Valence Bond Studies of Internuclear Coupling BY H. s. GUTOWSKY AND CYNTHIA JUAN No yes Chemical Laboratory, University of Illinois, Urbana, Illinois Received 18th June, 1962 Two studies are reported which involve valence bond calculations of internuclear coupling. The first, of the proton spectra for the -CH2CH2- bridges in (2,2) metacyclophane, shows con- clusiveIy that the relative signs of the geminal and vicinal proton coupling constants are opposite, which disagrees with the theoretical prediction that both are positive. In this compound, the C-CH2-CH2-C groups are locked in position with the dihedral angle between alkyl C-C-C bonds slightly less than the symmetrical, staggered 60". A complete analysis of the A2X2 and A2B2 type proton spectra, at 60 and 15 Mc/sec leads to the following assignments : JFH = f12.3, JFH (the coupling of the " central " pair of gauche protons) = i-3-2, = 112-0, and JFH = rt4.0, all f0-1 clsec.A second related study is concerned with an interpretation for the additivity of substituent contributions to the 13C-H coupling constant. Each atom or group X is assigned a characteristic " affinity " for s character in the carbon hybrid orbital of the C-X bond. The additivity can be derived if the s character is distributed among the four carbon orbitals in accord with the relative s affinities of the four substituents, provided that the total s character is conserved. The valence bond approach used with this model gives a linear relation between the s character of the carbon hybrid orbital involved in a C-H bond and the observed 13C-H coupling constant (JCH = 500 ah).Valence-bond methods have been used to calculate internuclear coupling con- stants for non-bonded 1 and also for directly bonded nuclei? For non-bonded nuclei, the a-electron contribution to the coupling has been expressed in terms of deviations of the molecular electronic structure from perfect pairing.1 Such calcula- tions for protons predicted the geminal coupling JgE to be + 12.5 c/sec in methane,1 and subsequent, more approximate, calculations 3 for vicinal protons in the HCCH ethanic fragment gave the trans coupling JFw to be about + 9.2 c/sec and the gauche J,", + 1.7 clsec. These magnitudes agree well with experiment except that the trans vicinal constants observed for ethanic groups 4 (and also the cis and trans constants for ethylene 3) are often about 50 % larger than predicted. Usually, only the magni- tudes of J have been obtained from experiment; but increasing attention is being given to the importance of their relative signs. Several substituted ethylenes have been reported 5 9 6 in which the sign of JZE (1 to 3 c/sec) is opposite to, and also the same as, that of JzF (5 to 11 c/sec) and J t s s (12 to 18 clsec).These results are com- patible with the valence-bond calculations for the CH2 fragment,s which neglect substituent and n-electron effects, and which predict that JgE should become negative for HCH bond angles larger than about 120°.53 7 Similarly, there are substituted ethanes in which the sign of the vicinal coupling JF (1 to 3 c/sec) is opposite to and also the same as, that ofJFH (10 to 16-5 c/sec).49 6 Again, the results seem compatible with the calculated dependence of the coupling upon the dihedral angle 4, because substituent effects were neglected and tetrahedral HCC angles were assumed.3 A more troublesome question has been raised by relative sign determinations, in diethyl sulphite 8 and in several dioxolane derivatives,g which conflict with the pre- dictions ~3 that large values of Jgg and J$F should both be positive.However, the 52 JZF N 9 C O S ~ 4 - 0.3, (1)H . S . GUTOWSKY AND C. JUAN 53 compounds studied are such that substituent effects, angular distortions and motional averaging are important, and their neglect in the theoretical treatment might be responsible for the apparent discrepancies in the relative signs.Therefore, we have made a detailed study of the proton spectrum of the -CH2CH2- groups in (2,2) metacyclophane,lo the conformation of which is given in fig. 1. This compound avoids the uncertainties of the cases reported earlier 899 because an x-ray structural determination of the solid11 has shown that the methylene groups are locked in virtually symmetrical, staggered positions, with tetrahedral bond angles. Nonethe- less, opposite signs are found for the large trans and geminal constants, in agreement with the previous experiments 8 9 9 and disagreeing with the theoretical predictions that both are positive.193 This disagreement may result either from inaccurate molecular wave functions or from the approximations made in calculating the coup- ling of the non-bonded nuclei, and both aspects require further theoretical study.FIG. 1.-The structure of (2,2) metacyclophane and the conformation of the -CHzCH2- “ bridges” whose proton spectra were analyzed. The protons in the -CH2CH2- groups are labelled A and B, and symbols are defined for the coupling constants. Thus far, the valence bond calculations for directly bonded nuclei appear to be more reliable. In this case, deviations from perfect pairing are relatively unimportant? and further simplification results when the coupling depends mainly on the Fermi contact term as in the 13C-H group.2 A number of theoretical and experimental studies indicate that JCH is determined by the carbon orbital hybridization and by the polarity of the C-H bond.29 12913 In fact JCH has been employed as a simple measure of orbital hybridization.More recently, attention has been turned to the effects of substituents upon JCH, and several interesting empirical relationships have been discovered,l4~ 15 the most basic of which is probably the linear additivity of group contributions to JCH in substituted methanes.14 We have found that this relation can be derived by assuming that a substituent changes the hybridization of the carbon 2s orbital in a characteristic fashion.16.17 Substituent effects have also been noted for H-H coupling in hydrocarbons. In particular, more or less linear relations have been found between the electronegativity of the substituent and the geminal and/or vicinal coupling constants in substituted ethylenes 18-20 and ethanes.21 As yet, no detailed, theoretical interpretation of these effects appears to have been advanced.However, it seems very probable that the effects of substituents upon JCH are related directly, or at least indirectly, to those for JHH. If our model is correct for the effect of X upon JCH in CHXYZ or CH2=CHX groups, it should contribute to a better understanding of JHH, inasmuch as the latter is also affected by the hybridization of orbitals in the C-H bonds. RELATIVE SIGNS OF J g z , JBHH AND J)IH A sample of (2,2) metacyclophane was provided for our experiments by Wilson, Boekelheide, and Griffin.10 The high resolution proton spectra were observed at54 INTERNUCLEAR COUPLING room temperature using 10 % solutions in CCle Spectra at 60 Mc/sec were observed with Varian Associates HR-60 and A-60 spectrometers.The 15.083 Mc/sec spectrum was obtained through the courtesy of Dr. J. N. Shoolery at Varian Associates, where it was observed with a V-4300 spectrometer system. The general procedure used to determine the magnitudes and relative signs of the coupling constants in the -CH2CH2- group is the following.22 At a resonance frequency of 60 Mc/sec, the chemical shift v06 between the A2 and B2 sets of protons, defined in fig. I, is sufficiently large that the quite simple observed spectrum is a good approximation to the A2X2 type. From it, the magnitudes of v06 and of the four coupling constants are determined readily, as well as the relative signs for each of two pairs of coupling constants.In part, the 60 Mc/sec spectrum is easy to analyze because it is insensitive to one of the relative signs. However, the latter becomes important at lower resonance frequencies, where the spectrum is of the A2Bz type. Therefore, the magnitudes and signs obtained from the 60 Mc/sec spectrum were used to calculate 15.083 Mclsec spectrum for the remaining relative sign permutations, and comparison of these with the observed spectrum completes the analysis. It is convenient to use the parameters where the coupling constants are defined in fig. 1. These four constants have three relative signs which we wish to establish. In terms of the parameters K, L, M and N, which we treat as positive quantities except for Kin the one circumstance noted below, the relative signs of each pair of coupling constants in eqn.(2) is determined by the relative values of the corresponding two parameters. Thus, if N> L, Jg and Jgem have the same sign ; and if N t L , the opposite. Identical relations involving K and M hold for Jt and J g . In addition, the spectrum is sensitive to the actual relative signs of K = (Jt+Jgt) and N = (Jg+Jgem). Whether the observed spectrum is fitted by K positive or negative, while treating N as positive, determines the third relative sign. If K negative applies, then the constant of largest magnitude in K is of opposite sign to the constant of largest magnitude in N, while they are of the same sign for a positive K. Finally, the magnitudes of the coupling constants are obtained by means of eqn.(2) from the numerical (positive) values for K, L, M, and N ; however, the spectrum alone does not tell which constant is which within each pair and supplemental in- formation about the relative magnitudes of the constants is required to complete the assignment. THE 60 Mc/sec SPECTRUM The proton spectrum observed at 60 Mc/sec is given in fig. 2. As a first approxi mation it is of the A2X2 type, with " mirror image " A2 and X2 multiplets whose centres are separated by [(v06)2+ N2]*. In general, each A2Xz multiplet has ten lines, two quartets and a doublet with a common centre. The outer splitting of one quartet is K, and of the other, M, while the central splittings are (Kz+L2)*-K and (Mz+L2)*--M, respectively. The lines of the doublet are the strongest transitions ; their splitting is N.In the observed spectrum, the A2 and Xz multiplets have two rather broad, very strong lines at the centre, with two weaker lines at each side. Therefore, the inner lines of the two quartets are not resolved from the strong N- doublet, and only the outer lines of the quartets are visible. Thus, the -8 clsec splitting of the strong centre pair of lines undoubtedly is N. Also, the outer splittings of the two quartets are - 9 and - 15 c/sec but at this point it is uncertain which is K and which is M. These values, in combination with the expressions for the centralH. S. GUTOWSKY AND C . JUAN 55 splitting of the two quartets and their observed values of -8 c/sec, give an unam- biguous value for L of 15+2 c/sec. Also, the separation between the centres of the two multiplets is approximately the chemical shift, which gives v06 = 60.3 c/sec.The values of the parameters were refined by varying them systematically, com- paring the resulting calculated spectra 23 with experiment, and then interpolating. In this manner, the following best-fit, numerical values were obtained : v06 = 59-1, N = 8.0, L = 16.0, and More important, the spectra calculated for the four possible permutations show that although the spectrum observed at 60 Mc/sec is too insensitive to the sign of K for its determination, the asymmetry in the splittings p and q in fig. 2 is governed by the relative magnitudes of K and M. In order to have p <q as observed, it is necessary to have K> M,22 which requires that K be 15-5 and M, 9.1 c/sec.K or M = 9.1 or 15.5, all in c/sec. L I I I I I 0 clsec FIG. 2.-The spectrum observed at 60 Mclsec for the -CHzCH2- group protons in (2,2) meta- cyclophane. This spectrum is fitted by v08 = 59.1, N = 8.0, L = 16.0, M = 9.1 and r t K = 15.5 c/sec. Spectra calculated for interchanged values of K and M have p >q, rather than p < q as observed. THE 15.083 Mc/sec SPECTRUM Figure 3 includes the spectrum observed at 15.083 Mc/sec and also spectra cal- culated for the two remaining sign permutations, K = k 15.5 c/sec. There is ex- cellent agreement between experiment and the spectrum calculated for K = - 15-5 c/sec, and very poor agreement for K = 15.5 c/sec. Therefore, the parameters which apply to the -CH2CHz- group are : K = - 15.5 c/sec, N = 8.0 c/sec, h!f = 9.1, L = 16.0. (3) Upon combining these results with the definitions in eqn.(2) we find from N and L that Jg and Jgem are 12.0 and 4.0 or 4.0 and 12.0 c/sec. Moreover, they are of opposite signs because N<L. From Kand M, Jt and Js. are 12-3 and 3.2 c/sec or the reverse. Also, they are of the same sign because K> M. (Here, both K and M must be treated as positive quantities.) Also K and N actually have opposite signs so the largest constant of the K, M pair (12-3 c/sec) is of opposite sign to the largest constant of the N, L pair (12.0 c/sec).56 INTERNUCLEAR COUPLING The assignment is completed by introducing the inequality I Jt 1 > I Jgt I , which is known with certainty from the nmr studies of substituted ethanesP.6 and the inequality I Jgem I > I Jg 1 which is equally certain from the experimental results 4 6 for substituted ethanes in Combination with those on Jgem in methane 1 and substi- tuted methanes.5 The final assignment is JyH = & 12.3 c/sec, .JF = 43.2, J!& = T 12.0 c/sec, JfH = k4.0 with probable errors of about 40.1 c/sec in the numerical values. A B I $1 I II I In I I1 II I ll A 0 (4) I[ I, I , I 1 I 1 I a I0 20 clsec FIG. 3.-The left-hand spectrum is that observed at 15083 Mclsec for the -CH2CHr group protons in (2,2) metacyclophane.The line spectra at the right were caIculated for the two sign permutations not differentiated by the 60 Mc/sec spectrum, i.e. for K = f 15.5 clsec. The spectrum for K positive disagrees with the wings and the central portion of the observed spectrum.COMMENTS The closeness of the 12.0+0.1 c/sec value found for Jgz to the 12.4+0.6 c/sec observed in methane 1 indicates that the former is not affected by angular distortion and substituent effects. The small difference between the 3-2 and 4-0c/sec values for JF and J," is consistent with a C-C-C-C dihedral angle of slightly less than the 60" for a symmetric, staggered -C&CH2- group, as is suggested by the X-ray data for the solid.11 Also, this could account for the value of 12.3 c/sec for JFH being smaller than most found for substituted ethanes.697 Therefore, our finding of large values of opposite sign for JCHH and .Ig%, as well as the less conclusive earlier studies,s* 9 show that either the calculation on CH4 1 or that on the ethanic (and probably also on the ethylenic) fragment 3 is in error.Which of the calculations is most likely to be in error, if not both, is another question. In some ways, the calcula- tions for the HCCH fragment present the best opportunities for error. These calcula- tions are more complex than for CH4 (or CH2), and it is possible for example that the non-neighbouring-atom exchange integrals should not have been neglected.3 A more direct approach to the question would be to determine the sign of JvF andlor Jgz with respect to JCH for there is little doubt but that it is positive.2.17 Such relative sign determinations could help decide which of the JHH calculations to redo first. Fortunately, the relative signs of JCH, J g z and can be determined by the sort of approach used here and also by double resonance methods, either on 13C en- riched (2,2) metacyclophane or other appropriate compounds.H. S.GUTOWSKY A N D C. JUAN 57 In fact, analysis of the 3 1 P and proton spectra observed for diphosphine H2PPH2 has given results,24 related to our problem. For this compound, JgE and Jpp were found to have values of 108.2 and 12 c/sec, respectively, and to be of the same sign, opposite to that of J z (cis and trans) which has values of 10.5 and 6.8 c/sec. By analogy to the results of the HCCH calculations,3 it was assumed24 that was positive in diphosphine, which, of course, made J p p and Jzz negative. A negative value for JPP is surprising because the coupling between directly bonded atoms due to the usually dominant contact term is positive.In view of the present findings it may be somewhat more plausible to take Jpp as positive, which leads to Jgg positive and JF (cis and trans) negative, at least in the diphosphine case. EFFECTS OF SUBSTITUENTS UPON JCH Malinowski has reported 14 that to a very good approximation the W-H coup- ling constant in substituted methanes, CHXYZ, is an additive property of the sub- stituents. This additivity has been expressed in two equivalent forms 149 17 employing different definitions of the " substituent parameters ". What is perhaps a better formulation may be obtained by returning to the basic experimental fact, namely,14.17 JcH(CHXYZ) = Jc,(CH,X) +JcH(CH,Y)+Jc,(CH,Z)-2Jc,(CH,), ( 5 ) and noting that it may be written as where, by definition JcH(CHXYZ) = Jc~(cH4) + 6~ + 8y + 82, Sx = Jm(CH3X) - JCH(CH4).In other words, each substituent X contributes a characteristic term &, to JcH(CHXYZ), which is independent of the other substituents. There are two general approaches to the theoretical interpretation of this empirical result. Previous work 2,129 13 is consistent with JCH being determined by the carbon orbital hybridization and the C-H bond polarity. Therefore, one can seek to derive eqn. (6) on the basis of hybridization and/or polarity changes produced in the C-H bond by the substituent. Or one can investigate the other contributions, such as n-electron and orbital polarization terms, which X could make to JCH without affecting materially the C-H bond. We are concerned here with the first approach. VALENCE BOND FORMULATION FOR JCH The general expression for JNN consists of several terms.25 However, in this paper we consider only the Fermi contact term which is dominant for the 13C-H coupling, at least in CH4,2 The symbols used above have their usual meanings.In the ground state wave function Y?o deviations from perfect pairing are not important for the coupling of directly bonded nuclei.2 We use the separated eIectron pair wave function, (9) y o = (8 !>-+I (- ~ ~ p ~ c \ y , x ~ ~ , ~ ~ ~ ~ ~ ~ ~ , ~ ~ i c l , , ~ ~ , ~ ~ with where ur(i,j) is of the valence bond form with inclusion of ionic terms,58 INTERNUCLEAR COUPLING In the latter, 4a, . . . q5d are carbon atomic orbitals ; &, . . . & are atomic orbitals on the atoms bonded to the carbon, and q is the normalization constant.The co- efficients of the ionic terms are il, and 1,. Substituting YO into eqn. (8) and using the Dirac identity S k Sj = (+)(2P&- l), in which P,& is an operator interchanging the spins of electrons k andj, one obtains We assume the four carbon hybrid orbitals to be formed from one 2 orbital and three 2p orbitals, e.g. where the s character, a&, a$, etc., of the orbitals depends on the groups or atoms H, X, Y or Z bonded to the carbon. Substituting 4 d , and #h = Is, into eqn. (12), one finds that +d = O~HS + (1 - ~1H')'p~ a d = a , ~ + (1 - aX2)'pG*, (13) where q - = (2 + (2 + &AH)[aiS: + (1 - ai)sg f 2aH(1- aG)'s,sp] + 4(& + AH) x [aHSs f (1 - ai)'sp] + 2; + 1;). (15) 2340) is the 2s wave function of carbon evaluated at the carbon nucleus, and l s ~ ( 0 ) is the corresponding quantity for the hydrogen 1s function.S8 and Sp are the over- lap integrals between the hydrogen 1s atomic orbital and the 2s and 2p carbon atomic orbitals, respectively. In eqn. (15) for q-2, i l ~ is much less than Ac, because the electronegativity of C is greater than that of H, so AH is neglected and the coefficient of the ionic contribution to the wave function is hereafter denoted by ~ c - H . Eqn. (14) leads to JCH = (Aq2/AE)ai = J,ai clsec, (16) where A is a collection of constants, and JO is 500c/sec, as determined from the observed value 129 13 of 125 clsec for Jc~(cH4). This value for JO is consistent with the valence bond theory inasmuch as Karplus and ($ant2 obtained a reasonable value of 0-374 for ilc-~, using the same approach, with JCH = 124 clsec, in combina- tion with an estimate of AE and calculations of the overlap integrals from Hartree- Fock functions.Eqn. (16), depending upon the sensitivity of AE and q2 to sub- stituents, affords an attractive semi-empirical way to obtain the s character of bonding orbitals from coupling constants. For the substituted methanes, or other classes of closely related compounds, one would expect AE to be very nearly constant. This follows from the fact that it is approximately twice the bond energy,;! which varies by only a few percent for C-H bonds. The constancy of q2 depends upon its sensitivity to il and a&. These dependences can be calculated relatively simply and directly by means of eqn.(15). For the C-H bond, q 2 was found 17 to be insensitive to the value of a&, the total change being only 0.2 % over a range of cx& from 0-24 to 0-45. q2 is also relatively insensitive to Ac-H. Substituents are expected to change the electronegativity of the C atom by at most 0.1 to 0.2 units according to estimates of effective electronegativities by proton chemical shift measurements.26 The empirical values of AB-H, AC-H and AN-H given by Karplus and Grant,2 indicate that an increase in electronegativity of the carbon by 0.2 units would change &!-H from 0.374 to about 0.44. This corresponds to a decrease in q 2 to about 0.95 @(CH4)H. S. GUTOWSKY AND C. JUAN 59 However, the increase in LC-H is accompanied by an increase of Zeff for the 2s and 2p electrons of carbon which leads to a decrease in the overlap integrals Ss, Sp, and to an increase in q2.Thus, the effects tend to cancel, and even though a&, &-R, and the overlap integrals all change with the substituents, q 2 is expected to remain about the same for the substituted methanes. This leads to JO zz 500 c/sec and the linear relation in eqn. (16) between JCH and a:. THE ADDITIVITY OF SUBSTITUENT EFFECTS The additivity relation observed by Malinowski 14 can be derived by means of eqn. (16) providing one assumes that the substituents redistribute the carbon 2s orbital among the four bonds in a particular manner. First of all, the 2s character must be conserved, that is Secondly, each atom or group X is assigned a " characteristic affinity for s character ", AX.Let AX be measured with respect to H so that AX is positive if the " s affinity " of X is less than H and negative if greater than H. Consider the four bonds to be four equivalent interconnected potential wells of possibly different depths. The difference in the depths of the wells for X and H is defined as AX. The 2s orbital will distribute itself among the wells to give a common 2s level, because of their interconnection. Moreover, this common 2s level, and the content of each well, can be obtained very readily via eqn. (17), i.e. by the assumption that the sum of the 2s content of the four wells is unity. In CH4 or CX4 the four wells are all of the same depth so that 2s character is distributed equally among them, and a2 = $. In CH3X, the H wells are deeper than that of X by the amount AX which is distributed equally among four bonds so an H well will have (+)Ax 2s character more than an H well in CH4.In general, the H well in CHXYZ will have [(i) AX + ($) Ay + (t) Az)] 2s character more than an H well in CH4. Expressed mathematically, this means that for CH3X a;+a;+a;+c!; = 1. (17) a$(CH3X) = ai(CH4) + (+)Ax or (+)Ax = a&(CH,X) - &(CH4), (18) &(CHXYZ) = ai(CH4) + (+)(Ax + Ay + Az). (19) (+)AXJO = JCH(CH3X) - JCH(CH4) 6X, (20) JcH(CHXYZ) = JcH(CH4) + + 6, + 6z. (6) ag(CHXYZ) = ($)(I +Ax+Ay+Az)-Ax. (21) and for CHXYZ, By means of eqn. (16), c!& can be eliminated from eqn. (18), giving which in turn converts eqn. (19) into the observed additivity relation, eqn. (6) In addition, a general equation, similar to eqn.(19), may be written for the s character of the carbon orbital in the C-X bond, COMPARISON WITH EXPERIMENT Experimental values 2314 of JcH(CH3X) and the resulting AX obtained from them by means of eqn. (20) are given in table 1 for a number of substituents. The AX tend to follow the electronegativity of X, being negative for electropositive substituents (- 0-096 for Al) and positive for electronegative (+ 0-2 for the halogens). However, at least another factor is important because for substituents with the same electro- negativity, AX is larger for those which have the greater number of lone pair electrons.60 INTERNUCLEAR COUPLING Moreover, AX is virtually the same for the four halogens in spite of their large range of electronegativity.Qualitatively, the AX values are consistent with charge and spin correlation effects 17 in CH3X, but their detailed significance remains to be determined. TABLE l.-SUBSTITUENT PARAMETERS Ax OBTAINED FROM JCH OBSERVED IN SOME CH3X COMPOUNDS CH3X A12(CH3)6 113 CH4 125 CH3CH3 126 CH34 126 CH3CHO 127 CH3CH2Br 128 CH3CH2C1 128 CH3COOH 130 CH3CHCl2 131 CH-jNHCH3 132 Si(CH314 118 CH3CH2I 132 a& 0.226 0.236 0.250 0-252 0.252 0.254 0-256 0.256 0.260 0.262 0.264 0.264 Ax - 0.096 - 0.056 0.000 + 0.008 + 0.008 +0.016 + 0.024 + 0.024 + 0.040 + 0.048 + 0.056 + 0.056 CH3X CH~CECH 132 CH3NH2 CHqCClq 133 134 136 138 138 141 143 149 150 151 152 a& 0.264 0.266 0.268 0.272 0.276 0.276 0.282 0.286 0.298 0.300 0.302 0-304 + 0.056 + 0.064 + 0.072 + 0.088 +0.104 +Oslo4 $0.128 +0.144 3-0-192 + 0.200 + 0.208 +0.216 The effects of substituents upon a& are additive to within an accuracy of 2 % for about 20 polysubstituted rnethanes.14.17 This may be seen in fig.4 where the observed coupling constants JCH are plotted against olz values predicted by means of eqn.(19) from the AX values in table 1. Also plotted in fig. 4 are the JCH values observed 129 139 27 for the 16 unsaturated hydrocarbons listed in table 2. The calcula- tions carried out for the methanes were extended to JCH in these sp2 and sp hybridized TABLE 2.-J(33 OBSERVED IN HYDROCARBONS WITH Sp2 AND Sp HYBRIDIZATION, AND VALUES " PREDICTED " FOR C& IN ETHYLENES USING THE Ax VALUES FROM SUBSTITUTED METHANES compound JCHc/sec a h compound JCHc/sec a& naphthalene benzene mesitylene cyclohexene ethylene CHCl=WH2 (cis) CHCl=WH2 (trans) (CH3)2C=C=13CH2 157 159 160 166 1 70 157 160 161 CH2=CC12 166 CH2=13CHCl 195 cis CHClSHCl 198 trans CHClSHCl 199 CClZ-CHCl 201 CH3C=13C-H 248 &kS3C-H 251 H--C-C<=C-H 259 0.349 0.402 0-408 0.408 0-41 6 SP SP SP compounds. Using AC-H = 0-374 and the overlap integrals28 appropriate to the C-H bond distances in ethylene and acetylene, we find y2 for these two compounds to be 0.987 y2 (CH4) and 0-977 y2 (CH4) respectively.Moreover, y2/AE for ethylene and acetylene is affected no more by substituent effects than it is for the methanes. Hence JCH E 500a& for sp2 and sp hybridized carbon, as well as for sp3, except for possible effects of the n electrons. There does not appear to be any simple way of estimating the substituent effects upon a& for the cyclic and acetylenic compounds, so the " pure " sp2 and sp values of -4 and 3 are used without correction in fig.4. The resulting points scatter somewhat more than those for the polysubstituted methanes, but the agreement with the theoretical line is still good. a& can be estimated for the substituted ethylenes by using the AX values obtained from the methanes. The main difference is that there are three cr bonds instead ofH. S. GUTOWSKY AND C. JUAN 61 four. Also, the substituent CYZ in CYZ = CHX has no counterpart in the methanes. However, it seems reasonable to use ACEYZ (methane) for ACYZ (ethylene). On this basis the s character for a monosubstituted ethylene is given by (22) which with eqn.(16) gives rise to c ~ ( C H ~ = 13CHX) = (+)[1+ ACH2 +Ax] = 0&CH2 = CH2) + (+)Ax, J ~ H ( C H ~ = 13CHX) = Jc~(cH2 = CH,)+($)[J,,(CH,X) -JcH(CHJ]. (23) Values of a& predicted by means of eqn. (22) are listed for eight substituted ethylenes in table 2 and plotted, as open circles, in fig. 4 against the observed JCH. FIG. 4.-Observed JCH values plotted against predicted values of ah. The straight line is JCH = 500 a$ c/sec, upon which all points would fall if the methods for predicting rx$ were sufficiently accurate. The points for sp2 and sp hybridization are from table 2, with no corrections for sub- stituent effects. The open circles are for the substituted ethylenes in table 2, for which a& was predicted using the A, values obtained from substituted methanes.The other points represent polysubstituted methanes for which I& was predicted by eqn. (19). It may be seen that these data are consistently 5 to 10 clsec below the theoretical line. It seems likely that this discrepancy may result from a n electron contribution to JCH. An estimate 17 of J& for ethylene gives a value of -2.6 clsec, which is of the same sign and magnitude as the discrepancy. A less satisfactory feature of our results is their relation to observed bond angles. The '' interorbital " angles 29 corresponding to the hybridization parameters obtained from JCH data are consistently smaller than the observed H-C-Y and X-C-X angles. In the methyl halides, CH3X, the calculated H-C-X angles are about 102" while those observed are 107" ; and for CH2X2 the calculated X-C-X angles are 100" and the observed, 112".In other words the a& values appear to be too large. These differences, at least in part, could reflect deviations from orbital following 30 of62 INTERNUCLEAR COUPLING the same nature as those found in CH2C12 for which both the H-GH and the Cl-C-Cl bond angles are greater than tetrahedral. Also, part of the substituent effect, 6x, may result from other than a change in a;. Interactions between electrons in the C-X bond and those in C--H can contribute to J m , without affecting aE2 and have the required additivity. The values for 6x range from - 12 to f27 c/sec compared to the 125c/sec value for JCH in methane itself. Even relatively small non-a& effects of about 5 c/sec would materially improve the picture.Such contribu- tions might come from the neglected 01 and 0 2 terms 2 and/or from overlap terms 15 which were assumed to be negligible in our calculation of the Fermi contact inter- action. Further studies of this question as well as of the nonadditivity of substituent effects found for JS~H in silanes 16917 are indicated. 140 I50 JCH (CH3X) C/S~C relation between JCH observed in CH3X and JHH observed in CHz=CHX. The three sets of points are for JP-, JF and J g z , from top to bottom. RELATION OF JCH TO .@ AND Jgg Both JCH and JHH in hydrocarbons depend upon the electron density at the proton and on the carbon orbital hybridization so one would expect there to be some relation between the coupling constants. Such a relation is implicit in the fact that JcR(CH~X)~~ and J~H(CH~=CHX),~~ 18919 cis, trans and geminal, individually have an approxi- mately linear dependence on the electronegativity of X. This may be seen in fig.5, where the three proton-proton coupling constants observed in a number of substituted ethylenes are plotted against the corresponding JCH(CH~X). The scatter is con- siderable but there is nonetheless a general linear correlation between JCH and each of the three types of JHH. It is noteworthy that the scatter comes mainly from the JCH values, which indicates that there are interactions affecting JCH which do not contribute significantly to JHH. Another point of interest is that all three types of J=H increase while JCH decreases, based upon the arbitrary assignment of JtZs as positive.A decrease in JCH implies a decrease in the s character of the C-H bond. In turn, this would tend to decreaseH. S . GUTOWUKY AND C. JUAN 63 the C-C-H bond angle. And, according to valence bond calculatioiis of JHH in the HCCH fragment,3 this would increase both Jzp and JES, as observed. It is surprising to find virtually the same dependences upon JCH for all three types of JHH in spite of the different structural features and magnitudes involved, particularly for J,"ef;t. These similar slopes in fig. 5 may be accidental; nonetheless they are one of many features of internuclear coupling which remain to be explained. Acknowledgment is made to donors of The Petroleum Research Fund, adminis- tered by the American Chemical Society, for partial support of this research.The work also was supported by the Office of Naval Research. 1 Karplus, Anderson, Farrar and Gutowsky, J. Chem. Physics, 1957, 27, 597. Karplus and Anderson, ibid., 1959, 30, 6. 2 Karplus and Grant, Proc. Nat. Acad. Sci., 1959, 45, 1269. See also Gutowsky, McCall and Slichter, J. Chem. Physics, 1953, 21, 279, for an earlier discussion of the coupling of directly bonded nuclei and its dependence upon the perfect pairing structure. 3 Karplus, J. Chem. Physics, 1959, 30, 11. 4 Gutowsky, Belford and McMahon, J. Chem. Physics, 1962, 36, 3353, and prior work cited SGutowsky, Karplus and Grant, J. Chem. Physics, 1959, 31, 1278. Barfield and Grant, J. 6 Banwell, Sheppard and Turner, Spectruchim, Acta, 1960, 16, 794. Banwell and Sheppard, 7 Gutowsky, Mochel and Somers, J.Chem. Physics, 1962,36,1153. 8 Kaplan and Roberts, J. Amer. Chem. Soc., 1961,83,4666. 9 Fraser, Lemieux and Stevens, J. Amer. Chem. Soc., 1961, 83, 3901. 10 Wilson, Boekelheide and Griffin, J. Amer. Chem. SOC., 1960, 82, 6302. 11 Brown, J. Chem. Soc., 1953, 3278 12 Muller and Pritchard, J. Chem. Physics, 1959, 31, 768, 1471. Muller, ibid., 1962, 36, 359. 13 Shoolery, J. Chem. Physics, 1959, 31, 1427. 14 Malinowski, J. Amer. Chem. Suc., 1961, 83,4479. 15 Malinowski, Pollara and Larmann, J. Amer. Chem. SOC., 1962, 84, 2649 ; we wish to thank 16 Gutowsky and Juan, J. Amer. Chem. Suc., 1962, 84, 307. 17 Juan and Gutowsky, J. Chem. Physics, 1962, 37, 2198. 18 Sheppard and Turner, Proc. Roy. SOC. A , 1959, 252, 506. 19 Cohen, Sheppard and Turner, Pruc. Chem. SOC., London, 1958, 118. 20 Waugh and Castellano, J. Chem. Physics, 1961, 35, 1900. 21 Glick and Bothner-By, J. Chem. Physics, 1956, 25, 362. 22 Grant, Hirst and Gutowsky, J. Chem. Physics, 1963, 38, 470. This reference reviews in considerable detail the nature and analysis of A2B2 and A2X2 spectra in general and serves as a basis for the approach used on (2, 2) metacyclophane. A fuller account of the latter is given by Gutowsky and Juan, J. Chem. Physics, 1962, 37, 120. 73 These calculations were made with the University of Illinois electronic digital computer, IIliac, using a programme written by Dr. Ger,eva G. Belford for the general 6-spin system. We are indebted to the staff of the Digital Computer Laboratory for their assistance. there for substituted ethanes. Chem. Physics, 1962, 36, 2054. Mol. Physics, 1960, 3, 351. See also the results on epichlorohydrin by Reilly and Swalen, J. Chem. Physics, 1961, 35, 1522. Dr. Malinowski for sending us a copy of the manuscript prior to publication. 24 Lynden-Bell, Trans. Faraday Soc., 1961, 57, 888. 25 Ramsey, Physic. Rev., 1953, 91, 303. 26 Dailey and Shoolery, J. Amer. Chem. Suc., 1955, 77, 3977. 27 Lauterbur, J. Chem. Physics, 1957, 26, 217. 28 Kotani et al., Table of Molecular Integrals (Maruzen and Co., Tokyo, 1955). 29 Coulson, Valence (Clarendon Press, Oxford, 1952), p. 194. 30 Linnett and Wheatley, Trans. Faraday SOC., 1949, 45, 33, 39. Whipple, Stewart, Reddy and Goldstein, ibid., 1961,34,2136, and Snyder and Roberts, J. Amer. Chem. Suc., 1962, 84 (in press).