Carbon-13 Isotope Effects on Proton Transfers from Carbon BY JOHN BANGER JAFFE AN-CHUNG ANNETTE LINAND WILLIAM JR.* H. SAUNDERS Department of Chemistry University of Rochester Rochester New York 14627 U.S.A. Receiiied 22nd April 1975 Carbon-13 isotope effects at C-2 have been determined on the rates of elimination from 2-phenylethyl-dimethylsulphoniumand -trimethylammonium salts with hydroxide ion in mixtures of dimethyl sulphoxide and water. The effects are consistently larger than those predicted from model calculations for a semi-classical (without tunnelling) isotope effect. The most reasonable inter- pretation is that the form of the dependence of the isotope effect on solvent composition is controlled by the semiclassical effect with a substantial tunnel effect superimposed.For some time deuterium and tritium isotope cffects ir? hydrogen-transfer reactions have been interpreted in terms of the Melander-Westheinier model,' * which predicts a maximum in the isotope effect when the hydrogen is half transferred. Bell and Goodall predicted that proton-transfer reactions should show this inaximgm when the pK values for the substrate and the conjugate acid of the attacking base were equal and presented evidence that this prediction was at least approximately true. Subsequently maxima in kH/kDvalues have also been achieved with sinzle substrates by varying the compositions of mixtures of aqueous hydroxide and dimethyl ~ulphoxide.~-~ Although this picture can be modified somewhat by tunnel effect^,^ non-linear transition states or inclusion of the proton transfer in a more complex reaction coordinate such as that for bimolecular eliii~ination,~.'~ it has stood without sub- stantial challenge until recently.Bordwell and Boyle argue that the maximuin in a plot of kH/kD against ApK is so broad and diffuse as to be of little value in determining transition-state syinmetry.ll Bell Sachs and Tranter conclude from calculations on an electrostatic model of the proton-transfer transition state that there is little variation in the stretching force constants of the base-proton and substrate-proton bonds as the base strength is varied and that observed kH/kDmaxima arise primarily from variations in the tunnel effect contribution. l2-I3 Rather large variations in the relative values of these force constants are needed to obtain isotope effects substantially below the maximum values from a semiclassical (without tunnelling) model.In view of the uncertainty currently surrounding the interpretation of hydrogen- transfer isotope effects we decided to undertake a study of carbon isotope effects on proton transfers from carbon. The reactions chosen to begin our study were the E2 reactions of 2-phenylethyl-dimethylsulphonium and -trimethylainmonium salts with hydroxide ion in mixtures of water and dimethyl sulphoxide. Both had been shown to give k,/k maxima.5* The dependence of the semiclassical isotope effect lo and the tunnel effect l6 for 13C as compared with 12C had been calculated as a function of the extent of proton transfer by the Wolfsberg-Stern-Schachischneider programs.' 7*1 These two contributions to the overall isotope effect appeared to differ sufficiently to permit a clear assessment of their relative importaiice from experimental data.113 CARBON-13 ISOTOPE EFFECTS EXPERIMENTAL MATERIALS 2-Phenylethyldimethy1sulphoniumbromide and 2-phenylethyltrimethylammoniumbro-mide were prepared as previously described. 19-2 Inorganic chemicals and the solvents used for extraction were analytical reagent grade. Dimethyl sulphoxide was purified by refluxing over calcium hydride followed by fractional distillation. Mixtures of water and dimethyl sulphoxide were prepared by weight. REACTIONS Reaction mixtures consisted of 50-75 ml of solution 0.1-0.2 M in substrate and 0.1-0.5 M in sodium hydroxide.The solutions were prepared and the reactions allowed to run in a constant-temperature bath controlled to 0.05"C. Two techniques were used. For the slower reactions an excess of base was employed the reaction allowed to run to the desired extent of completion as estimated from available rate con~tants,~~~ the reaction mixture cooled in ice water and the extent of reaction confirmed by titration of unconsumed base. For fast reactions an insufficiency of base was used so as to stop the reaction at the desired extent of completion and the mixture checked for any remaining base by titration. Titration of reaction mixtures containing 2-phenylethyltrimethylammoniumbromide used thymol- phthalein as indicator with added pyridine to repress interference from the tertiary amine present.2*2 The neutralized reaction mixtures were extracted with five 30-ml portions of benzene to remove styrene and then evaporated to dryness on a rotary evaporator with a mechanical pump. For reaction mixtures containing high proportions of dimethyl sulphoxide water was added to the residue and the extraction and evaporation process repeated. Tests with simulated reaction mixtures showed that the styrene was completely removed by this procedure. DEGRADATION OF UNREACTED SUBSTRATE The residue obtained above was dissolved in 100 ml of water. About 1.5 g of sodium carbonate was added followed by the cautious portionwise addition with stirring of potassium permanganate until its colour persisted (at least 10 g).After the reaction subsided the mixture was heated on a water bath for 3 h cooled in an ice bath and cautiously treated with sodium sulphite to destroy excess permanganate followed by acidification (litmus) and stirring for an additional half hour. The mixture was then extracted with three 100-ml portions of ether the extracts dried over magnesium sulphate and the ether removed. The residue was recrystallized from hot water to give benzoic acid in essentially quantitative yield. Its purity was checked spectroscopically on selected samples. A 30-40-mg sample of benzoic acid was dissolved in 6-9 ml of concentrated sulphuric acid in a 50-ml 3-neck flask. Dry nitrogen was bubbled through the flask and an attached collection trap for 30 min.The trap was then immersed in liquid nitrogen the flask heated to 40-60",and a side arm containing 20-30 mg of sodium azide rotated so as to add the azide to the flask. The reaction was allowed to proceed for one hour. The collection trap (still cooled by liquid nitrogen) was removed from the flask attached to a vacuum line pumped on carefully to remove nitrogen and then evacuated for 15 min with a mercury diffusion pump. It was then transferred to a gas chromatograph inlet and the contents swept by a helium flow of 25 ml/min onto a 30-ftx 1/4-in column of 20% adiponitrile on Chromosorb P. The carbon dioxide was collected in a trap cooled by liquid nitrogen. The trap was transferred to the vacuum line and the carbon dioxide condensed in a drying trap containing phosphorus pentoxide.The carbon dioxide was then transferred to a mass spectrometer sample tube. ISOTOPE RATIO DETERMINATION Sample tubes containing the carbon dioxide from the original substrate and from substrate recovered after partial reaction were attached to the dual viscous inlet system ofan J. BANGER A. JAFFEE A,-C. LIN AND w. H. SAUNDERS JR. 115 Atlas CH-4mass spectrometer equipped with dual Faraday cup collectors and the ratio of the m/e 44/45 values determined for each sample. There was some dependence of apparent isotope ratio on sample size. In the work with the sulphonium salt a plot of apparent isotope ratio against sample size (measured as total ion current) was prepared using tank carbon dioxide and was used to correct the sample isotope ratio to the value it would have at the same pressure as the standard.Improved precision was obtained in the work on the ammonium salt by keeping sample and standard sample total ion currents within f10% of each other and running the standard both before and after each sample. Observed 44/45 ratios were corrected for the natural abundance of 170 in the sample. CONTROL EXPERIMENTS Carbon isotope ratios (44145) from three samples of carbon dioxide from the same tank were the same to within rfrO.l%. Five samples of the same lot of benzoic acid were decarboxylated to give carbon dioxide samples of the same 44/45 ratio to within +0.2%. Two identical samples of 2-phenylethyldimethylsulphoniumbromide were dissolved in base- solvent mixtures containing pure water and 40% dimethyl sulphoxide respectively and recovered before any significant reaction could occur.They were degraded to give carbon dioxide of the same isotope ratio to within +0.2%. Another three samples of the sulphonium salt were degraded (without prior dissolution) to give carbon dioxide of some- what more variable isotope ratio (+0.4%) but the sample sizes as measured by total ion current varied over a 30%range. Finally there was no measurable attack of base on the glass reaction flasks over the time of the longest reactions. RESULTS The substrates Ia and Ib have been previously shown to react with PhCH2CH2X Ia X = -SMe2Br Ib X = -NMe,Br hydroxide in mixtures of dimethyl sulphoxide and water to give quantitative yields of styrene.Samples of each substrate were oxidized with potassium permanganate 9 0 00 0 20 40 60 80 100 mole % water FIG.1.-Observed j3-12C/13C 1)x 100 for the reactions of isotope effects expressed as (kI2/kl3-2-phenylethyl-dimethylsulphoniumion at 30°,open circles and -trimethylammoniom ion at 60°C closed circles with hydroxide ion in mixtures of water and dimethyl sulphoxide. to give benzoic acid which in turn was decarboxylated by treatment with hydrazoic and sulphuric acids to give carbon dioxide whose m/e 44/45 ratio was determined on an isotope-ratio mass spectrometer. Control experiments showed that the degradation was quantitative and gave isotope ratios reproducible to & 0.2 %. The elimination CARBON-13 ISOTOPE EFFECTS reactions were allowed to proceed to a specified extent and unreacted substrate isolated and degraded as above.The isotope ratio for the original sample (R"), the recovered sample (R),and the fraction of reactant remaining (F)were then substituted into eqn (1) to calculate the isotope effects. l4 The resulting values are collected k1&3 = log F/log(RF/R") (1) in table 1 and shown graphically as a function of solvent composition in fig. 1. Before the experimental results can be discussed the calculated values of the isotope effects must be considered. The transition-state model (11) was closely similar to that used earlier.g. lo The " extent of hydrogen transfer " was defined as the fractional weakening of the C-H bond.The extent of C-S bond weakening TABLE DIM CARBON ISOTOPE EFFECT FOR THE REACTION OF PhCH2CH2X WITH HYDROXIDE ION IN MIXTURES OF WATER AND DIMETHYL SULPHOXIDE X percent DMSOa ternp/'C* no. of detns. (klz/k13-l) x 100" SMe2 SMe SMe2 SMe SMe SMe §Me2 SMe SMe2 NMe NMe NMe NMe NMe NMe NMe NMe NMe 0.0 1.25 2.5 5.0 5.O 7.25 10.0 40.0 6.0 0.0 0.0 5.0 10.0 10.0 20.0 40.0 40.0 60.0 30 30 30 30 30 30 30 30 30 60 80 60 60 80 60 60 80 60 5 5 6 8 3 7 10 7 3 3 4 4 4 3 3 3 4 4 2.17$-0.18(0.50) 2.23f0.S4(0.39) 3.05 0.17(0.44) 3.40+ 0.14(0.33)d 3.15+ 0.08(0.34)e 1.925 O.OS(0.12) 2.32+ 0.09(0.20) 2.01 +0.09(0.22) 1.83+O.l l(0.47) 2.13 f0.05(0.22) 1.54+0.13(0.41) 1.64f O.Og(0.29) 1.61f0.04(0.13) 1.4650.03(0.13) 1.57+0.05(0.22) 1.61f0.14(0.60) 1.69f 0.13(0.41) 2.105 0.15(0.48) a mole percent ; b -t 0.1"C; C percent isotope effect.The figure immediately following the & is the standard deviation of the mean while the figure in parentheses is the 95% confidence limit. d results obtained by A. Jaffe ; e results obtained by A.-C. Lin under same conditions as for d. the extent of 0-H bond formation and the extent of C-C double bond formation were changed parallel to the extent of hydrogen transfer. A moderately curved potential barrier giving a maximum reaction coordinate frequency of ca. 9OOi cm-l was used.lg Other details of the model are described el~ewhere.~ lo The calculated isotope effects as functions of the extent of hydrogen transfer are given in fig. 2 for b-hydrogen as compared with deuterium and in fig. 3 for P-"C as compared with 13C.The figures also include the tunnel corrections calculated from the simple form of the Bell equation,13 which is valid for all values of the reaction-coordinate frequency of our model. This model should be valid for discussions of isotope effects for both Ia and Ib for the deuterium isotope effect is independent and the carbon isotope effect nearly independent of the nature of the leaving group.1° The effects of varying numerous parameters for I1 and related models have been explored.1° While numerical values can be changed by such manipulation the basic bell shape of the deuterium isotope effect curve and the S-shape of the carbon isotope effect curve remain essentially the same. J. BANGER A. JAFFE A.-C. LIN AND W. H. SAUNDERS JR.117 CH2-CH2 H H-0 I1 Intelligent comparison of the experimental results and the model calculations requires some knowledge of the relation between the solvent compositions used in the experiments and the " extent of hydrogen transfer ". No rigorous connection is possible but one can make the reasonable assumption that increasing dimethyl sulphoxide concentration leads to a decrease in the extent of proton transfer in the transition state because the hydroxide ion is becoming a stronger ba~e.~~'~' Second one can compare the experimental k,/k values (fig. 4) at the maxima with the smallest values on either side of the maxima. One then transfers these (kH/kD)max/(kH/kD)mi" values to the calculated kH/kDcurves of fig. 2. From such comparisons one can conclude that the pure-water result for the sulphonium salt represents an extent of hydrogen transfer of about 0.5 or a little more while 60% dimethyl sulphoxide represents about 0.3 extent of hydrogen transfer.Corresponding figures for the ammonium salt results (allowing for the temperature difference) are about 0.6 and 0.2 respectively. Whether or not the tunnel effect is included in the calculated values has only a minor influence on these ranges. 01 03 05 07 09 extent of H-transfer FIG.2.-Calculated values of k~/k~ for elimination from ethyldimethylsulphonium ion at 25°C. See text and ref. (9) and (10) for details of model. Closed circles semiclassical isotope effect ; open circles tunnel effects ; half-open circles combined semiclassical and tunnel effects.DISCUSSION The results for the sulphonium salt (Ia) in fig. 1 show a scatter at low proportions of dimethyl sulphoxide which considerably exceeds the combined standard deviations. The t-test 28 demonstrates that the results at 95.0 and 97.5% water are significantly higher with >99 % probability than all other results. Similar isotope effects (3.40 and 3.15 %) were obtained by two different workers at 95.0 % water. We can see no good reason however why the results at 100 and 98.75 % water should be so different from those at 97.5 and 95.0% water. Some systematic error perhaps arising from the slowness of the reactions in the highly aqueous media may be involved. We CARBON-23 ISOTOPE EFFECTS assume that the results follow a smooth curve of the sort depicted in fig.1 giving approximately equal weight to all points in the 95-100% water region. Even if one set should be incorrect only the slope not the basic shape of the curve would differ. The shape of the dependence fits best either the semi-classical isotope effect or the isotope effect with tunnelling of fig. 3. It might also fit though less well the tunnel effect curve over the restricted range of extent of hydrogen transfer (ca. 0.3-.05) covered by the results. A pure semiclassical isotope effect can be excluded by the magnitude of the observed effects. The lowest observed value is 1.8 % rather than the inverse effects predicted by the pure semiclassical model. Varying the parameters of the model can give larger numerical values than those depicted in fig.3,1° but no realistic set of parameters gives semiclassical effects as large as those observed in the 0.3-0.5 extent of hydrogen transfer region. The most reasonable interpretation of the results is that the shape of the dependence follows approximately the semiclassical isotope effect but with a tunnel correction somewhat larger (ca. 2.0-2.5%) than that in fig. 3 superimposed. A dependence dominated by the tunnel effect cannot be completely excluded however for the sulphonium-salt results alone. 0.1 0.3 0.5 0.7 0.9 extent of H-transfer Fro. 3.-Calculated ,9-1*C/'3C isotope effects expressed as (klZ/kI3-1) x 100 for elimination from ethyldimethylsulphonium ion at 25°C. See legend to fig. 2 for explanation of symbols.The results on the ammonium salt (Ib) provide a better test since they are more precise and cover a wider range (ca. 0.2-0.6) of extents of hydrogen transfer. Although they describe a relatively shallow curve as the solvent composition varies the t-test 22 gives a >99 % probability that the value in 80% water is lower than the value in 100%water and >95% probability that it is lower than the value in 40% water. The ammonium-salt data are clearly not consistent with an isotope effect controlled by the tunnel effect but they are also too large to result from a pure semiclassical effect. The best interpretation would seem again that the shape of the dependence on solvent composition is controlled by the semiclassical isotope effect but with a relatively constant tunnel correction of ca.1.5-2.0 % superimposed. For both Ia and Ib then an interpretation roughly consistent with the calculated curves of fig. 3 is possible. The model used for fig. 3 does seem to underestimate the tunnel effect somewhat and to give it too sharp a maximum at 0.5 extent of hydrogen transfer. A tunnel effect which is nearly constant over the range 0.2-0.6 extent of hydrogen transfer provides better fits to our results. J. BANGER A. FAFFE A.-C. LIN AND w. H. SAUNDERS JR. 119 The limited temperature-dependence data in table 1 also support an important tunnel effect contribution. The observed isotope effects at 80°C in 90 and 100% water are significantly smaller (>95 % probability by the t-test) than those at 60°C though the effects at 60 and 80°C in 60% water are not significantly different.The semi- classical model predicts a somewhat inverse temperature dependence over the 0.2-0.6 extent-of-hydrogen-transfer range while the tunnel correction is predicted to have a normal temperature dependence. 0 20 40 60 80 100 mole % water FIG.4.-Observed k~/k~ values for the reactions of 2-phenylethyldimethylsulphoniumion at 30°C open circles and -trimethylammonium ion at 60°C,closed circles? with hydroxide ion in mixtures of water and dimethyl sulphoxide. One might inquire whether the Bell Sachs and Tranter model l2 can be made to fit our results. Since it gives very small changes in the C-H and 0-H force constants with changes in the attacking base it would predict a nearly constant semiclassical isotope effect.Variations in its predicted tunnel correction depend primarily on changes in the activation energy (strictly speaking the barrier height in whichever direction the process is exothermic but all of the present reactions are exothermic in the forward direction). Activation energies for the sulphonium-salt reaction decrease monotonically as the water content of the medium decreases. While such a change would be consistent with a carbon isotope effect controlled by the tunnel correction it would be incon- sistent with the deuterium isotope effects. The Bell Sachs and Tranter model predicts that both the carbon and deuterium tunnel effects should decrease mono-tonically with decreasing water content.Even if one argues that the overall activation energy is not the appropriate figure for the calculation of the tunnel correction when the proton transfer is part of a more complex reaction coordinate the model would still seem to predict the same dependence on basicity of the attacking base of the tunnel effects for both H/D and 12C/13C. Both are after all of the same origin for the 12C/13Ctunnel correction doubtless reflects the effect of the carbon mass on the tendency of hydrogen to tunnel. In conclusion the Bell Sachs and Tranter model seems to be right in predicting a substantial tunnel correction. It does not seem to be right for the present reactions at least in ascribing to the tunnel effect a dominant role in variations in the isotope effect.This work was supported by the U.S. National Science Foundation. 120 CARBON-13 ISOTOPE EFFECTS L. Melander Isotope Efects on Reaction Rates (Ronald Press New York 1960) pp. 24-32. F. H. Westheimer Chem. Rev. 1961 61 265. R. P. Bell and D. M. Goodall Proc. Roy. SOC.A 1966 294 273. R. P. Bell and B. G. Cox J. Chem. SOC.By1970 194; 1971 783. A. F. Cockerill J. Chem. Soc. By 1967 964. K. C. Brown and W. H. Saunders Jr. unpublished results. E. F. Caldin Chem. Rev. 1969 69 135. R. A. More O’Ferrall J. Chem. Sac. By 1970 785. A. M. Katz and W. H. Saunders Jr. J. Amer. Chem. SOC.,1969 91,4469. W. H. Saunders Jr. Chem. Scripta 1975 8 27. l1 F. G. Bordwell and W. J. Boyle Jr. J. Amer. Chem. Soc. 1971 93 512. l2 R. P. Bell W.H. Sachs and R. L. Tranter Trans. Faraday Soc. 1971 67 1995. l3 R. P. Bell The Proton in Chemistry (Cornell University Press Ithaca New York 2nd edn. 1973) chap. 12. l4 R. P. Bell Chem. SOC.Rev. 1974 3 513. l5 N.-A. Bergman W. H. Saunders Jr. and L. Melander Acta Chem. Scand. 1972 26 1130. l6 W. H. Saunders Jr. unpublished results. l7 M. Wolfsberg and M. J. Stern Pure Appl. Chem. 1964 8 225. l8 J. H. Schachtschneider and R. G. Snyder Spectrochim. Acta 1963 19 117. l9 W. H. Saunders Jr. and S. ASperger J. Amer. Chem. Soc. 1957 79 1612. 2o W. H. Saunders Jr. D. G. Bushman and A. F. Cockerill J. Amer. Chem. Soc. 1968,90,1775. ’’ L. J. Steffa and E. R. Thornton J. Amer. Chem. Soc. 1967 89 6149. 22 W. H. Saunders Jr. and T. A. Ashe J. Ainer. Chem. SOC.,1969 91 4473.23 S. Siggia Quantitative Organic Analysis (John Wiley New York 1963) pp. 457-464. 24 W. H. Saunders Jr. chap. V in E. S. Lewis (ed.) Investigation of Rates arid Mechanisms of Reactions Part I (Wiley-Interscience New York 3rd edn. 1974). 25 G. S. Hammond J. Amer. Chem. Soc. 1955 77 334. l6 C. G. Swain and E. R. Thornton J. Amer. Chcm. SOC.,1962 84 817. 27 E. R. Thornton J. Ainer. Chem. Soc. 1967 89 2915. l8 E. L. Bauer A Statistical Manual for Chemists (Academic Press New York 2nd edn. 1971). l9 i = (-I)+.