Hydrogen-Bonded and Ion-Pair Complexes in Aprotic Solvents BY J. E. CROOKS Chemistry Department University of London King’s College Strand London WC2R 2LS AND B. H. ROBINSON Chemistry Building The University Canterbury Kent Received 2 1st May 1975 The proton-transfer reactions between acids and bases in aprotic solvents of low relative permit- tivity lead to the production of ion-pair complexes via hydrogen-bonded reaction intermediates. For most systems the rate-limiting step is the formation of the hydrogen-bonded intermediate. The rates of these reactions as measured by the temperature-jump technique agree well with those calculated by a refined theory of diffusion-controlled rates which takes into account rotation within the encounter complex.The reactions of Bromophenol Blue with pyridine basis are anomalously slow the rate-limiting step being proton-transfer within the hydrogen-bonded complex to form the ion-pair. Values of the enthalpy entropy and volume of activation and the primary kinetic isotope effect enable the structure of the transition state to be deduced. The reaction between a proton-donor and a proton-acceptor in an aprotic solvent of low permittivity may lead either to the formation of a hydrogen-bonded complex or an ion-pair. For example pyridine and phenol form a hydrogen-bonded complex whereas triethylamine and 2,4-dinitrophenol form an ion-pair. A considerable amount of charge generation and separation occurs in the forma- tion of an ion-pair as shown by the high dipole moments of these complexes,1 so that a considerable amount of energy must be supplied.Ionization is often observed in aqueous solution where the strong ion-solvent interactions provide the necessary energy but these interactions are much weaker for aprotic solvents. The con-sequence is that only hydrogen-bonded complexes will be formed unless energy can be supplied by some other process. Electron delocalisation may provide the necessary 29 HYDROGEN-BONDED AND ION-PAIR COMPLEXES IN APROTIC SOLVENTS energy. If the loss or gain of a proton by one of the molecules permits more extensive electron delocalisation or in other words establishes a conjugated system then ion-pair formation is favoured. For example the negative charge on the 2,4-dinitrophenol anion is delocalised over the nitro-groups.The establishment of a conjugated system is typically accompanied by a large bathochromic and hyper- chromic shift of the visible/u.-v. absorption spectrum so that ion-pair formation may be observed spectrophotometrically. For example the 2,4-dinitrophenol-triethylamine ion-pair is yellow having an extinction coefficient of 8130 dm3 mol-l cm-l at 400nm in toluene solution whereas 2,4dinitrophenol itself only has an extinction coefficient of 102 dm3 mol-1 cm-l at this wavelength. It seems reasonable that the formation of an ion-pair from an acid and a base must involve a hydrogen-bonded complex as reaction intermediate. An ion-pair differs from the corresponding hydrogen-bonded complex only in the location of the proton; the conversion of a hydrogen-bonded complex to an ion-pair usually requires only the motion of the proton along the hydrogen bond.A general scheme for the formation of an ion-pair may thus be written as k12 k23 AH+B +C +D k21 k32 where AH is the acid B the base C the hydrogen-bonded complex and D the ion-pair. If the structures of AH and B are such that charge delocalisation does not occur as a consequence of proton transfer the equilibrium constant for the second step K23 is extremely small If this is so the only observable product of the reaction is C. If on the other hand charge delocalisation does occur the predominant product is D. The existence of a small quantity of C in equilibrium with D may be overlooked as the absorption spectrum of the mixed products is dominated by that of D.However if K23 is near unity the value of the overall equilibrium constant K where (calculated assuming that [C] is negligible) is found to be concentration-dependent. 3-5 If the existence of C is taken into account the absorbance A of the ion-pair peak of a solution containing stoichiometric concentrations [AH] and [B] of acid and base is given by ti where E is the extinction coefficient of D. Thus a plot of [AH],e/A against [B] has gradient K-' and intercept (1 +K231-l. Hence values of Kl 2 the equilibrium constant for the formation of C may be found since K12 = K/K23. (4) Values of K12 may also be estimated for systems for which C is low by comparison with data from model systems. For instance it is found that values of KI2 for phenol with aromatic amines are on average 2.3 times greater than for Magenta E (I) with aromatic amines probably due to formation of an intramolecular OH .. .Br hydrogen bond in Magenta E. Values of K12 for Magenta E with the stronger aromatic amines can be measured directly by use of eqn (3) but values of K23 for Magenta E with J. E. CROOKS AND B. H. ROBINSON aliphatic amines are too large for K12to be evaluated in this way. However values of K1 for Magenta E with aliphatic amines may be estimated by dividing the values found for phenol with aliphatic amines by a factor of 2.3. OH I Corresponding values of K, for Bromophenol Blue (11) have been estimated from infra-red absorption measurements in CC14 solution by the use of 2,6-dibromophenol as proton-donor since it resembles Bromophenol Blue except in that it lacks the ability to form a conjugated system on proton loss.OH I1 A third way of measuring K12is to observe the hydrogen-bonded complex in the visible/u.-v. spectrum since a small bathochromic shift (-20 nm) occurs on hydrogen bond formation. Values of K, for Magenta E with the weaker aromatic amines have been measured by this method. Thermodynamic parameters obtained by these methods are listed in table 1. FAST REACTIONS INVOLVING THE FORMATION OF ION-PAIR COMPLEXES The kinetics of formation of ion-pair complexes in aprotic solvents for a range of acids and bases have been studied by the temperature-jump technique. The reaction is monitored by kinetic spectrophotometry of the ion-pair absorption peak.The experimental data takes the form of values of the relaxation time robs for solutions of various values of [AH]and [B]. For all the solutions studied it is found that each solution has only one observable relaxation time ;plots of 7%; against [AH]+[B] are straight lines with positive gradients and finite intercepts. This is in accordance with the simple kinetic scheme kr AH+B+D kb 32 HYDROGEN-BONDED AND ION-PAIR COMPLEXES IN APROTIC SOLVENTS for which 7-l = kf([AH]+[B]) +kb. (5) The ratio of the gradient to the intercept kf/kb,is predicted to be equal to the observed overall equilibrium constant K as defined by eqn (2) and this is in fact observed.For all systems studied except those involving Bromophenol Blue reacting with aromatic amines which are discussed later values of kf are found to be in the region TABLE OF HYDROGEN-BOND FORMATION 1.-THERMODYNAMICS K12 at 25°C -AH102 -AS92 /dm3mol-1 /kJ mol-1 /JK-1 mol-1 ref. phenol t rie thy lamine 71 33 74 4 (solvent CC14) tri-n-propylamine 18 25 59 4 tri-n-butylamine 23 29 71 4 2-met hylpyridine 61 29 63 4 2,6-dimethylpyridine 83 29 60 4 2,4,6-trimethylpyridine 117 31 66 4 2,6-dibromophenol pyridine 7.7 20 50 5 (solvent CC14) 2-met hylpyridine 7.7 21 53 5 2,6-dimethylpyridine 7.4 26 71 5 2,4,6-trimethyIpyridine 10.9 24 59 5 Magenta E (solvent C6H5C1) 2-methyl p yridine 28 25 55 4 2,6-dime thylpyridine 31 31 75 4 2,4,6-trime thylpyridine 55 32 74 4 Bromophenol Blue 3-chloropyridine 3 -9 19 51 5 (solvent C6H5Cl) Bromophenol Blue 2,4,6-trimethylpyridine 53 29 64 3 (Solvent C6H5Cl) (second complex)* pyridine 20 26 60 14 pyridine 25 27 64 pyridine 29 23 48 pyridine 35 32 77 *Bromophenol Blue is a dibasic acid.Strong amines react quantitatively with the first acidic group at the concentrations used and the data refer to reaction of the amines with the second acidic group. This reaction is very similar to that between Magenta E and bases. 10s-109 dm-3 mol-' s-l as shown in table 2. Values of kf are independent of K but decrease with increasing steric hindrance round the base. The results can thus be interpreted in terms of a simple mechanism in which the rate-determining step is the diffusion together of AH and B the subsequent proton-transfer being fast.However the possibility of a hydrogen-bonded intermediate cannot be ignored. A system involving two equilibria has in principle two relaxation times although only one may be experimentally observable. The general solution is complex but may be simplified by making either of two assumption^.^ J. E. CROOKS AND B. H. ROBINSON If the first equilibrium is established much more quickly than the second the relaxation times are given by A plot of Ti1 against [AH]+[B] thus gives a straight line for which the ratio of gradient to intercept is k12/k21,i.e. K12. As the observed ratio is K r1 cannot be robs. Eqri (7) is however compatible with the data if as is so in practice Kl2([AH]+ [B]) < I which implies K239 1.On this scheme the gradient of the r$ against [AH]+[B] plot i.e. k, is identified with k23K12. However if proton transfer were the rate-determining step k23 and hence k, should increase with increasing K which is not observed for the reactions in table 2. TABLE 2.-RATES OF FORMATION OF ION-PAIR COMPLEXES (CHLOROBENZENE SOLVENT) K 10-8 x kt temp. acid base /dm3 mol-1 /dm3mol-ls-l /"C ref. 2,4-dinitrophenol quinuclidine 119000 20 25 7 triet h yl ami ne 23 500 17 20 8 t ri-n-propylamine 4 900 5.1 25 8 tri-n- butylamine 3 350 3.O 25 3 tri-n-pentylamine 5 700 3.3 20 8 t ri-n-octylamine 4 800 2.4 24 7 t ri-n-nonylamine 9 700 3.3 20 8 Magenta E trimethylamine 18800 18 13 4 triethylamine 119OOO 16 25 4 tri-n-propylamine 21 600 8 25 4 tri-n-butylamine 33 loo 5.2 24 4 2,4,6-trimethylpyridine 12 800 7 -26 4 Bromophenol Blue trimet hylamine 3 400 13 25 6 (second complex) triet hylamine 33000 12 25 6 t ri-n-propylamine 4900 5.6 25 6 tri-n-butylamine 7 200 5.5 25 6 tri-n-octylamine 6 300 2.3 25 6 If the second equilibrium is established much more quickly than the first the relaxation times are given by Since -cobs is a function of reagent concentration eqn (8) cannot apply.Eqn (9) is compatible with the experimental data if as is usually found in practice K23 B 1. Thus k may be identified with kI2,the rate constant for formation of the hydrogen- bonded intermediate which accounts for its independence of K and its variation by steric effects.The experimentally observed variation of k with solvent and with temperature shows that k12is not a simple diffusion-controlled rate. For a simple diffusion- controlled reaction the observed activation energy should be due solely to changes in solvent viscosity with temperature and so be equal to the activation energy of s 10-2 34 HYDROGEN-BONDED AND ION-PAIR COMPLEXES IN APROTIC SOLVENTS viscosity of the solvent. Not only is this not so but for one reaction a negative value of AH has been observed as shown in table 3. On the simplest model the rate of a diffusion controlled reaction is given by the Smoluchowski equation l2 kD = 44Dm+DB)(rAH+rB) (10) where rAHis the radius of AH,considered as a spherical molecule and DAH is the diffusion coefficient of AH.Since D,H is related to the solvent viscosity by the Stokes-Einstein equation DAII = kT/4nqrAH k = q/(2+rBr,&+rAHr;l) kT fi17/4kT. Thus a plot of k;' (in units molecules m-3 s against (in units kg m-ls-') has gradient (4kT)-l (in units J K). If k and q are in the more conventional units of mol d~n-~ s and Poise respectively the gradient is (6.02 x x 4kT)-' mol dm-3 s Poise-' which has the numerical value of I .09 x lo-* at 25°C. The observed values of this gradient are much greater as shown in table 4 for solvents ranging in viscosity from chlorobutane (q298 = 4.27 x Poise) to iodobenzene = 15.8 x Poise). Furthermore the plots of k;' against q have a positive intercept on the k;l axis. TABLE 3.-ACTIVATION ENERGIES FOR ION-PAIR COMPLEXES FORMATION acid base AH^* AH& solvent /kJ rnol-1 /kJ mol-1 ref.2,4-dinitrophenol tri-n-butylamine chlorobenzene -3.5 +8.8 10 Magenta E trimet hylamine chlorobenzene +3 +8.8 4 Magenta E triethylamine chlorobenzene +9 +8.8 4 Magenta E tri-n-propylamine chlorobenzene +12 +8.8 4 Magenta E tri-n-but ylamine chlorobenzene $6 +8.8 4 Magenta E 2,4,6-trimethylpyridine chlorobenzene +2 +8.8 4 Magenta E tri-n-butylamine chlorobutane +5 +7.5 11 Magenta E tri-n- bu tylami ne chloropentane +13 +8.4 11 Magenta E tri-n-butylamine bromobenzene +8 +10.5 11 These anomalies can be resolved if the formation of the hydrogen-bonded complex C is broken down into two kinetically distinct steps. The first step is the translational diffusion together of reagent molecules to form an encounter complex AH B in which AH and B are oriented at random.The second step is a rotational diffusion so that AH and B rotate until they are correctly oriented for the formation of a hydrogen bond. The hydrogen-bonded complex AH.. . B,then reacts at rate k to give the ion-pair product. kt kr AH+B+AH,B+AH..B-+A-..HB+. k; trans-rotation reaction lational diffusion A detailed analysis of this process has been given by Solc and St~ckmayer,'~ J. E. CROOKS AND B. H. ROBINSON k is the rate of reaction which would be observed if the translational and rotational diffusive processes were infinitely fast and so is a bimolecular rate constant in eqn (1 3). It may be expressed as a unimolecular rate constant the rate for the unimolecular conversion of hydrogen-bonded complex to ion-pair i.e.k23,by dividing by the equilibrium constant for hydrogen-bonded complex formation K,2. The other parameters are defined as below a = (rAH +rB) 4AH = fraction of surface area of AH considered as a sphere available for reaction AAH = ($AH +k;z~H)l(l +kl~*H) zAH = correlation time for rotational diffusion ~-' = (1 -AAH)-'(l -AB)-' +(1 -AAH)-'(AB-&)-' +(1 -AB)-'(AAH-+AH)-' Values of rAH and rB may be estimated from space-filling molecular models (Catalin). The value of k may be taken as k K,& where k is identified with kDand evaluated from eqn (10) and KAHB the equilibrium constant for encounter complex formation may be evaluated from l2 KAHB = ha3.(14) (This is valid for dissimilar YAH and rB if rAH = rBr a value of 4na3is preferred for KAHB). TABLE 4.-PARAMETERS FOR THE SOLC-STOCKMAYER CALCULATIONS rm mI reaction 2 Magenta E+ tributylamine 560 400 1.6 1.57 0.15 0.15 6.2 1.6 36 10 2,4-dinitrophenol+tributylamine 560 400 2.8 3.00 0.08 0.15 3.3 3 72 19 *Using values of #AH and +B tabulated. The value of zAH may be calculated l2 from the Debye equation ZAH = hqriH/kT. Hence Ic~zAH = &(rid + ri ')/a2. (16) The gradient of the plot of k< against q according to eqn (13) is inversely propor- tional to $AH& and insensitive to the other parameters so that it is more convenient to adjust 4AH and 4Bto obtain the experimental gradient and see if sensible values are obtained.Table 4 shows values of the gradient calculated from the values of 4AH and $B given which inspection of molecular models shows are not unreasonable. The high value of the gradient for 2,4dinitrophenol as acid may be seen to be attribut- able to a low value of the fractional surface area of the molecule available for reaction. HYDROGEN-BONDED AND ION-PAIR COMPLEXES IN APROTIC SOLVENTS This may be due to the restriction of the rotation of the OH group by hydrogen bonding to the ortho NO1 group. The model implicitly ignores the possible efTect of the intramolecular hydrogen bond causing an activation energy for the formation of the hydrogen-bonded complex. Solvation effects are similarly ignored. It is not possible to use eqn (13) to derive a relationship between the observed activation energy and the activation energies for the final step and for viscosity.However the small or negative values for the observed activation energy may be explained in qualitative terms. The observed rate is a function not only of k but also of the concentrations of hydrogen-bonded complex and encounter complex. Increasing the temperature increases k, but decreases the concentrations of reaction intermediates since AH" for their formation is negative. Thus an increase in temper- ature may lead to an anomalously small or negative increase in the observed rate. ANOMALOUSLY SLOW REACTIONS INVOLVING THE FORMATION OF ION-PAIR COMPLEXES The indicator acid Broniophenol Blue 11 reacts with pyridine bases to form ion- pair complexes of type 111.0 Br HO Br 111 The kinetics of this reaction have been investigated using a laser tempera-ture-jump apparatus,l monitoring the progress of the reaction by spectro-photometric detection of 111which has an absorption peak at 405 nm. Relaxation times were found to be in the range 500 ps-25 ms whereas relaxation times for the systems listed in table 2 were in the region 2-5Op. The relaxation HO IV J. E. CROOKS AND B. H. ROBINSON times varied with concentration in accordance with eqn (5). The kinetic data obtained are listed in table 5. It can be seen that by contrast with the values listed in table 2 k is very dependent on base strength and well below the values expected for a diffusion-controlled reaction.Values of k are almost independent of base. Values of AH are negative for three of the four bases studied. TABLE 5.-THERMODYNAMIC AND KINETIC PARAMETERS FOR THE REACTION BETWEEN BROMOPHENOL BLUEAND PYRIDINE BASES IN CHLOROBENZENE SOI~UTION AT 298 K 10- 5 kr -AS" -Asf* amine 10-3 K /dm3rnol-1 /dm3 mol-' s-l kb Is-' -AH" /kJrnol-' -AH* /kJ mol-' /Jmol-' K-' /Jrnol-l K-' pyridine 2-methylpyridine 2,6-dimethylpyridine 2,4,6-trimethylpyridine 2.09 31.6 123 1 000 1.16 14.6 96.2 970 50 44 70 98 43 58 55 60 9.3 -5.3 -6.6 -15.4 81 108 87 88 117 145 133 144 The negative values of AH strongly suggest the kinetic significance of an inter- mediate complex which may be identified with the hydrogen-bonded complex IV.The kinetic scheme is thus kiz k23 AH+B$C+D k21 k3z in which C is the hydrogen-bonded complex IV D is the ion-pair complex 111 and the rate-determining step is the conversion of IV to 111. The formation of IV from Bromoplienol Blue and base is an exothermic process so that raising the temperature reduces the concentration of IV and hence reduces the rate of the overall reaction. The first equilibrium is rapidly established ; k, is of the order of the diffusion- controlled rate as shown for the analogous systems listed in table 2 for which kfhas been identified with k12. For the systems listed in table 5 the observed relaxation TABLE 6.-THERMODYNAMIC AND KINETIC PARAMETERS FOR THE INTERCONVERSION OF HYDROGEN-BONDED AND ION-PAIR COMPLEXES OF BROMOPHENOL BLUEIN CHLOROBENZE~E SOLUTION AT 298 K -AH53 AHA -AS53 -ASX 10-2 523 k3z !kJ /kJ /J K-1 /J K-l base K23 15-is-' mol-1 rnol-1 rnol-1 mol-1 3-chloropyridinea 1.2 2.6 220 14 34 44 83 pyridine 300 150 50 23 29 41 2-met hy I pyridi ne 4 200 1 900 44 37 16 55 92 2,6-dimethylpyridine 18 000 13 000 70 29 20 28 96 2,4,6-trimethylpyridine 92 000 89 000 98 37 8 29 85 Notes a from eqn (3) using 2,6-dibromophenol with base in CCI as model system for evaluation of KI2.time is then related to the individual rate constants by eqn (7). For all the bases studied except 3-chloropyridine K23 9 KI2,so that K,,([AH]+[B]) 4 1. There-fore k is identified with k23K12 k with k32,and AH with AH:2+AHG. Values of K, and AH:2 have been taken from the model systems listed in table 1 to give values for the kinetic parameters for the rate-determining step which are listed in table 6.A pronounced solvent effect on the kinetics has been observed." Values of kr and kb have been obtained by both stopped-flow and temperature-jump techniques HYDROGEN-BONDED AND ION-PAIR COMPLEXES IN APROTIC SOLVENTS which were found to be concordant and are listed in table 7. The primary isotope effect has been measured by the differential stopped-flow technique,'* and found to be close to unity. Values of AV? have been measured l9 by use of a high-pressure observation cuvette incorporated in the laser temperature-jump apparatus.'' These data are listed in table 8. TABLE7.-sOLVENT EFFECTS ON THE KINETICS OF THE REACTION BETWEEN BROMOPHENOL BLUEAND PYRIDlNE AT 298 K solvent relative permittivity ET /kJrnol-' 10-3~-10-39 /drn3 mol 1 /dm3 mol- s-l 1O-'?3 Is- a kb(= F2) Is- C6H5CH3 2.38 141.7 1.15 6.9 3.4 6.0 C6H6 2.27 144.2 1.82 13.8 5.6 7.5 C~HSC~ 5.62 156.8 2.12 117 40 55 CHZCI 8.89 171.8 6.2gb 641 184 71 b Notes a kz3 = kf/K, ; values of K, taken as those for the hydrogen-bonded complex between Magenta E and pyridine (see table 1).b K # kf/kbin this instance because of the presence of a further equilibrium involving dimerisation. TABLEPRIMARY ISOTOPE EFFECTS AND VOLUME DATA FOR THE REACTION BETWEEN BROMOPHENOL BLUEAND PYRIDINE AT 298 K -AV,* -AVO -AV$(= -At'&) solvent Ka/Kn (kf)E/(kf)D /cm3 mol -1 /cm3 mol-1 /cm3 mol -1 CrjHsCHs 1.04 1.04(+0.01) --C6HsCl -16 14 2 The formation of 111 differs from most other reactions in which proton-transfer results in ion-pair complex formation in that the negative charge on the deprotonated acid is located at some distance from the site of proton loss.The sultone ring in I1 has opened to form the new site of the negative charge. Five processes can be recognised as occurring along the reaction co-ordinate namely (i) formation of the hydrogen-bonded complex IV (ii) proton transfer along the hydrogen bond (iii) solvent re-organisation associated with (ii) (iv) opening of the sultone ring during which the negative charge disappears from the phenolate group and appears on the sulphonate group (v) migration of the protonated amine from the phenolate to the sulphonate site.It is clear from the data in table 7 that the solvent plays a dominant role in the kinetics of the reaction. The values of AS:3 and AVT suggest that there is extensive solvent reorganisation on forming the transition state for the reaction of IV to give 111. One reason why this reaction is slow in such non-polar solvents as chlorobenzene is the need for solvent involvement. This may be because proton transfer can only occur when the solvent has adopted a particular configuration that appropriate for the solvation of the ion-pair. The rate kZ3,will thus depend on the probability of this rearrangement occurring. The rate increases rapidly with increasing polarity of the solvent and there is a good correlation between log kz3and the ET polarity value of the solvent.21 Extrapolation suggests a value of 10l2 s-I for the rate in aqueous solution.The large value of -A V suggests considerable electrostriction of the solvent in the transition state. Furthermore the value of AV& suggests that the solvation of the transition state resembles that of the ion-pair complex. The negative J. E. CROOKS AND B. H. ROBINSON value of AS2 suggests that the transition state is more ordered than the ion-pair complex and as this is not due to solvation changes this may be associated with the existence of the sultone ring in the transition state. The closeness of the primary isotope effect to unity contrasts with the large effects recently observed for proton transfer from carbon acids to amine bases in similar solvents.22 This indicates that for Bromophenol Blue as acid either proton migration in the rate-limiting step is strongly coupled with other heavy atom motion (e.g.solvent rearrangement or sultone ring opening) or proton-transfer is not rate-limiting. If the latter is valid the actual proton migration step can only affect the observed rate via a pre-equilibrium constant. There are two plausible transition states HO V VI In V proton-transfer is synchronous with ring-opening whereas in VI these two processes are uncoupled. We believe that the weight of the evidence favours VI. VI is more ordered than 111 but solvated to a similar extent as required by the evidence from AS; and AVG. The kinetic isotope effect is close to unity because proton- transfer is almost complete in the transition state VI.The rate of the back reaction k32,is little affected by base strength because proton-transfer has hardly started in the transition state for the reverse process. The proton-transfer step is slow i.e. k23is low because proton transfer is opposed by both an entropy and an enthalpy of reaction. The negative values of AS2 are due to the need for solvent reorganisation around the highly dipolar transition state. The comparatively high values of AH2 are due to the need to supply energy for charge generation and separation which in the transition state is not adequately supplied by delocalisation energy. The dependence of AH2 on the base strength shows the effect of electron delocalisation in the amine.Aromatic amines are weak bases because delocalisation energy is lost on protonation but this loss is reduced by electron donation from substituent methyl groups. Proton transfer in the systems listed in table 2 is fast because delocalisation is synchronous with charge generation so that the energy of the system decreases continuously as the proton moves across the hydrogen bond. A. A. Maryott J. Nat. Bur. Stand. 1948 41 1. R. P. Bell and J. E. Crooks J. Chem. SOC.,1962 3513. J. E.Crooks and B.H. Robinson Chem. Commun. 1970,979. E. F. Caldin J. E. Crooks and D. O'Donnell J.C.S. Faraday I 1973 69 1000. J. E. Crooks and B. H. Robinson Trans. Faraday SOC.,1971 67 1707. J. E. Crooks P. J. Sheridan and D. O'Donnell J. Chem.SOC.B 1970 1285. 'E. F. Caldin J. E. Crooks and D. O'Donnell J.C.S. Faraday I 1973 69 993. HYDROGEN-BONDED AND ION-PAIR COMPLEXES IN APROTIC SOLVENTS * K. J. Ivin J. J. McGarvey E. L. Simmons and R. Small J.C.S. Faraday I 1973 69 1016. E. F. Caldin and J. E. Crooks J. Chem. Soc. B 1967 959. lo K.J. Ivin J. J. McGarvey E. L. Simmons and R. Small Trans Faraday Soc. 1971 67 104. l1 G. D.Burfoot E. F. Caldin and H. Goodman J.C.S. Faraday I 1974,70 105. l2 A. M. North The Collision Theory of Chemical Reactions in Liquids (Methuen 1964). l3 K. Solc and W. H. Stockmayer Int. J. Chem. Kinetics 1973 5 733. l4 B. H. Robinson unpublished data. l5 E. F.Caldin J. E. Crooks and B. H. Robinson J. Phys. E 1971 4 165. l6 J. E. Crooks and B.H. Robinson Trans. Faraday SOC.,1970 66 1436. l7 G. Gammons B.H. Robinson and M. J. Stern J.C.S. Chem. Commun. 1972 1157. l8 K. J. A.Hargreaves and B. H. Robinson unpublished data. l9 T. Altinata B.H. Robinson and C. J. Wilson unpublished data. 2o E. F. Caldin M. W. Grant B. B. Hasinoff and P. A. Tregloan J. Phys. E 1973 6 349. 21 K. Dimroth C.Reichardt T. Stepmann and F. Bohlmann Ann. 1963 661. 22 E. F. Caldin and S. Mateo J.C.S. Chem. Commun. 1973 854.