Chapter 5 The cause and calculation of proton chemical shifts in non-conjugated organic compounds

CHAPTER 5 THE CAUSE AND CALCULATION OF PROTON CHEMICAL SHIFTS IN NON-CONJUGATED ORGANIC COMPOUNDS R. F. ZCIRCHER CIBA Ltd. Base1 and University of Base], Switzerland CONTENTS Sunmary

205

1. Introabction

206

2. Theory 2.1. General

12

Discussion

of the Different Contributions

to the Relative Chemical

Shift 2.2. Detailed Discussion 3. Methyl Groups 3.1. Calculations 3.2. Results 3.2.1. The Carbonyl Group 3.2.2. Chloro Compounds 3.2.3. Alcohols 3.2.4. Nitriles 3.3. Discussion of Methyl Group Results 3.4. Applications

213 217 222 222 z 227 230 231 231 235

4. The Rigid System X/cx\,

239 239 247 255 255

4.1. Calculations and Discussion 4.2. Solute-Solvent Interactions Acknowledgement References

SUMMARY The replacement of hydrogen atoms in organic molecules by substituents may cause marked relative chemical shifts da of nearby protons.+ In high resolution proton magnetic resonance spectroscopy the chemical shift increments A6 of protons in methyl groups are brought about mainly by the action of the electric dipole moments of substituents. This is shown for -OH, -Cl, >C=O and -C=N groups in non-conjugated and non-aromatic compounds. In the case of the carbonyl group. its anisotropic magnetic susceptibility must also be taken into account. The rough agreement between the calculated and observed relative chemical shifts of methyl chloride, acetonitrile and the aldehydes and the precise agreement in the case of the ethyl derivatives and of acetone are proof that, despite some successful correlations with substituent electronegativity, no u-inductive effect causing proton chemical shifts is inf This definition of relative chemical shift is used throughout 205

the article.

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volved. This is further evidence suggesting that the often invoked inductive efkct is, in reality, essentially the linear electric field effect originating in the substituent dipole moment. Relative chemical shifts of single protons in the proximity of the newly introduced substituent in rigid systems, as opposed to the “rotating” methyl protons, cannot be calculated completely with the model applied to methyl protons. This is shown for the rigid system X /c-c\H

in which X is the substituent.

A further effect must he allowed for,

which is-proposed tooriginate in different solute-solvent interactions of the molecules with and without substituent X. Empirical rules for its assessment as a function of the torsion angle around the C-C

single bond of the system x/cc\H

are given. A model in

which the van der Waals interaction between the proton considered and that part of the solvent molecules which is excluded by the larger volume of the substituent, as compared with the replaced hydrogen atom, is considered to be the cause of this further effect, roughly describes the decisive part. With this model the relative chemical shifts due to methyl groups as substituents may also be roughly understood. These invtstigations con&m that for a quantitative calculation of the relative chemical shifts of single protons in rigid systems a deeper understanding of the solute-solvent interactions is necessary. Preliminary investigations demonstrate that, in addition to specific solute-solvent interactions, some sort of a reaction field may be important in the vicinity of a polar substituent. Some rules governing the solvent dependence of protons in the investigated compounds are given and parallels with similar infrared spectroscopic studies are shown. 1. INTRODUCTIONt

The calculation of the total chemical shift of a nucleus, that is the entire magnetic screening of a nucleus in a molecule by its environmeqt is one problem. The calculation of the change in chemical shift. of a proton in a C-H bond produced by neslrby or by distant substituents in the molecule, or by solvent molecules is another. In the tist case the bare nucleus is the starting point, in the second a compound like methane might be appropriate. Since proton chemical shifts canuot be measured absolutely with respect to the bare proton, it has become customary to determine the position of a signal relative to that of a reference compound, e.g. methane in the gas phase or tetramethylsilane in solution and to call that relative position the chemical shift. In 1950 Ramsey(‘e) derived, by means of a quantum mechanical perturbation calculation, an equation for the determination of the magnetic screening (total chemical shift) of nuclei in molecules. Thus in principle the calculation of the chemical shift of all magnetic nuclei is possible. In practice, however, even for small molecules (with the exception perhaps of some diatomic molecules) this has, until now, yielded only very approximate results. Quantum mechanical calculations are very desirable for quite a t This experimental study on selected substituents and selected compounds of a nonconjugated and non-aromatic character is by no means exhaustive but is intended to demonstrate the essential features. No attempt has be made to discuss the voluminous literature on this topic except when directly pertinent to a particular point.

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number of reasons yet the question must be raised whether the solutions are followed by a satisfactory physical interpretation and an understanding of the variation in chemical shift from molecule to molecule. One means of obtaining deeper insight into these matters, and for the present one of the more practicable, involves the use of relatively simple physical models for necessarily approximate calculations of chemical shifts?. The requirement of simplicity need not exclude models of an essentially quantum mechanical nature. For molecules of average complexity such simple models can be expected to explain at best chemical shift differences but never the entire magnetic screening of a proton. However, even the solution of this sub-problem, namely the understanding of the origin of the difference in magnetic screening of a proton, which comes about upon modification of the molecule, in terms of a simple physical model and the ability to calculate this difference would constitute progress of considerable practical consequence. A true understanding of the chemical shift of protons in H-Z bonds where Z may be any element of the periodic table capable of forming a bond with a hydrogen atom, will in all probability be obtained ultimately only with the help of detailed and elaborate quantum mechanical calculations. Next, the question arises how to explain the chemical shift differences of protons in C-H bonds of hydrocarbons with differently hybridized or substituted carbon atoms. Here, simple models might be expected to give rough, qualitative answers at best. The differences in the series ethane, ethylene, acetylene, benzene constitute such a case. A marginal case is that of the saturated hydrocarbons, .oi taking a speci6c example, chemical shift Werences between methane, ethane, propane and isobutane. Moritz and Sheppard(@) explained these and a number of other hydrocarbon chemical shift differences by assuming the anisotropy of the magnetic susceptibility of the C-C bond, AXC-C,to be the cause. The anisotropy thus determined, AXC-c = 4.2 x 10-a cm*/mole (7.0 x 10”s c&/molecule) is rather large. This would require that the longitudinal magnetic susceptibility be nearly zero, since the mean susceptibility is - 3-O x 10-s ems/mole. This and several inconsistencies, one of them with regard to the magnitude and sign of AXC-c as determined by different physical methods (cf. Bothner-By and Popleos)) shed some doubt upon this otherwise very satisfactory correlation. The last word about the origin of the chemical shift differences in saturated hydrocarbons, therefore, certainly has not yet been spoken. The same may be said of chemical shifts in compounds of the type C.,/H , ‘X where X is any substituent. Of this class, derivatives of methane, ethane, t Similar thoughts have been expressed by J. I. Musher. Musher for making his manuscript available before publication.

I am indebted

to Prof.

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R. F. ZtiRCHER

n- and &propane, ethylene, cyclohexane and norbornene, among many others, have received closer attention. As early as 1953 Shoolery(ss) correlated chemical shift differences between methyl and methylene protons in ethyl derivatives with substituent electronegativity. Correlations with electronegativity have since set the pattern, deviations being ascribed in general to the anisotropy of the magnetic susceptibility of the substituent.? When the substituent X is removed from the proton by one or more C-C (or equivalent) bonds truly long-range effects are present. This is the area in which additivity rules for the calculation of chemical shifts might be expected to hold and have indeed been found applicable in part. The existence of an additivity relation for chemical shift increments caused by the introduction of substituents into a molecule or due to other changes, such as a change of configuration, leads to the expectation that finally a physical model for the action of each substituent (in different solvents) will be found. Failure of the additivity rule indicates a modification or a breakdown of the model. Several physical models have been proposed and widely used. One is based on the anisotropy of the magnetic susceptibility of the substituent (McConnelI;@a) Pople(‘@), another on its electric dipole moment (Bothner-By and Naar-Colin;(g) Buckingham, Musher@‘)) and a third on the Londonvan der Waals interactiont between substituent and hydrogen atom (BothnerBy;(rO) Bothner-By and Naar-Colin;(il) Raynes, Buckingham and Bemstein@@). Extensions of these models include solute-solvent interactions. Chemical shifts of such distant protons have often been correlated. with good success with other quantities, such as substituent electronegativity (Shoolery;@s) Dailey and Shoolery(a4)), the electric dipole moment of the substituent (Bothner-By and Naar-Colin;@) Reddy, Boozer and Goldstein@l) or Hammett or Taft u-constants, the latter chiefly in the case of aromatic compounds (Spiesecke and Schneider,@e) Diehl@)). For these, correlations with the m-electron density of the adjacent carbon atom have been found (Fraenkel, Carter, McLachlan and Richards;@c) Schaefer and Schneide@)). In some cases empirical rules for the calculation of proton chemical shifts have been given, without an attempt to determine their origin, e.g. for open-chain compounds (Shoolery;@7) Primas, Ernst and AmdVs)), for olefins (Pascual, Meier and Sirno@)), for adamantanes (Fort and Schleyer@Q))and for steroids (Bhacca and Williams(r)). These correlations and empirical rules often are of considerable use for predictions within the respective classes of compounds, but they do not have a general prognostic value. In some cases the exact physical nature of the correlated quantity is not particularly clear. t A discussion of much of the work in this field together with a summary of the literature is given on pp. 665 et seq. of the book by Emsley, Feeney and Sutcliffe.(s4) : Only the so-called “dispersion forces” are involved here.

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With this arsenal of physical models at hand it is, of course, tempting to try to f%d out which of these mechanisms actually is important and to what approximation a calculation of proton chemical shifts in high resolution nuclear magnetic resonance is possible. The models are themselves inexact, involving the so-called point-dipole approximation (permanent or induced dipoles) and may, therefore, be expected to be most suited for the calculation of proton chemical shifts due to distant substituents. In addition, the (Iand r-inductive and mesomeric effects (Dewar and Grisdalec27)) have to be taken into consideration for molecules with easily delocalizable electrons and for molecules with substituents in the immediate vicinity of the proton. The ideal procedure would require hundreds of compounds with precisely known geometry together with their chemical shift increments due to the replacement of a hydrogen atom by a substituent. If the above mentioned set of models were to suf5c-e for the description of the chemical shift increments with satisfactory precision, that is, if no further important effects had been left out or counted twice then it should be possible to find experimentally, with the help of statistical methods, all the needed parameters and physical quantities. Because we are still far from this ideal position, these aspirations must be curtailed sharply. The following procedure has been adopted : molecules in which n-inductive and mesomeric effects may play a role, e.g. substituted aromatic or olefinic molecules with either the substituent or the proton located at a double bond have been disregarded, the.idea being, that if the importance of one or the other of the further effects has been assessed for aliphatic and alicyclic molecules, an analysis of the origin of proton chemical shifts in aromatic, heterocyclic or vinyl compounds will be more feasible. As already discussed, all effects should, in principle, be considered together in order to determine their relative importance. An exception to this statement may, however, be given in the case of distant substituents. In rigid cyclic molecules such substituents may cause appreciable chemical shift increments although separated by several bonds or by a distance of several Angstroms from the proton under consideration (O-2-0.3 ppm at a distance of four or five bonds or as much as 5 A). It is evident that neither an exponentially decaying u-inductive effect transmitting an electron-attracting power of the substituent through the bonds (Dewar and Grisdale(27)) nor a field effect decaying with the sixth (or higher) power of the distance between substituent and proton, e.g. the van der Waals and quadratic electric field effect, are capable of generating such chemical shift increments for this would result in much larger increments for less distant protons which is not observed. Numerous examples of such behaviour may be cited. A certain minor role for these effects cannot be excluded by this reasoning. To a first approximation, however, they may be safely neglected. These findings are contrary to what is reported for halo-

210

R. F. ZijRCHER

genated pertluorobenzenes and perfluorocyclohexanes (Boden, Emsley, Feeney and Sutcliffe@) and Emsley(m), where rsF chemical shift increments due to chlorine, bromine and iodine substituents replacing fluorine atoms seem to be a direct consequence of the van der Waals interaction and, to a lesser extent, of the quadratic electric field effect. In this article it will be shown that even chemical shifts of protons removed from the substituent by only two bonds may be calculated with satisfactory precision without recourse to the u-inductive, van der Waals or quadratic electric field effect. The latter two effects will be further discussed below in a more quantitative manner. The guiding idea of this investigation was to discover the origin of proton chemical shifts caused by distant substituents and to see how close to the proton in a C-H bond a substituent may be brought without a breakdown of the model. This was, of necessity, pursued with a limited number of compounds and substituents. Consequently, the number of models considered was also kept as small as compatible with the desired goal, for in least-squares calculations no significant results may be expected for a system of equations with too many adjustable parameters and quantities. For such a study, only rigid compounds with known geometry may be used. Combined with the requirement that substituents have to be more or less

FIG. 1, The four basic steroid configurations,

CAUSE

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distant and yet cause .significant and precisely known chemical shift increments, this restricts the number of available molecules severely. FGgid cyclic systems, such as steroids (Fig. I), terpenoids, some alkaloids, bicyclic compounds (Fig. 2) and conformationally stable cyclohexane derivatives are best suited. Only a limited number of rigid compounds with d&rent but known spatial arrangement of substituents and C-H bond together with the relevant chemical shift increments were available. Therefore, only four substituents could be investigated, namely the carbonyl (>C=O), hydroxyl (-OH), chloro (-Cl) and nitrile (-C-N) groups, that gave rise, however, to typical results. The hydroxyl group was of necessity assumed to be freely rotating, an assumption which certainly is not free from arbitrariness. $H3 (IO) (9W3C

7

CH, (8)

iffY EX3

6

2

END0

6

3

5

Fm:2.

Bornane.

Lack of suitable compounds with double bonds and of precise geometrical data prevented their inclusion in this investigation. Yamaguchi, Okuda and Nakagawa(ls@ and later Tori, Hata, Muneyuki, Takano, Tsuji and Tanida(as) rationalized the chemical &if? increments due to the introduction of a double bond into morphine alkaloids and bicyclo[2.2.1] heptanes and bicyclo[2.2.2] octanes by assuming the magnetic susceptibility of the sp2-hybridized carbon atoms to be anisotropic with an axial symmetry along the axis (2) perpendicular to the plane of the double bond. This model, however, is not in accord with the results of an approximate quantum mechanical a priori calculation of Poplen) and the assumed axial symmetry is not self-evident. The anisotropy thus determined is Ax = xz - x2 FW- 6 x 10-s ems/mole (- 10 x I O-80 cm*/molecule). It is probable that the anisotropy of the magnetic susceptibility of the double bond gives rise to chemical shift changes but this may not be the only cause. Chemical shift increments of distant single protons are seldom precisely known. Therefore, the increments of methyl protons which are known for a great number of steroids were employed in their place. Insofar as the

212

R. F. ZtiRCHER

methyl groups are rotating these compounds may no longer be called rigid. However, this circumstance may be allowed for by means of a simple and unequivocal averaging procedure. In the final calculations the corresponding ethyl derivatives and in some cases the bomane derivatives (Fig. 2) were also included. Subsequently the choice of methyl groups as indicators for the chemical shift increments instead of single protons turned out to be a great asset. The rotating methyl groups in many cases seem to be relatively insensitive to a change in specific solute-solvent interactions (and the ensuing change of the chemical shift) caused by the introduction of a substituent. This must be compared with the case of a proton in a fixed position near a substituent in a rigid molecule, where there may be an enormous further contribution to the chemical shift increment which originates, in our opinion, in an interaction between the molecule and the solvent. These relationships will be discussed c-c, ,H in rigid compounds, particularly for extensively for the system X/ different norbornene derivatives (Fig. 9).

2. THEORY

The replacement of a >CHz group in a molecule by a >C=O group, or of a > CH- group by a >CX- group, where X = -OH, -Cl or -C=N, may cause appreciable chemical shift changes (increments) of nearby protons. If U- and n-inductive, meso- and electromeric effects (for definitions see: Dewar and Grisdale@‘)) may be neglected, as is the case in this investigation for reasons already mentioned, then an attempt may be made to express the total, experimentally determined chemical shift change A8 of a hydrogen nucleus in the molecule due to the introduction of a substituent as AS = Ai& j

A& + &,agn + A&,,rv.

(1)

A.6= 6, - a,, where a8 and &, are the observed chemical shifts of the proton under consideration in the molecule with and without substituent, respectively. Hx: Proton replaced by the substituent X. Hc: Proton under consideration, which experiences a chemical shift as a consequence of the above substitution. h&r is that part of the total chemical shift difference, As, which has its origin in the difference between the electric dipole moments of the C-X bond, where X is the substituent, and of the C-Hx bond in the unsubstituted molecule. A6, comprises that part of A8 which is brought about by the difference in

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van der Waals interactions between the substituent and the hydrogen atom Hc on the one hand, and between the two hydrogen atoms Hx and HC on the other. AS,,,- is the contribution to A6 caused by the different anisotropies of the magnetic susceptibilities of the C-X bond and the C-HX bond. Alaotv encompasses that part of A8 in which a difference in the interaction with solvent molecules gives rise to a change of the proton chemical shift. As all the measurements have been made in dilute (0.1 molar) deuterochloroform solutions with internal tetramethylsilane as reference compoundwith the exception of some values taken from the literature, which were determined in carbon tetrachloride-no corrections for differences in the bulk diamagnetic susceptibility A&, of the solutions needed to be applied. The chemical shift 6 in this investigation is defined as 6=

HTMS-HJJ (

HTMS

1'

where HT~ and HS are the resonance field strengths of internal tetramethylsilane and the sample, respectively. With this definition a positive chemical shift increment AS corresponds to a shift of the NMR signal towards smaller magnetic field strength (reduced screening). 2.1. General Discussion of the DlJZerent Contributions to the Relative Chemical Shifit The term A& The electric field E at the position of a hydrogen atom, which has its origin in a polar group in another part of the molecule, may lead, as Buckingham(r7) has shown, to chemical shift increments which are proportional to the component of E in the direction of the C-HC bond, ECH, (or in general the Z-Hc bond, Z being any element), and to E*, thus Aa = A(EcH,~ - EcH,~) + B(E,? - I$),

(3)

where the subscripts s and o denote the electric field strengths at the proton Hc in the substituted and unsubstituted molecules, respectively. Henceforth the electric dipole moment of the C-Hx bond shah be neglected and EU thus set equal to zero whereupon the subscript s may be dropped. A and B are factors to be determined by experiment. An electric field parallel to the Hc + C bond direction gives rise to stronger magnetic shielding of the proton. A field in the opposite direction leads to reduced shielding as does Ez. t For a more extensive discussion and a summary of the literature see Em&y, Feeney and Sutcliffe(s4), pp. 59 et seq., and pp. 841 et seq.

214 The

R. F. ZijRCHER

term A&

Bothner-By(lO) and subsequently Raynes, Buckingham and Bernstein pointed out the effect of a fluctuating electric field F originating in surrounding molecules, whose square, p, is not averaged out and which, therefore, may also lead to a chemical shift change. Abraham and Holker@) applied this model to the van der Waals interaction between a substituent and a hydrogen atom within the same molecule and utilized it for the explanation of the relative chemical shift of a proton Hc in a steroid molecule, due to a methyl group in a 1,Ediaxial position. The newly introduced methyl group is assumed thereby to lead to a larger mean value of the fluctuating electric field squared, p, than the hydrogen atom Hx, which it replaces, causing a downfield chemical shift of the proton Hc in 1,3-diaxial position. Bothner-By and Naar-Coli@) however, came to the conclusion that in substituted I-alkenes the chemical shift of the vinyl protons cannot be the consequence of an intramolecular van der Waals effect. The same statement is made by Hruska, Hutton and Schaefer(**) for vinyl halides. The difference in van der Waals interactions leads to As, = B(q

- PO) = BAF,

(4)

where B is the factor also occurring in equation (3). It, too, must be determined experimentally. If the,fluctuating electric field squared, F;, due to the substituent were smaller than F. that due to the hydrogen atom Hx, then an upfield shift (AS, negative; enhanced screening) would resdlt, although an electric field squared, that is, E2 or p always leads to a downfield chemical shift. F may be determined by an approximate quantum mechanical calculation. According to Raynes, Buckingham and Bernstein it is given by p = 3aI/R’J,

(5)

where a and I are the static polarizability and the tist ionization potential of the substituent, respectively. R is rhe distance between the substituent and the proton Hc.

The term Aa,,

In a substituent with different principal magnetic susceptibilities xi (strong) magnetic fields Hr, in the i directions, induce different magnetic dipole moments x(Ht along the principal axes of the substituent. Their secondary magnetic fields at the position of the proton considered, Hc, lead (after averaging by the tumbling motion of the molecule) to the chemical shift

CAUSE

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215

Its change upon introduction of a substituent is

where the subscripts s and o refer to the substituted and unsubstituted molecules, respectively. R is the distance between the centre of the induced magnetic dipole and the proton Hc, the +r’s are the angles between the radius vector R and the axes of the three principal magnetic susceptibilities ~6. Didry and Guy (ss) concluded that the point-dipole approximation leads to results which may be wrong by more than 30% even at distances of 3 A from the assumed centre of the induced magnetic dipole and correspondingly more at smaller distances. This demonstrates that caution is necessary in the application of equation (6) to quantitative calculations of the chemical shift due to nearby substituents. increment A&The tam A&iv A polar molecule in solution polarizes the surrounding medium. This polarization leads to a further electric field at the solute molecule, the reaction field P. If the solute molecule may be approximated by a sphere, or by a prolate or oblate spheroid of revolution (models of Onsager, Dekker@s) and Scholte;(*s) cf. also Bbttcher)(is) with a point dipole of moment F at the centre surrounded by a continuous medium of dielectric constant 6, then P = c[(’ - l)/(r + mlir, where c and B are functions of the geometry of the cavity containing the solute molecule and of the refractive index of the solute. According to this model the resulting electric field P over the entire cavity is in the direction of the dipole moment P of the molecule. It is evident that this model can be expected to give an approximate description of the reaction field P only in very special cases. In general no mathematical expression for P canbe given. It is quite probable that in a larger molecule a change of the specific solutesolvent interactions due to the introduction of a polar group gives rise to a specific change of the reaction field P which, however, cannot be described by a simple model. In the opinion of Buckingham, Schaefer and Schneider(i*) “protons near polar groups undoubtedly experience ‘local’ electric fields as well as the overall uniform reaction field P of equation (7)“. Lumbroso, Wu and Dailey@@ find that highly polar solutes in highly polar solvents produce chemical shifts that are substantially larger than those calculated from equation (7). They believe that it is not possible to treat the solvent as a

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homogeneous medium characterized only by its dielectric constant. Their data, they feel, suggest strongly that aligned dipole solute-solvent pairs are being formed. Hydrogen bonds, we may add, merely constitute an extreme case of such solute-solvent interactions. A change of the shape of the solute molecule due to the introduction of a substituent, especially a bulky one, polar or non-polar, may give rise to a change of the solvent influence as well as of the reaction field. If the solvent molecules are polar a net change of the electric field E’, especially at proton positions near the substituent may result, even if the same solvent is always used, provided the movement of the solvent molecules is not entirely random. The electric field E’ also includes the above mentioned “local” fields due to specific interactions of solvent molecules with solute polar groups. Such interactions need not be restricted to strongly polar groups. Infrared spectroscopic studies on solvent shifts of molecular vibrational frequencies (Hallam@@) have led to the suggestion that even a proton of a solute C-H dipole may seek out a negatively charged polar group of the solvent with which to associate. This might be a lone pair orbital on a nitrogen or oxygen atom, a n-electron cloud or a halogen atom. Analogous behaviour may be expected for solvent molecules with an anisotropic magnetic susceptibility, resulting in an additional magnetic field. This is suggested by a dependence of the solute chemical shifts on the (rodor disk-like) shape of the solvent molecules, which form different collision complexes with the solute molecules (Buckingham, Schaefer and Schneider(is)). The chemical shift 8L,, of a solute proton due to such magnetically anisotropic solvent molecules is given by 3 %lagn

=iI;1xt<+~-3(3

cm2 bt -

l))av,

(8)

where the expression within the angular brackets is an average over all orientations and distances of the immediately surrounding molecules. Finally, a change of the averaged-out fluctuating electric field squared, F’, due to the solvent molecules may be visualized even when the same solvent is always used. Again, this behaviour is suggested by the solvent dependence of non-polar molecules in polar and non-polar solvents (Howard, Linder and Emerson(*‘)). The chemical shift increment h&iv thus may be expressed as M SOIV = A[PcrX,s f E&_rn]+ B[P; + Ef’ + E:‘] + SLw,, -

A[PCH,

o -r

E&,

,I - B[P: + E:’ A-E? - Sk,,, ,,,

(9)

where the primed quantities are the intermolecular analogues of the corresponding intramolecular ones, that is, they apply to the electric and magnetic fields originating in the solvent molecules. The subscripts s and o again refer

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to the field in the case of the substituted and unsubstituted solute molecules, respectively. 2.2. Detailed Discwsion The term A&i If in equation (3) the electric dipole moment of the C-H bond which is subsequently replaced by the C-X bond, is neglected, then there remains one linear and one quadratic term. The latter will be discussed in connection with the van der Waals increment A& and it will be made evident that neither can be important at distances greater than about 2.2 A. A further modification of equation (3) involves ECH, the component along the C-H bond of the electric field E, due to the substituent dipole moment P. The quantity &H is replaced by eCH, the component of E due to a substituent with unit dipole moment (in Debyes). Thus, equation (3) leads to A&i = AECH = Apec~ = KeCH (10) where p is the value of the substituent dipole moment and K = A&l/ecH. eCH is a geometrical factor given by equation (11) in the point-dipole approximation &H = FCH = /.4(3cos $1 cos +R - cos Q/P, (11) where +i is the angle between R and 1r0,$R that between R and Cn, and $r that between the directions of 1r0and CH (Fig. 3). The quantity CCH can be calculated easily if the relative positions of 1r0, the unit vector of the’substituent dipole moment (C- - X+), of Cu, the vector from the carbon to the hydrogen atom Hc, and of the radius vector R from the centre of the subs&tent dipole to the proton considered are given. cl0 is assumed to

n

H

FIG. 3. The relative positions of the vectors m, R and CH. 8

218

R.

F.

ZijRCHER

be parallel to CX, the vector from the carbon to the substituent atom X, where X is =0, -C=N, -Cl, or -O(H). The OH group is assumed to be freely rotating so that the averaged dipole moment, the vector ( IL)~” should coincide with the C-O bond. The term A& The quadratic term B(E: - Et) of equation (3) and A& = BAF (equation (4)) have been neglected. This was done firstly, because there is good evidence, as will be shown subsequently, that their contribution to the total chemical shift A6 at distances greater than 2.0-2.5 .& must be very small, if present at all, and secondly, because even for E. w 0 the determination of two more terms (BE2 + SAP) would have become necessary. Yet, with the limited number of equations available, the number of unknowns must be restricted as much as possible in order that the calculation may yield meaningful results. It should, however, be possible to obtain significant values for these quantities too, from more abundant experimental data. Bothner-By and Naar-Colinui) found that although equation (5) predicts the correct order of the chemical shifts of the olefinic protons in 1-alkenes due to the alkyl group any realistic choice of values for a and I yields shifts which are much too small. In vinyl halides and in ethylene itself the range of the chemical shifts of the truns protons is larger (2.2 ppm) than that of the cis protons (1.5 ppm) although the truns protons are more distant from the substituent than the cis protons. Hruska, Hutton’and Schaefer@@, therefore, conclude that this fact denies the importance of an intramolecular van der Waals effect. An analysis of the Cl- and &-proton chemical shifts of a large number of substituted octahydrophenanthrenes with different configurations and conformations shows that there is an increasing chemical shift difference between the Cl- and G-proton with decreasing distance between the C4- and &protons. This, Nagata, Terasawa and TorP) feel, can be best explained by invoking a van der Waals interaction between these protons. A further evaluation of their data leads to the conclusion that no van der Waals interaction detectable by means of NMR takes place between hydrogen atoms separated by more than about 2.2 A. This reasoning, of course, is only valid if the observed effect is indeed due to a van der Waals interaction. The term B(E2 + Ap) and equation (5) will now be discussed more quantitatively. The bond polarizability differences ha = a(C-X) - a(C-H) for the four substituents considered are listed in Table 1. They are average values obtained by calculating the differences of the mean optical polarizabilities of simple alkyl derivatives and the corresponding alkanes as given by Landolt-B6rnstein(52*) and Stuart.cgl) The first ionization potential of all the substituents was assumed to be 20 x lo-12 ergs. The deviations from that

CAUSE

.

AND

CALCULATION

TABLE 1. THE DIFFERENCESOF w s-

Substituent

da x 1W

cma

= 3Aal /

CHEMICAL

POL~~~BILITIE~, AND

ReAP

0 2”:; 2.3t

t VeIY approximate value estimated from HCN,

Aa,

ANDi-HE N-w

x 1086esu

SHIFTS

219

BETWEENTHE VALUES

R0E2 = ny3 s

+ 1).

I

PE2

-

x lo8aesu

I

I

I

>c=o

OwrcAL

AND THE PARENT hKANEs,

FOR THE &PRESSIONS RSAP

--OH -a -CEN

OF PROTON

0 30 120 138t

(CN)z,

20 2 :t

bemonitrile,

and pdibenzonitrk

value should not amount to more than 10 per cent. The electric field strength squared of a polar group with dipole moment or is given by I? = #!(3 cos2 $1 + l)/R6

(12)

where the symbols have the same meaning as before (Fig. 3). The values of the substituent dipole moments were taken from Smythcss) and McClellan.@l) In order to simplify this discussion the mean value cm = 4 has been inserted in equation (12). In the last column of Table 1 values of E2R6 from equation (12) with = 4 are given for the different substituents. The , component of the C-OH dipole moment along the direction of the C-O bond was assumed to have a magnitude of - 0.9 Debye according toSmyth@s) and Ivash and Dennison.@9). Marshall and Pople@@ have shown that for an isolated hydrogen atom B = $f&.S/mc2) = 0.74 x lo-18 esu. From NMR measurements of medium effects in non-polar gases B was determined for C-H -bonds to be 1.35 f 0.27 x 10-1s esu by Rummens and Bernstein. If this value and those for EzRa and Ape are of the correct order of magnitude this would imply that for small distances (<3 A) between the substituent and the hydrogen atom considered the expression B(E2 + AF) would be all-important in the case .of the chlorides and nitriles, and probably less so for carbonyl and hydroxyl groups whose optical polarizabilities do not seem to differ much from those of the >CH2 and >CH- groups, respectively. That such large chemical shift increments due to van der Waals interaction are unreasonable can be seen from a practical example. The relative chemical shifts of the 19-hydrogen nuclei (angular methyl group) in steroids due to 5a- and 6fihlorine atoms (Ziircher(lOs)) have considerable and very roughly equal magnitudes, namely A6 = 0.250 and 0.317 ppm, respectively. The 6g substituent is, however, much nearer to the angular methyl group than is the 5a- one (see Fig. 4). The distances from the methyl carbon atom to the chlorine atom are 2.53 and 4.09 A, respectively. The discrepancy is correspondingly larger if the hydrogen-chlorine distances are considered. With

220

R. F. ZijRCHER

the data of Table 1 and the value of B = O-15 x 10-1s esu, the entire chemical shift increment due to a 6@chlorine atom could be explained. This value for B is nearly ten times smaller than that proposed by Rummens and Bernstein.@) The increment due to a Sa-chlorine atom has a similar magnitude yet other causes must be sought, for AS, is negligible due to the larger distance from the angular methyl group. The electric field strength squared and the van der Waals term, therefore, can at most be responsible for the chemical

FIG. 4. The positions of 5a- and 6$-chlorine atoms relative to the 19-methyl group in steroids.

shift increments of protons which are very near to a substituent. However, such increments may equally well be a consequence of the linear electric field effect and the anisotropy of the magnetic susceptibility of the substituent, both of which fall off with R3 and, therefore, may also be the cause of the increments of more distant protons. Further examples could be given and have been in some cases (vide supra), which show that a consideration of the terms falling off with R6 is hardly necessary at distances greater than about 2 A. In Section 3.2.2 the results of some least-squares calculations with inclusion of the term B(l? + Ap) in the simpliGed form (const x B)/R6 will be discussed. The term AsrnaV Equation (6) may be $mplified somewhat. Nothing exact is known about the anisotropy of the C-H bond which probably is small (cf. Bothner-By and Pople(l2)). It is therefore the custom to neglect it. Then the last term of equation (6) may be dropped and the subscript s becomes superfluous.

CAUSE

AND

CALCULATION

OF PROTON

As the three angles +r are not independent may be transformed to A6mz+gn = 3RmS[Ax1(3~0s~ 41 -

CHEMICAL

SHIFTS

221

of one another equation (6)

1) + Ax2(3 COST42 -

l)]

(13)

with Ax1 = XI -

x2 and Ax2 = x2 - xs. For axially symmetric substituents and, therefore, Axe z 0. XI is the principal magnetic susceptibility in the C-X bond direction.

x2 E x2

The term ASrolv Although Ag,,l,, the change in chemical shift due to a different influence of the solvent molecules in the case of the substituted and unsubstituted solute molecule (but not that due to a change of solvent which is not included in A&W and not considered here) can certainly be important, especially in cases where the proton considered, Hc, is near to the substituent, it had to be neglected. In order to determine all the terms of AZ&i, with a fair chance of success a lot more experimental data would be necessary. The reaction field P probably may be neglected anyway for large molecules. In the Onsager model the solute is represented by a sphere of radius R, containing a point dipole of moment or at its centre, and the solvent by a continuum of dielectric constant d. P is given by .P = [2(~ - l)(ns - 1)/3(2~ + n2)](p/a),

(14)

where a = [(ti - l)/(n2 + 2)]Rs is the polarizability of the sphere and n the refractive index of the solute. If, for lack of a better value for the radius of the solute sphere, a is determined from the relation RS = 3M/4npN, where M is the molecular weight of the solute, p its density, and N Avogadro’s number, the reaction field according to equation (14) is about ten times smaller for a steroid (M = 3oo-400) than for a&on&rile, CHsCN (M = 41), for example, and is therefore negligible in solvents with low dielectric constant. Diehl and F reeman@e) were able to show that by using the appropriate shape factors the dependence of two selected molecules (rod-like acetonitrile (prolate spheroid) and disk-like paraldehyde (oblate spheroid)) on the dielectric constant of the solvents may be described satisfactorily with the reaction field theory of Buckingham.(l7) These authors, however, warn that in general this might not be possible with less symmetrical molecules where a non-uniform reaction field might be expected. Laszlo and Musher@s) examined the dependence of the chemical shift of selected protons in 2bromo- and cL.+2,6-dibromo-4,4-diphenylcyclohexanone on the dielectric constant of the solvent. They came to the conclusion that no reaction field model presently available describes the dependence on the dielectric constant adequately. If, however, the chemical shift changes of one proton are plotted

222

R.

F. ZiiRCHER

against those of another in a similar molecular environment and in the same solvent mixtures, with definite dielectric constants, linear plots are obtained. This procedure is a special case of a so-called BHW plot (Bellamy, Hallam and Williams@), well established in infrared solvent shift studies and proposed initially by Gordy,(Qd) where the relative frequency shifts of different solutes in the same series of solvents are compared with one another. In Section 4.2 this procedure is applied to proton chemical shift changes in a series of solutes and solvents. There it is demonstrated, that the curves thus obtained are not continuous with regard to the solvent dielectric constant, a behaviour observed also in infrared solvent shift studies. We thus prefer not to say, as do Laszlo and Musher in their special case, that the changes in chemical shift are linear in some reaction field, but to say rather that they are linear in some specific group interactions as well as a reaction field. That is to say that protons in similar molecular environments experience similar electric and magnetic fields due to solvent molecules along with similar possible reaction fields. We hold the optimistic view that with sufficient experimental data it will be possible eventually to find the refined physical models with which to ascertain quantitatively the chemical shift changes due to some reaction field and specific group interactions. At present the change in chemical shift due to solvent molecules, .?&I~, cannot be allowed for. For protons farther away from substituents this very probably will not introduce a serious error for reasons discussed above. However, nearby substituents definitely have a large effect as will be shown in detail for rigid compounds of the type /-c’,H* 3. METHYL

GROUPS

3.1. Calculations The various reasons which justify the cancellation of certain terms of equation (1) have been discussed in Section 2.2. The reduced form of equation (1) which should still be a good first approximation for the calculation of chemical shift changes due to relatively distant substituents is given by A8 =

KeCH

+

+R-3[&(3

COS2

$1

-

1)

+

I$&

COS’

‘42

-

I)]

(15)

where the symbols are those defined in connection with equations (6), (lo), (11) and (13). K, Ax1 and 1x2 are to be determined by least-squares calculations. The other expressions are given by experiment and geometry. With the limited experimental data available it is essential to restrict the number of unknowns to be determined to an absolute minimum even if small errors

CAUSE

AND

CALCULATION

OF PROTON

CHEMICAL

SHIFTS

223

may be introduced by such a procedure. For this reason, the electric dipole moment and the anisotropy of the magnetic susceptibility of the C-H bond to be replaced by the C-X bond have been neglected because they are probably small and not known exactly. In other words, the error introduced by considering the chemical shift increment AS as due exclusively to the substituent X has been judged to be small. Thus if the relative steric positions of the protons considered, Hc, and of a particular substituent X, together with the additional chemical shifts caused by its introduction into the molecule are known, then the geometrical expressions of equation (15) may be calculated and the two (or three) unknowns K and Axi (and Axa) determined for the particular substituent X. It is clear that these determinations become more significant the more supernumerary equations may be disposed of. The centres of the electric and induced magnetic dipoles were assumed to be identical in order to simplify the calculations. The coordinates of this common centre enter the calculations as a parameter. The best fit of the calculated (A?&,) and observed (A&be) chemical shift increments served as a criterium for the determination of the coordinates of this centre. It turns out that the best fit with the experimental data is obtained if the dipole centres are assumed to coincide roughly with the centres of the single (C-Cl and C-O(H)) and multiple (>C=O and -C=N) bonds. As already mentioned the calculations have been carried out mainly on steroids (Fig. 1). These compounds are ideally suited for such an investigation for several reasons.They are rigid and their geometry is usually well-known. Their 18. and 19.hydrogen nuclei (angular methyl groups) give rise to two prominent signals even in rather dilute solutions. These protons may, for the purpose of this investigation, be considered distant from most substituents. Since the steroids have high internal symmetry there are many equivalent sites relative to the angular methyl groups (Fig. 5) and the chemical shift increments due to identical substituents at equivalent sites may be compared with one another and averaged if necessary (cf. the discussionin Section 5 and Table 4 of reference 103). This check shows at the same time what degree of accuracy may be achieved at best. The limit will be of the order of & O-02 to & 0.03 ppm. Throughout this investigation it has been assumed that the steroid frame consists of perfect chairs and that the 5-ring D does not introduce appreciable deformations of the 6-rings. That this assumption is approximately justified follows from the small scattering of additional chemical shifts due to substituents at equivalent sites. The C-C and C-H distances were taken as 154 and l-09 A, respectively. According to the arguments of Moffitt, Woodward, Moscowitz, Klyne and Djerassi(~) the replacement of a >CH2 by a >C=O group should introduce only very minor deviations from a perfect chair. We therefore neglected them entirely, assuming the carbonyl

224

R. F. ZtjRCHER

carbon atom to be at the same position as the >CHs carbon atom, with the C=O bond bisecting the HCH angle.

Pro. 5. The equivalent positions in Sa-steroids relative to the 18- and 1Phydrogen atoms (dashed lines represent plants of symmetry).

In the case of the chloro substituents chemical shift increments of the tertiary methyl groups of bomyl- and isobornyl chlorides as investigated by Flautt and Errnan@@ have been included. The fact that the chemical shifts were measured in carbon tetrachloride instead of deuterochloroform solutions may introduce an error which was nevertheless considered small. The geometrical data for these compounds were taken from papers of Wilcox,(aQ) Ferguson, Fritchie, Robertson and Sim(ss) and Brueckner, Hamor, Robertson and Sim.(rs) The success in predicting the relative chemical shift of acetone and ethyl chloride through the use of data gained from steroids and bomyl chlorides prompted us to include the ethyl derivatives in the least-squares treatment on hydroxy, chloro and cyano compounds. 3.2. Results 3.2. I. The carbonyl group (>C=O) The relative chemical shift of the 19-methyl protons (Table 2) in eight different ketosteroids measured as O-1molar solutions in deuterochloroform (Ziircher(lm)) served as the basis for the least-squares calculations. As a consequence of the high internal symmetry of the steroids and the many equivalent positions, the number of independent chemical shift increments due to carbonyl groups is strongly reduced. Carbonyl groups far removed

CAUSE

AND CALCULATION

OF PROTON

CHEMICAL

SHIFTS

25

from the angular methyl groups cause only small relative chemical shifts as is expected. Therefore they were not included in the calculations as this would have led to no improvement. Initially, the reproduction of the observed chemical shift increments was attempted with a reduced model using (a) only the magnetic part and (b) only the electric part of equation (15). Whatever position on the C=O bond axis was assumed for the centre of the electric or induced magnetic dipoles, it was impossible to obtain a fit with the experimental data if only the electric dipole moment of the carbonyl group Tm

2. THE OBSERVEDAND CALSXJLA TEDIbLATIVE ~O.lQNcfiEM.lCALsfmprs A&b, AND AC& = A& i At&,, (ppm), WY, OFTHEh3GULAR METHYLGWUPS 0F~OlD.S

-

/ Position of the carbonyl group l[lPHj;

/ I

12[184q

11(19-H] (freely

rotating)

lW-W W-HI \ $WW-F (58-H)

1

I

I __

A&t.

A&tie

0.316 0.194 0.068 0.307 0.153 O-035 0.275

1

O-084

;

0.103

’

i / ,

0.096 -0.241 0.152 -0.104 -0.143 0.073

-0.054 0.031’ 0.055

0.412 -0.047 O-220 0.203 O*OlO 0.108 0.221 0,115 0.158

.

0.376 -0.033 0.259 0.217 0.217 0~100 0.217 0.117 0.208

-

or the anisotropy of its magnetic susceptibility was considered responsible for the chemical shift increments. The situation was much improved as soon as the least-squares calculations were carried out with a model in which both mechanisms acted simultaneously. Nevertheless there remained one large discrepancy between calculated and observed relative chemical shifts. This concerned the increment of the 19-methyl protons due to a carbonyl group in the Il-position. Up to this point the angular methyl groups had been assumed to be freely rotating and the relative chemical shifts had been found by averaging over 12 equidistant positions on the circle described by the protons of the rotating methyl groups. Good agreement for all the chemical shift increments was readily obtained when the calculations were done for angular methyl groups practically fixed in staggered positions. Rotational jumping provides for the averaging of the three different chemical shifts and thus leads to sharp NMR signals. This behaviour is very reasonable if the potential barrier hindering free rotation is similar for example, to that in neopentane, C(CH&, namely 4-2 kcal/mole (Aston and Messerly(Q and PitzeP)) where the eclipsed conformation is about a thousand times less probable at room temperature than the staggered one. For a much smaller

226

R. F. ZiiRCHER

barrier of 2.kcal/mole this ratio would still be about thirty. As a consequence of these considerations and results, all the further calculations have been based on a preferred staggered conformation of the methyl groups.

o.0250

; 0.2

G.4

C=O

0.6

5.8

distance

I.0

f&j

FIG. 6. Standard deviations (3 between calculated and observed chemical shift increments for the ketosteroids as a function of the distance of the assumed centre of the electric and induced niagnetic dipoles from the carbon atom along the carbonyl axis.

In Fig. 6 the standard deviations between calculated and observed chemical shift increments for the ketosteroids are given as a function ,of the distance of the assumed centre of the electric and induced magnetic dipoles from the carbon atom along the carbonyl axis. It clearly shows a minimum halfway between the carbon and oxygen atoms, which are separated for example by a distance of 1.21 A in formaldehyde (Lawrence and Strandberg(s The values for K and the Ax’s are therefore based on a distance of O-60 A from the carbon atom for the centre of the dipoles. The values so obtained are: K

AXI

=

-

12.2

x

lo-l2

esu

=

15.4 x 10-B cma/mole (25.7 x lo-30 cma/molecule)

Axa = 7.3 x 10-Gcm3/mole (12.2 x 1O-3ocma/molecule) With the principal axes 1,2,3 in the C=O bond direction, in the C-CO-C plane, and out of the C-CO-C plane, respectively (see Fig. 8), and Axi = xi -

x3,

4~2

=

~2

-

x3,

CAUSE

AND

CALCULATION

OF PROTON

CHEMICAL

SHIFTS

227

with the centre of electric and induced magnetic dipoles 0.60 A from C, halfway along the C=O bond. The eight measured relative chemical shifts ASobswhich range from - 0.03 to + 0.38 ppm are obtained with a standard deviation of & 04J27 ppm. Table 2 gives a comparison between the calculated (A&,) and the observed (A&s) chemical shift increments of the angular methyl groups due to the introduction of a carbonyl group into the steroid frame at different positions. It further shows the contributions of AS,1 and ASmssn to A&,rc. Clearly, A&b, cannot be explained by the action of the carbonyl group electric dipole moment alone (A&r = K&H), even if K were varied and even if the electric field squared were taken into consideration, which can cause only positive increments. Table 2 also demonstrates that the large difference between the chemical shift increments, due to the 1I-keto group, of a freely rotating and of a hindered angular 19-methyl group stems mainly from very different A&r terms. These may vary enormously for the different methyl hydrogen atom positions, in this case from - O-21 to + 1.07 ppm. The different averaging processes for the free and hindered rotator give rise to the large difference in A&tic. With these data at hand it was, of course, tempting to calculate the relative chemical shift of the methyl protons upon transition from propane to acetone or, more generally, upon replacement of a CHSCHT group in a n-alkane by a CHsCO- group, and to compare it with the measured increment. The methyl signals of n-hexane and n-heptane appkar at 6 = 0.89 ppm in dilute chloroform solutions. These signals do not seem to vary much in the different alkanes as shown by the data of Bothner-By and Naar-Cohn.(*) The corresponding methyl signals of acetone and methylethylketone solutions appear at S = 2.17 ppm. The chemical shift increment therefore is 1.28 ppm which is to be compared with the calculated increment AScarc = I.20 - 1.23 ppm, the difference being due to the assumption of a staggered or eclipsed position of the methyl group with respect to the carbonyl group. 3,2.2.

Chioro compoundr

The least-squares calculations were carried out at first with twelve, in the end with eleven different relative chemical shifts measured on chlorosteroids (as deuterochloroform solutions, Ziircher(lm)), bomane (S = 084 ppm for all angular methyl groups, measured in deuterochloroform and carbon tetrachloridet), bomyl- and iso-bomyl chlorides (in carbon tetrachloride, Flautt and Ennan,@@ cf. Fig. 2) and ethyl chloride (Bhacca, Johnson and Shook@@). For the same reason mentioned in connection with the ketosteroids (Section 3.2.1) only chlorine atoms relatively near to the angular

t

We are indebted to Dr. K. Heusler, ClBA Base], for the preparation of bornane.

R. F. ZtiRCHER

228

methyl groups were considered. The observed and calculated relative chemical shifts are listed in Table 3. The chemical shift increment, ASobs,of the methyl protons in ethyl chloride was again obtained by comparison of its signal with the corresponding signal of n-hexane, as was done for acetone. TABLE3. THEOB.WRVWANDCAUSULA ED

Ramw3

PROTON

Cppm)OF METHYL GROUPS PI CHLOROCOMPOIJNM

CmxcAL

SHIFT3

Substance Sa-Chlorosteroids 6a-ChlorosteroidP 6&Chlorosteroids 6/Whlorosteroids go-Chlorosteroidsb 2-exe-Chlorobomane 2-exe-Chlorobomane 2-exo-Chlorobomane 2-emfo-Chlorobomane 2-endo-Chiorobomane t-endo_Chlorobornane

Ethyl chlorideC

d&m

/ I

/ / I i

i I

/ I

AND

dSc.lC

Hc

j

Ah.

1

19 19 19 18 18 *

I

0.250 o-117 0.317 0.058 0.017 0.27

Abl.3

9 10 8 9

;

0.03 0.18 0.10

1 0.170 0.077 g.g2 * / / 0.017 0.288 i 0.058 1 0.233 I o-075

1;

/

;:z

; {:gj

/

aTori and Kuriyama.(g3) b Unpublished measurements. ’ CBhacca, Johnson and Shoolery.(*) Similar least-squares calculations were carried out on the chlorosteroids as on the ketosteroids. Again a fit with the experimental data could not be obtained when only the anisotropy of the magnetic susceptibility, Axi (AxPEO), was considered to be responsible for the chemical shift increments. However, the relative chemical shifts could, with one exception, be explained satisfactorily by the action of the electric dipole moment of the C-Cl bond alone. The results were only slightly improved by taking both effects into consideration simultaneously, which is also the case with the hydroxy and cyano compounds. A possible small magnetic contribution to the relative chemical shifts of chloro compounds has, therefore, been neglected. It must be concluded that the anisotropy of the magnetic susceptibility, Axi, is of minor influence on chemical shifts in chloro compounds compared with the substituent dipole moment IL Also, Axi can at best be determined very approximately for rather a limited number of compounds, its value ranging between about O-3 x 10V6cm3/mole (O-5 x 10T30cm3/molecule): the noteworthy feature is its positive value. The exception mentioned above concerns the relative chemical shift of the methyl protons in the lo-position in 2-endo-chlorobomnne. As discussed

CAUSE

AND

CALCULATION

OF PROTON

CHEMICAL

SHIFTS

229

below, similar deviations are found in camphor, bomeol and isobomeol. The most plausible explanation is probably that this is a consequence of the neglect of the term ALI, in equation (1). In the final least-squares calculations this relative chemical shift has been excluded. The centre of the electric dipole has been determined by the same criterion as before, namely a minimum standard deviation between caIculated and observed chemical shift increments. The values obtained are: K=9-O x 1O-U esu with the centre of the electric dipole 090 A from C, along the C-Cl axis. The eleven measured relative chemical shifts A&be which range from 0.02 to 0.60 ppm were obtained with a standard deviation of f 0.037 ppm. In order to find out the importance of the intramolecular van der Waals effect and the quadratic electric field effect, some least-squares calculations with chloro compounds were performed. The centre of the electric and induced magnetic dipoles as well as the centre of the polarizability ellipsoid have been assumed to be 0.90 and 1.10 A respectively from the carbon atom along the C-Cl axis. These calculations have been performed with chloro compounds because the expected change in polarizability, Au, upon introduction of a chlorine atom into a molecule, is relatively large (cf. Table 1) and, therefore, the effect should also be large. In half of the least-squares calculations the additional chemical shifts, AS, have been expressed as A6 = A& -t A&,,, -+-A&, in the other half the term ALegn hai been omitted. In the van der Waals term, A&, the previously neglected quadratic part of AS,1 has been included, so that 86, = B[Es + Am. Inspection of Table 1 shows that the average value of Eais much smaller than Ap. The angular dependence of Ea, therefore need not be considered. In the more complete term A& the quantity B must be determined by the calculations and the term in brackets is assumed to be dependent on the geometry only. Because of the many uncertainties [E2 + A’i;j was assumed to be 100 x 10-s6/S esu. The least-squares calculations show that, upon a change of the co-ordinates of the dipole and polarizability centre from 0.90 to 1.10 A, the quantities B, and when included Axi, but not K, vary strongly. Therefore, the value of these results is doubtful, and they hardly represent true physical quantities. The value of B varies in these calculations from 0*02-0*4 x IO-l* esu. Rummens and Bernstein obtain 1.35 x lo-18 esu for B in C-H bonds from measurements of medium effects in non-polar gases. In order to bring our B value into accord with theirs, the term [,!? + A2] would have to be reduced correspondingly. This would imply that the change of the polarizability due to the introduction of a chlorine atom is much smaller than has been assumed. These scarcely convincing results led us to neglect the term @.F + Am

R. F. ZijRCHER

230

in all the calculations. For the attainment of conclusive results much more experimental data are a prerequisite.

entirely

3.2.3.

Alcohols

The observed relative chemical shifts of the methyl groups due to the introduction of hydroxyl groups were taken from hydroxy steroids and from ethanol (dilute deuterochloroform solutions). The observed increment of ethanol was again obtained by a comparison with n-hexane and n-heptane solutions. The observed and calculated relative chemical shifts are compiled in Table 4. The calculated values for the 1la- and lfl-hydroxy-5u-H-steroids TABLE4. THE OBSERVEDAND CALCULATED RELATIVE PROTONCHEMICAL %4IFlYS d&b* AND A&a~c (ppm) OF METHYLGROUPSIN ALCOHOLS.

I

I Substance

HC

Ila-OH 12a-OH l/?-OH 2,%OH 3&OH 12&OH 68-OH

19 19 19 19 19 19 18

Ethanol

:

/ I

,

2

/

! !

j&bs

;

0.000 0~060 0.240 0’033 0.008 0.042

0.003 (O-162) ~ 0.225 i 0.033 0.022 : 0.020

0.050

1 0.028

0.330

/

I

&s1e

0.338

The observed additional chemical shifts, A&m, are mean values for equivalent positions (cf. Ziircher(lo3)).

are put into parentheses because they clearly do not agree with the observed ones. This behaviour is readily understood if a steroid model is examined. A hydroxyl group in one of those positions must interfere with a hydrogen atom in the other and this steric hindrance leads to the irregular behaviour. These two increments, therefore, were not included in the final least-squares calculations. The procedure was analogous to that for the chloro compounds. The hydroxyl group was treated as freely rotating and, in the average, axially

CAUSE

AND

CALCULATION

OF PROTON

CHEMICAL

SHIFTS

231

symmetric with respect to the C-O bond. Again, the chemical shift increments seem to be determined essentially by the electric dipole moment of the C-OH group. The inclusion of a AS,, term leads to practically no improvement. Whereas K varies only slightly with a change of the assumed centre of the electric and induced magnetic dipoles along the C-O bond axis, Ax1 runs through a range of values from about - 4 to + 1 x 10” ems/mole (- 6.7 to + I.7 x lo-30 cm3/molecule). Thus, no definite statement about the anisotropy of the magnetic susceptibility of the C-OH bond can be made. The centre of the electric dipole has been determined in the usual manner. K= 5.5 x lo-l2 esu, with the centre of the electric dipole 1.10 A from C, along the C-O axis. The twelve measured relative chemical shifts ASob6which range from 0 to 0.33 ppm were obtained with a standard deviation of If O-017 ppm. 3.2.4.

Nitriles

Only five different relative chemical shifts of methyl groups due to cyano groups were at our disposal. They are listed in Table 5. Again the electric dipole moment of this substituent is the element determining the relative chemical shifts. If the nitrile group possesses an anisotropic magnetic susceptibility it must be small according to this determination. KS. 14.8 x lO’l2 esu, with the centre of the electric dipole 2.10 A from the @hybridized carbon atom, along the C-C=N axis, that is halfway along the triple bond. The five measured relative chemical shifts A&& \;lhich range from O-05 to 0.45 ppm were obtained with a standard deviation of f 0.039 ppm. TABLE5. THE OBSERVEDAND CALCUUTED RELATIM PRoToN

@pm)

CHEMICAL OF

SUbStXlCC

Sa-Cyanosteroids* S/Kyanosteroids~ 6&Cyanosteroidsb 6/Kyanosteroidsb Ethyl cyanidec

&SIFTS

h%,,

AND

ddac

METHYLGROIJFSINNITRILES. I

I Hc

’’

) ~

&bs

/

x:;;;

1 8:;;;

19 19 19

I

18

:

o-050

2

:

0.450

i

0.283

A&&

0,262 i

0,039

0440

* Cross and Harrkon.(2sl b Jacquesy, Lehn and Levisaks. C Cavanaugh and Dailey.‘*O)

3.3. Discussion of Methyl Group Results According to equation (10) the quantity K is equal to AP, that is Kshould be proportional to the value of the dipole moment p of the substituent under

232

R.

TABLE6.

-C=N

thJhtMARY OF K AND

-14.8

F.

ZiiRCHER

Ax VALUES FOR

TW

-

DIFFERENTSuasTITuENTs

2.10

consideration, providing A is constant. A is a measure of the variation of the proton magnetic shielding with change of &H, the component of the electric field E along the C-H bond. In this work, A may be considered constant in so far as only protons belonging to methyl groups are dealt with and the same solvents (deuterochloroform and carbon tetrachloride) were used. If Kis plotted against p, whose values are known from dielectric relaxation measurements (Smyth@s) ,and McClellan@‘)), a straight line passing through the origin should result. That this is actually the case is shown in Fig. 7. The mean value of the C-OH group moment is / 1.7 DI. Its value along the C-O axis in methanol is - 0.89 D as determined by Ivash and Dennison(4g) from microwave measurements. The line. passes through a point between these two values. We consider this linear relationship as proof of the inherent consistency of the results and of the essential correctness of the model chosen. It stresses the fact that in molecules with polar substituents, their electric field is of prime importance in affecting chemical shifts of hydrogen nuclei. In comparison, the anisotropy of the magnetic susceptibility of a substituent or its shielding effect is often negligible. Musher@‘) has discussed the linear variation of proton magnetic shielding with electric field and has given a collection of theoretically and experimentally determined A values, ranging from 2-O to 3.4 x 10-1s esu. At the moment the most precise A values for $-hybridized C-H bonds are those of Petrakis and Bernstein(m) and Diehl and Freeman( which have been determined from medium effects. In Table 7 a collection of experimentally determined A values for C-H bonds with @-hybridized carbon atoms is given. In this investigation a value A = 4.2 x lo-i2 esu is found (from Fig. 7) which probably is still within the limit of error of Diehl and Freeman’s measurements. Higher A values are found in certain Z-H bonds. For the N-H bond of uracils A = 6.2 x lo-12 esut and for HCI, Raynes, Buckingham and Bernstein found A = (40.4 f 2.0) x lo-12 esu. t Private communication from Prof. Musher based on data of J. P. Kokko, L. Mandell and J. H. Goldstein, J. Amer. Chem. SW. 84, 1042 (1962).

CAUSE

AND

CALCULATION

OF PROTON

CHEMICAL

SHIFTS

233

.

P (Debye)

FIG. 7. ‘Ike relationship between K of equation (10) and the value of I(, the electric

dipole moment of the substituent. TABLE7. ExpEilIMwcAu~ FOR A OF &UATlON

Dm (lo)

IN

C-H

WITS spt-HYBRIDIZED t%lRON substance Methylbenzcnium ions* Fluoroformb Panddehydec AcetonitrileC This investigation

VALUES &BIDS ATOMS.

‘A x 10’~esu 2.8

2.9 -f 0.8 3.0 3.4 4.2

* Value estimated by Musher,‘s’J based on results of MIleLaan and Mackor.(‘g) b Pctrakh and Bernst~in.~‘~) c Diehl and Freunan.@O)

The order of the principal magnetic susceptibilities of the carbonyl group, XI > xs > xs (xl most paramagnetic or least diamagnetic), cxwresponds to the order of the principal optical polarizabilities, al > aa > w, as determined by Le FCvre(57)from Kerr effect measurements (see Fig. 8). This is in qualita-

234

R. F. ZijRCHER

x3

;l

0

X* +

/O\ FIG. S. The principal axes of the carbonyl bond.

tive accord with the theory of Gans and Mrowka@s) that states that the axis of largest (smallest) optical polarizability coincides with the axis of largest, that is most paramagnetic (smallest, that is most diamagnetic) susceptibility. An application of this theory to the determination of the magnetic susceptibility tensors of the C-C and C-H bonds has been given by Ziircher(lQQ); for a further discussion see Bothner-By and Pople.(lQ) The order of the principal magnetic susceptibilities is also in partial agreement with theoretical calculations of Pople,(n) the proposal of Jackman and the results of Narasimhan and Rogers,(QQ)insofar as x3 is most diamagnetic. On the other hand our results contradict those of Flygare(s7) and of Kaiser and Hooper.(sQb Finally, it is interesting to note that to a first approximation no anisotropy of the magnetic susceptibility AXI is found for the cyano group. This conflicts with the findings of Zeil and BucherWJl), Ax1 = - 34 x 10-S cm3/mole = -57

x lo-30 cm3/molecule

and Reddy and Goldstein( AXI = - 16.5 x 10-S ems/mole = - 27.5 x lo-30 cm3/molecule, who obtained large negative values for Axr. However, both sets of authors consider the relative chemical shifts of their compounds as a consequence of an anisotropy of the magnetic susceptibility of the cyano group alone. Their values for Ax1 of the cyano group are about as large as those for AXI of the C=C triple bond, that they also determined, and for which theoretical but widely diverging values are also available. Thus Tillieu and Guy(QQ)found, by a variational calculation, AXI = - 1.6 x 10-Qcma/mole (- 2.7 x lo-30 ems/molecule) whereas Pople(m obtained, by an approximate molecular

CAUSE

AND

CALCULATION

OF PROTON

orbital method based on gauge-invariant ems/mole (- 32.3 x IO-so ems/molecule).

CHEMICAL

orbitals,

SHIFTS

AXI = -

235

19.4 x 10-s

3.4. Applications There are relatively few non-aromatic and non-conjugated compounds with carbonyl and methyl groups, whose geometry is well defined. One such substance, however, is camphor (boman-2-one, see Fig. 2). The additional chemical shifts of the 8-, 9- and lo-methyl groups due to the carbonyl group in position 2 are A?LsObs = 0.01, O-14, and O-08ppm, respectively, according to Tori, Hamashima and Takamizawa,@4) but re-assigned according to Connolly and McCrindle.(21) These authors based this re-assignment of the 9- and IO-methyl signals on solvent-induced chemical shifts (benzene vs. chloroform). The calculated values are A&r, = O-085, O-203 and O-230 ppm respectively. The agreement between the calculated and observed additional chemical shifts of the 8- and 9-methyl protons is not overwhelming, and that of the IO-methyl protons is wholly unsatisfactory. As in the case of the chloroborrianes (Section 3.2.2) this behaviour may be a consequence of the proximity of the IO-methyl and the carbonyl group which no longer permits the neglect of the A&I, term. Another application may be found in the calculation of the relative chemical shifts of the 18-methyl protons of steroids due to carbonyl groups in the five-membered ring D (Fig. 1). ‘Dreiding@l) models of steroids have been constructed, in which ring D in the 14a-series is seen to exist in the half-chair conformation (with a CZ axis through the carbon atom 16, bisecting the C( 13)X( 14) bond), and in the 14@eries approximately in the envelope conformation (C,) (with carbon atom 13 “below” the plane through carbon atoms 14, 15, 16 and 17). (For the conformation of five-membered rings cf. Pitzer and Donath(75)). The results for the chemical shift increments due to carbonyl groups in positions 15 and 17 are given in Table 8. The increments in the lllpseries are reproduced satisfactorily in contrast with those of the l&-series. However, if ring D is also assumed to have approximately an envelope conformation (with carbon atom 15 “above” the plane through the carbon atoms 13, 14, 16 and 17) reasonable results are obtained. A further application, which concerns chemical shift increments due to a carbonyl group, of single rather than methyl protons, however, is mentioned by Ztircher.(r~) From the previously mentioned paper of Tori, Hamashima and Takamizawa,(g4) we gather that a 3-endo-chloro substituent in bomane (Fig. 2) should cause a relative chemical shift of the IO-methyl group A&b, = OG9 ppm to be compared with A6,,rc = 0.063 ppm. The quoted shift increments due to a 3-exe-chlorine atom are somewhat less consistent and therefore have not been used. The predicted shift increment for the I&methyl

236

R. F. ZtiRCHER TABL~~.OBWWED AND CALCULATED RELATIVE CHEMICAL%JlFlSOFTIiEhoTONSOFTZiE 18-Mmx~~ GROUPOFS~EROJDSDUETO CARB~N~GROUPSINRDJG Dw~llr

cz AND c.

CONFORMATION.

protons due to a 3-exe-chlorine atom is Asealc = 0.073 ppm. With two exceptions, the relative chemical shifts of the angular methyl protons of Zendo- and 2-exe-bomanol (Fig. 2) are also calculated satisfactorily (Table 9). These exceptions again involve the IO-methyl protons as in the case of the chlorobomanes and of camphor, where the neglect of Ai&rV was considered to be the cause of this discrepancy. TABU 9. OBSEWEDAND CALCULATED &LATlVE PMXON ChmmAL SHIFIs dbOti AM) ddwlc @pm)

substance 2-exe-Bomanol 2-e.wBomanol 2-exe-Bomanol 2-enab43omanol Zendo-Bomanol 24uiW3omanol

Hc f 10 8 9 10

hd’ 0.19 0.00 0.04

0.03 0.03 0.02

o-173 0.037 (O-153) 0.038 0.043 (0.122)

s Tori, H+mashima and Takamizawa.@~)

Some time ago Musher@@ surmised that the electric field effect due to the C-H bond dipole moment alone could probably account for changes in proton shielding with molecular geometry. There are not many clear-cut cases to test this proposal. One of them is the chemical shift difference between the 19-methyl protons of 5a- and 5fl-androstane (Fig. l), amounting to A8 = 0.133 ppm.t The geometrical changes are well known in contrast to those of the 5-ring D where the transition from 141~to 14j3-androstane causes t R. F. Zikcher (He/v. Chim. Acfa 44, 1755 (1961)) has given this difference less precisely as @148 ppm.

CAUSE

AND CALCULATION

OF PROTON

CHEMICAL

237

SHIFTS

a rather large relative chemical shift of the l&methyl protons (A6 = 0.300). With a C--H+ bond dipole moment of + O-3D @myth@@) and the centre of the dipole at 0.50 and 0.70 A from the carbon atom, respectively, and with A = 4.2 x lo-12 esu chemical shift increments A8 = 0.058 and 0.052 ppm, respectively, are calculated. This is roughly half the measured difference. These figures make it evident that the large chemical shift difference of the l%methyl protons of the 14a- and 14&-androstane conformational isomers cannot be explained with the field effect due to the electric dipole moment of the C-H bond. We do not think that the solution to this problem lies in a much larger C-H dipole moment than that customarily assumed, aa Musher@@ proposes, Rather, we suggest that changes in specific solute-solvent interactions accompanying the changes in conformation may play a dominant role, perhaps together with a minor effect of the anisotropy of the magnetic susceptibility of the C-C and C-H bonds. TABLE10. OBSERVJZDAND Cucu~~ TmRBLATrvEcHeMIcALsm,

L&M AND L%I~ (ppm), OFHYDRWENNUCLEIIN a-Posrrxo~~

-cl

-OH AN

2.83 3.17 I.75

2.62 2.73 148

2.57 2.58 l-38

2.80 2.60 1.33

2.87 2.75 1.18

2.83 (l-04& I.61 I.19

* Cavanaugh and Dailey.@@ b Laszlo and Schlcyer.f~s)

Following successful calculation of the chemical shift increments of the methyl protons in ethyl derivatives an attempt was made to extend calculations to hydrogen nuclei in a-positions relative to the substituents, as in monosubstituted methanes, for example. These results could in turn be expected to lead to more insight into the u-inductive effect. In Table 10 a collection of I

observed and calculated relative chemical shifts of protons

in X-C-H

positions is given. The large scattering of the observed chemical shift increments, all of which have been determined in carbon tetrachloride, clearly demonstrates that other effects beside the linear electric field effect must operate to different degrees in the different compounds. In these compounds

238

R. F. ZijRCHER

the protons considered are no longer in methyl groups, except in the methane derivatives. The calculated increment for chloro compounds lies about 0.60 ppm outside the range of the observed increments. If, however, the centre of the electric dipole is shifted from 090 A to I.04 A from the carbon atom along the C-Cl bond, the correct chemical shift increments of the chloro derivatives of methane, iso-propane and norbomene are obtained. This can be done without hesitation because this slight shift of the dipole centre leaves K unchanged. But the standard deviation between calculated and observed relative chemical shifts becomes a little greater. The relative shifts of the methyl protons are observed to be practically the same in both ethyl and iso-propyl chloride despite the difference in shifts of the protons in a-positions relative to the substituent. The calculated chemical shift increment for the nitriles is within the range of the observed increments, whereas that for the alcohols falls short of it. Too large a shift of the dipole centre along the C-O axis (toward shorter distances from the carbon atom) would be necessary to obtain agreement between calculated and observed chemical shift increments of the hydrogen nuclei in a-positions relative to the hydroxy group, and would, at the same time, lead to a large increase in the standard deviation. We do not think that a consideration of the terms falling off with R-6is the proper approach to this problem, for this would only make things worse in the case of the chloro and cyano compounds. However, it is possible that the model with the averaged dipole moment along the C-O axis is no longer applicable for such short distances. Finally, formaldehyde, CHsO, may be seen as a logical extension of this series of methane derivatives, although it has no methyl group. The transition from a methyl to an aldehydic hydrogen atom in general, is treated below. For this purpose deuterochloroform solutions of butyraldehyde, CHsCHsCHaCHO (6 = 9.74 ppm; Bhacca, Johnson and Shoolery(s)), and of n-hexane (S = 0.89 ppm) may be compared. The calculated chemical shift increment depends rather strongly on the geometry assumed. If all angles are assumed to be 120” and the C-H bond length 1.09 A then, with the centre of the electric and induced magnetic dipoles at 060 A from the carbon atom along the C=O axis, one obtains A&i = 6.21 ppm AS,,, = 2.32 ppm Ascsic = 853 ppm to be compared with A&-,s = 8.85 ppm. This rather good agreement between calculated and observed increment may be fortuitous, especially in view of the calculations of Didry and Guy (2s)who find that the point dipole approxi-

CAUSE AND CALCULATION

OF PROTON

CHEMICAL

SHIFTS

239

mation may lead to entirely wrong results for A&,, at such short distances. However, it demonstrates that the physical models chosen sufhce to calculate roughly the chemical shift increments even of such nearby substituents. The rough agreement between the calculated and observed relative chemical shifts of methyl chloride, acetonitrile and the aldehydes and the precise agreement in the case of the ethyl derivatives and of acetone demonstrate the importance of the linear electric field effect and, in the case of the carbonyl group, of the anisotropy of its magnetic susceptibility also. They also throw an interesting light on the so-called “inductive” effect adopted by organic chemists. Dewar and Grisdale@‘J)suggested from a careful analysis of the substituent effects on the acid dissociation constants of substituted 1-naphthoic acids that the propagation of inductive effects by the successive polarization of u-bonds (u-inductive effect) is unimportant and that it is, in reality, a field effect. Based on the equation A&i = A&H + BE2 of Buckingham,(i7) MusheP) estimated with reasonable values for A and B the relative chemical shift of the methylene protons in ethanol and found that it compares well with the observed one. He came to the conclusion therefore that it is explicable in electrostatic terms and that no. inductive effect is needed as had been proposed before from empirical correlations between magnetic shielding and electronegativity of substituents (Dailey and Shoolery(sQ). The results of this investigation demonstrate that, with few exceptions, the relative chemical shifts of methyl protons may be calculated in a quantitative way regardless of whether they are separated by few or many bonds from the substituent. Our findings therefore confirm the conclusion that the u-inductive effect is unimportant.

4. THE

RIGID

SYSTEM

x/‘-\~

4.1. Calculationsand Discursion It is quite natural that one wishes to apply the knowledge gained from the least-squares calculations on compounds with methyl groups to the study of other molecules. In order to determine relative chemical shifts two compounds are always needed, one with and the other without the substituent effecting the relative shift. Molecules with hydrogen nuclei in a-positions relative to a substituent Xi are especially attractive because these protons are generally shifted downfield and so easily recognizable in the spectrum. The introduction of a further substituent Xs into the molecule often gives rise to an appreciable relative chemical shift. We shall, however, refrain from discussing this topic because, as may be gathered from the discussion below, the proximity of the substituent Xi (not involved in the calculation) to the proton considered, Hc,

240

R. F. ZiiRCHER

may lead to further difficulties, especially if the second substituent Xz is nearby, Instead, another somewhat more lucid problem will be examined, the idea being again, that many relevant features can be made obvious with its I

help. The molecular system chosen is the arrangement

I

X-C-C-H, I

an

I

ethane-like derivative with fixed geometry in a sense, where X again may be one of the following substituents: =O, -OH, -Cl or -C=N. The relative positions of the proton considered, Hc, and the substituent X are fixed in bicyclic compounds, bicyclo[;! .2. llheptanes, bicyclo[2.2.2]octanes and adamantanes, for example, and in conformationally-stable cyclohexane derivatives. It is important to have small molecules for comparison, otherwise a determination of the chemical shifts and their increments is more dithcult. The extensively investigated norbornenes(bicyclo[2.2. llheptene derivatives (Fig. 9)) are especially suited for this purpose. The selection of such rigid

EXO

6 2

I X FIG. 9. Norborncne

(Bicyclo[2.2.l]heptene).

compounds allows the observation of chemical shift increments due to different substituents and at different torsion (dihedral) angles of the C-C single bond. One would surmise that these increments could be calculated as easily as those of the ethane derivatives. However, it turns out that the results obtained with the proven values for K and the Ax’s (Table 6) are entirely wrong. In this section the calculation of the correction term is dealt with and the reasons for these gross deviations are discussed. In Table 11 the observed relative proton chemical shifts of a number of suitable compounds are given as a function of the torsion angle @ around the C-C single bond. The large scattering of the observed values is immedi-

CAUSE

AND CALCULATlON

OF PROTON

CHEMICAL

SHIFTS

241

ately evident. Although the given torsion angles may be wrong by a few degrees, these small inaccuracies cannot be the reason for this large spread, nor should the different ring strains cause it. However, it is conceivable that the different steric environments and their interactions with the solvent molecules may lead to such spreads for a given torsion angle and substituent. The similar behaviour of the chemical shift increments of hydrogen nuclei in a-positions relative to a substituent as given in Table 10 may be recalled. Nevertheless the general tendency is quite obvious: the relative chemical shifts grow with increasing torsion angle a. This is exactly opposite to the trend of the calculated values (Fig. IO). For a torsion angle @ = 0” the discrepancy between calculated and observed chemical shift increments is largest

Torsion

FIG. 10. The calculated X/c-c\I-I

angle,

@

relative proton chemical shifts A&w

in the rigid system

as a function of the torsion angle @ and for different substituents

X.

and may be as much as about O-60 ppm. At about CD= 105” the calculated and observed increments cross over and diverge in the opposite directions for higher @ values. In Fig. 11 the term A&n which must be added to A&W, (Fig. 10) in order to obtain rough agreement between calculated and observed chemical shift increments is plotted against cos 4,,.

A&s = A&al, + &orr, where A&,1, is the term calculated according to equation (15) with the values for K and Ax from Table 6. The angle 4, is defined as in equation (1 I) as the 9

R.

242

F. ZijRCHER

TABLE11.OBSERVED RELATIVE PROTONCHEMICAL SHIFTSOFTHERIGID SYSTEM FORDIFFERENT SUBSTITUENTS X AND TORSIONANGLES@.

Torsion angle@

%h

(Ppm)

Substance/Proton

HC

Carbenyi Compounds Bicyclo[2.2.2]octan-2-one/i-H Adamantan-2sne/l-H Bicyclo[2.2.2]octan-2-one/3-H I-Bromocyclohexan-2-one/ 1-H

4.72 0.63 ho.73 1.00

0” 0 -42” 60” 60” 60”

-0.14 +0*15 -O*ll -0.14 -0.10 -0.09

60” ~63“ ~63” ~63” 43” -63” ~78” 120” 120” 120° 120”

+o. 12 -0.35 -0.27 -0.22 -0.13 -0.03 +0.07 +0.31 +0.4O +0.45 $0.50

Hydroxy Compounds 2-errdo-Norbomenol/3-endo-H 2-exe-Norbornenol/3-exe-H 2-exe-Norbornenol/l-H l-Hydroxyadamantane/2-H 1-Hydroxyadamantane/2-H Polysubstituted hydroxyadamantanes: mean value 2-Hydroxyadamantane/ 1-H 7-anri-Hydroxynorbomene/l-H 7-anti-Hydroxybenzonorbornane/ 1-H 7-syn-Hydroxybenzonorbomane/l-H 7-syn-Hydroxynorbomene/l-H 7-Hydroxynorbornadiene/l-H 2-endo-Hydroxynorbomene/ 1-H 2-exe-Norbomenol/3-e&o-H 2.endo-Norbomenol/3_exo-H 7-syn-Hydroxybicyclo[2.2.2]benzoctane 7-syn-HydroxybicycIo[2.2.2]oct-2-ene/8-unri-H

-0.24 TO.22 to.33 f0.35 +o* 15 ~0.24 i-O.68

Chloro Compounds 2-endo-Chloronorbomene/3-endo-H Sa_Chloro_6&hydroxysteroids/6&H I-Chloroadamantane/2-H I-Chloroadamantane/2-H 7Chloronorbomadiene/ 1-H 2-endo-Chloronorbomene/ I-H 2-endo_Chloronorbornene/3;exo-H

+0.26 +0*35 -+0*35 to.22 +0*25 +-0.35 iO.52 +0*56

Cyan0 Compounds 2_endo_Cyanonorbornene/3-endo-H 2_exoCyanonorbomene/3-exe-H 2-exo-Cyanonorbomene/ 1-H I-Cyanoadamantane/2-H I-Cyanoadamantane/2-H 2-endo-Cyanonorbomene/ 1-H 2-endo-Cyanonorbomene/3-exo-H 2-exo-Cyanonorbornene/3_endo-H

2: 60” 60” -63” -78” 120”

0” 0” -42” ;: ~78” 120” 120” I -

/ .‘ 30lVent _-

.I-

/ / / /

/

/cDc13

k

/cc14

C k

cDc13 c-DC13

j

cc14 cc14 cc14 cc14 cDc13

1, h, k L h, k L. h, k C k

CC14 cc14 cc14 cc14 cc14 CCL cc14 CCL CCL cc14 cDCl3 cDcl3

C C h :: h e. t3 h 1, h. k 1, h, k

i i

cc14 CDCIS ccl4 cDc13 CC14 cc14 cc14

e, h k

cc14 cc14 CC14

a, h a, h d k

/ i CC14

C k e. g d d, h

f d

I cc14

a, h

CAUSE

AND

CALCULATION

I ! Torsion Increment I angle @ / A&M (ppm) / O0 60” g: 60” -78” 180”

OF PROTON

CHEMICAL

SHIFTS

243

Substance/Proton Hc Me&y1 Compeunds 2sndo-Methylnorbornene/33ndo-H 2-rran&q)-Methylcyclohexanol/l-H(ax) 2-trans(ax)_Mahyl~lohexanol/l-H(eq) I-Methyladamantane/2-H 2-cis(eq)-Methylcyclohexanol/ l-H(q) 2-e&-Methylnorbornene/l-H 2-cis(ux)-Methylcyclohexanol/I-H&x)

-0.54 -0.47 -0.40 -0.30 -0.28 -0.16 J-o.19

L

G

a Davies and Van Auken~~J b Eliel, Gianni, Williams and Stother+) f Fort and Schleye9) d Laszlo and Schleyer@s) e Laszlo and Schleye+) r Simon and Pascual, private communication.* g Snyder and Franzus.‘*8) h Tori, Aono, Hata, Muneyuki, Tsuji and Tanida(O’l * Tori, Takano and Kitahonoki(D6) J Wellman and Bordwell@Q k Zilrcher, unpublished measurementst: * We are indebted to Prof. W. Simon and Dr. C. Pascual for the communication of their results prior to publication. t Prof. C. A. Grob has kindly provided samples of 2-0&o- and 2_exo-norbornenol, bicyclo[2.2.2)octan=&one, biiclo[2.2.2loctandiones, and bicyclo[2.2.2]octan-2,6,7-trione for which we are very obliged. z We are indebted to Dr. A Daeniker for providing the adamantane derivatives.

angle between the unit dipole moment, h, which is parallel to the C-X direction, and the vector CH, which is parallel to the C-H bond direction (see Fig. 3). For discussions of a possible action of the reaction field P the term cos +,, is appropriate. However, from molecular models the torsion angle 8 can more easily be inferred. Therefore, at the head of Fig. 11 the scales for these torsion angles are drawn for the case of two @-hybridized carbon atoms (@s) and of an sp2- and an q&hybridized carbon atom (es, carbonyl group as substituent). The transformations from the cosines @s and @Zto cos $r are given by @s:cos+~=gcos@3-~ (17) @2 : cos 93, =&cos@2-*

W)

In Fig. 11 straight lines are drawn, for the precise form of dependence of Aacorr on cos +P is not known. The values so determined may be wrong by about i 0.15 ppm.

244

R. F. ZiSRCHER

The question is, which of the hitherto neglected contributions may give rise to the term AS,,,. Following the successful calculation of the relative chemical shifts of the methyl protons in ethyl derivatives it seems to be an obvious postulate that the same effects, namely the linear electric field effect and, in the case of the carbonyl group, the anisotropy of its magnetic susceptibility too, must operate to the same extent in rigid systems. Therefore, the discrepancy it seems, can only be due to one or more further effects and not to an entirely new effect. The hitherto neglected quadratic electric field and

FIG. 11. The term JLrr

of equation (16) as a function of cos dILand the torsion angle @ (see text).

the van der Waals effects originating in the substituent are out of the question because they would lead to a reduced magnetic screening of the proton considered, Hc, whereas for most torsion angles 0, an enhanced screening (negative A&,,,) must be explained. If the lines in Fig. 11 were to pass through the point with the coordinates cos +P = 0 and A&, = 0 one would assume the action of some reaction field P. However, it is rather unclear why this reaction field might act only in rigid systems but not in molecules with internal (hindered) rotators. A further doubt is shed on the assumption of a strong reaction field if the behaviour of compounds with methyl groups is studied. Their electric dipole moment is too small to have any appreciable consequences. Besides, as the C-Hx bond dipole moment has been neglected in all the previous calculations, that is, as only the difference between the substituent and the C-Hx bond

CAUSE

AND

CALCULATION

OF PROTON

CHEMICAL

SHIFTS

245

dipole moment has been employed, and as the C-CHs dipole moment may be assumed to be approximately equal to the C-Hx bond dipole moment, no appreciable electric field nor reaction field effect is to be expected. Yet, such nearby methyl groups may cause rather large, chiefly upfield chemical shifts, which, as Muller and Tosch@s) state, cannot be rationalized with the concepts of inductive or bond anisotropy effects, ring deformations or ring currents. Eliel, Gianni, Williams and Stothers(sQ have compiled relative carbinol proton chemical shifts due to methyl groups in different positions in conformationally stable cyclohexanols. The chemical shift increments due to methyl groups are also listed in Table 11 and plotted in Fig. 11. As there is no physical model available for the determination of the term A&,ic, equation (16) becomes A&b6 = A&r, which has been plotted in Fig. 11 as a function of cos +,. Figure 11 reveals a further interesting fact. The straight lines for the chloro, hydroxyl and methyl substituents coincide very roughly. The same conclusion, but in quite different terms, has been reached by BrownsteirP) for 1,2 f3,4 , 5,Ckhexachloro- and 1,2,3,4,5,6_hexahydroxycyclohexane isomers. He found that, if a constant value of O-85 ppm is added to the inositol chemical shifts to allow for the different inductive effects of the chloro and hydroxyl substituents, the chemical shifts of the equivalent protons in the equivalent stereoisomers are roughly equal. Instead of invoking the inductive effect we would say that, after allowing for a difference in the terms A&i, for the chloro and hydroxyl compounds, a rough coincidence of the spectra is attained. This is possible because, according to Fig. 11, the quantities AaCorr for the two substituents approximately coincide. Further, a glance at Fig. 10 shows that the difference between the curves for the chloro and hydroxyl compounds is approximately constant, although amounting to much less than 0.85 ppm. This is to be expected, for in Brownstein’s compounds six equal substituents are present instead of one. We consider this rough coincidence of the three straight lines for the chloro, hydroxyl and methyl substituents in Fig. 11 as evidence that in all three cases the same effects are probably operative to a very similar extent. According to equation (1) only one more term is left which may be utilized for an explanation of AaCorr,namely the term A&i,, which is given in more detailed form by equation (9). The reasons why its reaction field term cannot be the most important part have already been mentioned. All the other quantities of equation (9) have their origin in the solvent molecules. With the following model and the subsequent short calculation a possible mode of action of the solvent molecules can be made evident. The newly introduced substituent forces the solvent molecules away from the position near the hydrogen atom Hx, which they previously held. Before the introduction of

R. F. ZtiRCHER

246

.

the

substituent these molecules caused a rather large downfield chemical shift of the nearby proton Hc. Buckingham, Schaefer and Schneider(l*J were among the first to show the importance of the intermolecular van der Waals effect as evidenced in gas-to-solution shifts of non-polar molecules, which, as is demonstrated by the experiments of Howard, Linder and Emerson(47) for cyclopentane, may amount to 0.2-0.7 ppm depending upon the different solvents used. Upon introduction of the substituent, that part of the intermolecular van der Waals effect due to the displaced solvent cloud is annulled leading to an upfield chemical shift (enhanced magnetic screening) as is found for A&, for small torsion angles @. TABLE ~~.CAL~~LATEDVANDERWAAL~PROTONCHEMICAL SHIFIS,dg;,DUETOASOLVENTCLOUD ATTHESAMEPOSITIONASASUBST~NT /c-c\ FOR THE RIGID SYSTEM X’ ‘H

Torsion angle @

Distance RinA

0”

I

120” 180”

’ / /

60”

2.54 2.85 3.38 3.61

j id

I

)

R6(ti6) :;; 1481 2221

&ii)

1 / , I

1::: -0.11 -0.07

In Table 12 the results of a short calculation for the determination of such intermolecular van der Waals chemical shift increments, As& as a function of the torsion angle @, are given. The centre of the solvent cloud to be displaced by the substituent X has been assumed to be 1.70 A from the carbon atom along the C-X axis. This corresponds nearly to the C-Cl bond length (1.76 A). The quantity B of equation (4) was taken as 1.35 x lo-18 esu (Rummens and Bernstein (83)) and the expression 3aZ from equation (5) was assumed to be 120 x IO-36esu which corresponds to a value a = 2-O x lo-24 cm3 (cf. Table 1). R is the distance between this centre of the solvent cloud and the proton considered, Hc. Table 12 shows that with AS& the general trend of A8COrrcan be reproduced roughly. The positive values of A&,,, attained at torsion angles of 120” and more may reflect the action of the electric and magnetic fields originating in the solvent molecules and of the reaction field P possibly present in polar molecules. The question immediately arises, why the term ASsOIV is not operative in the case of ethyl derivatives. The answer could be that due to the many collisions with solvent molecules the substituent is moved about in a manner which, in the end, leads to only a small difference between the substituent and the solvent cloud; in

CAUSE

AND

CALCULATION

OF PROTON

CHEMICAL

SHIFTS

247

other words, the substituent in this respect could as well be included with the solvent molecules. This behaviour is certainly entirely different from that of a rigid compound with constant local geometry and always the same spatial arrangement of substituent and proton considered. In conclusion it may be stated that the importance of the solvent in contributing to the additional proton chemical shifts in rigid systems has been recognized. At present there is still no quantitative theory for its calculation available. However, substituents with roughly similar van der Waals radii (Stuart@i)), as the chloro, hydroxyl and methyl groups seem to give rise to similar correction terms, ASeorr, in contrast to substituents such as carbonyl and cyano groups with different shapes and effective volumes. 4.2.

248

R.

F. ZiiRCHER

13 and 14 where the entries are arranged in the order of increasing solvent dielectric constant. In Table 14 the relative solvent shifts, AS*, are given with respect to the chemical shifts of the solute protons in cyclohexane, C.sHis, which is probably the most inert of the solvents chosen. A positive value of AS, corresponds to a downfield chemical shift relative to the shift in cyclohexane as solvent. The expression AS, has been used to stress the difference from A&,,,iV,which also originates in solute-solvent interactions, yet is not due to a change of solvent but to a modification of the solute. Only nonaromatic solvents were used in order to exclude gross effects due to the wellknown magnetic anisotropy of aromatic compounds. In Table 15 are listed, together with their ranges, the mean chemical shift increments, A&, for protons in a-positions relative to the respective substituents. The increments and solvents used are arranged in a manner which directs special attention to the fact that, for the four different kinds of solutes, the sequence of the three solvents cyclohexane, carbon tetrachloride, and deuterochloroform is the same. The other solvents occupy very different positions relative to the three solvents mentioned. The increments A& increase toward the top of the Table. Inspection of Table 15 clearly reveals that the reaction field effect can at most be one of several governing principles, for the chemical shift increments do not increase systematically with increasing dielectric constant E of the solvent. (The dielectric constants are given at the head of the Tables 13 and 14.) This fact was established several years ago by Buckingham, Schaefer and Schneideros) for acetonitrile. Diehl and Freeman,@@ however, were able to show for paraldehyde, that if the appropriate shape factor is taken into consideration and if the solvent dependence of the internal chemical shift differences between the methyl and methyne protons is plotted against a function of E, no irregularities occur for quite a number of non-aromatic solvents and the solvent dependence of these protons can be explained with the reaction field concept alone. We consider this case rather exceptional. Abraham(i) also found such regular behaviour for methyl iodide and for non-aromatic solvents. In the case of iodoform, CHIs, however, the solvent shift in acetone falls out of place. Laszlo and Musher@@ and also Fontaine, Chenon and Lumbroso-Bader,@s) in investigations of solvent shifts in twocomponent solvents of variable composition, whose dielectric constant varied continuously, came to the conclusion that the dependence on the dielectric constant of the solvent cannot be described satisfactorily with existing theories. In our opinion this does not exclude the existence of a simple reaction field to be described by presently available theories. However, other effects may be superimposed upon this reaction field effect, specific solute-solvent interactions for example, which lead to an apparently odd dependence on the solvent dielectric constant,

CAUSE AND C A L C U L A T I O N OF PROTON C H E M I C A L SHIFTS

8~

~6

~

~

~ ~ . ~ ~ . .~ .~. .. _.~

249

_ ~ ,. ,~~ - ~

0

°! m

.~ .~ 9 9 ~ 9

.~9 . ~

.~ .-~ .-.~ 9 9 .~ 9 9

.~ .~ ° . m 9 9

.~.~ T.- .~ ° ~

0 i-

0

~

9 .-9 ~ 9

b, ,,4 d

®A

~. 9 ~ 9

~. .~9 ~.9 9 .-9 .-~ 9 -, .~ ~

.=_ .o

~S/

~ = === == ~== ~ ~

==

== ~

‘-,

Solute

.-_.

Solvent ‘XX_ ,(E) ‘X.. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

I’

I_

EsHlz (2.01)

I

_-0.012 --0.012 0.067 --0.025 0,073 0.090 0.015 0.167 0.024 0.159 m~o.114 -~0.043 -0.013 0.053 --0.049 0.185 -4.002 0.093 0.020 0.150

Dioxane (2.21)

.

--0.002 -0.017 0.097 0.033 0.098 0.074 0.075 0.117 O-060 0.065 0.083 0.048 0.045 0.018 0.006 0.198 0.120 0.060 0.107 0.072

CCh (2.23)

__._....____

CHyOH CHsCHzOH CHsCHzOH (CHa)zCHOH (CCl&CHOH CHKN CHsCHzCN CHICHZCN (CH&CHCN (CH&CHCN

(CH3)2CHCI (CH3)3CHCI

CHLOCH3 CHzCOCHzCH3 CHsCOCHeCH3 CHsCOCHzCH3 CHKHzCI CHKHfl

CH$2HACH3 CHdCHa)sCHs

‘_

-0.015 -0.022 0.067 0.005 0.078 0.067 0.048 0.072 0.037 0.013 0.067 - 0.008 0.027 -0.018 -0.064 0.170 0.078 0.030 0.067 0.033

-

-0.007 -0.017 0.189 0.065 0.182 0.164 0.073 0.170 0.072 0. I64 0.123 0.095 0.138 O-077 0.105 0.218 0.110 0.115 0.105 0.145

(4.81)

cDc13

--0.015 --0.014 0.109 ---0.025 0.117 0.162 0.022 0.210 0.035 0.225 -- 0.055 - 0.018 0.002 - 0.027 0.001 0.287 0.028 0.197 0.052 0.275

(CD3)& 3 (20.7) -

-

0.002 0.002 0.172 o-021 0.173 0.212 0.034 0.165 0.039 0.167 0.008 0.035 0.038 O-025 0.026 0.288 0.053 0.185 0.070 0,188

CH30H (32.6)

-

--

-

-0.025 -0.034 0.109 -0.075 0.117 0.154 -0.005 0.307 0.005 0.280 -0.184 --0.087 -0.085 --0.088 -0.135 0.315 -0.042 0.222 --0.001 0.318

(46)

(CD&SO

TABLE 14. THE PROTONCHEMICALSHIRTINCREMENTS, A& (ppm), OF SOLUTES IN DIFFERENTSOLVENTS RELATIVETO THE CHEMICALSHIFTSOF THESAMESOLUTESIN CYCLOHEXANE.

?1

s .

CAUSE

Ah’D

CALCULATION

OF PROTON

CHEMICAL

SHIFTS

251

TABLE 15. THE MEANCHEMICAL SHIFT INCREMENTS, Ad, (ppm), AND RANGES, FOR PROTONS IN ~-POSITIONS RELATE TO A SUBSTKUENT. I Alcohols

C

I

0.122 & 0.017

T M

0.045 i 0.038 0.025 i 0.017

H A S X D

0 i & & &

-0.017 -0.052 -0.058 -0.135

Chlorides

D 0.293 6 0.013 A 0.222 5 0.012 M 0.175 $ 0.010 / c 0.168 & 0.002 / X 0.162 = O-005

1 T 0.100 & 0.017 ; / S 0.042 i 0.030 /H

0.038 0.025 0.055 0.050

A : Deuteroacetone. C : Deuterochloroform. D: Deuterated dimethyl sulphoxide. H: Cyclohexane.

0

Nitriles

Ketones

I ’

1 D 0.283 & 0.067 ( A 0.253 i 0.053 M c A D T

, / i I x I S

0.165 0.178 0.128 0.127 0.090 0.077 0.070

IH

5 * & & & & & O

0.027 0.015 0.033 0.027 0.017 0.013 0.008

/ M 0.220 & 0.068 j c 0.160 * 0.058 I X 0.145 & 0.045

j T

0.110 iO.088

j I S 0.078 & 0.092 / H 0 i

I M: S: T: X:

Methanol. Carbon disulphide. Carbon tetrachloride. Dioxane.

Table 15 shows at least two distinct features. The first, especially pronounced in the case of the chlorides and nitriles, is the relative importance of the solvent dielectric constant in causing solvent induced chemical shifts. This feature also has been encountered in studies on solvent-induced infrared carbon-halogen stretching frequency shifts by Hallam and Ray,(4s) who found by applying Buckingham’s theory (1s) of infrared solvent shifts and, by using a least-squares fit, that the dielectric shift may contribute as much as 40 to 50 per cent of the overall solvent shift. The second prominent feature of Table 15 is the constancy of the solvent sequence cyclohexanecarbon tetrachloride-deuterochloroform. This sequence is not changed, even for the alcohols, where the shifts in the remaining solvents are reversed compared with the shifts of the chlorides, ketones and nitriles in the same solvents. (Compare the increments AS, in deuterated dimethyl sulphoxide, for example.) Buckingham, Schaefer and SchneideG) noted that in a plot of the chemical shift of methane in various solvents (disk- and rod-like molecules were excluded) against the heat of vaporization of the solvent, the corresponding points for halogenated solvents were uniformly displaced below the common correlation line of the other solvents. .The heat of vaporization of the solvent at the boiling point was chosen as a measure for the van der Waals interaction energy. The significance of this deviation of the halogenated solvents is not understood. Lumbroso, Wu and Dailey,@*) too, noted that of five solvents and ten polar and non-polar solutes the largest

252

R.

F. ZtiRCHER

gas-to-solvent chemical shifts occur in the solvent carbon tetrachloride. In the case of non-polar solute molecules these shifts were assigned as van der Waals shifts. We doubt that this sequence of cyclohexane and the two halogenated solvents reflects an irregular behaviour in the van der Waals interaction, for this, one would surmise, should lead to similar shifts for the alkanes and tetramethylsilane, which, as these very shifts demonstrate, is not the case. So one is left with the conjecture that other electric or magnetic effects are responsible for this remarkable feature. In Table 16 empirical factors for the determination of the solvent induced chemical shifts of the methyl protons in alkanes, of the methyl protons in /3-positions relative to several substituents and of the protons in a-positions relative to a hydroxy group are listed. This is analogous to similar work of Bothner-By(l-0) who measured the excess solute proton shift, ,@,upon transition from the gas phase to the liquid phase (solution). The quantity /?i can be calculated empirically with the help of the formula /3: = xiyr,

(19)

where XI and ye are characteristic numbers assigned to the solute proton giving rise to the signal and to the solvent, respectively. The factors listed in Table 16 may, also be designated yj, insofar as they too describe solvent properties. The quantity fl{ in this investigation corresponds to the chemical shift increment (in ppm) of the solute proton i in the solvent j relative to the shift in deuterated dimethyl sulphoxide as solvent. In this solvent the solute protons i are most shielded, at least in the solvents investigated here. The quantity xz is the maximum chemical shift increment, namely for a proton i the difference xi = Si(CDCls) - Ss((CDs)sSO).

(20)

In the case of the chloro and cyano compounds instead of Si(CDCls), the mean value of &(CDCls) and &(CCl4) has been taken, and for the alkanes an arbitrary value xf had to be defined, namely alkanes: XI = 1.8 x [&(MeOH) - &((CDs)sSO)].

(21)

In this way the factors yi of Table 16 were determined. With one exception (propionitrile in cyclohexane) the observed values of ,@ for the individual methyl protons and the average values for the a-protons in hydroxyl compounds, as given in Table 15, are reproduced reasonably well. One feature of this table is especially interesting: the factors yj for the solvents dimethyl sulphoxide, dioxane, acetone and methanol are constant for all the /?-protons and alkane methyl protons. In the case of the a-protons in alcohols the solvents acetone and carbon disulphide have exchanged places. Some of the other factors are also remarkably constant, for example that for cyclohexane.

0.27

0.36

0.47 0.51 0.60

0.71 1.00

X

s

A H M

T C

T C

S :

A

X

D

-

--

M: S: T: X:

’

I.00

0.60 0.66

0.36

0.27

0

(O-079) (0.061) (O-157) (0.108)

Methanol. Carbon disulphide. Carbon tetrachloride. Dioxane.

C.T

M S

A

X

D,H

CHsCHsCl (CH&CHCl CHaCHzCN (CH.&CHCN

-i-

?

H M

D S X C A T

-~

I.00

0.51 0.60

0.20 0.27 0.33 0.36 0.38

0

CH&H&CHa (O+W CHa(CH&CHs (0.063)

The factors xr in parentheses at the head of the table correspond (with the exception of the alkanes; cf. equation (21)) to the maximum solvent-induced chemical shift differences (deuterated dimethyl sulphoxide-deuterochloroform). The individual solvent-induced proton chemical shifts, /?{.are given by equation (19).

0.71 l-00

0.47 0.51 0.60

0.36

0.27

0

CHsCHaCOCHs (0.140) (0.182) CHaCHaOH (CH&CHOH (0.165)

A: Deuteroacetone. C: Deuterochloroform. D: Deuterated dimethyl sulphoxide. H : Cyclohexane.

0

D

CHaOH CHsCHxOH (0.257) (CHs)aCHOH 1

-

TABLE 16. THE EMPIRICALFACXORSyf OF EQUATION (19) FOR TIIE DETERMINATION OF THE SOLVENT-INDUCED CHEMICALSHIFTSOF m METHYL PROTONSIN ALKANFS,OF THE METHYLPROTONSIN j?-PosmoNs RELATIVETO THE %asmua~~s, AND OF THEPROTONSIN a-PosmoNs RELATIVETO A HWROXY GROUP.

254

R. F. ZtiRCHER

The physical model which may describe these facts is not known nor is that which may explain the sequence cyclohexane-carbon tetrachloride-deuterochloroform of Table 15. It is obvious that much more data are needed before the general trend may be clearly recognized. It is noteworthy that the solventinduced chemical shifts of the a-protons of alcohols behave in many respects very similarly to those of the protons of ,Ssubstituted compounds and alkanes. One possible explanation could be that the dipole moment from the oxygen lone-pair electrons (cf. Coulson(22)) is in a similar steric position relative to the a-protons as is the C-X dipole moment relative to the &protons (where X is the substituent) and that these dipole moments or electric charges are mainly responsible for the interaction with the above mentioned solvents. As is to be expected, the dielectric medium effect seems to be relatively unimportant for these protons. As has been discussed several times, a method which has proven valuable in infrared solvent studies is that of Bellamy, Hallam and Williams (BHW),(s) in which the relative frequency shifts of different solutes are directly compared with one another in the same series of solvents (BHW plot; cf. Hallam@@). Such linear BHW plots are also well suited for NMR studies of solventinduced chemical shifts. They have two significant features, firstly, each has a characteristic slope indicating a more intensive or a less intensive interaction of the solute with the solvent molecules, and secondly, no discontinuity is found upon the transition from non-polar to highly polar solvents, provided protons in sufficiently similar molecular environments are compared with one another. Excellent examples are given by each of the categories of compounds (columns) of Table 16, with the exception perhaps of the a-protons in alcohols. If the observed relative chemical shifts, ,$, of the methyl protons in any of the compounds listed at the head of a column are plotted against the relative shifts of another compound in the same column a straight line results, in general with a slope different from 45”. A BHW plot of the relative chemical shifts, A&, of the methyl protons in a-positions relative to a carbonyl group shows a good correlation (see Table 14). The correlation of the methyl with the methylene proton shifts is less satisfactory. A BHW plot of the metbylene proton shifts in ethyl cyanide versus those of the methyne proton in iso-propyl cyanide exhibits an excellent correlation. The same plot of the equivalent chloro derivatives shows a satisfactory correlation. BHW plots of the relative shifts of all protons in a-positions relative to a hydroxyl group are satisfactory. These examples demonstrate that BHW plots are useful not only in infrared but also in NMR solvent shift studies. This rudimentary discussion of solute-solvent interactions was intended to indicate some paths along which, perhaps, a clearer understanding of these interactions, so important for chemical shift calculations, may ultimately be acquired.

CAUSE AND

CALCULATION

OF PROTON

CHEMICAL

SHIFTS

255

ACKNOWLEDGEMENT

This report is mainly based on investigations carried out in CIBA Ltd. Basel. The author is indebted to Mr. A. Borer, Dr. B. Somers and Dr. F. Stuber for their able and kind assistance.

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CAUSE

AND

CALCULATION

OF PROTON

CHEMICAL

SHIFTS

257

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