Nuclear quadrupole resonance of organic compounds

Tetrahedron, 1963, Vol. 19 Suppl. 2, pp. 123-141. P e r g a m o n Press Ltd. Printed in Great Britain

NUCLEAR QUADRUPOLE RESONANCE OF ORGANIC COMPOUNDS E. A. C. LUCKEN Cyanamid European Research Institute, Cologny-Gen6ve,Switzerland

(Received 13 December1961) Abstract The factors contributing to the field-gradients observed in covalent molecules by nuclear quadrupole resonance are discussed and the limitations of the method in yieldingsignificantinformation about chemical bonding are stressed. A number of the results obtained for organic compounds are critically surveyed. NUCLEARquadrupole resonance spectra 1 arise from the interaction between a nuclear electrostatic quadrupole moment, Q, and the electrostatic field-gradients, (a 2v)/(axi Oxj), produced by the surrounding electrons. It can be shown theoretically that only nuclei having a spin of greater than or equal to unity can have a quadrupole moment so that the principal nuclei of interest to the organic chemist are 14N ( / = 1), 35C1 (I = 3/2), 37C1 (I = 3/2), 79Br (I = 3/2), 81Br (I = 3/2) and 127i (I = 5/2). The deuteron, having a spin of one, is potentially the most interesting of all: the quadrupole moment is, however, so low that pure quadrupole resonance spectra of deuterium compounds have never been observed, although the deuterium quadrupole coupling constant has been measured for a few simple molecules where it gives rise to a hyperfine structure of the pure rotational spectrum. Measurement of a pure quadrupole resonance spectrum can, in principle, yield two parameters derived from the quadrupole moment and the field-gradient. These are the coupling constant,

e2Q[O2v~ \ azZ/ where z is the axis of maximum field-gradient, and the asymmetry parameter

\ az2 / For nuclei of spin 3/2 however the single resonance frequency o f a polycrystalline sample is given by

eZ-Q[a2V~[+ l!~Oz ~-3]2/l22] 1 For a discussion of the theory of nuclear quadrupole interaction see (a) C. H. Townes and A. L. Schlawlow, Microwave Spectroscopy, McGraw-Hill, New York (1955). (b) T. P. Das and E. L. Hahn, Nuclear QuadrupoleResonance Spectroscopy, 1st supplement, Solid State Physics, Academic Press, New York (1958). (c) N. F. Ramsey, NuclearMoments, John Wiley,New York (1953). 123

124

E.A.C. LUCKEN

so that the field-gradient and the asymmetry parameter are not known separately. 7/can however be obtained by observing the Zeeman effect on the pure quadrupole spectrum of a monocrystalline sample, where a small magnetic field splits the quadrupole lines by an amount depending on the field-strength and its orientation with respect to the field-gradient axes. Since this is rather a long and tedious procedure, many of the measurements of the spectra of nuclei with I = 3/2 have only been made on polycrystalline samples and this must be borne in mind when such frequencies are interpreted. In the text which follows, the distinction will be drawn between pure quadrupole resonance frequencies of polycrystalline solids and the quadrupole coupling constants of gaseous molecules or monocrystalline solids. It is apparent that the parameters of interest to the chemist are the field-gradient

02____~( Oz2 =q~) and the asymmetry parameter. The first of these can only be obtained absolutely from the coupling constant if the nuclear quadrupole moment is known. Unfortunately, the nuclear quadrupole moment only manifests itself by interaction with its electronic field-gradient, so it can never be measured separately. The most that can be hoped for is to measure the nuclear quadrupole interaction when the nucleus is in a particularly simple environment, e.g. as a gaseous atom or ion, when consequently it may be possible to calculate the electronic field-gradient from first principles, or at least to have an experimental measure of the field-gradient produced by a known simple atomic configuration. If for any reason this should prove unsatisfactory or even impossible (for example the electronic ground-state of atomic nitrogen is as having spherical symmetry), then it will only be possible to measure relative field-gradients. An electronic wave-function, W, produces an electrostatic field-gradient at the nucleus, qzz, given by the expression

qzz =

f

}p(3 cos20 z3

1) 7t. d~.

(1)

--o0

where 0 is the angle between the electronic volume element, dr, and the z-axis, and r is its distance from the nucleus. The interpretation of nuclear quadrupole coupling constants thus lies in going from an experimentally observed field-gradient to a suitable wave-function, W. Before proceeding to a discussion of the field-gradients observed in molecules, it is appropriate to discuss those observed in gaseous atoms or ions. Electrons in closed shells have an overall spherical symmetry, so that they produce no field-gradient, which thus arises only from the valency electrons. For a single valency electron moving in a central field it can be shown that qntm =

2,e 21+ 3

av

where lis the orbital angular momentum and (1/r3)av is the average inverse third power of the distance between the nucleus and the electron. Although it is, in principle, possible to calculate (1/r3)av, radial atomic wave-functions are so poorly known that the

Nuclear quadrupole resonance of organic compounds

125

calculated field-gradient would not be very accurate. Fortunately, a number of other spectroscopically determined quantities depend on this number, which may be thus eliminated, so that, at least for the lighter elements, the field-gradient may be calculated very accurately. Although eqn. (1), combined with an experimental determination of (1/r3)av, provides a fairly exact means of calculating the field-gradient for an electron moving in a central field, a close inspection of the situation in an actual atom reveals a nigger in the woodpile. The error lies in the assumption that the inner-shell electrons contribute nothing to the field-gradient. Sternheimer 2 has shown that there are two mechanisms by which the inner electrons contribute to the field-gradient. In the first place, the inner-shell electrons are repelled by the valency electron, so that they produce a fieldgradient opposite in sign to that of the valency electron, and secondly, the non-spherical nucleus polarizes the electrons near it--and it is these which contribute most to 1/r3avand destroys their spherical symmetry. These phenomena are illustrated in Figs. la and lb. The net effect is to alter the field-gradient f r o m q n l m to q,l,,, (1 - R ) , where R is a shielding or anti-shielding factor. s j

iI

I

I I I

| ! I

| t

I I %

(o)

•

(b} FIG. 1.

Sternheimer 2 has calculated this quantity for a number of cases and has shown that, for the lighter atoms in their ground-states, R is positive and of the order of 0-1. For heavier atoms and atoms in excited states, R becomes negative and very large, e.g. for Rb + and CS + it is - 7 0 . 7 and - 1 4 3 . 5 respectively. For electrons in molecules the calculations appear to be prohibitively complex, for here not even the unperturbed wave-function of the inner shell is known with much accuracy. At first sight, this would appear to at once preclude any reasonably accurate interpretation of coupling constants in molecules. This catastrophe is however largely averted, as far as organic chemistry is concerned, by the fact that one is mainly comparing two not too dissimilar molecules. The Sternheimer shielding effect must however always be borne in mind when the coupling constants of different nuclei are compared or when the same nucleus is looked at in widely differing environments. A final remark must be made to complete the gloomy picture of the possibility of interpreting quadrupole coupling constants in any significant manner. The majority of nuclear quadrupole resonance data are naturally derived from pure quadrupole resonance where the sample is a crystalline solid. In these circumstances, the neighbouring molecules change the electron distribution by an unknown amount from what it z R. M. Sternheimer, Phys. Rev. 84, 244 (1951); 86, 316 (1952); 95, 736 (1954).

126

E . A . C . Lucrd~rq

would be in the isolated state. There are a n u m b e r o f ways in which we can get an idea o f the order o f magnitude o f this effect. Thus a few coupling constants have been measured by both methods and a selection o f these is given in Table 1. TABLE 1. T H E COUPLING CONSTANTS OF MOLECULES IN THE GASEOUS AND SOLID STATES a

Molecule

Nucleus

Gas-phase coupling constant (%)

CH2C12 CH2~CHC1 CH3C1 CF3C1 CH3Br CF3Br CH3I CF3I

35C1" 35C1" 35C1" 35C1" 74Br* 79Br* 1271 1271 .f35C1 L14N f81Br* L14N f127I L 14N f127I L 35C1

78"0 72 74"74 78"05 577.15 619 1929 2143.9 f83.33 L 3.63 f573 L 3.85 f2420 L 3.80 ~'2930 L 82.5

C1CN BrCN ICN

IC1

Solid-state coupling constant (v~)

72"47 67-2 68"4 77"58 529 604 1766 2069 ;83-472 L 3.219 ~'598 L 3.37 f2549 L 3-40 ~'3037 L 74.4

A (v~- vg)

-

4-5 4"8 6-3 0"47 - 48 - 15 - 163 - 75 f +0-14 L - 0.41 ;+25 L -0-48 f + 129 L -0.4 ~"+ 107 L -8.1

-A- × 100 % (~)

- 5"8 - 6-7 - 8"4 - 0"6 - 8-3 - 2-4 - 8.4 - 3.5 f +0.2 L - 11.3 f +4"4 L-12"5 f + 5.3 L - 10.5 f + 3.6 L-9"8

a For nuclei which are starred, the solid-state coupling constant has been assumed to be twice the observed frequency.

The trend is for lower frequencies to be f o u n d in the solid state, and indeed it would seem that, where higher frequencies occur, these are due to specific intramolecular chemical bonds being formed in the solid state. The halogen cyanides have been exceptionally well studied in this respect. 3 A further aspect o f the same p h e n o m e n o n is the multiple resonances usually observed for molecules in which only one chemically distinct nucleus is present. These arise f r o m nuclei in crystallographically inequivalent sites. A few examples are shown in Table 2. The frequency-spread o f the last three c o m p o u n d s shown is typical o f th at caused by non-specific crystalline interactions. In chloral hydrate, 4 one frequency is significantly lower than the other two, and it is reasonable to look for a "chemical" explanation. The crystal-structure determination o f this c o m p o u n d 5 shows three different C - - C 1 distances, 1.79, 1.78 and 1.72 A, which m a y be due to h y d r o g e n - b o n d f o r m a t i o n ; it is 3 p. A. Casabella and P. J. Bray, J. Chem. Phys. 28, 1182 (1958). 4 H. C. Allen, Jr., 3. Phys. Chem. 57, 501 (1953). 5 S. Kondo and I. Nitta, X-Rays 6, 53 (1950).

Nuclear quadrupole resonance of organic compounds

127

TABLE 2. MULTIPLE NUCLEAR QUADRUPOLE RESONANCE FREQUENCIES PRODUCED BY CRYSTALLOGRAPHICALLY INEQUIVALENT SITES

Frequency (Mc/sec)

Compound

CC13CH(OH)2 CC14

15 resonances in the range

~37"513 438 "699 L38"781 40.465-40.817

CC13COOH I/~--CI

\j-Cl

~39"967 -]40"165 L40"240 r 35.824 435.755

L35.580

reasonable to suppose that the shorter bond-length corresponds to the chlorine atom having the lowest frequency. Finally, the average field-gradient seen by the nucleus depends on the amplitude of the thermal vibrations of the crystal, so that the nuclear quadrupole resonance frequency is temperature-dependent, increasing with decreasing temperatures. The majority of measurements are made at the boiling point of liquid nitrogen, 77°K, where they are between 0.5 and 1.0 Mc/sec higher than at room temperature. These crystal vibrations moreover modulate the field-gradient and so decrease the lifetime of a quadrupole state that the lines are so broad that at least half the time they are impossible to detect. At first sight, therefore, it would appear foolhardy to even attempt anything but the most qualitative and self-evident interpretation of nuclear quadrupole resonance frequencies. Surprisingly, however, it does not appear to be possible to detect quite subtle differences in bonding with this technique. Nevertheless, its limitations must always be kept in mind and small differences in nuclear quadrupole resonance frequencies between two molecules must not be invested with too great a significance. It is always wise to study a series of closely related compounds in order to obtain an averaging of the crystallographic effects. The isotope which has been studied to the greatest extent is 35CI, having a spin of 3/2, and this suffers from the difficulty in obtaining separate measures of e2 Qq and ~7mentioned above. It is however essential that both these parameters be known for a variety of selected compounds and a programme of Zeeman splitting measurements of monocrystals is under way in the author's laboratory. The analysis of the nuclear quadrupole resonance frequencies in molecules which follows is derived from that originally given by Townes and Dailey. 6 It assumes that the non-valency electrons have spherical symmetry and that the field-gradient at the nucleus arises only from the valency electrons. This is not the limitation which the previous discussion would perhaps imply, since it depends largely on an empirical 6 C. H. Townes and B. P. Dailey, J. Chem. Phys. 17, 782 (1949).

128

E . A . C . LUCKEN

evaluation of various integrals, so that, to some extent, the Sternheimer shielding is allowed for. The derivation is given for the z-component of the field-gradient, but it is exactly similar for the other components. We first make the usual simplification that the field-gradient is given by a sum of independent one-electron terms qz = ~ (qz)~ r

where the sum is taken over the " m " valency electrons. Then, from eqn. (1)

(q~), = f 7t, Hz 7j-dr where ~/t is the wave-function describing the motion of the rth electron. We then make the usual molecular orbital approximation

Eaj j where ~j is an atomic valence orbital. This may be re-expressed as 7tr = ~] aj q~ + Z ag ~ j

(2)

k

where,~b; is an atomic orbital of the nucleus at which the quadrupole interaction is being investigated and ~ is an atomic orbital of any other atom in the molecule. Then, by substitution of eqn. (2) in eqn (1), we obtain (qz)r =

~# f ~Hz#dr+

+ZZ j k

ESaja, f

ajakf ~]Hz~d~

(3)

The lastterm represents gradients produced by "overlap" distributions lying between A and another atom B. These can certainlybe neglected when A and B are not bound to each other, and there is perhaps some justification for neglecting them even when A and B are nearest neighbours. The third and fourth terms represent gradients produced by charges on or between atoms neither of which has the quadrupolar nucleus under investigation. It is certainly reasonable to neglect these, except perhaps when the gradient arises from a charge on the nearest-neighbour nucleus. The gradients of the second term arise from overlap between atomic orbitals of the same quadrupolar nucleus. Since these are assumed to be spherical harmonics, they are identically zero unless the difference in the orbital quantum numbers of ~i and ~j is equal to two. If only s- and p-orbitals are considered, the second term is identically zero, if d-orbitals are also postulated, the s-d integral has a small finite value which is usually in fact neglected. The Townes and Dailey approximation consists then in neglecting all terms except the first one which will be seen to be just the weighted sum of the field-gradients produced by the atomic orbitals. That this is, in fact, a reasonable approximation can be seen by a simple calculation of the field-gradient produced by a point charge of, say,

Nuclear quadrupole resonance of organic compounds

129

0"5 electrons 2 A from the nucleus. Most of the integrals we have neglected in eqn. (3) will have a value of less than this, 3 × 1013 e.s.u., whereas an electron in a chlorinep-orbital produces a gradient of the order of 1016 e.s.u. A neglect of these terms could, however, produce very significant errors in the analysis of deuterium coupling constants~, where the orbital field-gradients are much lower. Since s-orbitals produce no fieldgradient and that of a d-orbital is less than 10 ~o of that of a p-orbital, the Townes and Dailey equation is usually written •

.

j

= Z aZ[P~[z+ Y~ a2lPy[z+ Za~,[Pzlz

(4)

i

Let us now examine a simple molecule, C12, with the aid of the Townes and Dailey equation. The resonant frequency of solid C12 at 20°Kis 54.475 Mc/sec and, neglecting solid state effects and assuming axial symmetry for the bond, this gives a coupling constant of 108.95. The coupling constant of atomic chlorine is 109.6 Mc/sec and, since we know that the ground-state configuration of C1 is sZp 5, from eqn. (3) we may at once express this as 109.6 = 2]pxlz+2]pylz+ IPz[~ From the symmetry properties ofp-orbitals [Pxlz = [Py[~ = - l l p z ] z

(5)

[P~[z = - 109.6

(6)

so that This illustrates the way in which field-gradient integrals may be solved empirically. For a chlorine-like atom forming a pure single-bond using only s- and p-orbitals, we obtain, by rearrangement of eqn. (4) and inserting the value of the integrals obtained from eqns. (5) and (6) c2 Qq = - 4 ( 1 - a 2 ) . 109.6 1 e 2 Qq

i.e.

a 2 = 1 - ~ (1-~.6)

From the observed coupling constant then a 2'~ 0"5. If it is assumed that the bond has been formed using pure p-orbitals, i.e. ~C1,

=

a(pl+P2)

from simple molecular orbital theory a2

1 2(1 + Saa)

where Saa is the overlap integral between two chlorine p-orbitals and from Mulliken's table 7 has the value 0.34. Thus a 2 would be 0.36. If we wish to achieve agreement with experiment, we must postulate 30 ~ s-hybridization, which seems so high that various arguments have been proposed for assuming that Sa~ should be set equal, or nearly equal, 7 R. S. Mulliken, J. Amer. Chem. Soc. 72, 4493 (1950).

130

E.A.C. LUCKEN

to zero, which would then reconcile theory and experiment with little or no hybridization. For example, it has been suggested that, in fact, the re-normalization procedure resulting from the introduction of a finite value of Saa affects only the outer part of the atomic orbital, whereas the main part of the field-gradient arises from a largely undisturbed orbital lying close to the nucleus. This appears to the author to be a classic example of "double think". It certainly seems clear, however, that a much more reasonable interpretation of nuclear quadrupole resonance frequencies is obtained if Saa is set equal to zero and we must now consider why this should be so. It seems to the author that the trouble lies in the fact that we are happily using oneelectron orbitals to calculate electron distributions, while these are known to be unsatisfactory even for energy calculations. One-electron orbitals are bound to exaggerate peaks and valleys in electron distribution, inclusion of electron repulsion would smooth it out considerably. Indeed, it is significant in this respect that, if the Heitler-London description of the bond is used in the chlorine molecules--and this approximation is known to underestimate charge separation--then only 12 ~ s-hybridization is sufficient to reconcile theory and experiment. A simple model shows that electron-repulsion will redistribute the charge in the desired way so as to make the effective overlap integral close to zero. Thus consider a molecule formed by pure p-orbitals with overlap integral unity. The molecular orbital then has two nodes and is illustrated in Fig. 2. The total electron density in each of the three regions is also indicated.

FIG. 2.

If we now assume that the second electron goes into this orbital in such a way as to get as far away as possible from the first electron, the average instantaneous electrondistributions will be as shown in Fig. 3.

4

(3C(3 EEE)

2

FIG. 3.

Nuclear quadrupole resonance of organic compounds

131

The overall electron distribution is then that shown in Fig. 4, which, in fact, corresponds to an effective overlap integral of minus one third !

FIG. 4.

It goes without saying that a simple model of this sort greatly overestimates electronrepulsion effects. Nevertheless, in the author's opinion, it goes a long way towards justifying the neglect of overlap in these calculations and indeed any others which have electron distributions in mind. Without further ado then, we may now state the general form of the Townes and Dailey equation for the one of the cases of most interest to us, namely the gradient at a nucleus forming a pure single-bond with s-, p- and possibly d-orbitals in which it is the most electronegative partner, eZQqm°lecular =__p = ( 1 - s + d ) ( 1 - i )

(7)

e2 Qqatomic where s is the fractional s-character of the bonding orbital, d is the fractional d-character of the bonding orbital, i is the fractional ionic character of the bond. The derivation is quite straightforward from eqn. (4). It is at once evident that we are in the usual position of having more parameters than experimental data, even with the simplifications we have so far made. It is obvious that any absolute calculations of electron-density must be viewed with the greatest suspicion, but fortunately we will probably be fairly happy if we can interpret changes in field-gradient. As a starting point, it is reasonable to assume that the extent of s- and d-hybridization is governed mainly by overlap considerations so that, for a bond formed with an sp 3hybridized carbon atom, the factor ( s - d ) remains constant. We must, however, be prepared for it to change abruptly when we form the bond with an sp 2- or sp-hybridized carbon atom. It could perhaps be argued that the hybridization will change with the ionic character of the bond when the bond is formed between the same two atoms. However, it would be difficult to allow for this in any but the simplest of molecules and it seems more reasonable to ascribe all changes which occur when the two atoms remain in the same basic state to changes in ionic character, i.e. to inductive effects. The effects of hybridization and ionic character on the reactivity of, say, a halogen atom are in any case likely to be similar. At this stage, it would be as well to have recourse to experiment and see whether the theory gives reasonable results in this simplest of all cases. Consider methyl chloride. From the foregoing discussion it would be expected that progressive substitution of the hydrogen atoms by an electron-withdrawing group would produce an approximately linear increase in coupling constant, while the substitution with an electron-releasing group would produce a corresponding decrease. The coupling constants for chlorine and methyl substituents are shown in Fig. 5. These, and indeed those of a variety of substituted alkyl halides, are in good accord with the theory.

132

E . A . C . LUCKEN 42

f

40

f

38 ~ 36 g ~ 0 Z d

~

f

CCL4 CHCL

CH~CLz

34

~cL 32

~(CH#3CCL 30 I

I

I

Compostion,(arbitrary units) FIG. 5.

The frequencies of fluoro- or methoxy-substituted methyl chlorides are however anomalous in that these, at first sight electron-withdrawing, substituents lower the 35C1 coupling constant (Table 3) when substituted for chlorine. TABLE 3. ANOMALOUS EFFECT OF FLUORO AND METHOXY SUBSTITUENTS ON 35C1 RESONANCES

Compound

Frequency (Mc/sec)

CH2C12 FCH2C1 CH3OCH2C1

35"99 33"7 30"18

The effect is well-established, particularly for fluoro derivatives# We must now choose between two alternatives; either we abandon nuclear quadrupole resonance as a means of providing useful information about chemical bonding, or we accept that these frequencies have a "chemical" significance and that we must revise our idea that a fluoro or methoxy substituent in this environment behaves as a simple electronwithdrawing group. Since the choice is between standing still and at least attempting to go forward, we choose the latter, but with the mental reservation that, if the results are too ridiculous, we must reconsider abandoning nuclear quadrupole resonance. The most notable thing that the groups M e O - and F - have in common is that they are both members of the first short period and have unpaired electrons. As such, they can efficiently conjugate with a pi-electron system and this property is usually invoked to explain their effect on the dissociation constants of aromatic carboxylic acids. The 8 E. A. C. Lucken, J. Chem. Soc. 2954 (1959).

Nuclear quadrupole resonance of organic compounds

133

author has suggested that an analogous hyperconjugative effect could explain the results here, i.e. in resonance terms that there are contributions from the structure F~H 2

ClO

A simple molecular orbital calculation has shown that quite a small amount of interaction would explain the observed results. The overlap integral between the fluorine lone-pair orbital and the carbon-chlorine bond has been calculated from the Tables of Mulliken et aL 9 to be 0.10 so that the suggestion does not seem to be unreasonable. The reactivity of the ~-chloro ethers is usually explained bypostulatingan SNI pre-ionization facilitated by resonance stabilization of the CHaO+=CH2 cation; the present hypothesis would explain why the rate of ionization is so great in these compounds. The fluorine and methoxy anomaly does not then seem to be too serious; nevertheless we must continue to build up our confidence in nuclear quadrupole resonance by measurements on compounds in which the effects of the various substituents can be fairly clearly anticipated. A very valuable series of measurements of this sort was that undertaken by Bray and Barnes I0 where the correlation between the 35C1nuclear quadrupole resonance frequencies of over fifty substituted chlorobenzenes and the corresponding Hammet sigma-constants were investigated. The relationship f = 1"024cr+ 34"826 Mc/sec was obtained by a least-squares analysis of the data and the standard deviation of frequencies predicted by this equation is 0.36 Mc/sec, i.e. approximately 7 ~ of the range observed in these compounds. A similar correlation has been made for bromo, iodo and chloromethyl compounds, but the data are not here quite so extensive. When a halogen atom is adjacent to a double-bond, the lone-pair electrons can, in theory, interact with the pi-orbitals to give the carbon-chlorine link and partial doublebond character. In these circumstances, eqn. (7) is considerably modified by the introduction of an additional parameter to describe this double-bonding which, however, destroys the cylindrical symmetry of the field-gradient tensor so that, at least in principle, an additional piece of information, ~], is made available by the nuclear quadrupole resonance measurement. We may illustrate these remarks by reference to vinyl chloride where, for once, the quadrupole coupling data are available from measurements of microwave spectra 11 and have the values e 2 Qq = 72 Mc/sec, r / = 0.14. A simple extension of eqn. (4), due to Bersohn, 12 relates the double-bond character of a carbon-halogen bond, p, to the asymmetry parameter by the relationship 2 e 2 Qqmolecular

P = 3 e 2 Qqatomic

"~

Thus the carbon-chlorine bond in vinyl chloride has approximately 6 ~ pi-character, a figure which is in agreement with approximate molecular orbital calculations. It is perhaps worth stressing that it is likely that the observed asymmetry parameter does arise from a real transfer of charge from the chlorine atom. Polarization of the outer parts of the lone-pair electron-lobes by the acylindrical charge distribution around the 9 R. S. Mulliken, C. A. Rieke, D. Orloffand H. Orloff, J. Chem. Phys. 17, 1248 (1949). 10 p. j. Bray and R. G. Barnes, J. Chem. Phys. 27, 551 (1957). 11 j. H. Goldstein, J. Chem. Phys. 24, 106 (1956). 12 R. Bersohn, J. Chem. Phys. 22, 2078 (1954).

134

E.A.C. LUCKEN

carbon atom would not produce very much effect on r/because of the 1/ra-dependence of the field-gradient on charge density. From the coupling constant and asymmetry parameter we may calculate the total pz-electron density at the chlorine atom in vinyl chloride as 1.296, corresponding to a frequency for an axially symmetric bond with unshared electron-pairs of 77.1 Mc/sec. Although the gas-phase data for ethyl chloride are not available, we can estimate the coupling constant by multiplying the solid-state value by 1.09 to obtain 71.9 Mc/sec. Thus the effect of the change of hybridization has been to decrease the pz-electron density and this could have arisen in two ways, (i) the ionicity of the bond has decreased, i.e. sp2-carbon is more electronegative than spa-carbon; (ii) the degree of s-hybridization of the chlorine-bonding orbital has decreased. It has been suggested on a number of occasions that the electronegativity o f carbon in its three possible hybridized states varies in the sense s p > s p 2 > s p a. As far as nuclear quadrupole resonance is concerned, this sequence is well illustrated by the data in Table 4, where there are no complications due to conjugation. TABLE4. 35C1NUCLEARQUADRUPOLERESONANCE FREQUENCIESAT 77°K (illustrating the variation of the electronegativity of carbon with its degree of hybridization)

Compound

Frequency (Mc/sec)

CHaCH2CH2C1 CH2~CHCH2C1 CH~CCH2C1

32.968 33.455 34.812

When the carbon atom directly attached to the chlorine changes its hybridization, the effect will be larger than when a C H 2 group separates the two atoms. We might guess the frequency change to be as much as four times as great. The uncertainty in this and in the gas-phase frequencies of ethyl chloride, n-propyl chloride and allyl chloride makes it just conceivable that the higher pz-electron density in vinyl chloride is solely due to the change in electronegativity. There is, however, room for a d e c r e a s e in s-hybridization which would similarly increase the p-electron density, but it does not seem likely that the observed coupling constant is the result of two opposing effects. Thus, if we accept that an sp2-carbon atom is more electronegative than an spa one, then, if there is any change in the hybridization of the chlorine atom, it must be in the sense of decreasing s-character. Further comment on this point must await the result of more detailed calculations which, I understand, are being carried out by Jaff6 and Whitehead. 13 We have so far been more or less implicitly concerned with monovalent quadrupolar nuclei, i.e. the halogens. It is in fact for these, particularly chlorine, that the great majority of experimental data is available. A detailed discussion of nitrogen resonances will therefore be deferred to the end of this article, and some results for the halogens will now be discussed in a more qualitative way. la M. A. Whitehead. Private Communication.

135

Nuclear quadrupole resonance of organic compounds

A useful way of looking at the measurement of halogen resonances is to consider the halogen a t o m as a probe inserted in the molecule and to compare the response to the probe in a reference molecule with the response of the molecule under investigation. We have really progressed about as far as we can with a priori interpretations of halogen resonances, so henceforward the results will be discussed from the viewpoint just outlined. Thus, in Table 5, are shown a selection of pure quadrupole frequencies for molecules of the type RCHzC1 which demonstrate the effective electronegativities of various substituents. They will be seen to be, at least qualitatively, those expected on general chemical grounds. TABLE 5, 35CI NUCLEAR QUADRUPOLE RESONANCE FREQUENCIES AT 77°K OF COMPOUNDS OF THE TYPE R.CH2C1 DEMONSTRATING INDUCTIVE EFFECTS

R CH3_ CH3SHC1CH2NH2COCH3COC2H5OCOC1-

Frequency (Mc/sec) f32.649 1.32.759 33.104 34"029 34-361 34.882 f35.071 L35.485 35-962 35"991

The chlorinated nitrogenous heterocycles have been extensively investigated and a selection of frequencies is given in Table 6. TABLE 6.

35C1 NUCLEAR QUADRUPOLE RESONANCE FREQUENCIES AT OF CHLORINATED NITROGENOUS HETEROCYCLESa

Frequency (Mc/sec)

Compound Chlorobenzene 2-Chloropyridine 3-Chloropyridine 4-Chloropyridine 2-Chloroquinoline 6-Chloroquinoline 7-Chloroquinoline 4,6-Dichloropyrimidine 2,4,6-Trichloropyrimidine 2,4,5,6-Tetrachloropyrimidine

77°K

{ {

34"60 34"17 35.24 34-89 33-29 34.60 34"68 35"426, 35.308, 35.132, 35.102 35.702, 36-166, 36-250 36.281, 36.560, 37"068, 38"020, 38-420

a Note the high. frequency (38"020, 38.420) of the chlorine at position 5 in the last compound where no conjugation with the nitrogen atom is possible.

136

E.A.C. LUCKEN

An adjacent nitrogen atom would be expected to withdraw electrons from the chlorine single'bond--and hence increase the nuclear quadrupole resonance frequency - - b u t at the same time to increase the conjugation of the chlorine atom with the ring w h e n the t w o atoms are ortho or p a r a t o each other, thus decreasingthe frequency. These effects are quite well illustrated by 2- and 3-chloropyridine. The frequency of 4-chloropyridine--in which the direct inductive effect will be negligible--does not show the expected decrease. This may imply some sort of bond-fixation in pyridine which prevents the transmission of electronic effect over long distances. This is to some extent borne out by chemical evidence in that pyridine appears to undergo nucleophilic substitutlon only in the 2-position. Another suggestion of bond-fixation is found in the frequency of 2-ehloroquinoline which is much lower than that of the analogous pyridine derivative. Both theory and experiment suggest that the order of the 1-2 bond in naphthalene is high and the same should be true of quinoline. Thus the conjugative interaction with the chlorine should be much higher in 2-chloroquinoline than in 2chloropyridine for the ~ N pi-bond order is much higher. This argument implies that in the analogous acid chlorides, where the

)c=o pi-bond order is approximately unity, the conjugation with the chlorine atom should be much higher. It is noteworthy that in these compounds tile nuclear quadrupole resonance frequency (29-30 Me/see) is much lower than in vinyl chloride, although the oxygen exerts a considerable inductive effect. Indeed, in this case we have direct evidence of carbon-chlorine double-bonding in that the asymmetry parameter in gaseous COC1214 is 0.25 (cf. vinyl chloride, ~7= 0.14). It is perhaps worth repeating that the majority of the data have been obtained for polycrystalline solids; there is therefore no direct evidence of C--CI bond asymmetry. This is true for all the nitrogen heterocycles shown in Table 6, however there are available single-crystal data for cyanuric chloride, is i.e. 2,4,6-trichloro-l,3,5-triazine, and here ~ = 0.24 compared with ~ = 0.10 for 1,3,5trichlorobenzene.a6 This figure is in excellent accord with that obtained by an analysis of a number of chloropyrimidine frequencies 17 which indicate an average carbonchlorine double-bond character of 10 ~. This survey illustrates the kind of information which can be obtained from halogen resonances and, I think, states clearly the very serious limitations which are imposed on a priori calculations based on nuclear quadrupole resonance measurements. In some ways, the asymmetry parameter is a more fundamentally interpretable quantity than the coupling constant itself, and it is to be hoped that many more halogen derivatives will have their asymmetry parameter measured. A recent paper by Morino and Toyama 18 rouses hope in this connection. There it was shown that asymmetry parameters could be measured for polycrystalline samples having not-too-small values of ~?, provided that a sufficiently sensitive spectrometer was available, since the envelope of the magnetically broadened nuclear quadrupole resonance-line has sharp maxima at positions + (1 + ~7)(7H)/2% where 7 is the nuclear gyromagnetic ratio and H is the a4 G. W. Robinson, J. Chem. Phys. 21, 1741 (1953). a5 F. J. Adrian, J. Chem. Phys. 29, 1381 (1958). 16y. Morino and M. Toyama, J. Phys. Soe. Japan 15, 288 (1960). 17p. j. Bray, S. Moscowitz, H. O. Hooper, R. G. Barnes and S. L. Segel,J. Chem. Phys. 28, 99 (1958). 18y. Morino and M. Toyama, J. Chem. Phys. 35, 1289 (1961).

Nuclear quadrupole resonance of organic compounds

137

field-strength. This may make it possible to measure ,/for substances which are liquids at room temperature and may be particularly useful for bromo derivatives where the resonances are usually much stronger than for chloro compounds. One of the greatest barriers to a fundamental interpretation of halogen nuclear quadrupole resonance frequencies is the apparent impossibility of separating s-character from ionicity. A recent note by Bloembergen 19 has indicated that there may be a way out of this difficulty by the observation of the effect of a large electrostatic potential gradient (104 V/cm) on the nuclear quadrupole resonancefrequency. Heretheelectrons around the nucleus are polarized by the electrostatic field and the field-gradient altered. Armstrong et al. 2° have shown that they must postulate at least 5 ~o s-character to explain their results for p-dichlorobenzene. Their results were obtained with a polycrystalline sample; single-crystal measurements would be more informative. It will be well worth while to have these data for a variety of types of molecule, and when these and more extensive asymmetry parameter measurements are available, nuclear quadrupole resonance measurements will begin to give the theoretician some quantitatively significant data to interpret. One of the most interesting quadrupolar nuclei for the organic chemist is 14N. Nitrogen resonances are unfortunately weak and difficult to detect so that not many measurements are, in fact, available. Moreover, since atomic nitrogen has a spherically symmetric 4S1 ground-state, it is impossible to measure the field-gradient produced by ap-electron directly, although it has been possible to estimate it indirectly. Nevertheless it has been shown, 21 mainly from a consideration of the 14N-asymmetry parameters observed in pyridine, 4-picoline and cyanuric chloride, that the sigma-bond electron density at the nitrogen atom in pyridine is greater than the pi-electron density by about 0.1 electrons, a rather surprising result. The asymmetry parameters for the three compounds mentioned are only consistent with the accepted electronic effects of a methyl and a chlorine substituent on this hypothesis. Nevertheless it should be stressed that these results are based on a formal analysis of the bonding in pyridine, assuming sp 2hybridization and also that the field-gradient produced by an electron in a pTr-orbital is the same in absolute magnitude as that produced by an electron in a per-orbital. Much more data on simple nitrogen heterocycles is essential, particularly those having an axis or plane of symmetry through the nitrogen atom where the analysis is considerably simplified. A programme of this sort is being attempted in the author's laboratory and it is hoped that it will soon be possible to decide on the significance of the results discussed above. Before leaving the subject completely, a last word must be said about deuterium resonance. Although no results for organic molecules are available, the deuterium coupling constants for HD, ND3 and D20 are known from microwave data. Since accurate wave-functions for H D are known, the quadrupole moment for the deuteron can be calculated exactly and hence the field-gradients in N D 3 and D20. The most accurate wave-functions for these molecules give quite inaccurate values of the fieldgradient so that here at least the theoretician is provided with food for thought. It should be emphasized that the deuteron does not suffer from Sternheimer effects, since there are no inner-shell electrons. It is unfortunately unlikely that pure deuterium 19N. Bloembergen,J. Chem. Phys. 35, 1131 (1961). 20 j. Armstrong, N. Bloembergen and D. Gill, J. Chem. Phys. 35, 1132 (1961). 21 E. A. C. Lucken, Trans. Faraday Soc. 57, 729 (1961). 10

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E . A . C . LUCKEN

r e s o n a n c e s will be o b s e r v e d , unless t h e r e is a v e r y significant i m p r o v e m e n t in t h e signal/ noise ratio of radiofrequency spectrometers. T o c o n c l u d e , it is h o p e d t h a t this d i s c u s s i o n has b r o u g h t o u t clearly t h e r e a l p a s t successes o f n u c l e a r q u a d r u p o l e r e s o n a n c e a n d i n d i c a t e d the d i r e c t i o n s in w h i c h it m u s t g o i f it is to s u r v i v e as a useful t e c h n i q u e . Its g r e a t a t t r a c t i o n is t h a t it is o n e o f t h e r a r e p h e n o m e n a w h i c h give precise i n f o r m a t i o n a b o u t e l e c t r o n d i s t r i b u t i o n at a welld e f i n e d p o i n t in a m o l e c u l e . T h e t a s k o f t h e t h e o r e t i c i a n is to s e p a r a t e t h e u s e f u l f r o m t h e trivial i n f o r m a t i o n a n d to i n d i c a t e to t h e e x p e r i m e n t a l i s t h o w this i n f o r m a t i o n m a y best be o b t a i n e d .

GENERAL

DISCUSSION

Comment by H. H. Jaffd As mentioned by Dr. Lucken, Dr. Whitehead and I have recently done some re-evaluation of N Q R data on halogens. These calculations are admittedly extremely crude, since they are based on a large number of arbitrary but necessary assumptions. They are made possible by our recent evaluation of electronegativity as a function of hybridization. 1 They are based on the basic formula of Townes and Daley, with all its shortcomings and in addition on the assumption, following Gordy, that ionic character is equal to one half the electronegativity difference. These assumptions permit expressing the N Q R frequency (really the ratio px of the molecular to the atomic frequency) in a halogen atom X in a diatomic molecule XY as a function of the hybridization of X. Application to such molecules as FC1 and HC1 has permitted to determine the hybridization in chlorine. 2 In contrast to the assumptions of Gordy (no hybridization) and of Townes and Daley (hybridization of the more negative dement), it is found that hybridization of the element with the higher lying valence orbital must occur. Such hybridization invariably leads to a better match of the energies of the orbitals forming the bond, in accord with Coulson's requirement of energy matching. In the cases of compounds of the heavier halogens, solution of the resulting equations is often impossible, or leads to too low hybridization, which we have interpreted as indicating evidence for involvement of C1 orbitals. Thus, the Townes-Daley equations predict thai the product PxPy~< 1, but this product 3 for BrC1 is larger than 1. Similar calculations were performed on the carbon tetrahalides, 4 again leading to an assessment of hybridization of the halogens (10 ~ in CCL, 17 ~ in CBr4, and 0 ~ in CI4); again in CI4, and possibly CBr4, some involvement of C1 orbitals is likely. Calculations for the tetrahalides of Si, Ge and Sn lead to much greater hybridizations, probably because of w-bonding involving the Cl-orbitals of the central atom was neglected. Maximumrr-bondordersoftheorderof0'3wereestimated. A treatment of the series CXnC14--n with X = H and F also leads to reasonable assessment of chlorine hybridization, varying smoothly from 19 ~ in F3CC1 to 4 ~o in I--[3CC1. The data have been interpreted to lend support to Lucken's suggestion of hyperconjugation of F and antibonding CC1 orbitals. Further refinements of these calculations are being made. In particular, a new definition of ionic character based on a new definition of electronegativity will be introduced, 5 and empiric estimation of group electronegativity will be replaced by theoretical calculation. 1 j. Hinze and H. H. Jaff6, J. Amer. Chem. Soc. 84, 540 (1962). 2 M. A. Whitehead and H. H. Jaff6, Trans. Faraday Soc. 57, 1854 (1961). M. A. Whitehead, J. Chem. Phys. (in press). 3 M. A. Whitehead and H. H. Jaff6, J. Chem. Phys. 34, 2204 (1961). 4 M. A. Whitehead and H. H. Jaff6 (in preparation). 5 j. Hinze, H. H. Jaff6 and M. A. Whitehead (in preparation).

Nuclear quadrupole resonance of organic compounds

139

Comment by A. Julg J'AI toujours 6t6 chagrin6 par le probl6me de la mol6cule Clz. En effet usuellement, comme le rappelle le Dr. Lucken, on rend compte de la valeur exp6rimentale pour la constante de couplage de C12 solide (108.95) en admettant que la liaison est assur6e par une hybride (3s, 3p), la valeur obtenue pour l'atome isol6 (109.6) correspondant h une orbitale (3p) pure. Or en g6n6ral les valeurs obtenues h l'6tat solide sont inf6rieures h celles obtenues en phase gazeuse, c'est-h-dire pour les mol6cules isol6es. Si bien que si l'on interpole les valeurs exp6rimentales obtenues pour C1F, C1Br, CII ~t l'6tat gazeux pour C1C1, on obtient une valeur de l'ordre de 116, c'est-a-dire bien sup6rieure ~t celle du chlore atomique. Cette interpolation parait raisonnable puisqu'~t 1'6tat solide les valeurs obtenues pour C1F, C1C1, C1Br, CII forme une suite r6guli&e. Que devient alors l'interpr6tation de la pr6tendue diminution de la constante ' de couplage ? L'hybridation entre les orbitales 3s et 3p ne peut expliquer cette 616vation. A mon avis, il faut comme je l'ai sugg6r6 d6j~tplusieurs fois en conclure que dans les mol6cules les orbitales atomiques entrant dans les liaisons cr sont d6form6es. Moyennant quoi, il est possible de rendre compte de la valeur exp6rimentale. Je dois bient6t publier le calcul.

Reply to comments f r o m A. Julg DR. JULG'S suggestion of a method for estimating the gas-phase coupling-constant of molecular chlorine is an excellent one and certainly produces an answer of the expected order of magnitude. It is however, in my opinion, possible to find a n " explanation" of this frequency within the framework of the present simple theory without having recourse to deformed orbitals. According to the LCAO description of the chemical bond if the chlorine atom uses an s-p hybrid in bond-formation,

7J¢1 = a3s + b3p, then it can be readily shown that, within the framework of the Townes-Dailey theory,

eQq = 110.4 ( l ~ s - 2 b Z ) , where S is the overlap integral S Wc~7JcBlbetween the two hybrid chlorine orbitals. If, however, we use the Heitler-London description of the bond, then it may be equally readily shown that b2 2

eQq= llO'4(l+Sa-2b ).

With an interatomic distance of 2-01/k and using the values of overlap integrals taken from the Tables of Mulliken et al. (J. Chem. Phys. 17, 1248, 1949), we obtain the two curves shown in the attached Figure for the two descriptions of the bond. With Professor Julg's estimate of 116 Mc/sec this leads to an s-hybridization in molecular chlorine of 9 ~ or 21 ~ by the Heitler-London and LCAO methods respectively. Thus we have two very different answers corresponding to the two simplest ways of describing a chemical bond. In addition to this, the Sternheimer shielding constant will probably be slightly different for atomic chlorine and molecular chlorine, and we may also reasonably suppose that the bonds have a small amount of d-character,

11Jcl = a3s + b3p + e3d. In the LCAO approximation therefore the frequency of molecular chlorine will be given by

/

-}-Rmolecular/

]

where R is the Sternheimer shielding constant. There is a corresponding equation for the Heitler-London method with S 2 replacing S. We thus have to choose (i) which description we use for the chemical bond; (ii) values for two of the three parameters in the above equation in order to calculate a third.

140

E . A . C . LUCKEN

It is for these reasons that I do not think apriori calculations on such a complex molecule as C12 are worth while at present. When one is dealing with frequency differences between two fairly similar molecules, then most of the above difficulties disappear. Nevertheless I repeat that I think Professor Julg's estimate of the coupling constant of C12 to be correct, but that I would hesitate to make any very significant deductions from it.

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C o m m e n t by D. Peters THE author's interesting conclusion that the crcharge per hybrid AO at the N atom in pyridine is greater than the z, charge in the rrz AO is perhaps not so surprising. Even more unexpected results have been obtained from some SCF LCAOMO calculations on the linear molecules HCN and CzN2. These computations, carried out at the University of Chicago by R. S. Mulliken and C. C. J. Roothaan and their colleagues, are very much more detailed than any previous ~relectron calculation since all electrons

N u c l e a r q u a d r u p o l e r e s o n a n c e o f organic c o m p o u n d s

141

are included a n d all integrals accurately evaluated. Nevertheless, even these wave f u n c t i o n s are still s o m e w a y away f r o m t h e molecular H a r t r e e - F o c k calculations, so t h a t the conclusions m u s t be accepted with caution. T h e unexpected feature o f these results is t h e atomic charges, particularly t h e division o f these between t h e a a n d ~r electrons. I n b o t h H C N a n d C2N2, t h e N a t o m s are negative, the N a t o m in t h e molecule being p o p u l a t e d by m o r e electrons t h a n is the free N a t o m in its g r o u n d state. This negative charge, however, c o m e s f r o m the c~electrons, n o t f r o m the 7r electrons. T h e 7r charge is, in fact,positive so t h a t there are fewer 7r electrons o n t h e N a t o m in t h e molecule t h a n in the free a t o m in its g r o u n d state. T h e ~ charge is negative a n d numerically larger t h a n t h e 7r charge, so t h e N a t o m is overall negative, b u t towards t h e ~r electrons in b o t h H C N a n d C2N2, t h e N a t o m is electropositive c o m p a r e d with the c a r b o n atoms. This suggests that if we are to carry o u t a 7r-electron c o m p u t a t i o n which really does refer to the 7r electrons only, we should m a k e the N a t o m less electron attracting t h a n the c a r b o n atoms. W h e n we c o m p a r e the results with experimental quantities, however, we m u s t allow for t h e electron effects in order to get the N a t o m overall negative. Details o f these results will be given by Clementi a n d E. Clementi in a f o r t h c o m i n g p a p e r in J.

Chem. Phys.