Structural and Solvent Influences on Tunnelling in Reactions of 4-Nitrophenylnitromethanewith Nitrogen Bases in Aprotic Solvents BY E. F. CALDIN* AND C. J. WILSON University Chemical Laboratory University of Kent Canterbury Kent Received 2nd June 1975 Exceptionally large kinetic isotope effects are observed in the proton-transfer reaction of the carbon acid 4-nitrophenylnitromethane with the strong nitrogen base tetramethylguanidine (TMG) in solvents of low polarity such as toluene ; values of W/kDup to -50 and of AD/AH up to -100 have been reported. The volume of activation has been determined in several of these solvents and shows only small variations. In solvents of higher polarity such as THF dichloromethane or acetonitrile the isotope effects are smaller.With tertiary amines in place of TMG as base the isotope effects show a similar solvent-dependence but are all smaller. These effects are interpreted in terms of tunnelling. The factors influencing the tunnelling correction are discussed (i) the dimensions of the barrier to proton-transfer (ii) possible changes of configuration in the reactant molecules and (iii) solvent motions coupled to the proton-transfer. The data on other reactions exhibiting tunnelling are considered in the light of this discussion. A study is being made 1-4of the influence of variations of the base and the solvent on the kinetics of the proton-transfer reaction of the carbon acid 4-nitrophenyl- nitromethane (RH = NO2.C6H4.CH2NO2)with uncharged nitrogen bases (€3) in aprotic solvents (eqn (1)).The product is deep yellow and convenient for spectrophotometric study. The reaction is shown by p.m.r. to result in a proton-transfer and spectrophotometric determinations of the equilibrium constant are in accord with the scheme (1) in which the product is an ion-pair. The kinetic behaviour also agrees with scheme (1). Rates are conveniently measured by stopped-flow methods '; a wide range of temper-atures can be covered because the activation enthalpies are relatively low. A range of bases can be studied in the less polar solvents 2p especially in chlorobenzene or anisole for which the equilibrium constants are relatively high. Isotope effects are readily measurable.'. 2* 4* Volumes of activation can be determined in some solvents (where the equilibrium constant is ~uitable),~ by measurements of rates at high pressures with a laser temperature-jump apparatus.The rate constants at 25" in a series of solvents increase with solvent polarity; the plots of log kHagainst the reciprocal dielectric constant are somewhat scattered suggesting that specific inter- actions are involved as well as electrostatic forces. The deuterium isotopic effects that have been observed are exceptionally large ; the highest values of kH/kDare about 50 and those of AD/AHare of the order of 100. Such values can only be interpreted in terms of tunnelling. The evidence for tunnel-ling in transfers of H+ H and H-has been reviewed from time to time 6-10 ; a 121 TUNNELLING ; STRUCTURAL AND SOLVENT EFFECTS considerable number of reactions are now known lo which show deviations from classical theory attributable to tunnelling.(Given that atoms have wave properties such deviations are to be expected and the only question is whether they are large enough to be detectable.) The height and width of the potential-energy barrier for pro ton-transfer can be calculated from the temperature-dependence of the is0 tope effect provided we assume a particular shape for the barrier such as a truncated parabola. The base and the solvent have been systematically varied in order to examine their effects on the barrier dimensions. The largest effects are found when the base is tetramethylguanidine or benzamidine containing the grouping HN-C < rather than a tertiary amine ; and when the solvent is of low polarity.In this paper we review the data obtained so far on these reactions and report some new experimental results on the reactions in anisole. The factors that may influence tunnelling effects are considered. EXPERIMENTAL Kinetic isotope effects have been determined by the methods already described '* 2* for the base N,N-diethylbenzamidine (HN=CPhNEt2). The stopped-flow apparatus was the one used earlier.' This work will be more fully described el~ewhere.~ Calculations of the barrier dimensions were carried out by fitting Bell's equations for an unsymmetrical truncated parabola by computer as before.' The original calculations '9 were carried out on two different assumptions (a) that only the proton moves so that MH = 1 and m~ = 2 a.m.u.; (b) that heavy-atom motions are coupled to the proton-transfer so that m~ > 1 with the futher assumption that MD-MH = 1a.m.u.CALCULATIONS In most of the calculations of barrier dimensions reported in ref. (l),it was assumed that the width of the barrier at the base is the same for transfer of H+ and of Df. Because of the different barrier heights for the two isotopes this assumption is not exact; the more correct assumption is that the curvature of the parabolic barrier is the same. Dr. S. Mateo has recalculated his data on this assumption; we are much indebted to him for allowing us to quote his results. RESULTS The results obtained on varying the solvent with TMG as the base throughout are summarised in table 1 which includes new data on the reaction in anisole.The table has three sections (1) solvent properties ; (2) experimentally-determined kinetic quantities and (3) the barrier dimensions calculated from them. For given values of the rate constants the optimum barrier height can be given to k0.05kcal mol-l and the optimum width to +0.002 A. The results obtained on varying the base in a given solvent are summarised in table 2. The results of the calculations of barrier dimensions assuming equal curvature for H and D due to Dr. S. Mateo are shown in table 3 with the results of the previous calculations for comparison. The barrier dimensions are not greatly changed. The new values of the barrier width 2bHare smaller than the previous values of 2b by less than 0.04k The new values of the barrier heights EHand EDare smaller than the previous values by 0.1-0.5 kcal mol-' ; the difference (ED-EH)is usually close to the previous value and is physically reasonable.In general the results confirm the earlier calculations; the differences in 2bH are small and we shall continue to use this as a measure of the barrier width. E. F. CALDIN AND C. J. WILSON 123 TABLE 1.-REACTION OF 4-NITROPHENYLNTTROMETHANE WITH TETKAMETHYLGUAMDINE IN VARIOUS SOLVENTS. RATES,ARRHENIUS PARAMETERS VOLUMES OF ACTIVATION AND BARRIER DIMENSIONS CALCULATED FOR UNSYMMETRICAL PARABOLIC BARRIER cyclohexene mesitylene toluene dibutyl ether anisole D dielectric constant 2.22 2.28 2.38 3.06 4.33 p dipole moment/D 4.5 0.0 0.38 1.22 1.30 a polarisability/cm3moI-' 27 40 30 40 33 103p(n2Va)-' /D mol CM-~ 2.4 0 1.5 3.7 5.2 ETlkcal mol-' 33.0" 33.Y 33.9 35.0 37.2 lO-'k? at 25"C/dm3mol-1s-1 164.5k4 166f5 229 k1 305k8 60723 krf/kD,at 25°C 32.6k1.4 31+1 45k2 41f2 35.7+1 AHJH/kcal mol-' 4.0 &1.4 3.72 &0.03 3.62 k0.05 3.63+0.08 3.2+02 AHlD-AHJHlkcal mol-' 5.4 k0.25 4.7f.0.2 4.3 f0.3 4.2k0.2 --ASJH/cal K-' mol-' 30.4 +0.5 31.3 &0.1 31.0 k0.2 30.4 40.3 30.6 42 log, AD,IA 2.4f.0.2 1.94+0.06 1.5k0.2 1.43kO.13 -3 Vt at 30"C/cm3mol-' -13.2& 1.0 17.8 1.2 -16.34 0.5 -A V" at 30"C/cm3mol-1 -15.9+ 1.7 28.2 &4.6 -29.3 5 1.7 EHlkcal mol-I 11.05 9.8 8.6 8.4 -2b/A 0.820 0.796 0.788 0.786 -267A 0.820 0.796 0.788 0.786 -ni a.m.u.1.oo 1.oo 1.oo 1.oo -chlorobenzene THF dichloromethane acetonitrile D dielectric constant 5.62 7.39 9.08 37.5 p dipole moment/D 1.56 1.7 1.55 3.37 cx polarisability/cin3mol-1 31 18 13 11 103p(n2V")-'/D mol ~m-~ 6.6 12 14 37 ET/kcal mol-1 37.5 37.4 41.1 46.0 10-'ky at 25"C/dm3mol-1s-' 708k20 482k8 52453 589f6 kH,/kD,at 25°C 50+8 12.750.3 11.4f0.2 11.8k0.3 AH!H/kcal mol-1 3.57kO.16 3.44k0.05 3.4940.5 4.3720.04 AHiD-AHJH/kcal mol-I 3.7k0.4 1.8k0.2 1.9f0.2 1.46k0.2 -ASiH/cal K-1 mol-I 28.940.5 30.1 50.2 29.8k0.2 26.640.1 10210 &/AT 1.0k0.3 0.2k0.2 O.35kO.1 O.O+O.1 -A Vt at 3O0C/cm3mol-' 13.04 1.4 -4 V" at 30"C/cm3m01-' 21.9rf 3.5 -EH/kcal mol-' 8.55 4.55 4.85 5.85 2b/A 0.794 0.900 0.954 0.960 2b7A 0.794 0.782 0.786 0.794 m&/a .m.u. 1.oo 1.17 1.24 1.27 E =barrier height ;26 =width of barrier at base ;D =dielectric constant at 25°C ;p =dipole moment ;n =refractive index ;0 =molar polarisability ;ET =empirical solvent-polarity para- meter (some values estimated*).1 cal =4.184 J. DISCUSSION FACTORS INFLUENCING TUNNELLING EFFECTS IN PROTON-TRANSFER REACTIONS In previous discussions 7* of the factors that might favour tunnelling in reactions of carbon acids and the like no simple correlations have been found with the nature of the atoms other than carbon concerned in the reaction (0,F N) nor with the charges on the atoms nor with the electronic properties of the neighbouring groups. It has however been suspected for some time that the effects are influenced by bulky substituent groups l19 l2 and by the solvent.The results summarised above permit TUNNELLING ; STRUCTURAL AND SOLVENT EFFECTS 2.-&UILIBRIUM RATE AND ARRHENIUS TABLE PARAMETERS FOR REACTION OF LGNITRO-PHENYLNITROMETHANE WITH VARIOUS BASES IN TOLUENE ANISOLE AND ACETONITRILE N,N-diethyl-TOLUENE log KHat 25"C/dm3mol-1 TMG t 2.25 benzamidine* quinuclidine 1. 1.61 NEt3 §0.60 NBu~ 6 0.04 -AH"H/kcal mol-1 -AS"H/cal K-I mol-1 10.6f 1.7 25+ 4 8.2f0.6 20+ 2 10.2f0.5 32f1 7.8f0.2 26f1 kr at 25"C/dm3mol-1s-1 2290f 9 2200f 15 132f2 43.okO.4 k"fk; at 25°C 45+ 2 15.6f0.6 11.0k0.7 14+1 AH?"-AH:H/kcalAH,"H/kcal mol-I mo1-l 4.3 +0.3 3.62f0.005 4.5450.09 2.8k0.6 3.51f0.07 5.61fO.14 2.2f0.6 1.7f0.5 -ASFH/cal K-lmol-l 31.Of 0.2 28.0f0.3 37.2f0.2 32.1f0.5 log o(AD,/A';) &/A? 1.50f0.2 32f 14 0.86f0.12 752 0.6k0.45 4f 2 0.04f0.4 1.1 ,QH at 25'C 28f2 4.110.1 3.350.1 3.6k0.1 EH/kcal mol-1 2b/W 2b'/8 m;I/a.m.u.8.6k0.15 0.788 0.788 1.oo 0.96 0.79 1.32 %Oaf 0.05 0.97 0.79 1.30 5.3ofO.05 0.97 0.78 1.35 6.65f0.05 ANISOLE logKH at 25"C/~lm~mol-~ 3.2220.07 -AH"H/kcal mol-' 14.5f 0.8 -AS"H/cal K-lmol-' 38.5f 2.5 1.34f0.05 9.7f0.5 31.3f2.5 2.15f0.02 9.7k0.5 23.0k2 1.05f0.03 10.1k0.9 29.0f3 k,H at 25"C/dm3mol-1s-1 AH,fH/kcal mol-' -AS:H/cal K-lmol-' kp/ky at 25°C 6070k 30 3.2f0.2 35.7+ 1 30.6f2 283f 7 32+ 3 4.2f0.4 33.6f 1 7670f 80 18.8+0.6** 3.25k0.3 30+ 1 620 22.52 1** 3.2f0.4 35-1-1.5 ACETONITRILE log KHat 25"C/dm3mol-1 -AH"H/kcal mot1 -AiS"H/cal K-lmol-l 3.5 4.3 & 0.8 -2f3 2.14 ky at 25"C/dm3mol-1s-1 5890k 60 kTlkp at 25°C 11.8f0.3 AH,"D-AH:H/kcal moP 1.46f0.2 -ASzH/cal K-l mol-' 26.6f0.1 AHf,H/kcal mol-' 4.37 f0.04 1% (AD,IA?) O.O+O.l APIA? l.Ok0.2 12.2k0.9 7.3f0.3 6.7f0.1 6.0f0.1 l.Of0.2 O.Sf0.2 22.150.4 25.2f0.3 1.8f0.3 1.7f0.3 3.12fO.242.17fOO7 0.2~f0.1 0.2~ 0.1 QHat 25°C 2-56 1.67 1.42 EH/kcal mol-l 2b/A 2b'lA 5.8 0.96 0.79 7.7 1.23 0.97 6.85 1.38 0.99 rn&a.m.u.1.27 1.39 1.52 2b"/ArnL/a.m.u. 0.79 1.27 0.79 1.82 0.79 2.05 * This work. 'f Ref. (1). $ Ref. (2). 0 Ref. (5). ** Ref. (4). Symbols and units as in table 1. E. F. CALDIN AND C. J. WILSON a tentative discussion of the influences of the following factors (i) the barrier width and height and the molecular properties that affect them (bonding solvation and steric factors) ; (ii) configurational changes involved in the formation of the transition state and (iii) solvation changes in which the motions of solvent molecules are coupled to the transfer of the proton.(i) THE BARRIER DIMENSIONS The barrier width is the distance that the proton moves in the change from +/ /ICH . .NL to lC ..HN-.\ (It is assumed that the C-N distance does not \/ change appreciably in the very short time concerned.) It must therefore depend (a) on the lengths of the C-H and H-N bonds which probably vary by only a few pm in our systems and (b) on the C-N distance at which proton-transfer occurs which is probably comparable with the length of a hydrogen bond and may be expected to vary appreciably from one system to another depending on the electron- distribution around the nitrogen atom in the base l4 Unfortunately the CH ..N distance has been determined for only one hydrogen-bonded system (HCN),l3.so we cannot argue directly from experimental data. On theoretical grounds however we should expect this distance to be shorter for TMG in which the orbitals of the N atom are sp2-hybridised than for amine bases where the hybridisation is sp3. The overlap integral for the interaction CH ..N will be smaller for sp2 than for sp3 hybridisation unless the distance is less both because the electron density at a given distance from the N atom is smaller and because the orbital is of higher energy; moreover since only two groups are attached to the sp2-hybridised N atom the steric hindrance to formation of a hydrogen bond will be less. The carbon atom will therefore approach more closely to sp2-hybridised N than to sp3-liybridised N before proton-transfer begins to occur.The CH. .N distance will therefore be shorter and the barrier-width smaller for TMG than for amine bases. If the barrier-width depends largely on the type of hybridisa- tion we can understand why the values of 2b calculated from the isotope effects in toluene are about the same for the reactions of all the amine bases regardless of steric considerations and why the value for TMG is appreciably smaller. Steric crowding of the reaction site does not appear to be a major influence on the barrier width which shows only minor variations in the series quinuclidine NEt, NBu, in which the reaction site is progressively more obstructed by the carbon chains.The barrier height will be affected by the changes of bonding by steric factors and by solvation. For TMG and benzamidines the sp2 hybridisation will lead to a shorter C-N distance than that for amines and the additional repulsion energy will increase the barrier height ; we can thus understand the trend in EHfor the reactions in toluene (table 2). For the three amine bases in toluene the variations in EHmay be attributed to steric factors. The barrier height is greater for NBu than for NEt ; this may be attributed to the longer carbon chains in NBu, which will lead to greater repulsion and may also lead to exclusion of solvent molecules from the reaction site so reducing any lowering of the barrier by solvent reorganisation.l0?l2 The still greater barrier height for quinuclidine might arise from a different effect of steric bulk the cage structure of the quinuclidine molecule will prevent the approach of solvent molecules to the N atom in the reaction complex k..H ..N-,/\ and so / could reduce the increase in solvation compared with other amine bases. The less negative entropy of activation is in accord with this suggestion. TUNNELLING ; STRUCTURAL AND SOLVENT EFFECTS Solvent effects on the barrier height (table I) are attributed to solvation partly electrostatic and partly specific (see below).6* lo*12* l6-l8.l9 The effect of asymmetry of the barrier (measured by AH') would be interesting to investigate but at present the data are insufficient. (ii) CHANGE OF CONFIGURATION In the preceding section we have considered only the values of 2b calculated for the various bases by method (a),on the assumption that only the proton moves during the reaction so that the effective mass is that of the proton nzH = 1 a.m.u.If motions of any other nuclei occur and are coupled to the proton-transfer they will contribute to the effective mass along the reaction coordinate and so reduce the tunnelling correction. There may well be changes of configuration of the reacting molecules as a result of the proton-transfer ; for instance the bond angles in NEt and NBu will change slightly when a proton is added.20 Such changes may be coupled with the proton-transfer (though they could alternatively precede the proton- transfer,2' as solvent molecules are thought to do in outer-sphere electron-transfer reactions 22 and in some proton-transfer reactions in water 23).Coupling should in principle be detectable by finding values of the effective mass mfr,by calculations based on method (b)gin which mfr is optimised as well as the barrier width. These I 30 35 40 45 ET/kCal mol-' FIG.1.-Plots of barrier width against the empirical solvent polarity parameter ET for the reaction of 4-nitrophenylnitromethanewith TMG in various solvents. Open circles 2b calculated by method (a) ; filled circles 26' calculated by method (b) ; squares methods (a)and (6); see text. Solvents (2) cyclohexene (3) mesitylene (4) toluene (5) di-n-butyl ether (6) chlorobenzene (7) THF (8) dichloromethane (10) acetonitrile.calculations (table 2) give new values of the barrier width (2b')and of the effective mass (mk) which are just as compatible with the experimental results as are the values of 2b calculated by method (a). For TMG there is no change in the barrier width (2b' = 2b) or the effective mass (mi= 1.00 a.m.u.) ;but for the three E. F. CALDIN AND C. J. WILSON amine bases 2b' is smaller than 2b and nearly equal to the value for TMG while the effective masses mfI are 1.30-1.35 a.m.u. The values of 2b and 2b' are shown in fig. 2. "I e 1' I I I I 2 3 log K FIG.2,-Plots of barrier width against log K for the reaction of 4-nitrophenylnitromethane with various bases in toluene. Open circles 26 calculated by method (a); filled circles 26' calculated by method (b); square methods (a) and (b); see text.Bases (1) TGM (2) quinuclidine (3) triethylamine (5) tri-n-butylamine. TABLE 3.-COMPARISON OF CALCULATED BARRIER DIMENSIONS ASSUMING THAT BARRIERS FOR H+ TRANSFER AND D+ TRANSFER HAVE (a) SAME WIDTH AT BASE (b) SAME CURVATURE FOR REACTION OF 4-NPNM WITH TMG IN VARIOUS SOLVENTS cyclohexane mesi tylene toluene di-n-butly ether barrier parameters (a) (b) (a) (b) (4 (b) (4 (b) CH/kcal mol-l A-" 209 203 172.5 170 208 198 190 182 CD/kcal mol-I A-" 212 210 188 185.5 EH/kcal rno1-l 11.05 10.90 9.80 9.60 8.60 8.45 8.40 9.10 EDlkcal mol-l 11.30 11.15 10.30 9.75 9.40 9.55 8.10 0.818 0.800 0.746 0.744 0.820 0.796 0.788 0.780 0.826 0.814 0.774 0.776 chlorobenzene THF dichloromethane acetonitrile barrier parameters (4 (b) (4 (b) (4 (b) (a) (b) CH/kcal mol-' A-2 165 85.4 76 68 196 86 78.3 70 CD/kcal mol-I A-2 180.5 97.6 86 78 EH/kcal mol-1 8.55 8.45 4.55 4.30 4.85 4.50 5.85 5.55 ED/kcal mol-1 9.75 9.40 5.70 5.40 6.00 5.60 7.00 6.65 2bH/A 0.726 0.882 0.920 0.928 0.794 0.900 0.954 0.960 2bD/A 0.752 0.938 0.978 0.998 CH and CD are curvatures of the parabolas; EHand EDare the barrier heights for the forward reactions ; 2bH and 2bD are the barrier widths.128 TUNNELLING ; STRUCTURAL AND SOLVENT EFFECTS If only NEt3 and NBu were concerned it would be tempting to adopt the results of method (b) and explain the high values of mfr as due to configurational changes. It is difficult however to explain the results for quinuclidine and TMG on this basis.The effective mass m;I calculated for quinuclidine by method (b) is about the same as for NEt and NBu, whereas it should be smaller if due to configurational changes which must be hindered in quinuclidine. For TMG the calculated effective mass mfr (1.00 a.rn.11.) would imply that there is no coupled configurational change although protonation of TMG leads to a change of hybridisation which must alter bond lengths and angles and so affect mfI if configurational change is relevant. These anomalies in the results of method (b)make us incline to the view that the true barrier widths are those given by method (a). with m;I = 1.00 a.m.u. so that there is a real difference between the barrier widths for TMG and for amine bases; and that there is no clear evidence from the present results for effects of coupled configura- tional changes.(iii) SOLVENT MOTIONS COUPLED TO PROTON-TRANSFER The formation of a dipolar transition state in a solvent of low dielectric constant would be expected to lead to reorientation of solvent molecules. Rotation of solvent inolecules might therefore be coupled to the proton-transfer.l* l2 This would increase the effective mass. The results for TMG in table 1 section 3 and fig. 1 show a marked difference between the less polar and the more polar solvents. (Effects with other bases (table 2) are smaller but similar.) For the reaction with TMG in the less polar solvents (dielectric constant < 6) the barrier widths 2b calculated by method (a) i.e.assuming m = 1.00 a.m.u. are nearly constant (0.80+0.02 A) ; the same values are obtained for 2b’ by method (b) and the optimum value of the effective mass remains 1.00 a.m.u. It appears there- fore that in these solvents there is no coupling of solvent motions with the proton- transfer. This conclusion is also in accordance with the values of the volumes of activation (AV*) for the reaction of TMG determined from rate measurements at high pre~sure.~ In mesitylene toluene anisole and chlorobenzene AV* is approximately constant (table 1) ; all the values lie within the range -15k3 cm3 mol-I. A value of this order (ca.-12 cm3 mol-I) is obtained by a rough calculation from a simple model for the decrease in volume of the reacting pair of molecules when the CH .. N distance decreases from the van der Waals distance to the hydrogen-bonded distance omitting all consideration of solvation changes. The values vary less than the overall volumes of reaction AVO in the several solvents which range from -16 to -29 cm3 mol-’ ; and they are smaller than the values of AV* for typical Menschutltin reactions,24* 25 in which charge-separation associated with transfer of heavier nuclei occurs (-20 to -50 cm3 mol-I). This evidence is compatible with the view that in these solvents the proton-transfer is neither accompanied nor preceded by any considerable rotation of solvent molecule?. It does not support the view that solvent molecules move first and the proton-transfer occurs when the solvent environment is suitable for the product as in outer-sphere electron-transfer reactions in water.For the reaction of TMG in the more polar solvents (THF dichloromethane acetonitrile) calculations by method (a) lead to values of the barrier width 2b markedly larger than for the less polar (0.90-0.96 A). Since there is no obvious physical reason for so large a difference (though the effect of dielectric constant on the initial hydrogen-bond distance CH . .N may account for part of it) calculations were carried out by method (6). These gave optimum values of the barrier width in close agreement with those found for the less polar solvents (26’ = 0.78k0.01 A) E. F. CALDIN AND C. J. WILSON and the corresponding values of the effective mass are mk = 1.17 to 1.27 a.m.u.(table 1 section 3b). Such values can be understood in terms of coupling of the reorientation of solvent molecules with the proton-transfer. These solvents are the ones in which the field due to a dipolar transition state on adjacent molecules will be largest. This field according to a simple model due to Dr. N. J. Bridge (personal communication) will be proportional to p/Von2,where p is the dipole moment of the molecules of solvent Yoits molar volume and n its refractive index; the values of this function (table 1 section 1) are much greater for the three solvents mentioned than for the less polar ones. The numerical values found for rnI; are in reasonable agreement with those expected from a simplified electrostatic model of the coupled motion due to Prof.R. P. It is possible that another factor influencing the behaviour of the three more polar solvents is that each of them has a relatively low moment of inertia about at least one axis while the less polar molecules have not. Experimental difficulties have so far prevented us from extending the range of solvents to investigate this point. It was also found impossible to determine volumes of activation in the more polar solvents because the product was not stable for the relatively long periods required. The picture that emerges for the reaction with TMG in the more polar solvents is that when the proton-transfer occurs the field due to charge separation in the transition state exerts a torque on the polar solvent molecules so that they begin to rotate; their motion is therefore coupled to the transfer of the proton and this coupling leads to an increase in the effective mass which is reflected in a smaller tunnelling correction and hence in smaller isotope effects.For the reaction in the less polar solvents the corollary of this view is that for some reason the fleld due to the transition state does not bring about rotation of solvent molecules although some interaction is indicated by the variations of the barrier height EH. The reason may be that in these solvents the effect of the field is only to bring about electron polarisation in the solvent molecules rather than rotation. These solvents have relatively high molar polarisabilities and relatively low values of the quantity ,u/n2/Vorepresenting the field (table l) compared with the more polar solvents.Electron polarisation is set up in -10-I' s and will be coupled with the proton-transfer but will exert a negligible torque and will leave the effective mass unaltered. REQUIREMENTS FOR LARGE TUNNELLING EFFECTS IN REACTIONS OF CARBON ACIDS The main factors that produce large tunnelling effects in reactions such as that of 4-NPNMwith TMG in certain solvents thus appear to be (1) the unusually narrow barrier attributable to the sp2 hybridisation of the orbital of the basic N atom; (2) the barrier height which may be increased by steric bulk in the base; (3) the low polarity of the solvent which appears not to undergo rotations coupled to the proton- transfer and (4) the apparent lack of a configurational change coupled to the proton- transfer.It is of interest to enquire whether these factors also characterise the other reactions that exhibit anomalous isotope effects attributable to lo and what other factors may be involved. (1) Evidence on the width of the barrier in a given reaction is not generally available ; indeed part of the interest attaching to tunnelling calculations is that they provide such evidence. But if it is accepted that the barrier is narrower for sp2-hybridisation of the nitrogen orbitals than for sp3-hybridisation then it may be significant that of the 18 proton-transfer reactions (excluding that of 4-NPNM with S 10-5 130 TUNNELLING ; STRUCTURAL AND SOLVENT EFFECTS TMG) listed in Bell's tables of reactions lo showing anomalous hydrogen isotopic effects on Arrhenius parameters four are reactions of pyridine bases.(2) As regards the barrier height it may be significant that five are reactions of hindered bases such as collidine or t-butoxide. (3) Reactions in which the solvent reorganisation is small or unusually easy will be favourable cases for large tunnelling effects. (a) It is noteworthy that 10 of the proton-transfer reactions listed do not involve a change of charge on forming the transition state so the solvation change will be less than in an ionogenic reaction. (b) The solvent is aqueous for 16 of the reactions including 6 of the 8 ionogenic reactions other than 4-NPNM +TMG. Water is unique among common solvents in the small moment of inertia of its molecules ; small motions in water appear to be almost ~nhindered,~~ and solvent reorganisation will have relatively little effect on mA.(c) The effect of steric bulk in the base molecule may be to exclude solvent from the reaction site (cf. above) and so reduce effects due to solvent reorganisation. Hydrogen-atom transfers are particularly favourable from this point of view since they involve no charges and can be carried out in non-polar solvents. An example is the reaction of oxygen (0,)with dihydrophenanthrene in a hydrocarbon which has kH/kD= 64 at -10°C corresponding to about 30 at 25"C and has been the subject of a very full theoretical investigation. The reactions of sub-stituted phenols with radicals in vinyl acetate give kH/kDup to 19 at 50°C.18* 29 Eighteen such reactions are listed by Bell.O (4) Evidence on configurational changes might be sought by comparing rigid with non-rigid systems (though the results for the reactions of 4-NPNM with bases have so far been negative). It is of interest that the proton-transfer reactions of 2-carbethoxycyclopentanone 30 (the first established case of a large tunnelling correction) and the H-atom transfer reaction of dihydrophenanthrene 28 involve ring systems. CONCLUSION The general results of this investigation of the reactions of 4-NPNM with nitrogen bases so far may be summarised as follows. (1) The isotope effects vary widely with base and solvent. The largest are explicable only in terms of tunnelling. (2) When the base is varied much larger effects are found with tetramethyl- guanidine or diethylbenzamidine than with amine bases.The larger effects can be attributed to a smaller barrier width due to the more compact electron-distribution in the sp2-hybridised orbital. Among the amine bases there is little difference in the calculated barrier dimensions between quinuclidine and NEt or NBu3 ; this suggests that configurational changes accompanying proton-transfer do not alter the effective mass appreciably. The main factor influencing the effect of a base thus appears to be the electron-distribution around the nitrogen atom. (3) When the solvent is varied the largest effects are found in solvents of low polarity (B< 6). The explanation proposed is that in the more polar solvents the solvent molecules interact with the field set up by the separation of charges in the transition state and begin to rotate so that their motion is coupled to that of the proton ; the effective mass is thereby increased and the tunnel effects decreased.In the less polar solvents which are also the more polarisable we may suppose that only electronic polarisation occurs so that the effective mass is nearly that of the proton and the tunnelling effects are not appreciably reduced. The main factor influencing the effects of the solvent appears to be its polarity. The size of the molecule could be significant. E. F. CALDIN AND C. J. WILSON 131 (4) When we consider the data on other reactions which involve transfer of Hf PI or H-to or from carbon and have large isotope effects attributable to tunnelling it appears that the expected effects of the solvent and of bulky substituents can be seen but that effects of configurational change are not clearly discernible.We acknowledge helpful discussions with Prof. R. P. Bell Dr. N. J. Bridge Prof. C. D. Hubbard and Prof. F. Ann Walker and an S.R.C. research fellowship to C. J. W. E. F. Caldin and S. Mateo J.C.S. Faraday Z 1975 71 1876. E. F. Caldin and S. Mateo J.C.S. Faraday Z 1976,72 112. C. D. Hubbard C. J. Wilson and E. F. Caldin J. Amer. Chem. SOC.,1976 98. E. F. Caldin D. M. Parbhoo C. J. Wilson and F. A. Walker J.C.S. Faraday I 1976,72. E. F. Caldin A. Jarczewski and K. T. Leffek Trans Faraday SOC. 1971 67 110. R. P. Bell The Proton in Chemistry (Chapman and Hall London 1973) chap.12. E. F. Caldin and M. Kasparian Disc. Faraday SOC.,1965 39,25. E. F. Caldin Chem. Rev. 1969 69 135. 9 E. F. Caldin in Reaction Transition States ed. J. E. Dubois (Gordon and Breach London 1972) p. 247. lo R. P. Bell Chem. SOC.Rev. 1974 3 513. l1 E. S. Lewis and L. H. Funderburk J. Amer. Chem. SOC.,1967,89,2322. E. S. Lewis in Proton-transfer Reactions ed. E. F. Caldin and V. Gold (Chapman and Hall London 1975) chap. 10 l3 G. C. Pimentel and A. L. McClellan The Hydrogen Bond (Freeman San Francisco 1960). l4 S. N. Vinogradov and R. H. Linnell Hydrogen Bonding (van Nostrand New York 1971) chap. 7. l5 R. D. Green Hydrogen Bonding by C-H Groups (Macmillan London 1974). F. H. Westheimer Chem. Rev. 1961 61 265.l7 J. R. Keeffe and N. H. Munderloh Chem. Comm. 1974 17. l* M. Simonyi I. Fitos J. Kardos I. Lukovits and J. PospiSil Chem. Comm. 1975 252. l9 R. A. More O’Ferrall in Proton-transfer Reactions ed. E. F. Caldin and V. Gold (Chapman and Hall London 1975) chap. 8. 2o H. C. Brown H. Bartholomay and M. D. Taylor J. Amer. Chem. SOC.,1944 66,435. 22 J. L. Kurz and L. C. Kurz J. Amer. Chem. SOC.,1972,94,4451. 22 R. A. Marcus Ann. Rev.Phys. Chem. 1964,15,155; J. Phys. Chem. 1968,72,891. 23 (a) W. J. Albery A. N. Campbell-Crawford and J. S. Curran J.C.S. Perkin ZZ 1972 2206 ; (6) M. M. Kreevoy and D. E. Konasewicli Adv. Chem. Phys. 1971 21,243 ; (c) M. M. Kreevoy and Sea-wha Oh J. Amer. Chem. SOC. 1973,95,4805 ; (d)A. J. Kresge Chem. SOC.Rev. 1973,2,484 ; (e) M.H. Davies J. R. Keeffe and B. H. Robinson Ann. Rep. Chem. SOC. A 1973 123 ; (f)W. J. Albery in Proton-transfer Reactions ed. E. F. Caldin and V. Gold (Chapman and Hall London 1975) chap. 9. z4 H. Hartmann H. D. Brauer H. Kelm and G. Rinck Z.phys. Chem. (Frankfurt) 1968,61,53. 25 H. Heydtmann A. P. Schmidt and H. Hartmann Ber. Bunsengesphys. Chem. 1966 20,444. 26 R. P. Bell personal communication. 27 (a) D. W. G. Smith and J. G. Powles Mol. Phys. 1966 10 451 ; (b)H. G. Hertz Aizgew. Chem. (Int. Ed.) 1970 9 124; (c) D. Eisenberg and W. Kauzmann The Structure and Properties of Water (Clarendon Press Oxford 1969). p. 214. 28 A. Bromberg K. A. Muszkat E. Fischer and F. S. Klein J.C.S.Perkin ZI 1972 588 and earlier papers. 29 M. Simonyi and F. Tudos Adv.Phys. Org. Chem. 1970 9 127 ; 3O K.P. Bell J. A. Fendley and J. R. Hulett Proc. Roy. SOC.A 1956 235 453. S10-5*