R. J. ABRAHAM
1192
Medium Effects in Rotational Isomerism. VI. Inclusion of Dipole-Dipole Interactions in Polar Solvents12 by R. J. Abraham The Robert Robtnson Laboratories, The Untoerstty, Lirerpool 7 , England
(Received May 21. 1968)
An electrostatic theory of the effect of the medium on the energy differences between rotational isomers is extended by the inclusion of solvent-solute dipole-dipole interactions in polar solvents. This extension permits the calculation of the energy differences of rotational isomers in the vapor ( A P ) and liquid (AEI) from measurements of the solvent dependence of the coupling constants in a molecule. In 1,1,2-trichloroethane the theory is in agreement with the observed energy differences in the vapor and liquid. For meso-Z13-dibromobutane these are obtained as AEv = 2.0 ( f O . 1 ) kcal/mol and AE1 = 0.90 ( f 0 . 1 ) kcal/mol. The trans and gauche vicinal HH couplings in the latter are 10.3 (f0.1) and 2.9 (f0.4) cps, respectively, and the trans and gauche oriented Me-C-CH couplings are 0.5 (f0.2) and -0.3 (d~O.1)cps, respectively. The long-range couplings are similar to those found in related molecules and agree with present theories of these couplings.
+
Introduction Previous papers in this s e r i e P have been devoted to calculating the energy difference between the rotational isomers of a molecule as a function of the dielectric constant of the medium. These calculations are based on the classical theory of dielectrics but evaluate both the molecular dipolar and quadrupolar electric fields to give the basic equation
AE‘
AEv - k ~ / ( l- 22)
=
+ 3h2/(5 -
2)
(1)
AEv and AEa are the energy differences between the isomers in the vapor (v) and any solvent (8) , 2 equals (e - 1)/(2e 1) where B is the dielectric constant of the solution, 2 is the solute polarizability and is given by 2 (nd2 - 1) / (nd2 1) , and k and h are functions of the dipole (p) and quadrupole ( q ) moments of the isomers and the molecular radius a.
+
+
k
= kA
- kB; h
ha =
5
[4qii2
i i-s a,e
=
kA =
hg
/.LA2/aa;
- ha;
+ 3(qij +
qji)2
- 4qiiqjj13/2a5
(2)
Equation 1 gave values of AE’ - AE1 (1 = pure liquid) in excellent agreement with the observed values for all the haloethanes for which thereare reliable data.2v4 The theory was further tested by measuring the coupling constants of a number of ethanes in various solvents. The observed coupling (J) in any solvent (8) is the weighted mean of the couplings in the individual isomers (JAand JB), e.g.
J
= nAJA f nBJB
Eliminating n A and n B from
+
?%A nJnB
=
nB =
-
1
G exp ( AEB/RT)
The Journal of Physical Chemislry
(3)
-
+
gives J = JB (JA J B ) / ( 1 exp(AE8/RT)/G), where G is the statistical weight factor (usually 2 or 3). Equations 1 and 3 give the variation of the measured coupling with solvent dielectric constant in terms of only three unknown parameters, AEV, JA, and JB. These equations have been tested on a variety of compounds of known AEv;l-a thus the variation of the coupling constant now becomes a two-parameter fit. The results obtained confirmed the general validity of these equations and gave very reasonable values of the coupling constants in the individual rotational isomers. In principle these equations could be used to obtain values of AEv,JA,and JBfrom the soIvent dependence of the coupling constants and if successful this would be a very useful method for obtaining AEV. At present, the only general methods are by ir or microwave techniques616and both of these become very difficult for complex molecules. In this investigation we wish to test this approach on a suitable compound. A compound satisfying all the requirements is meso2,3-dibromobutanea This has only two rotational isomers of different energy, the trans and the gauche isomers, the gauche isomer consisting of two identical forms, These isomers have very different dipole moments and therefore would be expected to show a considerable solvent dependence. Also the value of A E v for this compound is unknown. We then give further results for 1,1,2-trichloroethane in highly polar media. However, before considering these results, it is (1) Part V: K.G. R. Pachler and P. L. Wessels. (2) Part IV: R. J. Abraham, K. G. R. Pachler, and P. L. Wessels, 2.Phys. Chem., 5 8 , 257 (1968). (3) R. J. Abraham and M. A. Cooper, J. Chem. SOC.,B , 202 (1967). (4) R. J. Abraham and M. A. Cooper, Chem. Commun., 688 (1966). (5) 9. Miaushima, “Structure of Molecules and Internal Rotation,” Academic Press. New York, N. Y.,1954. (6) E. B. Wilson, Advan. Chem. Phys., 2 , 367 (1969).
MEDIUMEFFECTS IN ROTATIONAL ISOMERISM
1193
necessary first to develop the basic equation (1) to take into account very polar solvents.
Let c = mlm2/r~kT; then ( W ) = -mlm2fo/ra; ie., (W)/kT = -cfo, where
Theoretical Section Equation 1 is developed from the Onsager reaction field theory7 and contains the same basic assumptions. In particular the solvent is treated as a continuum of given dielectric constant. Thus the solute reaction field and therefore the external molecular electric fields, which are integrated t o obtain eq 1, follow instantaneously the orientation of the solute dipole. In very polar media the Onsager theory and therefore eq 1 tend to break down and this can be clearly demonstrated as follows. If the solvent was infinitely polarizable (ie., c 4 00 ) , then the energy difference between the isomers should also approach m. However, in eq 1 when E - + to, x -+ 0.5 and AEe is finite. This is confirmed from the dependence of the coupling constants with dielectric in our previous work. It is found that although the calculated curves for the correct value of AEv are in good agreement with the experimental data, an even better fit is obtained using higher values of AEv, but now the J values become unreal. The reason for this is that the experimental curve is more curved than the calculated curve, showing that the value of AE1 is increasing faster in solvents of high dielectric constant than is predicted from (1). As the solvent polarity increases, the dipole-dipole interactions between the solvent and the solute become increasingly important. The energy of interaction of two dipoles ml and m2,a distance r apart (I) , is given by78 W
=
-3(fiil@P)( r i ’ 2 . ~ ) / r b
+ (fil*fii2)/r3
= -m1mzr-~{2 cos O1 cos e2
- sin 61 sin 02 cos (cpl - cpt) ] =
-mmlmtr-3f (e,
These integrals cannot be evaluated explicitly except for some limiting cases. If c > 1, then the only orientation which contributes is the most stable one (01 = e2 = 0) and therefore fo 2 and (W)/kT + -2c. The calculation can be extended to include more than one solvent molecule. If the solvent shell contains six molecules in an octahedral arrangement, then for c > 1, fo 4 8. These calculations show that if the dipolar interaction is very small compared to the thermal energy, c + O and therefore (W)-+O. This is of course the result obtained by integrating eq 4 over all orientations. As c increases from zero, ( W ) initially increases as c2 but eventually for large values of c becomes proportional to c. A solute molecule of dipole moment 2 0 surrounded by an octahedral arrangement of equally polar solvent molecules at a distance of 4 A gives (W) equal to 8 kcal/mol. Thus in very polar solvents the interaction energy will become proportional to c. The dipole moment of the solvent may be related to its dielectric constant by the Onsager f0rmu1a.l~
This equation gives a good value of the dipole moment of nitrobenzene from the liquid dielectric constant, so that it is of sufficient accuracy for our purpose even in high-dielectric media. The value of nd is very constant for most liquids. Taking this as equal to 21/2 gives
(4)
cp)
In eq 7 NOis the number of molecules per unit volume ( =N/Vm where V m is the molar volume). Combining eq 5 and 7 gives (W)
= -bofof@
where
I
and
The average energy ( W ) is obtained by integrating W over 0 and cp (at constant r ) , taking into account the thermal motions of the dipoles. This gives
(w)=
JWexp( -W/kT)dNldNz $ exp( - W/kT)dNldN2
(5)
f.
=
I (e - 2) ( E
+ l)/e}1’2
There are two possible developments from eq 8. The crudest approximation is to assure that this extra (7) 0.J. F. Bottcher, “Theory of Electric Polarisation.” Elsevier Publishing C o . , Amsterdam, 1952: (a) p 141; (b) p 323. Volume 73,Number 6 Mag 1969
R. J. ABRAHAM
1194 term ( W ) is only significant in very polar media, in which fc is a constant. For an octahedral arrangement of solvent molecules fa = 8 and eq 8 becomes simply
(W) =
(9)
-hfe
However, we wish to apply this correction to all the solvents, including both polar and nonpolar solvents. For this it is necessary to evaluate fa. The integrals in eq 6 were calculated using a numerical integration technique for c values of 0.01, 1, and 3. Values of fa obtained were 0.00669,0.631, and 1.276 (T. Vladimiroff, private communication). The lowest value is in excellent agreement with the value of 2c/3 predicted for small values of c, but the other values are well below the limiting value of 2.0 for c 4 co. A curve giving the correct functional dependence of fc is a simple exponential. The function fc = 2( 1 - exp( -c/3)) gives f c values for the above c values of 0.00667, 0.563, and 1.264, in close agreement with the numerically calculated values. Thus the integrals may be replaced by a function of this form without introducing any appreciable error. For the more probable model of an octahedral arrangement of solvent molecules the function satisfying the boundary conditions (vide supra) is fa = [l - exp( - c / 2 ) ] . Incorporating this in eq 8 gives Removing c in eq 10 by using eq 5,7, and 8 gives finally
W
=
- exp( -bofe/16kT)]
-bofe[l
(11)
Equation 11 is for one molecule of solute. The corresponding equation for 1 mol of solute is
where
b,=-
{=I
3m2 2 K R T ___
r8
‘I2
For a solute molecule of 3-D dipole moment with r equal to 4 A and a solvent molecular volume of 80 ml b, is 5.0 kcal/mol. Thus the calculations show that an extra term of the form of eq 12 needs t o be included in eq 1 to take account of the nonzero averaging of the dipole-dipole interactions. These calculations ignore the important solventsolvent interactions. Fortunately, we are only concerned with the differences in energy between the rotational isomers. To a good approximation all solvent-solvent interaction8 are constant for the two isomers and therefore do not affect BE#. A further point is that eq 4 and the subsequent treatment has been obtained without introducing an effective dielectric constant into the denominator. The introduction of the dielectric constant of the medium into eq 4 is only valid when both the dipoles considered are completely The Journal of Phyaieui Chemistry
surrounded and therefore solvated, in the electrostatic sense of the word, by the solvent. The use of this equation using “artificial” values of the dielectric constant, e.g., to calculate conformational equilibria,* is incorrect. In order to apply eq 12 directly to our solvent theory, specific assumptions would have to be made concerning the structure of the solvent shell for each solvent. I n particular, it would be necessary to evaluate an effective r for each solvent-solute interaction. In order to achieve a general theory, we make the simplifying assumption that the variation in r can be ignored for the different solvents considered in comparison to the variation in the solvent dipole moment (which is explicitly accounted for in the fe term). Also in order to evaluate the difference in energy between two rotational isomers we make the convenient assumption that the mz/r3 term, or more strictly the new term (m2&- m2b/ra),is proportional to IC (eq 2). Therefore eq 1 is now modified by the inclusion of the term
(AW) = -bICfe[l - exp( -bkfe/16RT)] (13) where the parameter b is a constant to be determined experimentally. This is the only arbitrary parameter in eq ,13 and our approach will be to test this for a compound of known AEv and AE1and then use this value in a compound of unknown energy differences, Note that eq 13 overcomes the theoretical objections to eq 1, as now when e + 0 0 , the final term --$ co. Experimental Section and Results The 1,1,2-trichloroethane (I) was obtained commercially and the sample of rneso-2,3-dibromobutane (11) was provided by Dr. A. A. B~thner-By.~ The proton resonance spectra of the two compounds were obtained in dilute solutions in various solvents on Varian A-60, HA-100, and A-56/60A spectrometers. The sample temperature was ca. 30”. All spectra were recorded three or four times, using the side-band technique, and the transition frequencies were averages of these spectra. The rms error in these averages was always less than 0.05 cps and commonly ca. 0.02 cps. The spectrum of 1,1,2-trichloroethane is almost a first-order AX2 case at either frequency (a small secondorder splitting of the center peak of the CH triplet can just be resolved in some cases) and the coupling is given directly from the measured separations. The analysis of the meso-dibromobutane spectrum has been given@+ by regarding it as an XAA‘X,’ case (8) E. L. Eliel, N. L. Allinger, 8. J. Angyal, and G. A. Morrison, “Conformation Analysis,” Interscience Publishers, New York, N. Y., 1965, Chapter 7. (9) A. A. Bothner-By and 0 . Naar-Colin, J. Amer. Chem, Soe., 84, 743 (1962). (10) F. A. L. Anet. i b f d . , 84, 747 (1962). (11) P. Dfehl. R . K. Harris, and R . G. Jones, “Progress in N. M . B. Spectroscopy.” Vol 3, Pergamon Press, Oxford, 1967, Chapter 1.
1195
MEDIUMEFFECTSIN ROTATIONAL ISOMERISM in which JXX, is zero. This provides explicit expressions f ~ the r transition frequencies from which the couplings can be obtained directly. Apart from the pure liquid, the signal to noise ratio of the methine region of the spectrum in these dilute solutions was not good and the spectral parameters were obtained directly from the methyl spectrum. The analysis given9-" shows that this spectrum consists of two strong lines of separation JAX JAX, and a number of AB type quartets. In only one of these quartets are all four lines clearly seen, and in this quartet the "effective" AB coupling equals JAA, and the"effective" chemical shift eqUalSJAx-JAx~. Thus all the coupling constants can be obtained explicitly. The results for these two compounds are given in Tables I and 11. Table I includes the previously reported results for the trichl~roethane~ plus further results in very high-dielectric solvents. The dielectric constants in Table I are measured values for the solutions, while those in Table I1 are calculated on the basis of additive-volume dielectric constants. This gives results in much better agreement with experiment for a variety of solvent mixtures12*than the equation previously used based on additive-volume polarizabilities.2 The coupling constants of I1 show the expected solvent dependence. The CHa-CH coupling JAX is constant (6.60 f 0.02 cps) to within the experimental error for all the solvents investigated. In contrast, the CH-CH coupling J A A changes ~ con-
+
Table I: Proton Coupling Constant of 1,1,2-Trichloroethane in Various Solventsa Solvent n-Hexaneb Pentane %-Hexane Decalin CCln
cs2 CClzCHCl GPrzO EtzO CHCls C7HlsBr Neat liquid CHzClz CHaCl-CH2Cl Mesityl oxide CHsCO-Et Acetone CHsCN CHaNOz CKaCNb DMF CHsCO-NMeZ Sulfolane DMSO
€
J. CPS
1.95 2.07 2.10 2.32 2.45 2.95 3.55 4.10 4.50 4.90 5.38 7.15 8.25 9.75 15.0 17.3 19.2 32.0 32.6 34.4 35.0 35.8 42.2 44.9
6.24 6.25 6.21 6.17 6.17 6.13 6.13 6.04 6.05 6.03 5.99 5.92 5.93 5.87 5.64 5.53 5.52 5.52 5.51 5.52 5.34 5.28 5.31 5.17
Solutions contained 1 mol of solute to 10 mol of solvent. eolutions.
Table 11: Proton Coupling Constants and Chemical Shifts (cps) of meso-2,3-Dibromobutane in Various Solvents" Solvent n-Hexane c-Hexane CCla
cs2 CHCl-CCIz CHCla Neat liquid CHzClz CHzC1-CHaCl Acetone CHsCN DMSO
e
2.281 2.399 2.589 2.945 3.599 4.762 5.93 8.44 9.67 18.79 32.90 44.60
JAA'
JAX
9.16 9.07 8.93 8.82 8.59 7.97 7.94 7.45 7.33 6.65 6.36 5.72
6.63 6.58 6.60 6.61 6.62 6.62 6.58 6.64 6.63 6.62 6.57 6.64
JAX'
GCHab
-0.31 -0.25 -0.23 -0 25 -0.23 -0.22 -0.20 -0.20 -0.18 -0.15 -0.13 -0.09
110.71 110.39 113.05 110.97 110.62 111.55 109.92 110.01 109.08 108.60 106.94 104.16
I
Solutionscontained 1 ml of solute in 10 ml of solvent. TMS at 60 Mcps.
* Cps from
tinuously with the dielectric constants from ca. 9 to 6 cps. Also the four-bond coupling J A X ~shows a parallel behavior, which is in agreement with the known dependence of this type of coupling on the molecular configuration (vide infra). The results of Table I1 are in complete agreement with earlier reliable r e s u l t ~ . ~ JThe ~ values quoted for JAA are~7.87 and 7.85 cps for the pure liquid and 8.81 cps for the solution in CS2, compared t o the above results of 7.94 and 8.82. However, these results do not agree in detail with some results recently reported from for~ our laboratory.12b E.g., in ref 12b the value of J A A trichloroethylene solution is reported as anomalously low (7.75 cps). In contrast, the present measurement (8.59 cps) shows that this solvent behaves quite normally, as it has done for every other solute in~ e s t i g a t e d . ~ JIn all the other solvents common to Table I1 and ref 12b, there are disagreements of 0.1-0.2 cps. This is probably due to a combination of the different concentration used and experimental errors. More seriously the theoretical treatment is also incorrect (vide infra) so that the conclusions reached in ref 12b are incorrect. ~,~,d-TrichZoroethane. The results in Tables I and I1 can now be used to test eq 1 and 6. The experimental data and calculated molecular constants needed in these equations are given in Table 111. The molecular radius a is obtained directly from the molecular volume (mol wt/Np). The calculation of k and h follows the normal procedure of placing point dipoles a t the center of the C-X bonds of magnitude given by the corresponding methyl derivative. For the CH2Cl fragment we use ethyl chloride (2.03 D), for the CHCl2 fragment,
* 5% (12) (a) D. Decroocq, Bull. SOC.Chim. France, 127 (1964); (b) K. K. Deb, J . Phys. Chem., 71, 3095 (1967). Volume 73, Number 6 Mag 1969
R. J. ABRAHAM
1196
Table 111: Molecular Constants and Calculated Parameters for Trichloroethane (I) and meso-Dibromobutane (11) Molec radius,
Isomer
Density
nd
A
I gauche
1.4357233
1 .4706*0
3.33
trans
I1 gauche trans
1.774626
1.5092*6
3.64
ethylidene dichloride (2.06 D) , and for the CHBrCHa fragment, isopropyl bromide (2.20 D) .la Normal bond lengths and angles are assumed with the dihedral angle of the trichloroethane (trans isomer) taken as 70". The values of k and h for I1 again differ appreciably from those in ref 12b. The application of eq 1 and 13 to these results is conveniently performed using a computer program. This takes as input the values of le, h, 1, etc., and the experimental values of the coupling constant and the dielectric constant of the solutions. AEv is then varied over any given range and for each value of AEV the least-squares best-fit values of J t and J , are obtained from eq 1, 13, and 3, together with the rms error of the calculated and observed couplings. The Trichloroethane Results. In the case of trichloroethane the values of the energy differences in the vapor and pure liquid are known. AEv is variously quoted as 2.314t o 3.015kcal/mol. The energy difference in the liquid obtained from infrared studies of 0.3 f 0.1 kcal/mol15 ( AE$) is not the true energy difference in the liquid ( A E ' ) as no correction is made for the variation in dielectric constant with temperature. Writing eq 1 (or 13) as, for the pure liquid AE'
=
A.Ev - H
then AE'o
=
AE'
+ T(dH/dT)
The variation of dielectric constant with temperature is known and therefore dH/dT is immediately calculable. These results alone are sufficient to define the constant b in eq 13. However, this must also give the correct solvent data and it is more convenient to consider this first. There are two nonequivalent isomers of I, the trans isomer consisting of two identical forms. Thus G in eq 3 equals 0.5.
;.;
; + aH H
H
gauche
trans
Using eq 1 and 3 with the results in Table I, it is shown that although a reasonable fit is obtained if 6 E v is within the stated range,3 the calculated curve is The Journal of Physical Chemistry
Dipole moment
k. kcal/mol
h, kcal/mol
1
3.64 1.63
5.18 1.03
1.18 4.00
0.560
3.59 0
3.86 0
1.55 4.98
0.596
more in agreement with the observed results for higher values of AEv although unreal values of the couplings are obtained (e.g., for AEv = 3.4, J t = 6.38, J, = -21.6, and the std dev = 0.074). The inclusion of the dipole-dipole term in eq 13 gives a different result. It is found that a value of b satisfying the solvent data is obtained and furthermore that this value is well defined. For b = 0.06 the program converges to the result AEV = 2.60, J t = 6.30, J , = 0.48, std dev = 0.062 cps. Both below and above this value of AEV the agreement is worse. For b = 0.07 the program converges to AEq = 2.20, J t = 6.33, J, = 3.12, std dev = 0.062 cps. The value of AEV obtained is in Satisfactory agreement with the experimental data. The calculated values of AElo are 0.56 and 0.14 kcal/mol for b equals 0.06 and 0.07, respectively, and these are again in excellent agreement with the more accurate ir data for the liquid. (The true values of the energy differencesin the liquid AE1 at 30" for the two cases are 0.15 and 0.74 kcal/mol, respectively.) These values also reproduce the observed variation of the coupling constant in the pure liquid with temperature. The coupling constant changes from 5.92 (30") to 5.87 (90'). The calculated values are 5.92, 5.92 (30") and 5.88, 5.90 (90") forb equals 0.06,0.07. Outside these limits of b all the data cannot be fitted simultaneously. For b = 0.08 the value of AE'o is too low (-0.1 kcal/mol) and for b = 0.05 the value of J, is unreal (-9.32 cps). The range of values of b could be extended by not taking the precise best-fit solution of the solvent data. However, we may conclude that the inclusion of the dipole-dipole interaction in eq 13 is sufficient to give a satisfactory quantitative explanation of all the existing experimental data with a value of b of 0.06-0.07, and that no other value so complete satisfies all the data. The final values of the parameters obtained from this treatment are AEV, a',and M'Oequal 2.4, 1.0, and 0.35 ( k 0 . 2 ) kcal/mol, J t equals 6.32 f 0.05 cps, and J, equals 2.0 f 0.6 cps, meso-9,S-Dibromobutane. The experimental results for I1 can be treated in a similar fashion. There are again only two nonequivalent isomers of this compound, (13) "Handbook of Chemistry and Physics," 45th ed, Chemical Rubber Publishing Co., Cleveland, Ohio, 1965. (14) R. H. Harrison and K. A. Kobe J. Chem. Phys., 26, 1411 (1957). (15) N. Sheppard Advan. Spectrosc., 1, 288 (1959).
1197
MEDIUMEFFECTSIN ROTATIONAL ISOMERISM the gauche isomer in this case having two mirror image forms. Thus G (eq 3) now equals 2.
M Br e&:
H
trans IIA
:he Me
gauche IIB
The use of eq 1 and 3 on the experimental results for again does not give any real the vicinal coupling JAA, result. The agreement between the observed and the calculated couplings becomes better and better as E" increases even though completely unreal values of J, and J t are obtained. In this case as AEv is not known; without further evidence none of the molecular parameters can be obtained from eq 1. However again the inclusion of the dipole term of eq 13 gives a completely different result. For values of the constant b in eq 13 equal to 0.06 and 0.07 the best-fit values of the three unknown parameters are A E v = 2.00 and 1.90kcal/mol, Jt = 10.26 and 10.30 cps, and J, = 2.53 and 3.33 cps. The standard deviation is 0.10 in all three cases. Both above and below these values of AB" the agreement between the observed and calculated couplings is much worse. It is encouraging to note that the value of AEv is relatively insensitive to the exact value of b as this of course increases the accuracy of this method. The solvent dependence of J A X ~could be treated similarly. However, because the variation in J A X is ~ so small (ca. 0.2 cps) , a better method of obtaining the couplings in the isomers is as follows. There is a linear relation between any two couplings, such as J A Aand ~ JAX'which depend solely on the per cent of the rotational isomers present.2 A plot of J A A f os. J A Xshows ~ that this is so, within the accuracy of the experimental data and follows the equation
+
JAX =~ - 0 . 0 5 9 J ~ ~ t 0.262 Using this equation with the values of JAA, in the of -0.35 distinct isomers (above) gives values of JAX, cps for the trans isomer and f0.09 cps for the gauche isomer. The value for the gauche isomer is the average of the couplings for the two orientations of the methyl groups relative to the methine H (IIB). Assuming that the coupling in the gauche orientation has the same value as in the trans isomer gives the Me-C-CH coupling in the trans orientation equal to 0.53 cps. The results can be summarized as A E v = 2.0 f 0.1 = 2.9 f 0.4 kcal/mol, JIHH= 10.3 f 0.1 cps, JQHH cps, JoMeH = -0.3 f 0.1 cps, and JtMeH = 0.5 ~t 0.2 cps. Detailed discussion of the coupling constants will be deferred to the next section.
Discussion The calculated values of the coupling constants in I and I1 are plotted against the experimental results in
.I
I
0.2
I
0.3 (E-I)/(2ttl)
I
0.4
I
Figure 1. The solvent dependence of the vicinal proton coupling constants in 1,1,2-trichloroethane (I) and meso-2,3-dibromobutane (11) with the calculated best-fit curves.
Figure 1. The agreement is excellent and worthy of some comment. Using 24 solvents in I and 12 solvents in I1 with a range of dielectric constants from 19 to 50 and excluding only aromatic solvents, hydrogenbonding solvents, and anisotropic solvents ( i e . , solvents containing a long hydrocarbon chain and a small polar group) , the results give calculated curves with mean deviations of only 0.06-0.10 cps, which is roughly the combined experimental error of the coupling constant and dielectric measurements. This lends considerable support to the validity of the reaction field theory for these solvent effects. It is of interest to note that solvents with very high dielectric constants are not necessarily the best solvating agents. E.g., fonnamide (e 109) and N-methylformamide ( e 190.5) give coupling constants for I of 5.40 and 5.50 cps, respectively, much higher than DMSO. This is because the former are strongly associated by hydrogen bonding and their high dielectric constants reflect this association in solution rather than the solvent polarity. In contrast, DMSO cannot hydrogen bond to itself and therefore its dielectric constant is a true measure of its Volume 75, Number 6 M a y I960
R. J. ABRAHAM
1198 solvating powers. These results agree entirely with observations recently obtained for ionic solutions.lB A basic assumption of the above treatment is that the coupling constants in the individual rotamers are solvent independent. This cannot be tested expermentally for I and I1 nor for any ethane which consists of an unknown mixture of rotational isomers. The coupling constant in the CH3-CH fragment in I1 is independent of the solvent (Table I I ) , and in measurements in our laboratory the coupling in 1,ldichloroethane is 6.03 f 0.03 cps in both CC1, and CHaCN. However, these couplings are average couplings which may behave differently to the gauche and trans couplings. Recent investigations with cyclic compounds and ethanes predominantly in one conformation confirm the above assumption. In the rigid hexachlorobicyclo[2.2. llheptenes the variation in J , is Q 0.1 (in 9 cps) and in J t 0.2 (in 3 cps) , for a variety of substituents.17 In 3,3-dimethylbutyl iodide, which exists almost entirely as the trans rotamer, the variation in J , is
