MAGNETIC RESONANCE IN CHEMISTRY, VOL. 29, 946954 (1991)

Intermolecular and Intramolecular Effects on the 'H and 13C Shielding in Some Gaseous Hydrocarbons at Various Tempera tures-Experimental Results

Brian Bennett and William Thomas Raynes* Department of Chemistry, The University, Shefield S3 7HF, UK

The proton and "C shielding constants in CH, , C,H,, C,H, and some other gaseous hydrocarbons have been studied as functions of density at temperatures in the range 180-370 K. The linear coefficients describing the density dependence of the shielding, after correcting for bulk susceptibility, increase substantially as the tem- perature is reduced, indicating stronger intermolecular interactions. (Some of the required magnetic susceptibilities were determined in this work by an NMR method). The "C measurements for CH, are close to those of an earlier study; the results for the other gases are new. The linear coefficient is substantially greater for the carbon shielding of the methyl group in propane than for the methylene group at any temperature, but there is virtually no distinc- tion between tbe linear coefficients for the proton shielding in this gas. Values for du,/dT, the temperature depen- dence of the shielding extrapolated to zero density, are also presented for both proton and "C shielding in the bydrocarboos. They are positive and negative in different instances. It is shown from this and earlier gas-phase studies that standard literature values of the methane "C shielding relative to the ''C shielding in tbe other bydrocarboos are in error.

KEY WORDS Intermolecular effects Intramolecular effects 'H and shielding Hydrocarbons

INTRODUCTION

Apart from a few exceptions, the nuclear shielding con- stants a(p, T ) of pure gases vary linearly with the density p. Thus

(1) 77 = oo(T) + a m p

where T is the temperature and uo is the shielding con- stant at zero density, which varies with temperature on account of the temperature dependence of the popu- lation distribution of the vibration-rotation levels and the variation of the shielding with the degree of vibration-rotation excitation. Ultimately oo varies with temperature because of the bond length and bond angle dependence of the hi el ding.'-^ ul, which is normally negative, is determined by the effects of intermolecular interactions on the shielding and consequently becomes numerically greater at lower temperature^.^^^ Excep- tions to the linearity of the density dependence have been observed for a few gases: notably xenon.' u1 can be divided into two parts, (ul),, and (ul)loc.

The former part, due to the bulk susceptibility effect, i.e. the polarization of the gas by the external magnetic field, can be readily calculated if the magnetic suscepti- bility of the gas is known. (ol)loc is due to the 'local' interaction between the molecule containing the nucleus of interest and a second, perturbing molecule. It is given

* Author to whom correspondence should be addressed.

where N is the Avogadro constant and U is the inter- molecular potential function for a pair of interacting molecules. U is a function of the mutual orientation and separation of the two molecules, denoted here by T. The integration is taken over all orientations and separa- tions of the two molecules. npair denotes the functional dependence on z of the shielding of interest. It is the goal of studies such as this to obtain data that -will enable upair to be determined. This is, in fact, a very difficult task4#* and it is more likely that experimental values of u1 at various temperatures will serve to test theories of upair. Up to the present time progress towards this end has been made by models which break (ul)loc down into separate contributions, viz. uw due to van der Waals forces, oE from polar and other electro- static interactions and ua arising from molecular mag- netic ani~otropy.~.'

In a previous paper," values of (ul)loc were reported for the proton shielding in the gases CH,, C,H,, C,H6, CH,F and H,S. That work was carried out over the temperature range -40 to +80°C, although for each gas a shorter range was taken; e.g. CH, was studied over the range -40 to +30°C whereas c& was examined over the range - 10 to + 80 "C. (ul)loc in all cases became more negative at lower temperature, in agreement with earlier studies of protons and other nuclei in a wide range of compound^.^^^'^'^ This work

0749-1 581/91/090946-09 $05.00 0 1991 by John Wiley & Sons, Ltd.

Received 4 M a y 1991 Accepted (revised) 31 May 1991

INTER- AND INTRA-MOLECULAR EFFECTS ON ‘H AND 13C SHIELDING 941

was undertaken to obtain data for ( o ~ ) ~ ~ ~ for proton shielding over a much wider temperature range (180- 370 K) than previously and to extend the study to I3C shielding. The principal gases investigated were CH, , CzH6 and C,H,, although some other hydrocarbons were also studied. Of particular interest is propane, which offers the prospect of obtaining the temperature dependence of o1 for two different sites for each of two different nuclei in the same molecule. In order to deter- mine ( o ~ ) , ~ ~ for these gases we found it necessary to measure a number of magnetic susceptibilities by an NMR method.

A second part of our work was to measure do,/dT for the hydrocarbons both in ‘H and I3C resonance. The results are of importance since the direct ab initio calculation of this quantity is now feasible for nuclei in the simpler hydrocarbons. It has already been accom- plished for methane and its i~otopomers.’~ We have also obtained data at 348 K which enable the ‘absolute’ shielding constants, uo , of these hydrocarbons to be easily calculated. Further references and discussion of gas-phase NMR are given in Jameson’s review,, which covers work up to 1980. More recent work is discussed in her annual reviews of the physical and theoretical aspects of nuclear shielding.’,

In the following paper” we discuss the present results in terms of the concepts that are used to under- stand intramolecular and intermolecular effects on nuclear shielding.

EXPERIMENTAL

All the gases studied except isopentane were obtained from Matheson; isopentane was purchased from Aldrich. Reference solvents were obtained from Fluoro- chem.

Sample tubes were made from Pyrex tubing and drawn out to fit comfortably inside standard Wilmad 507PP tubes of 5 mm 0.d. For the high-density samples thicker walled tubing was used. The volumes of gas samples varied from 0.08 an3 for the thicker walled tubes to 0.3 cm3 for the normal tubes. Careful measure- ments were made to obtain the volumes of the sample tubes and it was estimated that the error in a sample volume was less than 2%. Gas densities were in the range (1-20) x lo-, mol an-, for CH,, C2H, and C,H6 and (0.3-4.0) x mol for the other hydrocarbons. The number of different sample densities varied from ten to twenty for the various gases.

Measurements were made on Bruker AM 250-MHz and WP80-SY spectrometers. The I3C studies were carried out in natural abundance except for methane, for which results were obtained using the same enriched samples employed in our simultaneous study of the temperature dependences of the isotope shifts’ and the spin-spin coupling constants of the methane iso- topomers.16 The principal reference and lock signal used was the CD, deuterium resonance of toluene-d, because of the larger temperature range of this liquid, although secondary references such as acetone-d, and cyclohexane-d,, were used on the WP80-SY spectro- meter. These liquids were placed in the Wilmad tube and surrounded the gaseous sample. Temperatures were

measured using the internal chemical shift between the alcohol and alkyl proton signals of methanol and ethyl- ene glycol accompanied by the data of van Geet” and more recent studies.”-”

The proton spectra of the two butanes and iso- pentane consisted of two broad regions. No analyses of these were possible and the central peak of each region was taken as the point for measurements. A second- order analysis based on the work of Corio and Hurst” was used for propane. The I3C NMR spectra were obtained with full proton decoupling employing the WALTZ- 16 composite pulse sequence which minimizes heating effects. Values of c1 and O, were obtained for each temperature by fitting to a linear function of the form of Eqn (1). A weighting factor of (error)-’ was applied to each point as the low-temperature values of O , were often less accurate than those for temperatures close to ambient. A more detailed account of our experimental procedure has been recorded.’

MAGNETIC SUSCEPTIBILITIES

We have measured the magnetic susceptibilities of the hydrocarbon gases employing the method introduced by Becconsall et al.’, and developed by Homer and Whitne~.’~ This makes use of the fact that in supercon- ducting spectrometers, where the magnetic field is applied parallel to the axis of the sample tube, (b1)b = - 47txJ3, whereas on spectrometers with an iron elec- tromagnet, where the field and axis are perpendicular,

= 2qJ3. xm is the molar magnetic susceptibility of the sample. It is obtained from the difference in ol measured on two such spectrometers. Thus,

where I and 11 denote measurements for the appropri- ate spectrometer and the second equality follows from the independence of ( o ~ ) , ~ ~ on orientation in normal fluids.

Our results are given in Table 1, where they are com- pared with a selection of earlier results, both experimen- tal and theoretical. Some further values are given in Landolt-BOrn~tein.~~ It is clear from Table 1 that precise and reliable values of xm for even simple com- pounds are yet to become available. This is a serious matter for the study of ol, especially for protons with their small c1 values, since a relatively small error in (GI),, leads to a relatively large error in (uJlOc. Fortu- nately, the problem should disappear in the next few years as the new SQUID (superconducting quantum interference device) magnetometer^^'.^^ are applied to the measurements of xm for diamagnetic molecules.34

RESULTS

Intermolecular effects

Values of ( o , ) , ~ ~ for proton shielding in the gases CH, , C,H,, C,H, and CzH4 were obtained from the meas- ured u1 values by correcting for ( b l ) b using the zm

948 B. BENNETT AND W. T. RAYNES

Table 1. x, measured in the present work, literature values and the values adopted to calculate (u,),, , with all results in units of 1 x c.gs. units mol-'

Other work Gas This work Exptl

CH4 -19.1 (*0.9) -17.4 (*0.8)' -18.7 (*0.4)b

'ZH4 -20.1 (i0.6) -18.8 (*0.8)" -19.7 (i0.4)b

C,H, -28.4 (i0.6) -26.8 (i0.8)"

C,", -40.3 (*0.9) -38.6 (i0.8)"

n- Butane lsobutane

-50.3 (*0.8)" -50.5 (*0.8)"

Neopentane -62.1 (i4.1) -63.0 (*l.O)'

lsopentane -63.0 (*1.0)"

a Barter et a/.'' "Trappeniers and O l d e n ~ i e l . ~ ~

Bernstein,z8 empirical value. Raynes et a/.," combination of an ab initio diamagnetic part

the J = 2 level. d

Calc

-1 8.8" - 1 9.459d -22.6"

-27.2" -30.9" -40.1' -40.2" -50.4"

-52.7" -52.1' - 64.6 -79.6" -63.5'

Values chosen to calculate

(U7)b

-1 8.7

-1 9.7

-28.4

-40.3

-50.3 -50.5

-63.0

-63.0

* Schindler and Kut~elnigg,~~ ab inifio calculation by the IGLO method. ' Burnham et a/.,30 empirical value.

n experimental paramagnetic part for

values given in the final column of Table 1. They are shown in Table 2 for the range 180-370 K. The esti- mated error (one standard deviation) in these results is + 3 ppm cm3 mol-I (except where shown explicitly), apart from the systematic error for each gas originating from the uncertainty in xm. The major features of the

results are the expected increase in the magnitude of (oJlOc as the temperature is lowered and the notably smaller numerical value of (oJlOc for methane compared with the other gases at any one temperature. There is only the slightest suggestion that the methyl protons in C,H, possess a numerically greater than the

Table 2. Values of (ul),= for the proton rmnance of some simple hydrocarbons over the temperature range 180-370 K'

Temperature C3H8 (K) CH4 C2He CH3 CHZ CZH,

180 -16.6 190 -16.6 21 0 -14.0 230 -12.1 250 -25.0 255 -10.3 -16.1 ( i 4 ) 260 -19.5 265 -14.4 (*4) 270 -17.3 275 -14.0 ( i4 ) 280 -9.1 290 -6.0 -14.0 -13.4 295 -14.5 (*4) 300 -13.8 -17.0 (*4) -15.3 (*4) -1 2.8 305 -1 2.6 -10.9 31 0 -7.9 320 -5.0 -17.5 (*5) -17.6 (+5) -9.5 330 -13.2 345 -4.5 350 -12.3 -14.5 -1 3.3 -1 1.7 370 -5.9 -11.5 (*4) -9.1 -9.7

'All results are in units of ppm em3 mot-' and have error *3 in these units except where stated.

INTER- AND INTRA-MOLECULAR EFFECTS ON 'H AND "C SHIELDING 949

Table 3. Values of (uJlOc for proton resonance in CH,, C,H, and C,H, at room temperatures measured in this work and by other workers'

Reference CH4 C2He cih4 Gordon and Dailey (1961)35 Raynes et a/. (1 962) Widenlocher (1 966)" Meinzer (1965)37 Mohanty and Bernstein (1 971)j8 Rummens (1971)39 Trappeniers and Oldenziel (1 975) 27

Rummens and Mourits (1977)40 Smith and Raynes (1983)" This work

-4.8 (*2.2) -6.7 (*2.2) -2.9 (*2.2) -14.5 (*2.2) -3.8 (*3.1) -5.5 (*4.2) -8.7 (i3.1) -6.6 -2.6 (i2.2)

-7.7 (*0.8) -9.9 (*0.9) -13.8 (k1.3)

-3.4 ( i l .8) -8.7 (*2.4) -1 5.4 (h2.5) -21.1 (zt1.8) -7.6 (*3.0) -13.8 (*3.0) -11.9 (*3.0)

"The results are listed in date order. All values are in ppm cm3 mol-'.

methylene protons, but it is clearer that (ol)loc for either kind of proton in C3Hs is greater numerically than for the protons of either C2H, or C2H4.

Although (ol),oc for these gases has not, as far as we are aware, been measured at different temperatures, a number of workers have measured (ol)Loc for CH,, C2H4 and C2H6 at room temperature. Their results are listed in Table 3. There are relatively large differences among these results. This cannot be attributed to the small differences in 'room temperature' stated by the various workers (ours is 300 K) since variations due to this are within experimental error. In constructing Table 3 we have used our chosen x,,, values (see Table 1) to obtain (ol),, for all the results, not just our own. It

must also be remembered that there is a constant, sys- tematic error unique to each gas due to the uncertainty in x,,. Putting this to one side, it does seem reasonable to state that the room temperature values of (ol),oc are about -8, -14 and -10 ppm cm3 mol-' for CH,, C2H, and C2H4, respectively.

Our results for the temperature dependence of (ol)loc will be discussed later." We note here that for CH, and C2H6 it is probably valid to equate (ol)loc with ( c ' ) ~ . However, for C2H4 this is less certain since due to quadrupole-quadrupole interactions and (o& due to magnetic anisotropy effects may be significant.

Values of (ol)loc for 13C shielding in the four hydro- carbon gases are listed in Table 4 for the temperature

~ ~ ~ ~~~~~

Table 4. Values of (ul),= for "C resonance of some gaseous hydrocarbons in the range 180-370 K and results for some other hydrocarbons'

Temperature ( K)

180 1 90 21 0 230 250 255 260 265 270 275 280 290 300 305 320 325 330 345 350 370

CH4

-314 (*lo) -312 (*11) -275 -265 (17)

-253

- 245 - 242

-239 -234 - 234

-233

- 230

-243

-234

-226 (*7)

-21 1

- 202

-184 -184

-181

-219 (*lo)

-203 ( i l l )

-21 1

- 327 -182 -320 -1 55 -1 64

-1 64 -283 -149 -1 64

-259 -144 -169 (*8) -255 -135

Other results: at 350 K: n-Butane C-1, -404 ( i 8 ) ; C-2, -180 ( i8) lsobutane C-1, -399 (*26); C-2, -119 (+26) Neopentane C-1, -600 (*40); C-2, -418 (*26)

at 370 K: lsopentane C-1 , -590 ( * P O ) ; C-2, -1 31 (*22) ; C-3, -245 (*22) ; C-4, -590 ( i40 )

"All results are in pprn cm3 mol-' and have an error of *6 in these units except where stated.

950 B. BENNETT AND W. T. RAYNES

range 18C370 K. Some additional results for n-butane, isobutane and neopentane at 350 K and for isopentane at 370 K are also given. The error here (one standard deviation) is estimated to be 1 6 ppm cm3 mol-' down to 250 K, and to be somewhat larger at lower tem- perature. Again, the most obvious feature of the results is the numerical increase in (ul)Ioc for each gas as the temperature is reduced. In contrast to the proton shield- ing results in Table 2, the numerical value of (ol)Ioc for carbon shielding in CH, is greater at any one tem- perature than that in C&, C2H4 and for the methy- lene carbon of propane, and only slightly smaller than that of the methyl carbon of propane. There is now a very clear distinction between the two carbon nuclei of propane, with I ai(CH3) I being almost twice as large as I a1(CH2) I at any temperature. The results for a single temperature for the butanes and pentanes given at the bottom of Table 4 again show marked differences between (ol),oe values for the different carbon nuclei in a given compound. The I (ol)lQc 1 values for the methyl carbon nuclei of isopentane and neopentane are the largest so far determined for carbon nuclei.

( c T ~ ) , ~ ~ for the carbon nucleus of CH, gas was meas- ured at 10 K intervals in the range 220-380 K by Jameson et al." Their results are presented in units of Hz amagat-' for measurements at 22.63 MHz. Using a conversion factor of 1 Hz amagat-' at 22.63 MHz = 990.3 ppm cm3 mol-', we calculate that they obtained - 267 ( f 60), - 224 ( f 8) and - 209 (k 90) ppm cm3 mol-' at 220, 300 and 380 K, respectively. These results are close to, but slightly smaller than, our results at each of these temperatures.

There are four literature results for (ol)loc of the proton resonance in C2H4, all at room temperature: -6.7 (f2.2),35 -8.7 (+3.1),36 -9.9 (+0.9)27 and -21.1 (+ 1.8)" ppm cm3 mol-'. Our results at 300 and 305 K are -12.8 and -10.9 ppm cm3 mol-', respec- tively, and are therefore closest to those of Trappeniers and Olden~iel.~, For C2H6 the literature results are also for room temperature only, and are - 5.5 ( f4 .2 )p -13.8 (+2.2)6 and -15.4 (f2.5)" ppm cm3 mol-'. Our results of -13.8 and -12.6 ppm cm3 mol at 300 and 305 K, respectively, are close to that of rum men^.,^ All the literature results for C2H4 and C2H6 were obtained by us from the original data using the susceptibility values given in the final column of Table 1. The concepts used to explain these r e s ~ l t s ~ ~ * ~ ' involve the electric field dependence of shielding.,, They will be discussed separately."

Intramolecular effects

Let us first consider the temperature dependence of no. This cannot, of course, be measured directly since one can only measure the temperature dependences of shielding differences. Therefore, to obtain values of da,/dT it is necessary to know the temperature depen- dence of the reference shielding. The most straightfor- ward way to do this is to follow the procedure introduced by Jameson et aL4, of measuring the appro- priate nuclear shielding of the reference liquid with respect to the I2'Xe shielding for a range of tem- peratures. At each temperature a graph is plotted of the

shielding difference against the xenon density and then this graph is extrapolated to zero density. In this way one obtains the temperature dependence of the refer- ence shielding, since the shielding of xenon gas extra- polated to zero density is independent of temperature.

In this work we chose methane gas at zero density as the reference. Earlier we had made a careful study' of the proton isotope shifts and their temperature depert- dence for CH,D and CHD, with respect to CH, . From the results it was possible to deduce the dependence of proton shielding in CH, on the bond stretching and angle bending, and hence to predict the temperature dependence of the proton shielding over the tem- perature range of the present experiments. For zero density we calculate a value of -0.05 x ppm K-'. This is a true experimental result in that it depends on a combination of experimental NMR measurements' and on an experimentally determined force field.44 No the- oretical assumptions are made, apart from the expan- sion of the shielding surface and force field as Taylor series in internal coordinates with truncation after the second order for the shielding surface and after the third order (i.e. including cubic anharmonic terms) for the force field.

As mentioned earlier, our principal reference was liquid toluene-d, . We first measured the temperature dependence of the shielding of the protons of the CHD, group in the appropriate isotopomer of toluene-rl, present in the toluene-d, with respect to the proton shielding of methane for several methane densities, anid then extrapolated to zero density. A further small cor- rection was necessary because of the small difference in do/dT for the proton of the CHD, group in the toluene-d, and the deuteron of the CD3 group of the toluene-d, . We obtained a value of - 3.66 (fO.08) x

ppm K-' for the temperature dependence of the shielding of these deuterons using the 250-MHz spec- trometer. This result was confirmed by independent measurements on two separate samples involving methane at fixed low density with respect to toluene-d, and then correcting for the value of da,/dT for the methane gas at these low densities. An identical result was obtained. It was clear from these experiments that it is reasonable to neglect intermolecular effects when methane gas is used as an external reference, provided that the methane pressure is lessthan 10 atm.

Values of doo/dT in proton resonance for the other gases studied are given in Table 5 and show estimated errors in each case. For ethane and propane results were obtained by both extrapolating to zero density of the gas (method 11) and by taking a single sample with low density gas and then correcting for da,/dT (method 111). It can be seen that the values are very small, being of the same order as the experimental error. However, apart from the C2H4 result, they are all negative. There appears to be an experimentally significant discrepancy between the results for both the shielding constants in propane obtained by the two methods. The reason for this is not yet known,

shielding in various gases are given in Table 6. These results for methane were obtained using I3C-enriched samples and two methods as before. We found that the CD, carbon nucleus of toluene-d, has do/dT = +0.75 (f0.09) x ppm

Results for dao/dT for

INTER- AND INTRA-MOLECULAR EFFECTS ON 'H AND SHIELDING 951

Table 5. Experimental values of du,/dT for protons in various g-'

Range of Gas temperature (K) do,ldT Method

CH4 200-370 C2H4 253-350 C2H6 250-370

21 8-372 CaH, H-1 289-370

H-2 289-370 261-370

261 -370

-0.05 +0.05 (i0.22) -0.1 0 (*0.9) -0.07 (*O.lO) -0.23 (i0.12) -0.07 (*O.l 1 ) -0.29 (i0.i 1) -0.09 (*O.ll)

'All results are in units of 1 x ppm K-'. Calculated from experimental isotope shift data.5 Obtained from extrapolation to zero density of the gas. Obtained from a single sample after correcting for do,/dT.

K - ' for the 250-MHz spectrometer. These methods were repeated for the other gases, except for the butanes and pentanes for which method I11 was used involving no correction for do,/dT. The results in Table 6 give experimentally significant values of da,/dT for most carbon nuclei with positive and negative values occurring. The value of do,/dT for the carbon shielding in methane, viz. -0.30 (k0.14) x lo-' ppm K-', has not previously been measured. Jameson et ai.' ' esti- mated it to be smaller than -0.2 x lo-' ppm K-' and

with respect to a primary or secondary reference com- pound whose shielding constant is known. Secondary references for proton and ''(2 shielding in this work are the nuclei of methane for which o(H) = 30.61 1 (f 0.024) ppm at 25°C45 and G('~C) = 194.8 (k0.9) ppm at 27°C.46 Although we have measured our shielding dif- ferences with respect to toluene-d, , for the purposes of comparison we given them in Table 7 relative to the secondary reference methane for several of the com- pounds studied in the present work. Our values for both 'H and 'jC shielding, which are for 348 K, are more precise than earlier values but are generally in agree- ment with them. However, there are differences between gas- and ~olution-phase~~ data in proton resonance. Agreement is better in ''C resonance apart from iso- butane, where some uncertainty about the assignments of the signals still exists, and in isopentane, where there is disagreement on the relative positions of the C-2 and C-3 resonances in the gas phase. Our ordering is the same as that from solution-phase work. In the lower part of Table 7 we give internal shielding differences with respect to the appropriate nucleus of the methyl group of each compound. This permits some additional work to be introduced for comparison. The gas-phase results in Table 7 are in fairly good agreement among themselves, but there are serious differences with the solution-phase values of some standard literature tabu- lations as discussed in the next section.

our ab initio cal~ulation'~ gave -0.26x lo-' ppm K-'.

DISCUSSION uo values

The cro values of chemical compounds cannot be mea- sured directly. One measures the shielding difference

Table 6. Experimental values of da,/dT for the carbon nuclei in various g d

n- Butane

lsobutane

Neopentane

lsopentane

c-1

c-2

c- 1 c-2 c-1 c-2 c-1 c-2 c-1 c-2 c-3 c-4

Range of temperature (K)

180-370 190-370 253350 250-370 21 8-372 289-370

289-370

300-369 300-369 300-370 300-370 300-370 300-370 330-371 330-371 330-371 330-371

261 -370

261-370

do,/dT

-0.30 (*0.14) -0.32 (iO.19) -0.33 (*0.18) +1.67 (i0.20) +1.74 (hO.10) +0.07 (iO.11) +0.42 (+0.14) +2.33 (*0.12) +2.76 (*0.21) +1.80 (iO.17) +3.10 (iO.14) -0.92 (*0.26) +2.21 (*0.37) -2.65 (i0.20) +0.38 (i0.24) -0.25 (*0.25) +1.41 (*0.15) +0.71 (*0.14) +2.15 (i0.22)

'All results are in units of 1 x lo-' ppm K-'. Obtained from extrapolation to zero density of the gas. Obtained from a single sample after correcting for daJdT As b except no correction for do,/dT.

Method

I l b 111' II I I Ill II Ill II Ill I I l d l l l d l l ld

Illd l l ld l l ld l l l d l l ld l l l d l l l d

We start with (ol)loe. As noted for proton resonance, it is probably valid to equate this with (u&, for the 'H and resonances of all the compounds listed in Tables 2 and 4. The most likely exception is C,H4, where (a& may be significant in both 'H and 13C resonance and (~7 ' )~ in proton resonance.

Although we believe that our results present a major step forward in yielding (ol)loe as a function of tem- perature for the nuclei investigated, we also take the view that some significant improvemements in the pre- cision of measurement is necessary before (ol),oc and its temperature dependence can be used to determine crpair for a particular molecular pair. It is to be expected that many possible functions upair will produce the same (ol)loc as a function of temperature within the present experimental error. It appears from the results of Tables 2 and 4, and also from the work of Jameson et al." on the "C shielding in CHI, that ( o ) , ~ ~ is less temperature dependent at room temperature and above than at low temperatures. It would be desirable to establish this firmly by carrying out measurements at higher tem- peratures. This would also permit the determination of (ol)loc for nuclei in less volatile compounds such as those mentioned at the bottom of Table 4. It is hoped to carry out such measurements in this laboratory in the near future. In the following paperI5 we discuss the results in Tables 2 and 4 in relation to existing quanti- tative models of intermolecular effects on nuclear shield- ing.

Ideally, the values of do,/dT given in Tables 5 and 6 are for use in the extraction of molecular coeficients

952 B. BENNETT AND W. T. RAYNES

n-Butane

lsobutane

Neopentane

lsopentane

Table 7. Proton and 13C shielding differences of some hydrocarbons studied in the present work with respect to the corresponding nuclei of methane (all substances in the gaseous state at 348 K) and literature values for the same compounds in gaseous and liquid phases near 300 K (all results in ppm)

'H '3C Hydrocarbon Au (this work) Au (other work). Au (this work) ,b (other work).

C2H4 -5.165 (*0.010) -5.16747 -1 30.456 (*0.015) -1 30.535 -1 30.653 -1 29.7955

C*H' -0.739 (*0.004) -0.75' -1 3.973 (*0.006) -14.2553

-14.0755 -1 4.225e

C3H8 H-1 -0.797 (*0.005) -0.6804' c-1 -24.146 (*0.006) -24.2553 -24.1655 -24.31 5e

H-2 -1.245 (*0.005) -1.11748 c-2 -25.731 (i0.006) -25.8853 -25.8355 -25.965e

n- Butane H-1 -0.802 (*0.005) c-1 -21.298 (*0.008) -21 .585e H-2 -1.228 (*0.005) c-2 -34.767 (i0.008) -35.0g5'

lsobutane H-1 -0.772 (*0.005) -0.66448 C-1 -32.643 (i0.008) -32.7gS3 -32.685'

H-2 -1.591 (*0.005) -1.51448 c-2 -33.450 (i0.008) -32.31 53 -33.525e

Neopentane -0.81 5 (*0.006) -0.701 48 c-1 -39.660 (*0.013) -39.71 53

-0.841 49 -39.71 5e

c-2 -36.788 (*0.011) -36.9853 -36.955e

c-2 -40.1 89 (*0.011) -41 .675e c-3 -41.668 (iO.011) -40.1 85' C-6 -19.380 (*0.011) -1 9.325e

-0.6304' - 1 4.254

lsopentane c-1 -30.109 (*0.011)

Internal shielding differences with resped to the appropiate nucleus of the methyl group (C-1 for isopentane)

-0.448 (*0.004) -0.43748 -1.585 (*0.006) -1 .6353 -0.43550 -1 .6755 -0.4275' -0.51 850

-0.4857 -0.426 (*0.007) -Q.40352 -1 3.469 (iO.011) -1 3.51 ''

-0.3985' -1 1 .6658 -1 1 .8057 -1 1 .go5'

-0.81 9 (*0.004) -0.8504' -0.807 (*0.008) -0.845e -0.82g5' +0.4853

-0.8357 +2.872 (*0.016) +2.7656

+2.7353 +3.657

-8.0" -7,957.65 c-2 -1 0.08 (k0.02)

c-3 - 1 1.56 (*0.02) -9.785 -9,857.63

c-4 +10.73 (*0.02) +1 0.4e5 +10.557*e3

a Refs 6 and 53-56 are gas-phase values; Refs 48-52 and 57-59 are solution- and pure liquid-phase values. -

describing the dependence of nuclear shielding on geometry in the shielding surfaces. To obtain the full shielding surface of a nucleus in a molecule one needs to determine oo as a function of temperature for the chosen nucleus, not only in the given molecule but in most (if possible, all) of its isotopomers. For hydrocar- bons this has to date only been accomplished for the carbon shielding in methane for which three of the deu- terated isotopomers were studied.' Wesener et aL6'

obtained carbon isotope shifts for two deuterated iso- topomers of C2H6 but no temperature variation was carried out. On the theoretical side, Chestnut et aL6' predicted that the torsional motion in C2H, will con- tribute to dao/dT for the carbon shielding.

We close with a discussion of uo for the carbon shielding of the compounds in Table 8. Most chemists requiring the carbon shielding in these compounds would obtain the necessary data from one of the four

INTER- AND INTRA-MOLECULAR EFFECTS ON 'H AND ''C SHIELDING 953

Table 8. Carbon-13 chemical shifts (in ppm) relative to tetra- methylsiane as tabulated in three standard works of refer- ence for some alkane molecules.

Levy el a/ 03 Breitmaier and

Stothed' Voelter- Kalinowokt ef c-1 c-2 c-1 c-2 c-1 c-2

CH, -2.1 - -2.3 - -2.3 C,H, 5.9 5.9 5.7 5.7 6.5 6.5 C,H, 15.6 16.1 15.4 15.9 16.1 16.3 lsobutane 24.3 25.2 24.1" 25.0 24.6 23.3 Neopentane 31.5 27.9 27.4 31.4

a 24.3 according to Ref. 64.

standard works on 13C NMR.62-6s In Table 8 we give those data in the form of chemical shifts relative to tetramethylsilane, and with the scale direction such that the smaller the shielding the more positive is the chemi- cal shift. A more recent work66 gives data identical with those of Stothers.62 All these results were obtained on liquid-phase samples. Those given by Stothers, Levy et al. and Breitmaier and Voelter are taken from the mea- surements of Paul and Grants7 supplemented by those of Spiesecke and S~hneider.~' The tabulations of Sto- thers and Levy et al. differ throughout for the nuclei of interest here by a constant amount of 0.2 ppm. The results of Kalinowski et ~ 1 . ~ ~ are stated to be 'mea- sured on a 1 :1 mixture of alkane with 1,cdioxane'. There are two points we wish to make. Evaluation of the shielding differences with respect to methane using the data in Table 8 gives very different results from the data in Table 7. Consider the shielding of C,H6 with respect to methane. This is - 8.0 ppm according to Sto- thers, Levy et al. and Breitmaier and Voelter and -8.8

ppm according to Kalinowski et al. However, the several, independent gas-phase measurements reported in Table 7 all show that the true value is about -14 ppm. This difference cannot be attributed to differential solvent effects on C2H6 and CH,, as is clear from gas-to-liquid We believe that the discrep- ancy is due to faulty measurements on methane in the early liquid-phase work. The second point is the poor agreement, possibly due to differing assignments, between the data of Stothers, Levy et al. and Breitmaier and Voelter on the one hand and Kalinowski et al. on the other. Our results, whilst admittedly for the gas phase, are in much closer agreement with those of Sto- thers and Levy et al.

Acknowledgement

The authors acknowledge the support of an SERC postgraduate stu- dentship to B.B.

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