuterium atoms should give the same organic radical.
Furthermore, all the spectra observed may be reasonably assigned to the corresponding cyclohexadienyl radicals formed by the nearly random addition of the atoms to the six positions on the aromatic ring.4Jo The radical spectra observed with 4-isopropylstyrene polymer indicated some preference for addition a t the para position. However, the rather marked asymmetry of the deuterium atom induced spectrum is not understood. The dominance of addition to 3-methylstyrene polymer strongly suggested that addition to the aromatic ring occurred in the reaction of hydrogen atoms with toluene. In previous work with polystyrene, it "" possible to argue that the a-hydrogen Of styrene was not as reactive as the methyl hydrogen atoms in toluene because the other bonds of the (ycarbon in polystyrene are not entirely free to move to a position most favorable to the resonance stabilization of the radical produced by abstraction. No such
Although a qualitative study of the rotamer populations in meso-2,3-dibromobutane has been made by A n e P and Bothner-By, et a1.,2b no detailed quantitative investigation of the rotameric states has previously been reported. Recently, a classical theory of the solvent dependence of the coupling constants of rotational isomers has been developed3 which has been used with high accuracy to evaluate the energy difference between the two rotational isomers of a few 1,2-disubstituted ethanes. More recently, the theory3 has been successfully used to determine the H-H coupling constants of the individual isomers of a few complex molecules such as 1,1,2-tri~hloroethane~ and 1,2-bromo~yanoethane.~ It is the purpose of the present work to analyze the spectra of naes0-2,3-dibromobutane in different suitable solvents and to use the classical theory3 to derive the couplings between H-2 and H-3 protons for different conformations of the molecule. (1) The work was supported by a grant from the Science Research Council of Britain. (2) (a) F. A. L. Anet, J. Am. Chem. SOC.,84, 747 (1962); (b) A. A. Bothner-By and C. Naar-Colin, ibid., 84, 743 (1962). (3) Part I1 : R. J. Abraham, K . G. R. Patchler, and L. Cavalli, Mol. Phys., 1 1 , 471 (1966). (4) Part 111: R. J. Abraham and Ll. A. Cooper, J . Chem. SOC.,t o be published. ( 5 ) K. K. Deb and R. J. Abraham, J . Mol. Spectry., in press.
Volume 7 1 , Number 5 August 1567
3096
NOTES
Table I : Nuclear Magnetic Resonance Spectral Data of meso-2,3-Dibromobutane in Various Solvents" z = I)/ (2f 1)
(e
Solvents
n-Pentane n-Hexane Cyclohexane CClr
cs2
CZHCIi CHCli CHzC12 1,2-Dichloroethane Methyl chloroacetate Acetone CHiCN
-
+
Spectral data
JAA',~
JAX,~
-J A X ' , ~
7
CH,C
CHa
- CH,
Hz
Hz
CHsC
ppm
ppm
0.178 0.184 0.201 0.224 0.259 0.307 0.354 0.418 0.429
9.02 9.00 8.93 8.69 7.75 8.00 7.42 7.39
6.57 6.57 6.59 6.54 6.55 6.59 6.60 6.48 6.59
0.23 0.22 0.21 0.16 0.20 0.13 0.20 0.18 0.16
4.050 4.047 4.044 4.109 4.087 4.207 4.186 4.212 4.223
1.846 1.843 1.838 1.878 1.852 1.831 1.857 1.834 1.819
2,204 2.204 2.206 2,231 2,235 2.376 2,329 2.378 2.404
0.443
7.04
6.66
0.15
4.295
1.822
2.473
0,464 0.480
6.68 6.55
6.63 6.66
0.14 0.10
4.326 4.318
1.812 1.789
2.514 2.529
8.70
HZ
" All spectra are recorded a t 12% by volume solutions in the solvents. a J A Aand ~ JAXare assumed positive; J A Xthen ~ requires negative sign as shown. Parts per million increasing to high field with TMS used as internal standard a t 10.00 ppm. Experimental Section
J X X ~= 0) system of spectrum is conveniently de-
The meso-2,3-dibromobutane obtained from Eastman Organic Chemicals was purified from impurities by the use of gas-phase chromatography. The solvents listed in Table I were of AR grade and were thoroughly dried immediately before use. It was expected that these solvents would not form chemical bonds with the solute molecule. The spectra of the solutions of the compound were recorded on a Varian HA-100 spectrometer operating a t 100 MHz at 30" (probe temperature) and in each of the solutions a small amount of TMS was added as an internal reference. Solutions of strength 12% by volume were usually used and in some cases solutions of varying concentrations were also examined, but no substantial changes5 were noticed in the values of the observed couplings with the solvent concentration. All samples were degassed in order to achieve good resolution in the spectra. Calibration of the spectra was accomplished using a Hewlett-Packard 5212 A electronic counter provided with the instrument and the peak positions were the average of a t least five measurements, using a 50-HZ full-sweep width. The coupling constants are accurate to h0.05 Hz and chemical shifts to *0.01 ppm.
scribed2 in terms of the chemical shift between the A and X nuclei and the three coupling constants J A A J , ~ J A X ,and J A X ~ .The latter couplings J A Xand J A Xare referred to as the short-range and long-range (A,X) coupling constants. Except when J A A t is very small, the lines in the X spectrum usually appear to be well resolved, although if J A Ais~ very large the outer lines are quite weak. Thus the observed couplings J A A ~ , J A X , and J A x ~can easily be obtained from the X spectrum using the expressions given by Harris6 for the X part of an X,AA'X,' system (with J X X I= 0). The predicted spectra are calculated using these coupling constants by programming the KDF-9 computer followed by the method of calculation already described by Bothner-By, et a1.2b In each solution, the calculated spectra give a very good fit with the observed spectra within the limit of experimental error of line measurement. Figure 1 represents the observed and calculated spectra of meso-2,3-dibromobutane in dilute solution in CSz. The meso-2,3-dibromobutane consists of rapidly interconverting mixtures of three rotamers T, G and G' of which G and G' are mirror images' as shown in Figure 2. It is fairly well knownE-11~12 that the size of the
Results and Discussions The spectra of meso-2,3-dibromobutane were analyzed in various solvents by comparison of the spectra with those expected from XaAA'X3' system (with J X X I= 0) and the results are summarized in Table I, which also includes the data for the dielectric constants of the pure solvents at 30". The XaAA'X3' (with The Journal of Physical Chemistry
(6) R. K. Harris, Can. J . Chem., 42,2275 (1964). (7) S. I. Mizushima, "Structure of Molecules and Internal Rotations," Academic Press, Inc., New York, N. Y., 1964. (8) M. Karplus, J. Chem. Phys., 30, 11 (1959). (9) H.Conroy, private communication. (10) R. U. Lemieux, R. K. Kullnig, H. J. Bernstein, and W. J. Schneider, J . Am. Chem. Sac., 79, 1006 (1957).
NOTES
3097
a
b
_ilr
Methyl signa[
I
w 3
M*hhJonal
Figure 1. The 100-MHz proton magnetic resonance spectra of rneso-2,3-dibromobutane a t 12% by volume solution in CSZ: a, observed; b, calculated.
coupling constant of protons on adjacent carbons should primarily be a smooth function of the dihedral angle describing the degree of rotation about the bond joining carbons. Therefore the rotamer T in which the H-2 and H-3 protons are trans oriented should have a large value of J A A ~ ( =J T ) . In G and G’, H-2 and H-3 are gauche, and should have small and equal values of J A A ~ ( =J G ) . Changing the solvent changes the dielectric constant, thus affecting the conformer p o p ~ l a t i o n s ~ - since ~ * ’ ~the forms T and G have different dipole and quadrupoIe moments. On the other hand, there is a very small change3ol4 in the coupling const,ants of the rotamers T and G or G’ for
varying solvent. I n fact, the change in the values of JT and J G with solvent is so small as to be less than the experimental error of measurement of CH. CH coupling constant for compounds of this type. Thus the observed coupling J A A in ~ a solvent(s) is the weighted average of the coupling constants JT and JG and has been related3by
(1) where AES = EG’ - ET’ is the excess of energy of isomer G in the solvent and has been shown to be related3 to the energy difference in the vapor phase, ~~~
T Figure 2.
~~~
~
(11) J. A. Pople, W. G. Schneider, and J. J. Bernstein, Can. J. Chem., 35, 1060 (1957). (12) M. Bafield and D. M. Grant, Aduan. Magnetic Resonance, 1, 149 (1965); A. A. Bothner-By, ibid., 1, 195 (1965). (13) P. L.Wessels and K. G. R. Patchler, private communication. (14) R. J. Abraham, L. Cavalli, and K. G. R. Patchler, “Nuclear Magnetic Resonance in Chemistry,” Academic Press, New York, N. Y., 1965,p 111.
Volume 71, Number 9
August 1967
NOTES
3098
Figure 3. Plots of the observed J A Afor ~ meso-2,3-dibromobutane us. x in various solvents with the calculated curve.
AEV, and the bulk dielectric constant, medium by eq 2
+
E,
of the solvent
where x = (E - 1)/(2e 1) and1 = 2 { [ ( n ~-) 1]/ ~ [ ( n ~ ) 2 21 n~ being the refractive index of the solute. k and h are given by ( P T ~- C ( G 2 ) / a 3 and ( 4 -~4 T~2 ) / a 5 , respectively, FT,G and q T , G being the dipole and quadrupole moments of the two isomers, T and G, and a being the molecular radius. Therefore, the variations of J A A t (see Table I) can be fitted using eq 1 and 2 to calculate AEs and hence the relative population of the two rotamers T and G in the solvents. The dipole
+ 1,
The Journal of Physical Chemistry
and quadrupole moment terms of the molecule have been calculated in the usual way4 assuming normal tetrahedral angles, with the dihedral angle between the two C-Br bonds in the isomer G or G’ equal to 70°.15 The dipoles have been considered as point dipoles placed a t the centers of the dipolar bonds. The calculations give a value of k equal to 3.91 kcal/ mole and that of h equal to 4.45 kcal/mole. These values of k and h have been used with eq 2 to obtain a best fit computed curve of the observed data for J A A ~ us. x (see Figure 3). The important thing to notice about the relative energies of the rotamers is that the isomers T and G are almost equally predominant in dilute solutions in polar solvents while the proportion of the nonpolar form T comparatively increases in the solutions of the compound in nonpolar solvents. The computer fit of the observed data gives the value of AE’ equal to 1.0 kcal/mole and the couplings between H-2 and H-3 protons of the two isomers as 11.35 =t 0.20 Hz for 0.38 Hz for isomers G and G’. isomer T and 5.90 It is pertinent to note that there is some scatter of experimental points from the calculated curve (see Figure 3)) and such small discrepancies are obviously due to the preferential solute-solvent interaction4 not involved in the classical the or^.^
Acknowledgment. The author expresses his hearty thanks to Professor G. W. Kenner for his encouragement during the progress of the work, and to Dr. W. A. Thomas for many fruitful discussions. (15) H. J. M. Bowen, J. Donohue, and 0. Kennard, “Interatomic Distances and Configurations in Molecules and Ions”, The Chemical Society, London, 1958.
