Isotope Effects and the Nature of Proton-TransferTransition StatesBY R. P. BELLPhysical Chemistry Laboratory, OxfordReceived 12th January, 1965The magnitude and variability of hydrogen isotope effects in proton-transfer reactions indicatesthat some of the modes of the transition state must involve considerable motion of the proton.These may include stretching vibrations (especially when the process involves the movement ofother atoms in the system), bending vibrations, or the " vibration " of imaginary frequency whichleads to reaction : in the last case the tunnel correction is isotope-dependent. There will be somecancellation between the contributions to the isotope effect of transition state bending and of thetunnel correction. It is suggested that non-equilibrium solvation of the transition state may alsocontribute.As shown by the contributions to this discussion, there is now ample evidencethat many physical and chemical processes involve the transfer of a proton betweentwo atoms.The present paper attempts to speculate about what information maybe obtained about the transition state, especially by the study of kinetic hydrogenisotope effects. The following questions may reasonably be asked. (i) What isthe nuclear configuration of the transition state, and in particular where does theproton lie? (ii) What are the forces acting in the transition state; in other words,what are its frequencies, or the shape of its energy surface? (iii) Can the answersto (i) and (ii) be predicted or interpreted by theories of interaction between bondedor non-bonded atoms? (iv) What part is played by solvation, or by change ofsolvation, in the formation of the transition state?The short life of the transition state precludes the use of the usual methods ofstructural investigation, such as spectroscopy, and the only useful experimentalevidence is that derived from the kinetic measurements themselves.A purelytheoretical approach is difficult, since it necessarily involves non-classical structureswith partly broken bonds, and for this reason an electrostatic model has often beenused.Kinetic investigations of a single process give only general information aboutthe transition state, such as its enthalpy or entropy of formation, and it is only inthe simplest systems that this information can be given a structural interpretation.A more hopeful approach is to investigate the variation of velocity with the structureof the reactants.In proton-transfer reactions this principle was first applied toacid-base catalysis, where the Bronsted relation between acid-base strength andcatalytic power, and deviations from this relation, can be given a molecular inter-pretation.1 More recently, the development of techniques for studying fast reactionshas made it possible to extend the same ideas to a wide range of acid-base reactions,and an excellent summary of this general field has been given recently by Eigen.2Isotopic substitution is a particular type of structural variation, and in proton-transfer reactions particularly valuable information may be obtained by replacingthe proton being transferred by deuterium or tritium (the primary isotope effect),1R.P. BELL 17though it may also be useful to substitute other hydrogen atoms in the reactants(secondary isotope effect) or to change the solvent from H20 to D20. These sub-stitutions will not affect the shape of the energy surface, but will modify the energylevels in a way depending upon its shape, thus providing some hope of answeringquestion (ii) above.Swain and Thornton 3 recently stated " If the transition state isotope effectof every atom were determined, valence force constants could presumably be deter-mined," and it will be shown later that this includes the negative force constantassociated with motion along the reaction co-ordinate.In practice this would demandan accurate study of deuterium and tritium isotope effects over a wide temperaturerange, but it is of interest to see what can be deduced from the more limited informationactually available.Considering a proton transfer represented by AH + B+A+ HB (charges beingomitted) the most important factor determining the primary isotope effect is thezero-point energy of the A-H bond, and the simplest expression for the isotopeeffect is k ~ / k ~ = exp (Aiso/kT), where A E ~ represents the difference in zero-pointenergies between A-H and A-D, and is derivable from spectroscopic data. Inthe common case of proton transfer from carbon, Aeo is about 1.15 kcal/mole ifonly the stretching vibration is considered, and the predicted value of k ~ / k ~ is 6.9at 25".In the transition state the stretching frequency of A-H changes into motionalong the reaction co-ordinate, A . . . H . . . B, which has no real frequencyand hence no zero-point energy. The simple picture therefore predicts that k ~ / k ~should be independent of the nature of B : moreover, since the C-H frequencyin a series of similar organic compounds is almost constant, k ~ / k ~ should vary littlein such a series.The rather fragmentary data available for proton abstraction from carbon(mostly obtained from the rates of zero-order base-catalyzed halogenation re-actions) 4 show that this simple expectation is not realized. For a given organicspecies there is definite evidence that k ~ / k ~ increases with the strength of the basewhich is abstracting the proton.This is shown particularly clearly by recent workin this laboratory 5 on the abstraction of protons or deuterons from ethyl a-methyl-acetoacetate by the anions of carboxylic acids of varying strength. The resultsare summarized in table 1, and show a smooth variation of k ~ / k ~ with the basicc -+ 4-TABLE 1 . - h T E OF IONIZATION OF ETHYL a-METHYLACETOACETATE AT 25°Ccatalyst Kl kH (M-* sec-1) kHlkDCHCl2CO 2 3 . 3 2 ~ 10-2 3 . 5 7 ~ 10-5 3 . 8 5CH2ClCO 2 1 . 3 8 ~ 10-3 3 . 0 0 ~ 10-4 5 . 1 8CH2ClCH2CO; 1 . 0 4 ~ 10-4 1 . 7 6 ~ 10-3 5.72CH3C0; 1 . 7 5 ~ 10-5 3 . 2 3 ~ 10-3 5-92Me3CCO; 9.35x 10-6 5-75 x 10-3 6.45strength of the catalyst.It is not practicable to study proton abstraction byhydroxide ion in the reaction of table 1, but we have recently found 6 k ~ / k ~ = 9.6by direct measurement of the reaction between nitromethane and hydroxide ions,which may be compared with the values 6.5, 4.3 and 3.8 previously found 7 in thezero-order bromination of nitromethane catalyzed by CH3CO 2, CH2CICO; andH20 respectively; there is again a large increase of isotope effect with increasingbase strength18 ISOTOPE EFFGCTSThere is also good evidence 4 of variation of isotope effect in a series of similarcompounds AH when 3 remains the same in the reaction AH + B+A + HB. Table 2contains results for proton transfer to water at 25", mainly from work in thislaboratory.TABLE 2.-RATES OF IONIZATION IN WATER AT 25°C(p = Bronsted exponent for base catalysis)ref.kH(sec-1) ~ H I ~ D P substance5 2.45~ 10-5 2-0 0.79CHMe(C02Me)2 5 3-53 x 10-7 2.4CHBr( CO2Et)2 5 2-15 x 10-4 2.7 0.73- CH2(C02Et)2 ;yy2,TflC"'"' 20 2 . 3 0 ~ 10-3 3.4 0.64\- (MeC0)2CHMe 8 9.7 x 10-5 3.5MeCOCH2C02Et 5 1 . 1 6 ~ 10-3 3.5 0.59MeCOCHMeC02Et 5 1 . 1 4 ~ 10-5 3.8 0.60MeN02 7 6 . 5 ~ 10-8 3.8 0.67(MeC0)zCHBr 5 3.35x 10-2 3.9 0.42MeCOCHBrC02Et 5 1 . 5 6 ~ 10-2 4.3 0.42(MeC0)2CH2 5 1 . 3 2 ~ 10-2 4.5 0.48The isotope effect varies between 2.0 and 4.5, but bears no relation to the reactivity.It does, however, correlate fairly well with the exponent of the Bronsted relation be-tween catalytic constant and base strength, probably within the experimental errorsof both quantities.Values so far obtained for the reaction between nitroparaffinsand hydroxide ions 6 show a smaller variation : MeN02, k13[ = 28 M-1 sec-1,k ~ / k ~ = 9.6 ; MeCH2N02, k~ = 5.2 M-1 sec-1, k ~ / k ~ = 9-3 ; Me2CHN02, k H =0.31 M-1 sec-1, k ~ / k ~ = 7.5. Another series of interest was investigated byStewart and Lee,g who measured k ~ / k ~ for the oxidation of five ring-substitutedphenyl-trifiuoromethyl-carbinols by CrVr in 77 % aqueous acetic acid, and founda regular increase from 7-4 to 12.9 as the reactivity of the carbinol decreased by afactor of 50. This last reaction probably involves the transfer of a hydride ion ratherthan a proton, but the principles involved should be similar.The facts described in the last two paragraphs show that isotopic substitutionmust affect not only the initial states but also the transition states of proton-transferreactions, and the obvious suggestion is that the latter involve vibrations whosefrequencies (and hence zero-point energies) are affected by the mass of hydrogen.*Such vibrations would decrease the kinetic isotope effect, and since the observedeffects are usually (though not always) smaller than those predicted in terms of theinitial state only, the problem is sometimes referred to as " small isotope effects ".I1It is, however, by no means clear what kinds of transition state vibrations are in-volved, and it is necessary to clarify this point if we are to use observed isotope effectsfor obtaining information about the transition state.If the transition state is regarded as a linear, tri-atomic species, its normal modesof vibration can be represented as follows :* Because of the short life of the transition state, doubt has sometimes been expressed 10 whetherit is legitimate to consider quantization of vibrational levels.This objection should be less validfor the zero-point energy, which is a direct consequence of the uncertainty principleR. P. BELL 19UNSYMMETRICAL STRETCHc -b cA . . . H . . . B (imaginary frequency iv3, reaction co-ordinate).“ SYMMETRICAL ” STRETCH4- -bA . . . & . . . B (v1, motion of H indeterminate).BENDINGt tIA . . . H . . . B (v2, doubly degenerate).Early explanations of small and variable isotope effects supposed that the A-Hbond was “ incompletely broken ” in the transition state, so-that some of its vibra-tional zero-point energy is retained.This is equivalent to assuming a real finite valuefor v3, and it was pointed out by Westheimer 12 that this is inconsistent with thedefinition of the transition state, which must have one normal mode correspondingto a maximum in the energy surface, and hence lacking a real vibrational frequency.Westheimer further pointed out that when the force constants for A . . . H andB . . . H are unequal, the “ symmetrical ” stretching mode v1 will in fact involvea considerable motion of the proton and can be a source of mass-dependent zero-point energy. This view has been generally adopted, and leads to the predictionthat in a series of similar reactions k ~ / k ~ will have a maximum value when the transi-tion state is symmetrical, since v 1 will then not involve any movement of the proton.This prediction is consistent with some of the experimental results mentianed above.Thus the anion of ethyl a-methylacetoacetate is certainly a stronger base than acarboxylate anion, so that in the transition states of the reactions listed in table 1the proton will be closer to the carboxylate; increase in the basic strength of thecarboxylate catalyst will therefore render the transition state more symmetricaland should increase k ~ / k ~ , as actually observed.This idea receives support fromthe correlation between k ~ / k ~ and p shown in table 2, since the latter may also bea function of the position of the proton in the transition state.34Westheimer’s treatment is certainly qualitatively sound, but closer examinationshows that the “ symmetrical ” vibrations of a three-centre system can hardlyaccount for the observed effects.If the distances A . . . H and H . . . B arerespectively r1 and r2, he writes for motion along the line of centresand the usual treatment gives a quadratic equation for v1 and v3 in terms of themasses rnl and m2 and the force constants. Westheimer now makes the simplifyingassumption k: -klk2 = 0, which corresponds to v3 = 0, and obtains a simpleexpression for v1 which shows a large isotopic dependence. For example, if kl =10 kz, ml = 12, m2 = 16, then vy/vF = 1.32, which is not much less than themaximum value of 2+. However, this result is dependent on the assumption v3 = 0 :actually we must have k: > klk2, when the equation has an imaginary root iv3, where-v$ is ameasure of the curvature of the energy barrier along the reaction co-ordinate.The assumption v3 = 0 is thus an artificial one, suggesting an activation energyof zero, and it would be more natural to suppose that the energy surface has curvaturesof similar magnitude in different directions.It is therefore of interest to calculatethe effect of varying kI2 on the magnitude and isotopic dependence of V I inWest heimer’s treatment20 ISOTOPE BFFBCTSTable 3 shows the results of calculations on the basis of eqn. (1) for variousvalues of k12, assuming as before kl = 10 kZ, ml = 12, m2 = 16.The first rowcorresponds to Westheimer's assumption k& -klk2 = 0. It is clear that an increaseof k12 produces a decrease both in v1 and in vT/vy, both of which will diminish theeffect of the " symmetrical " vibration in decreasing the isotope effect. It is im-possible to predict the value of k12 corresponding to real cases, but it would haveto be at least 2(klk2)* if the barrier curvature (measured by 23) is to be similar toTABLE 3.-bNGlTUDINAL MOTIONS OF TRANSITION STATEA = 4712~2, kl = 10 k2, mi = 12. m2 = 16k d k i kd* q - + y I k i "H 1 7 lki V l H I V 11 0.558 0 1 -321 *27 0-415 - 0.024 1.281.74 0.233 -0.136 1.143.16 0.138 - 0.952 1 a08the other curvatures of the energy surface. A similar conclusion follows from anelectrostatic treatment of the motion of a proton between two unequal negativecharges.13 If we take rn = 10 for the repulsive exponent in eqn.(10) of ref. (13),and z = 1 (corresponding to a total charge of -1 on the transition state), then inorder to make kl = 10 k2 we must put y = 0.535, which leads to k1223-5 (klkz)*.A similar result is obtained for any reasonable choice of m and z. All the abovecalculations have involved the rather extreme assumption kl = 10 k2: a smallerratio between the two force constants will diminish both the frequency and theisotopic dependence of the " symmetrical " stretching vibration. It seems doubtful,therefore, whether this vibration can account for the low values of kH/kD oftenobserved and for the variation in a series (cf.table l), at least in terms of a three-centre model.The three-centre model may, however, be a misleading one for many of theproton-transfer reactions studied in practice. This is particularly clear when thetransfer of the proton is concerted with the making or breaking of another bond inthe system, for example in the E-2 mechanism for base-catalyzed fl-eliminationreactions, for which there is good evidence.14 The transition state can be writtenasII!C . . . H . . . BIx . . . c -and it seems intuitively obvious that the degree of breaking of the C-H bond inthe transition state may vary greatly from one system to another, although thesystem as a whole must be passing through a maximum of potential energy: thisinvolves a return to the organic chemist's concept of an '' incompletely broken "C-H bond, rightly criticized by Westheimer on the basis of a three-centre model.A more precise picture is obtained by considering an idealized model in which thetransition state is linear.There will now be four normal stretching modes whichmay be represented as follows, a query denoting a small displacement which maybe in either direction. Mode (i) represents the reaction co-ordinate, in which thetransfer of the proton to the base is accompanied by a lengthening of the C-X bondand a shortening of C-C: it will correspond to a maximum in potential energR. P. BELL 21and will have no real frequency. Mode (ii) is analogous to the “ symmetrical”vibration of the three-centre model, and according to the arguments of the lastsection will have a low frequency and a small isotope effect.The new feature isrepresented by mode (iii) in which the motion of the B-H-C part of the systemresembles that in the reaction co-ordinate (i), but the motion of the C-C-X unitis no longer concerted with it, and reaction does not result: instead, the modeTABLE 4.-NORMAL MODES OF A TRANSITION STATE( i ) + t -+ t +B-H-C-C-Xf ? + c 4(ii) B- H4-C-X(iii) -+ +- ? -+ -+B- H- C- C- Xt f ? + +(iv) B-H- C- C- Xwill have a real frequency which is clearly highly dependent upon the mass of thehydrogen, even when it is symmetrically situated in the transition state. Mode(iv) will also have a real frequency, but it will be lower and may be less dependentupon the hydrogen mass.The general result of these considerations is that the concerted nature of themechanism leads to a real vibration of the transition state which is “ unsymmetrical ”as far as the system B .. . H . . . C is concerned, and therefore permits largevariations in the magnitude of the isotope effect. In fact, in the reaction C&5CH2X+C~HSCH = CH2 in presence of sodium ethoxide, the effect of replacing the CH2-groupby CD2 varies from 3.0 to 7-1 according to the nature of the group X.14 Moreover,the same arguments apply in reactions where the proton-transfer is concerned notwith the cleavage of another bond, but only with a change in its multiplicity. Thissituation is a common one in slow proton transfers; for example, in reactions ofI Ithe type B+H-C-C = O-+BH+C = G O - such as those in tables I and 2.I I I 1The transition state modes for this system will be entirely analogous to those intable 4, and the same conclusions may be drawn.Similar considerations may applyin quite simple systems : for example, the loss of a proton from RC02H or HCX3will involve changes in the C-0 distance and XCX angle respectively, and onlyone of the normal modes will lead to reaction.In practice, transition states will usually be non-linear, so that the vibrationsinvolved cannot be classified in terms of stretching and bending. However, thepart of the system represented by A . . . H . . . B is probably close to linearin many cases, and it is of interest to consider the bending vibrations of a linearthree-centre model, represented by the doubly degenerate v2.As usual, we haveno direct evidence for the magnitude of this frequency, but the bending frequencyof the ion HF; is 1225 cm-1,15 and calculation on the basis of an electrostatic model 13gives a simiiar value for a transition state.*This degenerate vibration will contribute doubly to the zero-point energy of thetransition state, and its frequency clearly depends upon the isotopic mass even ina symmetrical transition state. It therefore provides another reason for low andvariable values of k ~ / k ~ : it seems intuitively likely that the frequency of such a%-** It is sometimes stated 16 that the assumption of central forces predicts a zero frequency forthe bending vibration of linear triatomic molecules, but several authors 179 18 have shown thatthis is not the case22 ISOTOPE EFFECTSvibration will be at a minimum when the proton is symmetrically placed, and thisagrees with the results of the electrostatic treatment (eqn.(7) and (14), ref. (13)).There is, moreover, an additional reason why transverse frequencies may be quitehigh and may vary in a series of transition states. The central-force treatmentaccounts for the bending force constant in terms of non-directional forces betweenthe proton and the centres A and B, and the same picture will apply to the bifluorideion. An initial state such as -C-H will possess bending frequencies around1400 cm-1 which can be attributed to changes of hybridization with bond angle, orto interactions between non-bonded atoms.These factors will diminish as the bondis stretched, but they will still be present in the transition state, especially if it isclose to either the initial or the final state. Their result will be to increase thefrequency of the bending vibration, and also its sensitivity to the configuration ofthe transition state.So far nothing has been said about the tunnel correction for motion along thereaction co-ordinate. This is a quantum correction having exactly the same logicalstatus as the correction for zero-point energy in the transition state, both beingdirect manifestations of the uncertainty principle. In fact, it has been shown 19that under most conditions the tunnel contribution to the isotope effect can becalculated merely by inserting the imaginary frequency iv3 in the exact expressionfor a vibrational contribution (rather than the approximate expression exp (A&o/kT)).There are now several investigations of proton-transfer reactions in solution, mainlyinvolving deuterium or tritium isotope effects, which appear definitely to establishthe part played by the tunnel effect,20-24 and there is no logical justification foromitting its consideration. Its effect will always be to increase k ~ / k ~ , and treat-ment of a rather general central-force model 13 predicted that this increase wouldalways be at least as great as the decrease due to the bending vibration v2, cancella-tion being exact for a model in which the proton moves between two non-polarizablenegative charges.However, this conclusion should not be taken too seriously.The predictionmentioned in the last sentence is valid only if the bending force constant is due tocentral forces between the proton and the two basic centres, and any contributionfrom valency bending forces will not be cancelled out by the tunnel correction.Moreover, there are two reasons why the tunnel correction may be less importantthan previous calculations suggest. In the first place, the usual treatment 1 9 ~ 2 5expresses the correction solely in terms of the curvature of the energy surface alongthe reaction co-ordinate, which implies that its value is the same for symmetricaland unsymmetrical barriers. This is very nearly true when the correction is small,but it is physically obvious that a large tunnel correction will be reduced when thereis a large energy difference between the initial and final states (since no tunnellingcan take place from systems with energies lower than the higher of these states),and this is confirmed by calculations for unsymmetrical parabolic 26 and Eckhart 27barriers.* In the second place, there is no real justification for applying tunnelcorrections based on a one-dimensional barrier to systems where the correctionsare not small, and there are indications that the one-dimensional treatment mayconsiderably over-estimate the correction289 29 Nevertheless, the contribution ofthe tunnel correction to the isotope effect will certainly oppose that of the bending\/* This effect might provide an additional contribution to the variation of the isotope effect withthe configuration of the transition stateR.P. BELL 23vibrations, and is probably of the same order of magnitude : thus it may not be abad approximation to ignore both these contributions.Finally, there is one more factor which may influence the magnitude of the isotopeeffect in proton-transfer reactions. It has recently been pointed out 309 31 thatthe dielectric relaxation time for water, about 10-10 to 10-11 sec,32 is probablygreater than the time involved in a proton transfer between two properly orientatedand activated molecules, estimated at 10-12-10-13 sec. This implies that the re-orientation of water molecules cannot keep pace with the transfer of the proton,so that the free energy of the transition state will be greater than that correspondingto equilibrium orientation.Since the deuteron moves more slowly than the protonthe departure from equilibrium will be greater in proton transfer than in deuterontransfer, leading to a decrease in k ~ l k ~ . Moreover, in a series of similar reactionsthe amount of reorientation involved in passing from the reactants to the transitionstate will depend upon the distance through which the proton has to move, and thenon-equilibrium effect may therefore contribute to the variation of k ~ / k ~ in sucha series. Unfortunately, it seems impossible to make any estimate of the importanceof non-equilibrium behaviour, since this would demand a knowledge of the timeinvolved in the proton transfer and the relaxation time of water molecules in thevicinity of the reacting system.It is of interest here that many proton or deuterontransfers take place 20-40 % more slowly in D2O than in H20, even when no solventspecies are formally involved in the reaction and no isotopic change is made in thereactants. This is the case for proton or deuteron transfers from acetone to acetateions,33 from nitromethane to acetate or monochloroacetate ions,7 from methyl-acetylacetone to acetate ions,8 and from 2-carbethoxycyclopentanone to monochloro-acetate ions.20 Since the relaxation time for D20 is greater than that for HzO,32these observations might be accounted for by non-equilibrium solvation of thetransition state.There are thus many factors which may affect the magnitude of hydrogen isotopeeffects in proton-transfers, and more systematic experimental work is needed todecide their relative importance.Ultimately, however, the study of isotope effectsshould prove a most useful means of elucidating the detailed structure of transitionstates.This paper was written while the author was on Sabbatical leave at Brown Uni-versity, Providence, Rhode Island, U.S.A., and he is grateful to the Brown ChemistryDepartment for hospitality and to the National Science Foundation for a Fellowship.1 Bell, The Proton in Chemistry (Cornell University Press, New York, 1959), chap. 10.2 Eigen, Angew. Chem., 1963,75,489.3 Swain and Thornton, J. Amer. Chem. SOC., 1962, 84,817.4 ref. (l), table 24, p. 201.5 Bell and Crooks, to be published.6 Bell and Goodall, to be published.7 Reitz, 2. physik. Chem., A , 1936, 176, 363.8 Long and Watson, J. Chem. Soc., 1958, 2019.9 Stewart and Lee, Can. J. Chem., 1964,42,439.10 Kassel, J. Chem. Physics, 1935, 3, 399.11 Thornton, J. Org. Chem., 1962, 27, 1943.12 Westheimer, Chem. Rev., 1961, 61, 265 ; see also Bigeleisen, Pure Appl. Chem., 1964, 8, 217.13 Bell, Trans. Faraday SOC., 1961, 57,961.14Bunnett, Angew. Chem. (Int. Edit.), 1962, 1, 225.15 Cot6 and Thompson, Proc. Roy. SOC. A, 1951,210,206.16 Herzberg, Infa-red and Raman Spectra of Polyatomic Molecules (Van Nostrand, N.Y., 1945),p. 16124 ISOTOPE EFFECTS17 Longuet-Higgins, Phil. Mag., 1955,46,98.18 Pearson, J . Chem. Physics, 1959, 30, 1537.19 Bell, Trans. Faraday SOC., 1959, 55, 1.20 Bell, Fendley and Hulett, Proc. Roy. SOC. A , 1956, 235,453.21 Hulett, Proc. Roy. SOC. V, 1959, 251, 274.22 Caldin and Harbron, J. Chem. SOC., 1962, 3454.23 Lewis, J. Amer. Chem. SOC., 1964, 86, 2531.24 Shiner and Martin, Pure Appl. Chem., 1964,8, 371.25 Wigner, 2. physik. Chem. B, 1932, 19,203.26Bel1, Proc. Roy. SOC. A, 1935, 148, 241.27 Johnston and Heicklen, J. Physic. Chem., 1962, 66, 532.28 Johnston, Adu. Chem. Physics, 1961, 3, 131.29 Johnston and Rapp, J. Amer. Chem. SOC., 1961,83, 1.30 Kreevoy and Kretchmer, J. Amer. Chem. SOC., 1964, 86, 2435.31 Grunwald and Price, J. Amer. Chem. SOC., 1964,86,2965,2970.32 Hasted, Prog. in Dielectrics, 1961, 3, 103.33 Reitz and Kopp, 2. physik. Chem. A , 1939,184,429.34 Lefflex and Grunwald, Rates and Equilibria of Organic Reactions (Wiley, New York, 1963),p. 158