Nonequivalence of Protons and Related Phenomena in Some

Chem. , 1966, 70 (7), pp 2249–2256. DOI: 10.1021/j100879a028. Publication Date: July 1966. ACS Legacy Archive. Cite this:J. Phys. Chem. 70, 7, 2249-...
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PROTON NONEQUIVALENCE IN ORGANONITROGEN AND -PHOSPHORUS COMPOUNDS

the acids show only one band in the region of interest. It is reasonable to believe that it is a composite of both bands since the hypsochromic shift for I from ethyl or methyl alcohol tjo the acids is reflected in the spectra of V. The hydrogen bond conceived to be responsible is between the solvent acidic hydrogen and the imine nitrogen. It is believed that the hydrogen bonding provides a basis for hydrogen transfer to the imine nitrogen. Also, it was found that the formation of the additional long wavelength band with solvent was a reversible process. The strength of the intramolecular hydrogen bond between the o-hydroxy group of N-(o-hydroxybenzy1idene)aniline and the imine nitrogen16 is evidently not sufficient to initiate tautomerism in the first group of solvents. The possibility of an intramolecular hydrogen transfer with this compound in other solvents is being studied further.

2249

Two other facts are immediately evident besides the hydrogen bonding. They are that the tautomerism increases with the acidity and the dielectric constant of the solvent. The aforementioned azo-hydrazone tautomerism also increases with solvent polarity. l 1 The largest factor, however, seems to be the acidity. It is then proposed that the stability of the quinoid isomer is found through intermolecular hydrogen bonding with the solvent. The stability furthermore increases with the dielectric constant of the solvent. The enamine nitrogen of the quinoid isomer is expected to be more basic than the imine nitrogen. In addition, an increase in tautomerism with the ~ K N Hof+the corresponding aminophenol is observed. Increasing both the nitrogen basicity and the solvent acidity would increase a tautomerism of this type where solute-solvent hydrogen bonding is the critical feature.

Nonequivalence of Protons and Related Phenomena in Some Organonitrogen and Organophosphorus Compounds1

by T. H. Siddall, 111 Savannah Rivm Labaratmy, E. I . du Pont de Nemours and Co., Aiken, South Carolina (Received January 10, 1966)

Proton nonequivalence was rationalized in a variety of molecules in terms of the symmetry properties of the nonequivalent protons, groups, or radicals. The compounds that were studied included amides, an amine, a carbamylphosphinate (VIII) , carbamylmethylenephosphonates (IX-XIII), and diphosphonates (XIV-XVIII).

Introduction Nonequivalence Of magnetic nuclei, Or even of whole groups or radicals that contain such nuclei, has Observed* We have now Observed equivalence for protons in a still further variety of compounds. The purpose of this paper is to report these observations and to show how they can always be explained in terms of the symmetry properties of the protons, groups, or radicals.

Experimental Section The proton magnetic resonance (pmr) spectra were measured on a Varian Associates A-60 spectrometer fitted with the Varian variable temperature probe and dewar insert, Except where noted, measurements (1) The information contained in this article was developed during the course of work under Contract AT(07-2)-1 with the U.S. Atomic Energy Commission.

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T. H. SIDDALL, I11

2250

were made on solutions that were made by diluting 250 mg of compound to 1ml with CDCb. The chemical compounds were all prepared by conventional synthetic technique^.^^^ All compounds were purified by vacuum distillation and/or crystallization until no extraneous signals could be observed in the pmr spectra.

Results and Discussion Conditions for Nonequivalence. In view of the variety of compounds for which proton nonequivalence is reported here and in order to help in organizing the discussion, it seems desirable to state the conditions that are necessary for nonequivalence to be observable, even though many investigators may be aware of these conditions. The most precisely defined condition for protons (or groups or radicals) to be nonequivalent is (1) that there must not be any molecular motions that correspond to a symmetry operation for the protons which are completed in a time that is short compared to the nmr signal width. The symmetry operations are the familiar symmetry operations of ~tereochemistry.~,~ Even in the presence of one or more symmetry elements corresponding to the above operations, protons may still be nonequivalent provided that the molecular motion(s) that corresponds to the symmetry operation is slow on the nmr time scale. Two other conditions, which cannot be stated so precisely as the symmetry condition are: (2) there must be a field gradient between the protons, and (3) there must not be any rapid internal molecular motions that produce an approximation of symmetry that is good enough to prevent the observation of nonequivalence. Condition 3 has been the subject of considerable discussion.6 The analysis’ of rotation around an ethane-like bond is an example of the achievement of approximate, but incomplete, symmetry. Another

could arise when there are two asymmetry centers in a molecule, one not inverting and the other inverting rapidly. The rapid inversion of only one of the two centers does not correspond to inversion as a symmetry operation. As a consequence, nonequivalence might still be observable in spite of rapid inversion of one of the two asymmetric centers. Amides. Slow rotation around the carbonyl to nitrogen bond (called the amide bond in the following discussion) removes the possibility of any molecular motions that correspond to a symmetry operation for

0

I1

R-C--N

R1

/ \

RZ

the radicals that are attached to nitrogen. As a consequence these radicals are nonequivalent as entire radicals.* I n general, the geminal protons or groups within a radical are equivalent, since there is a molecular symmetry plane. This is true even when the bonding to nitrogen is pyramidal, since rapid inversion of the nitrogen atom corresponds to the symmetry operation of reflection. However, if the molecule possesses an asymmetry center, no symmetry plane exists and geminal nonequivalence could be observable. The observations for the amides in Table I show that this prediction is fulfilled (see Figure 1 as an example). I n compounds I, 11, and 111, the asymmetry center is in the carbonyl substituent (R group) of the molecule. Similar effects were achieved when the asymmetry center was

H O

I* I/ CH3-C-CI c1

C6H6 0

I* I/ I

and H-C-C-

c1

At lower temperatures the four methyl groups in the nitrogen substituents with R1 = Rz each has its own

I f (Lo

f

ao

I 4.0

ppm

Figure 1.

The Journal of Physical Chemistry

1

3.0

f

1

I

(2) (a) W. J. Hickinbottom, “Reactions of Organic Compounds,” Longmans, Green and Co., New York, N. Y., 1957; (b) R.B.Wagner and H. D. Zook, “Synthetic Organic Chemistry,” John Wiley and Sons, Ino., New York, N. Y., 1953. (3) G. M. Kosolapoff, “Organophosphorus Compounds,” John Wiley and Sons, Inc., New York, N. Y., 1950. (4) F. A. Cotton, “Chemical Applications of Group Theory,” John Wiley and Sons, Inc., New York, N. Y., 1963. (5) G. W. Wheland, “Advanced Organic Chemistry,” John Wiley and Sons, Inc., New York, N. Y., 1960. (6) G. M. Whitesides, D. Holtz, and J. D. Roberts, J. Am, Chem. SOC.,86, 2628 (1964).

(7) H. S. Gutowsky, J . Chem. Phys.. 37, 2196 (1962). (8) H.S. Gutowsky and C. H. Holm, ibid., 25, 1228 (1956).

PROTON NONEQUIVALENCE I N ORGANONITROGEN AND -PHOSPHORUS COMPOUNDS

2251

Table I: Pmr Data" for Amides

RI

Rl

Compd

Data

I

Ethyl

Ethyl

4 H g - of ethyl just barely nonequivalent. About the same a t -40' as +40"

I1

2-Propyl

ZPrOpyl

Four &methyl seta (2-propyl) 1.42, 1.33, 1.17, 0.98; two methine seta 4.39, 3.33 a t $40".

At 75' in

C&hH, all fl collapsed into a hump; methine lost in noke. 6 two sets a t loo", 1.27, 1.15. 9, two seta 1.25, 1.18 at 145'. Methine still collaped a t 1W0,but eherp a t 130', 3.85 I11

Isobutyl

IV

Methyl

V

I

Isobutyl

No definite nonequivalence even a t -40"

2-Propyl

CeH6 *CHCHn

VI

I

CEHI*CHCH~

VI-u

Four ?-methyl sets (0.94, 0.89, 0.82, 0.78); N-CH2nonequivalent a t -40". At +40° only one NC H r set, 3.20; 7, two sets 0.87, 0.82 (1:3 intensity). At 75" in C2CLH2 one N-CH2- set, 3.14; one y set, 0.83

Uranyl nitrat'e adduct of VI

One amide isomer from -40" (CDCla) to 145' (C~CLHS),but two sets of methyl (%propyl) signals over entire range. Chemical shift between sets lies between 0.032 and 0.040 for whole range. Lowfield set at 1.22 a t -40°, a t 1.34 a t 145' Only one amide isomer down to -40". 2.14, 1.87 at $40' Only one amide isomer a t $40". 1.88

o-Methyl a t

o-Methyl a t 2.49,

a Unless specified otherwise, all data are for solutions of 250 mg of compound made up to 1.0 ml in CDCls. All chemical shifts are in PPm from tetramethylsilane; all coupling constants in c p (same for other tables and figures),

doublet for the isobutyl (111) and 2-propyl (11) derivatives. The radicals are nonequivalent as also are the geminal methyl groups within the radicals. As the temperature is raised, rotation around the amide bond becomes rapid and the radicals become equivalent (-75" for I1 and slightly less than 40" for 111) ; but even then, the geminal methyl groups remain nonequivalent in I1 up to 145", since the only possible molecular motions that correspond to symmetry operations for them involve inversion of the asymmetric carbon atom, which does not occur. With more freedom of motion in the longer isobutyl chain, geminal methyl nonequivalence in I11 disappears between 40

and 75" but still is observable at a higher temperature than is radical nonequivalence. The geminal proton8 in I and I11 are nonequivalent in these compounds but to a much smaller extent than the geminal methy1 groups in I1 and 111. Evidently either condition 2 or 3 or both are not well satisfied. I n compound IV there was possibly some broadening of the methylene signals, but no definite indication of the outer components for the quartets that would arise from an AB pattern. Compounds V and VI demonstrate the effect of having the asymmetry center in one of the radicals attached to nitrogen (R1).In both cases the signals Volume 70,hTumber7 July 1966

T. H. SIDDALL, I11

2252

from only one of the two possible amide isomers was observed. (From work in this laboratory with many similar compounds, this effect probably results from a great preponderance of one isomer over the other rather than from rapid rotation around the amide bond.) I n both cases nonequivalence was observed. The chemical shift is small, but remarkably near to constant from -40 to 145" for V. Methyl nonequivalence would be anticipated for V, but for VI, even with an asymmetry center, there is a molecular motion that corresponds to a symmetry operation for the methyl groups on the benzene ring, ie., rotation around the benzene to nitrogen bond. However, this rotation probably has a half-time of many hours, even well above 100°.9 Consequently, these methyl groups are nonequivalent. The protons in the 3 and 5 positions in this benzene ring should also be nonequivalent, but no analysis could be made because of interference from signals from the other benzene ring. Slow rotation around the benzene to nitrogen bond can itself provide the required asymmetry center, since with unsymmetrical substitution in the benzene ring there is no molecular symmetry plane. We have reported our examination of this special situation in other publications.10311 This situation is of considerable interest since the molecular motions that make geminal groups equivalent correspond to the symmetry operation of molecular inversion a t the nitrogen atom. Compound VII. The behavior of compound VI1 as the temperature is increased illustrates condition 3 stated at the beginning of this discussion. It also CH3 CHs

I

CBH~CHZ-N-CH

*I

I

C6H5

which presumably have different energies and different abundances. However, increasing temperature tends to populate the less abundant isomer and helps to produce approximate symmetry. The AB pattern contains the information for following this process down to small chemical shifts, even beyond the direct resolution of the instrument. Even when the inner components of the AB quartet have amost merged, the high-field outer component is detectable. the low-field outer component is lost in the I

The Journal

of

Phgsical Chemistry

But the relative intensity,

I

+

outer-to-inner component, is R = (Q - J ) / Q J),12 where Q is the distance between the first and third (or second and fourth) components of the quartet and J is the geminal coupling constant; and the chemical shift Av (in cps) is calculated by the formula Av = (Qz - J2)'/'or

Av = J

2J (R)"' 1-R

(1)

Chemical shifts between the benzyl methylene protons (Av) are plotted as a function of temperature in Figure 2. The points designated were calculated from eq 1; the points designated A, from signal separation. The geminal coupling constant, J A B , was 13.8 f 0.2 cps over the range 60-180". Resolution of this compound (undiluted) becomes very poor below 60" because of increasing viscosity. However, Av continues to increase in CDC13 solution at least down to -40" (at -40" in CDC13 Av = 24 cps, J A B = 16 cps). As would be expected, the A points fall below the points as Av becomes small, since as the central signals begin to merge, the apparent signal separation is less than the real separation. Compound VIII. In the carbamylphosphinate

VI1 shows that the effects of an asymmetric center can be demonstrated in amines. The geminal protons of the methylene group in the benzyl radical are nonequivalent. However, the chemical shift between these protons decreases in a gradual and regular manner over the whole temperature span (-40 to 180") that was studied. There is no molecular motion (that corresponds to a symmetry operation) that becomes rapid. The only available motion would be inversion a t the asymmetric carbon atom. Instead, a combination of internal motions apparently approaches approximate correspondence to a symmetry operation (condition 3) as the temperature rises. Inversion of the nitrogen may be the most important motion in this combination. Inversion of the nitrogen atom produces diastereomers

I

signals from CsH5CH-C-.)

0

I1 I

0

I1

(Et0)-P *-C-N

(2-Pr)z

CB& VI11 the asymmetry center is the phosphorus atom. At temperatures below 90" four equal sets of methyl signals (1.45, 1.33, 1.25, and 0.92 ppm in CDC13 a t (9) R. Adams, Record Chem. Progr. (Kresge-Hooker Sci. Lib.), 10, 91 (1949). (10) T.H.Siddall, 111,and C.A. Prohaska, Nature, 208, 582 (1965). (11) T. H.Siddall, 111, and C. A. Prohaska, submitted for publica-

tion.

(12) K. B. Wiberg and B. J. Nist, "Interpretation of NMR Spectra,'' W. A. Benjamin Inc., New York, N. Y., 1962.

PROTON NONEQUIVALENCE IN ORGANONITROGEN AND -PHOSPHORUS COMPOUNDS

Colculatrd from Signal Areas (Equotlon I). Flog is rstimote of meon error. A Colculoled from Apparent Sipnol Soparotion A V in eps

I 0.0020

0.0022 0,0024

0.0026

0,0028

0.0030

2253

Figure 3. 0.0032

VT', K

Figure 2. A v for methylene protons of the benzyl group.

40") and two sets of methine signals (5.04 and 3.37 ppm) are observed for the 2-propyl radicals (see Figure 3). The signals of both sets of methine signals are further split at 40" by about 2 cps (perhaps by coupling to phosphorus). The methylene protons of the ethyl group are nonequivalent with a chemical shift of about 0.1 ppm. Nonequivalence of geminal protons in a radical attached to a phosphoryl group does not appear to have been reported before, although it has in a thiophosphoryl analog [(EtO)2P(=S)CHs].l3 At about go", with undiluted compound VIII, the methyl signals of the 2-propyl radical begin to coalesce and the methine signals become broad humps and lose all detail. At 170" the methyl signals have coalesced into two sets 01' sharp signals (Av 0.088 ppm), while the methine signals have become one set with broadened components that, is partly overlapped by the methylene signals from the ethyl radical. The behavior of the signals from the 2-propyl radical is easily explained, as with the amides, on the basis of the onset of rapid rotation around the amide bond above about 90". Below that temperature the 2propyl radicals are nonequivalent as entire radicals, since rotation around this bond is required for correspondence to aay symmetry operation. The methyl groups within a radical are nonequivalent because the asymmetric phosphorus atom removes all molecular symmetry planes:. The signals from the ethyl radical never lose their sharpness, even during coalescence of the 2-propyl signals. However, there is a continuous change for the methylene signals as the temperature is raised. The main feature of this change is apparently a decrease in the chemical shift between the methylene

protons. At 170" these protons are nearly, if not completely, equivalent. This gradual decrease in chemical shift is very similar to that observed for the methylene protons in VI1 and may be connected with increasing rate of rotation around the amide bond. If so, the connection is not direct or simple, since at 120" (well above the coalescence of the 2-propyl signals) the methylene protons are still nonequivalent. Carbamylmethylenephosphmates and Related Compounds. These compounds can be regarded as amides with a phosphoryl-containing substituent. Only five comparatively simple examples of this class are in-

RO 0

\ll

R3

I I1

RO/p-Y*-c-N R4

R1

0 '/

\

Rz

eluded in Table 11. We have synthesized and examined the spectra of many others and from this can state certain generalities. One such generality is that as a rule R radicals are nonequivalent as radicals, and geminal methyl groups within an R radical are nonequivalent whenever the bridge carbon atom (i) is an asymmetry center. The a geminal protons (ii) in RI and RZ

R3

I -c*-

I

R4 i

H

-N-C-

I

I

H ii

often exhibit a very complex and not readily analyzable signal pattern, which we take as indicative of geminal proton nonequivalence. (For geminal methyl groups (13) H. Finegold, J . Am. Chem. Soc., 82, 2641 (1960).

Volume 70,Number 7 July lQ66

T. H. SIDDALL, I11

2254

~~~

~

Table I1 : Pmr Data for Carbamylmethylenephosphonates

RO 0 R3 0

RI

RO

RI

\I1 I P-C/ I

Compd

IX

R

H

/ C-N \

Itr

RI

C6HaCHz

CH3

R1

CH3

Ra

I/

Data

R a t 3.84, 3.80; R1a t 2.85, 2.75 (2.85 further split 1.6 cps, by coupling to bridge H?)

X

I

H

CHI

R a t 3.83, 3.79, 3.51, 3.44; R1a t 2.99, 2.67, both

CH3

very broad; bridge CHI a t 1.49, 1.32

CsHsCHCHs

XI

H

2-Propyl

CeHsCHz

Isobutyl

R methyl a t 1.39, 1.38, 1.35, 1.36; R1 y methyl a t 0.85, 0.80, 0.65, 0.53

XI1

XI11

mCHzEthyl

2-Propyl

2-Propyl

CH3

(b) Signals

occur as weak, complex multiplet, under the (a) signal8

CeHsCHz

CH3

+--

Figure 4.

in R1 and R2 that are conspicuously nonequivalent, see compound XI as an example.) Compound X (see Figure 4) shows the effect of two asymmetry centers. This is clearest for the R signals which occur as four sets. Evidently, asymmetry causes the R groups to be nonequivalent in both diastereoisomers. Compound XI11 is interesting in that the CeHr CH2- protons attached to the bridge are nonequivalent. The rather large degree of nonequivalence suggests that there may be rather strong rotamer preference 11

around the CsH6CH2-C- bond. This same pheI

nomenon for XI (Rs = H) would help to account for the rather large effects on groups as far away as the The Journal of Physical Chemistry

R methyl a t 1.46, 1.43, 1.38 (ratio 1:2:1); R1 methyl a t 0.91, 0.35

R methyl a t 1.35, 1.32; R1 a t 3.18, 3.16 ( 3 : l ) ; bridge CH3 1.40; CsH&Hz nonequivalent; center of pattern a t 3.33; Av between first and fifth peak 0.96 ppm; JAB= 13.6 CPS, JH..P= J H ~ ,=P 9.2 CPS

y-methyl groups. However, when RB = H, the overlap from the signals from this proton has prevented our analyzing the signals from the aryl-CH2- protons. The stiffness of the amide bond is probably also a factor in producing large effects at a distance. The chance of internal motion producing approximate symmetry would be reduced by these restrictions. The shift to high field of two of these y signals suggest that the y-methyl groups of one isobutyl radical are on the average in a plane that is substantially perpendicular to the plane of the benzene ring. The effect is even more pronounced in compounds with a naphthyl group in the place of this benzene ring. This is seen in XI1 where one methyl signal center is at 0.35 ppm. Rotamer preference may be increased with the larger naphthyl group and the fused ring system certainly provides a larger magnetic field than does the simple benzene ring. Diphosphonates. So long as Rz = R1,the R radicals are equivalent as whole radicals in these diphosphonates, since there is a symmetry plane. Even so,

RO 0 Rz 0 OR

\I1

/

RP

I I// I R1 \

P-c-P

OR

geminal protons (or groups) within an R radical may be nonequivalent, since they possess no symmetry element. (This situation has been studied for the

PROTON NONEQUIVALENCE IN ORCANONITROGEN AND -PHOSPHORUS COMPOUNDS

2255

Table 111: Pmr Data for Diphosphonates

RO 0 R1 0 OR

\II

I

k~

RO’ R

Compd

RI

H

It/

P-c-P

Rz

‘OR

a Proton

Additional data

4.79

1.35

5.19

1.37, 1.58

4.77

1.32, 1.28, 1.26; intensity 2: 1: 1

GH~CHZCH overlaps

Uranyl nitrate chelate

5.14

1.57, 1.50, 1.33, 1.22

CBH~CHZCH overlaps

XV-T

Thorium nitrate chelate

4.9

1.47, 1.44, 1.23, 1.08

XVI

2-Propyl

4.75

1.19

CeH5CH2- a t 3.35, J H P = 16.2

XVII

2-Propyl

1.10,1.20

05

XIV.

2-Propyl

XIV-u

Uranyl nitrate chelate*

XV

2-Propyl

XV-u

CBH~CHZ

CBH~CHZ

H

Signals ,%Methyl

H

CBH~CHZ

I

,

CH,-

a t 3.92,

JHP = 18, center peak broad XVIII

Ethyl

Ca&CHz

XVIII-U

Uranyl nitrate chelate

H

4.04

I

1.26

CeHsCH&H overlaps

1.37, 1.32

CBH~CHZCH overlaps

I

a

10% by volume.

Complex

* All chelates 250 mg/ml in CDCl3.

simple esters, (R0)zPOR1.14,15With the simple esters, only groups are nonequivalent, and not whole radicals.) However, as soon as R1# Rz the two R’s attached to a phosphorus become nonequivalent, since there is now no molecular symmetry plane that is also a symmetry plane for the R’s. These various considerations as well as condition 2 are illustrated by the series given in Table 111. (The first two entries are from a previous study.I6) Evidently there is not enough field gradient in XIV itself to produce any nonequivalence, but the uranyl group in the urimyl nitrate chelate (XIV-U) provides a strong anisotropic magnetic field. The chelate ringI6 that is formed by bonding of the uranium atom to the phosphoryl oxygens reduces the flexibility of the molecule, even though the bonding is mobile and exchange is rapid. The P-methyl groups within a 2propyl radical become nonequivalent in the uranyl nitrate chelate, but since there is a symmetry plane for the 2-propyl radicals, as a whole, the radicals are equivalent. With compound XV the appropriate symmetry plane is lacking, and potentially both the entire radicals and the p-methyl groups are nonequivalent. However, only three P-methyl signal sets are observed, but

with an intensity ratio of 2: 1:1. Two of the four pmethyl groups (for each phosphorus) happen to be equivalent. In the uranyl nitrate adduct (XV-U) there are four equal sets of p-methyl signals. Again through condition 2, and almost certainly (3) as well, greater multiplicity is realized. The formation of the chelate ring is now probably very important in making the maximum multiplicity observable. It is unlikely that the bridge grouping (CeH&H&H-) can be rotated through the chelate ring. This would tend to fix the CaH,CH2- group on one side of the chelate molecule, thereby diminishing motions that approximate symmetry operations. This effect is illustrated in the thorium nitrate chelate where presumably there is little or no additional contribution to condition 2 over XV, but about the same change in condition 3 as there is for XV-U. With XVI, the molecular symmetry plane is restored. Since there is only one signal set for the &methyl groups, (14) T.H.Siddall, 111, and C. A. Prohaska, J . A m . Chem. Soc., 84, 2502 (1962). (15) T. H.Siddall, 111, and C. A. Prohaska, ibid., 84, 3467 (1962). T ~ .4, 783 (16) T. H.Siddall, 111, and C. A. Prohaska, I ~ o Chem., (1965).

Volume 70, Number 7

July 1966

T. H. SIDDALL, I11

2256

it is evident that an approximate symmetry is also achieved within a 2-propyl radical. However, with XVII, the approximate symmetry within a radical is lost and two @-signalsets are observed. The fused naphthyl rings enforce a high rigidity on this molecule. This factor, plus the larger magnetic field from these rings, must account for the loss of approximate symmetry as compared to XVI. Unfortunately, we have not been able to isolate the naphthyl analog of XV; this compound would allow interesting comparisons. Compound XVIII and its uranyl nitrate adduct add no new conclusions but do confirm those found with the 2-propyl analog. The uranyl nitrate chelate XVIII-U gives two sets of methylene signals, presumably one set for each radical on a phosphorus atom. The methine signals of the 2-propyl radicals are already so complex (14 lines) that it is hard to say whether or not there is still further multiplicity. Also, it is possible that the methylene protons of XVIII and XVIII-U should be nonequivalent within an ethyl radical). This would lead to a theoretical total of 64 lines [4 (for JHH) X 2 (for JHP)X 2 (for nonequivalent radicals) X 4 (for nonequivalence within a radical)]. There does not appear to be that much multiplicity for XVIII-U. The CBH~CHZprotons should be equivalent (a symmetry plane) for all the compounds in Table 111. However, for XVIII, the expected triplet is so broad

The Journd of Physical Chnnktry

in its center component that this component is no higher than the wing components. Possibly the rotation I

around the CaH5CHz-CH bond may be slow (the symI

metry operation that corresponds to reflect.ion in a molecular symmetry plane). However, a t -40°, this component is much the same as at +40°.

Conclusions The power of elementary symmetry considerations to rationalize nonequivalence in a variety of circumstances is perhaps adequately demonstrated by the examples cited above. The chief problem that remains is the weakness of this formalization in predicting nonequivalence. It is evident that increased predictive ability can arise only as conditions 2 and 3 can be made more explicit. Gutowsky’s “asymmetry effect”’ is a beginning in that direction. It seems that chelates with uranyl salts may be especially useful as model compounds for studies of conditions 2 and 3. The geometry of the cheiate ring system is often well known, and the anisotropic field of the uranyl group is subject to measurement. Further studies along these lines are in progress in this laboratory.

Acknowledgment. The author wishes to thank M. A. Davis for the preparation of several of the diphosphonates used in these studies.