J. Phys. Chem. 1981, 85,3772-3775
3772
Nuclear Magnetic Resonance Solvent Shifts of Xenon. A Test of the Reaction Field Model Thomas R. Stengle," Nicholas V. Reo, Department of Chemlstty, University of Massachusetts, Amherst, Massachusetts 0 1003
and Kenneth L. Williamson Department of Chemistty, Mt. Holyoke College, South Hadley, Massachusetts 0 1075 (Received: July 9, 198 1)
The medium shift of 129Xewas measured in a number of liquid alkanes, monosubstituted benzenes, and a set of ten test solvents where the magnetic anisotropy is negligible. The shifts arise from van der Waals shielding, but in the test solvents they do not correlate well with the predicted reaction field. A good correlation is found for the n-alkanes where the repulsive part of the shift is assumed constant. Branched alkanes show positive deviations which are ascribed to enhanced repulsive interactions. Shifts in monosubstituted benzenes correlate well with prediction except for solvents with low-lying excited states which show negative deviations. It is concluded that the reaction field model is valid within a group of closely related solvents, but it fails when extended to collections of randomly selected solvents.
Introduction Recently we undertook an NMR study of the interaction of xenon with biological systems. In the course of this work we expect to utilize the chemical shift of lBXe to determine the locus of xenon when it is present in complex systems such as cell membrane suspensions. For this work, it is important to have an understanding of the factors responsible for xenon shifts in the absence of specific interactions. In order to elucidate the mechanism of the nonspecific medium shift, we measured the 129Xeshift in a number of simple solvents, and we have attempted to explain the results in terms of a reaction field model. The magnetic shielding of a molecule dissolved in a solvent differs significantly from its value in the isolated state. Part of this difference is connected with the bulk magnetic susceptibility of the sample. The remaining shielding, urn, is a true medium effect. The medium effect is important from both theoretical and practical points of view, and it has received much attention over the past 20 years. The solute-solvent interactions responsible for the medium effect are usually classified as specific or nonspecific.l Specific interactions involve the formation of definable molecular associates with their own peculiar shift; hydrogen bonding is a common example. Nonspecific effects arise more from the solvent in the aggregate than from individual intermolecular interactions. This report deals exclusively with nonspecific effects. In fact, we have chosen the solute xenon partly because it exhibits no specific interactions with common solvents. The nonspecific part of the medium shift is usually taken to be the sum of several individual terms following the proposal of Buckingham, Schaefer, and Schneidera2 In expanded form the relation is =
ga
+ 632 -k (TE +
+ urep
(1)
Here ua is the shielding originating in the magnetic anisotropy of the solvent molecules, uE2 is the shielding caused by the permanent electric dipole moment of the solvent, UE arises from the reaction field induced in the (1)M. I. Foreman, Nucl. Magn. Reson. Spec. Period. Rep., 5, 292 (1976). (2) A. D. Buckingham, T. Schaefer, and W. G. Schneider, J. Chem. Phys., 32,1227 (1960). 0022-365418 112085-3772$0 1.2510
solvent by the permanent electric dipole of the solute, u, is the shielding due to the dispersive part of the van der Waals interaction, and ureParises from the repulsive part of the van der Waals force. Frequently, these various terms are treated in terms of models which assume the solvent to be a continuum. Often solute/solvent systems can be chosen for which some terms are negligibly small; then certain individual terms in (1) can be isolated. Perhaps the most interesting terms in (1)are the van der Waals terms. They can be isolated from the other contributions to the medium shift by limiting consideration to solutions of nonpolar solutes in nonpolar and magnetically isotropic solvents. Unfortunately, this restricts one to a very small group of solvents. However, it is generally true that UE2 is small except in solvents which have a large, localized dipole such as HCL3 Then, if urepis ignored, uw can be obtained for a large number of solvents. This quantity has often been treated in terms of a reaction field model: According to this approach the system is pictured as a solute molecule immersed in a continuum. Spontaneous electric moments which arise in the solute induce a reaction field in the solvent. In turn, the reaction field affects the magnetic shielding a t the solute nucleus. The reaction field concept was introduced by Onsager5 who dealt with the field induced in the solvent by a solute with a permanent dipole. Later Linder6 extended the idea to include the reaction field induced by spontaneous electric moments which arise in the solute from normal fluctuations in its charge distribution. He showed that the magnitude of the field is proportional to (2n2- 2)/(2n2+ 1) where n is the refractive index of the solvent. The calculations of Marshall and Pople' and Stephen8 showed the connection between the magnetic shielding of an atom and the electric field acting on it, so it was an obvious extension to attemp a correlation of the medium shift with a simple function of refractive index. Various modifications of the continuum model have been proposed in the intervening years. For example, if the magnetic nucleus (3) F. H. A. Rummens, Can. J. Chem., 54, 254 (1976). (4) F. H. A. Rummens,"NMR Basic Principles and Progress", Vol. 10, SDrineer Verlae. New York. 1975. =(5)OL. OnsaGr, J. Am. Chem. SOC., 58, 1486 (1936). (6) B. Linder, J. Chem. Phys., 33, 668 (1960). (7) T. W. Marshall and J. A. Pople, Mol. Phys., 1, 199 (1958). (8) M. J. Stephen, Mol. Phys., 1, 223 (1958).
0 1981 American Chemical Society
NMR Solvent Shifts of Xe
is not at the center of the solute molecule, such as the proton in CH4, a "site factor" has been included in the medium shifta3Slightly different refractive index functions have also been advanced. In this work we have elected to follow a recent suggestion of Rummensg and use the function [(n2- 1 ) / ( 2 n 2+ 1)12. The continuum model predicts a correlation between uw and the refractive index function. This idea has been tested by a number of workers. In a recent report, Rummens and MouritslO present the proton shifts of CHI in a series of 11 test solvents. The data fit the model to an acceptable precision. Later, anisotropic solvents were included, and the deviations from the model were used to estimate u,. However, when 13C shifts were obtained on the same systems, the fit was quite poor, and the line did not pass through the origin as predicted. Apart from the suggestion that repulsive forces may play a role here, no explanation could be advanced for the failure of the model. The applicability of the reaction field model is limited by the repulsive term in the medium shift. This term varies from solvent to solvent in a way that cannot be predicted a priori. However, it is possible that urepcould be nearly constant within a homologous series of solvents; then the reaction field model would be valid within that set. To test this idea it is necessary to study the medium shift in a large number of liquids. Unfortunately, the u, term complicates this procedure since there is no way to distinguish it from ureY If the orientation of the solvent molecule with respect to the solute is not completely random, and if the magnetic susceptibility of the solvent is anisotropic, there will be a residual susceptibility shielding which is not included in the usual bulk susceptibility correction.2 The magnitude of u, is determined primarily by the properties of the solvent; it is only slightly affected by the nature of the solute, and it is rarely greater than 1 ppm. If we use a solute which exhibits chemical shifts on the order of lo2ppm, the contribution of u, can be neglected. Then the medium shift will be made up almost entirely from uw and urep. The noble gas xenon fits all the requirements for a test of the reaction field model. It has no permanent dipole moment, and its simple structure eliminates the need for a "site factor". It is unreactive under the conditions used here, but it is soluble to some extent in most liquids, and its medium shifts extend over a range of ca. 200 ppm. The isotope lZ9Xehas a natural abundance of 26% and its NMR frequency is just slightly greater than I3C. It has no quadrupole moment and its spectrum consists of a single sharp line. Its shift can be measured accurately and compared to a sample of the pure gas as reference so that true medium shifts can be obtained. Experimental Section Materials. Most of the solutions were prepared by shaking xenon gas (Linde, 99.995%) with the solvent in a syringe. Solutions in especially volatile solvents, such as tetramethylsilane, were prepared on a vacuum line, and the NMR tube was sealed off. The solvents were reagent grade, and they were used without further purification. Most of the liquids dissolved an equal volume or less of xenon. The shifts from these solutions (10.04 M) may be taken to be infinite dilution values. Xenon is especially soluble in decane, and this system was studied at several higher dilutions. The chemical shift exhibited no change with concentration. (9)F.H.A. Rummens, Chem. Phys. Lett., 31, 596 (1975). (10)F.H.A. Rummens and F. M. Mourits, Can. J. Chem., 55, 3021 (1977).
The Journal of Physical Chemistry, Vol. 85,No. 25, 198 1
3773
TABLE I: Medium Shifts of Iz9Xein Ten Test Solvents a t 23 "Ca no. 2 3 4 5 6 7 8 9 10 11
solvent Me,Si cyclopentane cyclohexane
cc1,
CC1,H CH,I CHA CS, ethyl ether ethyl acetate
nDZ3 1.3564 1.4044 1.4244 1.4583 1.4438 1.5288 1.7451 1.6250 1.3505 1.3708
-Om
b
157 157 164 22 1 215 207 333 223 159 167
a Solvent numbering, refractive indexes, and bulk susceptibilities are taken from ref 10. Chemical shifts in ppm from xenon gas at zero pressure corrected for bulk susceptibility.
Apparatus and Procedures. Xenon spectra were obtained on a JEOL FX-9OQ spectrometer at a center-band frequency of 24 789 225.0 Hz. Usually a 30" pulse and a 1-2-5 repetition rate were employed. With a sweep width of 2000 Hz and 4 K data points, a resolution of 0.5 Hz was achieved. Each sample contained a concentric capillary filled with DzO as a spectrometer lock. The experimental resonance frequencies were compared with a sample of xenon gas at 10.0 atm. The shift with respect to the gas at zero pressure (24 784 771.0 Hz) was calculated from the known pressure dependence of the gaseous xenon shift.'l All the shifts observed in this work lie downfield from the gas. They are reported in ppm from the resonance of the pure gas at zero pressure. A bulk susceptibility correction has been applied, so that the tabulated values are true medium shifts. Most of the spectra were obtained at a controlled temperature of 25.0 "C, although one series of solvents was examined at the ambient probe temperature (23.5 "C). The lZ9Xeshift is quite sensitive to temperature; a one degree rise causes an upfield shift of ca. 0.3 ppm in most organic solvents. The probe temperature was monitored by recording the lZ9Xeshift in a standard methylcyclohexane solution. This, in turn, was calibrated against the proton shift difference in CH30H.lZ The sensitivity of the shift to temperature caused the thermal stability of the system to be the limiting factor determining the precision of the measurements. The probe temperature could be kept within a range of f0.3 "C resulting in a shift uncertainty of f O . l ppm. Shifts which were measured a t the ambient probe temperature are reported to the nearest ppm only. The refractive indexes were measured on the same solvents used in the NMR study. They were determined at 25.0 "C with a precision Abbe'refractometer. Refractive indexes at 0 "C were calculated by assuming that the molar refraction, [(n2- l)/(n2 2 ) ] ( M / p ) is , independent of temperature. The densities at 25 and 0 "C were taken from the American Petroleum Institute tables.
+
Results and Discussion Earlier workers have tested the reaction field model by studying medium shifts in a selected group of test solvents. It is important to select solvents which have negligible anisotropy, since this term cannot be estimated a priori. We have used the same set of solvents that were chosen by Rummens and Mourits (with the exception of dimethyl (11) A. K. Jameson, C. J. Jameson, and H. S. Gutowsky, J. Chem.
Phys., 53, 2310 (1970).
(12) A. L. Van Geet, Anal. Chem., 40, 2227 (1968); 42,679 (1970).
3774
The Journal of Physical Chemistry, Vol. 85, No. 25, 1981
Stengle et al.
TABLE 11: Medium Shifts of lz9Xein Saturated Hydrocarbons and Substituted Benzenes at 25 "C
no. 1 2 3 4 5 6 7 8 9 10 0
I
I 2.0
1
1 4.0
I
I 6.0
I
I
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
I
8.0
Flgure 1. "'Xe gas to solution shifts in ten test solvents at 23 O C corrected for bulk susceptibility. The numbering is given in Table I. The n = 0 intercept occurs at u = 60.7 ppm and the correlation coefficient is 0.912.
sulfoxide). The solvents and the lz9Xemedium shifts are reported in Table I. Several of the solvents are not spherically symmetric, but earlier work established that they do not contribute a significant ua term.3 Furthermore, some have an electric dipole moment, but it has been claimed that the uE2 terms are ~ m a l l . ~ J ~ The xenon medium shifts in the ten test solvents are plotted against the appropriate function of refractive index in Figure 1. The large scatter of the points from the line and the failure of the line to pass through the origin indicate a serious weakness in the model. Roughly the same behavior was observed earlier for the 13C shifts of methane.1° However, the proton shifts of methane gave a much better fit.1° It seems that the heavier atoms are more difficult to treat, presumably because the repulsion term is more important. Elsewhere we have reported 129Xemedium shifts in a collection of 37 randomly selected s01vents.l~ The correlation was no better than that shown in Figure 1. There was a significant scattering of the points and the line did not pass through the origin. However, medium shifts in monosubstituted benzenes did fit the line well. This could be explained by assuming ure to be constant within that group. Thus, the reaction fiefd model could be successful over a group of related solvents, while it fails for a set of randomly selected solvents. The medium shifts of lz9Xein saturated hydrocarbons are reported in Table 11, and the reaction field plot is given in Figure 2. The straight chain aliphatics are often taken as the paradigm of a homologous series, and Figure 2 shows that medium shift correlates almost exactly with the reaction field in these solvents. However, the line does not pass through the origin, and the intercept of 60.2 ppm presumably reflects the common value of uIeP in these media. In branched hydrocarbons, higher values of urep are observed. All of the isomeric hexanes and some of the octanes are included in Figure 2 which shows that the more methyl groups contained in a hydrocarbon, the higher is the xenon shift. This idea is supported by the data for cyclic alkanes which have no methyl groups and produce a lower medium shift. These results can be understood in terms of a van der Waals shift which is made up of contributions from dispersive and repulsive interactions. The repulsive term is essentially constant within any series (13) K. W. Miller, N. V. Reo, A. J. M. Schoot Uiterkamp, D. P. Stengle, T. R. Stengle, and K. L. Williamson, Proc. Nutl. Acud. Sci. U.S.A., 78, 4946 (1981).
solvent n-pentane n-hexane n-heptane n-octane n-nonane n-decane n-dodecane n-tetradecane n-hexadecane 2,2-dimethylbutane 2,3-dimethylbutane 2-methylpentane 3-methylpentane 2-methylheptane 2,5-dimethylhexane 2,2,4-trimethylpentane cyclohexane cycloheptane cyclooctane cyclodecane fluorobenzene tert-butylbenzene toluene anisole benzene pyridine chlorobenzene nitrobenzene bromobeiizene aniline iodobenzene
nD2s a
1.3558 1.3731 1.3853 1.3954 1.4031 1.4096 1.4198 1.4271 1.4327 1.3674 1.3733 1.3697 1.3752 1.3934 1.3910 1.3891 1.4244 1.4432 1.4568 1.4689 1.4639 1.4910 1.4940 1.5154 1.4988 1.5079 1.5225 1.5503 1.5575 1.5840 1.6178
-am
b
154.1 160.9 166.0 169.9 173.0 17 5.4 179.4 182.4 184.5 174.7 169.2 167.4 165.1 175.9 181.7 190.5 163.7 171.4 176.2 182.9 174.6 201.6 188.5 191.1 193.0 203.6 200.1 187.4 217.2 215.8 246.7
a Refractive index at 25 "C measured on actual solvent used for NMR experiment, Chemical shift in ppm from xenon gas a t zero pressure corrected for bulk susceptibility.
2 00
c 0 10 3
I
2
160 I
LINEAR
(-Jx
100
Figure 2. '*'Xe gas to solution shifts in saturated hydrocarbons at 25 OC corrected for bulk susceptibility. The line fitted to the shifts in linear alkanes shows an intercept at 60.2 ppm and a correlation coefficient of 0.9999. The numbering is given in Table 11.
of hydrocarbons of equal branching, but it increases with increasing branching. The dispersive term which arises from the reaction field induced in the solvent is proportional to [(n2- 1)/(2n2+ 1)12. Medium shifts in the monosubstituted benzenes afford a more stringent test of the model. These data are also collected in Table I1 and plotted in Figure 3. tert-Butylbenzene shows a positive deviation from the correlation due to the enhanced urepof the methyl groups. All the other solvents which deviate significantly do so in the negative direction. In the absence of any information to the contrary, we assume that urepis the same for all aromatics except tert-butylbenzene and we ascribe the neg-
The Journal of Physical Chemistry, Vol. 85,No. 25, 198 1 3775
NMR Solvent Shifts of Xe
TABLE 111: Medium Shifts of lz9Xein Straight Chain Alkanes at 0 "C
4
no,
24
solvent n-pentane n-hexane n-hep tane n-octane n-nonane n-decane n-dodecane
1 2 3 4 5 6 7
--Oma
162.2 168.6 173.3 176.8 179.6
181.9 185.5
a Chemical shift in ppm from xenon gas at zero pressure corrected for bulk susceptibility.
I 4.5
I
I
5.0
I
1 6.0
5.5 I
n
(-)p
1
I 6.5
I 7.0
$2
100
Flgure 3. '*'Xe gas to solution shifts in substituted benzenes at 25 O C corrected for bulk susceptibility. Points indicated by filled in circles have not been used in fitting the line. The intercept is 16.9 ppm and the Correlation coefficient is 0.989. The numbering is given in Table 11.
ative deviation to a decrease in the strength of the reaction field. This field strength depends on the magnitude of the spontaneous moments of the xenon atom and the polarizability of the solvent. In this connection, the dynamic rather than the static polarizability must be used. The dynamic polarizability of the solvent molecule depends on frequency, and it is a maximum a t the "oscillator frequency" of the molecule. Thus, when solute and solvent are identical (xenon dissolved in xenon) an especially large medium shift is observed since the frequencies are equalall In other systems the shift will depend on the match between solvent and solute frequencies. This effect is often treated by use of the London approximation vi = I J h , where I; is the ionization potential of the molecule i. Various functions of Il and I2 have been proposed to correct observed medium shifts for this effect with indifferent s u c c e ~ s . ~ Although these ideas have not been successfully applied in a quantitative sense, they can explain the deviations in Figure 3 in a qualitative way. Rather than using the ionization potential, we focus on AE,the energy difference between the ground and first excited state. In a closely related series of solvents it is possible that uIePand aE values will be the same for all members of the set. This is the case for the straight chain alkanes and many of the substituted benzenes. However, certain aromatics have low-lying excited states, and these are the ones which show a negative deviation in Figure 3. Furthermore, the magnitude of the deviation is proportional to the difference aE(benzene) - U(so1vent); for example, the deviations lie in the order nitrobenzene > aniline > anisole. In this connection it is interesting to note the position of CS2 in the set of test solvents. The medium shift in this solvent is consistently below the correlation line for both 'H and 13Cin methane and also for lz9Xe. This behavior must be the result of the low-lying excited state of CSz. It should be noted that the London approximation will break down here. Whereas CS2has a slightly lower ionization potential than the saturated hydrocarbons, its first excited state lies a t much lower energy, and that is the quantity of importance in determining the medium effect. It would be valuable to have some experimental method of separating the effects of uwand urepother than fitting a line to a group of related solvents. Some time ago the
180
-
-
-,I;
bE 160
I 3.2
I 3.6
I
I
1
4.0
Figure 4. laXe gas to solution shifts in linear alkanes at 25 and 0 O C corrected for bulk susceptlbility. The intercept of the 0 O C line is 64.5 ppm and the correlation coefficient is 0.9999. The numbering is given in Table 111.
suggestion was made that uEPwould be especially sensitive to temperaturea2It was proposed that the repulsive term would increase at higher temperature as the "buffetting" of the solute increases due to departures from equilibrium solvent configurations. Abcordingly, we obtained lZ9Xe medium shifts in a number of hydrocarbon solvents a t 0 "C. These data are presented in Table I11 and plotted in Figure 4. The plot is almost identical with the one obtained at 25 "C. The slope is the same within 2.2% and the intercepts differ by only 4 ppm with the 0 "C data giving the larger value. If the intercept is identified with ore,this trend is not in the predicted direction. It seems unfikely that this approach will be successful in sorting out uw and urePin liquid systems. In the past the reaction field model has never been successful with nuclei heavier than hydrogen. It is particularly poor when extended over sets of widely different solvents. However, our results show that the model does have validity, and that it can be used within limited groups of related solvents. Even then, there may be deviations from the predicted shift, but it is possible to understand these in qualitative terms. An unequivocal resolution of the medium shift into dispersive and repulsive terms has not yet been accomplished.
Acknowledgment. Some of the data in the early stage of this work were collected by Dr. Diane P. Stengle and Beth M. Weiner. This research was supported in part by a grant from the National Institute of Arthritis and Metabolic Diseases to K. L. Williamson (AM-21381), and by a Faculty Research Grant from the University of Massachusetts to T. R. Stengle. The cost of publication was supported by the National Science Foundation through grant CHE-8103004 to T.R.S.
