A theoretical study of the proton affinities of water, alcohols, and ethers: absoluteversusrelative basicities

摘要

J. CHEM. SOC. PERKIN TRANS. 2 1990 A Theoretical Study of the Proton Affinities of Water Alcohols and Ethers Absolute versus Relative Basicities Jose-Luis M.Abboud lnstituto de Quimica Fisica 'Rocasolano ;C/Serrano I 19 euro;-28006 Madrid Spain Jose Elguero lnstituto de Quimica Medica C/Juan de la Cierva 3 E-28006 Madrid Spain Daniel Liotard Universite de Pau et des Pays de I'Adour 64000 Pau France M'Hammed Essefar and Mohammed El Mouhtadi Laboratoire de Chimie Theorique Department de Chimie Universite Cadi A y yad Marrakech Morocco Robert W. Taft Department of Chemistry University of California lrvine CA 9277 7 In this work we report the proton affinities (euro;pa) of water seven alcohols and seventeen cyclic and acyclic ethers as measured by ion cyclotron resonance spectroscopy (ICR) with respect to the same 'basicity ladder.' The Epafor selected compounds have been calculated by MNDO AM1 and ab initio (3-21 G and in some cases 4-31 G*//4-31 G and 6-31 G*//6-31 G) methods. These results are used for a comparison of the various computational techniques and for the analysis of structural effects on the neutral and protonated species.Methyl and other alkyl affinities of aliphatic alcohols are determined and discussed. The experimental euro;pa are treated by correlation analysis methods. Alcohols and ethers are common and useful compounds neutral and protonated species is necessary if meaningful Epaare bridging the structural gap between water and cyclic or acyclic to be obtained.13 Thus full geometry optimizations have been polyethers.The gas-phase proton affinity (Epa),of a base B is performed on all the species and by the three methods. The defined as the standard enthalpy change for reaction (1) in the corresponding Epaare given in Table 1. Although we shall not deal here with a detailed case-by-case comparison of the experimental and calculated geometries we report in Table 2 results for (2) (2)H+ (ll),and (11)H' that are useful for the gas-phase. In this work the Epafor water and a variety of next discussion. alcohols and ethers are reported. These experimental results are then analysed in terms of structure-reactivity relationships Discussion using both quantum mechanical and correlation analysis Molecular Geometries.-It has been reported that the 3-techniques.This study is aimed at (i) providing a better 21G method leads to optimized geometries that compare quite understanding of structural effects on the basicity of these favourably with the experimental structures. This is indeed the compounds and (ii) assessing the ability of advanced semi- case for the neutral forms of the compounds studied herein. In empirical techniques to describe these effects. This should general bond lengths agree within 0.02 A or better and planar facilitate future insights in the field of crown ethers. and dihedral bond angles are reproduced to within 3 and 4"' respectively. Although conformational barriers have not been calculated Results in this work the majority of the most stable conformations have Experimental values.-These values were obtained with the been correctly assessed.Of particular interest are the cases of same instrument namely the U.C. Irvine Ion Cyclotron (a) 2,2,2-trifluoroethanol (8) for which the gauche (defined by Resonance Spectrometer and have been anchored to the same 'basicity ladder'.' Full experimental details are given el~ewhere.~ t 1 cal = 4.184J.Unless stated otherwise relative proton affinities 6Ep,(B) $ ab initio E,, values are obtained as the negative differences between defined as 6Epa(B)= Epa(B)-Epa(HzO)are believed to be the energies at the potential-energy minima for the protonated (BH +)accurate to within 0.2 kcal mol-'.t and neutral (B) species as in equation (2). Because of the Computational Methods and Results.-(a) ab initi0.S The E,,(B) = -AE = AE(B) -AE(BH+) (2) choice of the basis set was severely limited by the size of many of parametrization features built into the NDDO methods MNDO andthe molecules studied herein.Thus we selected the 3-21G split- AM1 Epp were calculated according to equation (3) where AHf is the valence basis set4 as a compromise between flexibility and computational tractability. In a few instances calculations were E,,(B) = -AH = -AHamp;BH+) -AHf(B) -AHf(H+) (3) also performed at higher levels.' In all cases the MONSTER- enthalpy of formation for the various species in the gas-phase at 298 K.GAUSS 806 package was used. In this formalism the value of AHf(H+) is determined by the one-centre (b) Semiempirical. Two of the most advanced NDDO' core-electron attraction integral Uss.Its empirical value is quite differ- techniques were applied namely Dewar's MNDO * and AM1 ent from that appropriate to an isolated hydrogen atom.Thus following as implemented in Thiele's and Stewart's computer previous workers'* we used the experimental value AHf(H+) = 367.2 program. Complete optimization of the geometries for the kcal mol-'. J. CHEM.SOC. PERKIN TRANS. 2 1990 Table 1. Experimental and calculated proton affinities for water and selected alcohols and ethers. ROR' R H I I I' i Experimental 167.3 STO 3-21G 191.6 MNDO 172.1 AM 1 164.5 Ii 182.5 204.8 175.0 171.9 I-I 187.8 208.7 177.1 178.8 I-I 189.6 210.3 178.2 179.0 I-I 190.2 21 1.8 178.8 179.5 I-I 192.0' 2 14.0 180.2 182.8 I-I 193.4' 215.5 181.8 186.5 CF3CH2 1-I 169.3 186.8 155.8 157.9 191.1 213.1 177.4 177.4 195.2 216.7 179.4 183.4 196.1 197.3 198.6 220.4 181.1 187.8 201.1 223.0 183.6 190.9 l-Adamantyl 206.0 198.5 219.8 181.0 188.7 202.3 205.1 201.1 204.8 2 12.0 232.8 188.7 200.9 186.4 203.8 179.4 177.2 193.2 220.4 183.3 187.0 197.6 221.3 182.0 185.9 198.5 219.1 182.9 186.5 'From ref.3(c). See the text. 'Experimental proton affinities based on Ep,(NH3)= 204.0 kcal mol-' (ref. 2). Table 2. Experimental and calculated geometries for (2) (2)H+ (ll) and (11) H'." Parameter f Experimental 3-21G (Base) 3-21G (Base H+) AM1 (Base) AM1 (Base H+) 1.4244 1.440 1.532 1.4104 1.496 0.9630 0.967 0.974 0.964 0.999 1.0937 1.083 1.074 1.119 1.120 108.53 110.25 1 19.98 107.16 109.95 108.63 108.53 124.44 105.11 112.43 3.20' 3.7 3.3 3.9 3.5 180.0 180.0 179.9 179.9 62.1 61.5 61.5 62.5 1.415' 1.425 1.504 1.416 1.478 1.404 1.428 1.527 1.427 1.517 1.520 1.528 1.519 1.51 1 1.494 0.971 0.995 1.084 1.085 1.076 1.118 1.1 19 1.100 1.085 1.076 1.119 1.120 1.101 1.087 1.076 1.123 1.123 1.092 1.082 1.083 1.116 1.119 1.089 1.082 1.083 1.116 1.122 111.49 114.86 121.28 112.57 1 13.22 108.15 106.75 108.07 106.99 106.69 109.33 108.97 111.78 110.50 11 1.92 110.95 110.47 113.14 111.12 114.12 110.10 110.87 108.59 109.31 108.10 180.0 180.0 178.9 179.9 178.3 2.24 2.6 1.5 2.2 0.8 109.90 107.23 105.78 104.55 104.59 'Bond lengths in A angles in degrees.All experimental values for (2) are from ref.14(a). Methyl tilt angle as defined in ref. 14(6). Corrected OC(methy1)H angle as defined in ref. 14(b). All experimental values for (11) are from ref. 14(b). I = bond length; L = bond angle; cp = torsion angle; 6 y = methyl tilt angles the orientation of the G-H bond) conformer G is found to be and other ab initio (4-31G) calculations;" (b) (24) and (25) the most stable form as a consequence of the lone pair-lone pair predicted to have puckered (C,) and chair (C,)structures in repulsion existing in the trans conformation and the weak qualitative and quantitative agreement with the experimental chelation (O-H F) present in G. This agrees with IR data l6 evidence as well as for (24) with very thorough ab initio (4- J.CHEM. SOC. PERKIN TRANS. 2 1990 3 1G) calculations.' 'More subtle features such as the tilt angles of the alkyl groups relative to the C(a)-0 bonds in alcohols and acyclic ethers ' are nicely reproduced. As expected the description of the smallest cycles is somewhat poorer. For (22),the calculated (1.465A) and experimental (1.436A) C-0 bond lengths differ substantially (a study at the 6-31G ** level 2o also falls short of reproducing this value); (23)is slightly puckered '' but the calculated potential-energy minimum pertains to a planar structure. Other relevant structural features deduced from this study are as follows. For alcohols (2) to (7).(i) The calculated C-0 0-H and C(a)-C(p) bond lengths are nearly constant and respectively equal to 1.437 f 0.003,0.965f0.002and 1.531 f 0.004 A (the corresponding averages of the available experimental values are 1.430 f 0.005 0.954 f0.006 and 1.526 amp; 0.003 A).(ii) The COH angles are practically constant with an average value of 110.9 f 0.5" (appreciably larger than the experimental average 107.4 f1.6"). For acyclic ethers. (i) In the ROCH series (R = CH3 CZH5 i-C3H7 t-C,H,) the H3C-0 bond length is essential1 constant the average value being 1.429 amp; 0.004 A (0.013 x longer than the experimental values). The 0-C(H) (CH3) and O-C(CH,) bond lengths are calculated to be slightly longer (1.443 A). The average of the C(a)-C(p) bond distances for (9),(lo) (13) (14) and (16)is 1.530 f 0.004 A i.e. practically the same as for the alcohols.(ii) In the same series LCOC increases with the bulk of the R moiety possibly as a consequence of increasing back-strain. Except for H30+ in crystals,'4b no experimental geometries are available for the protonated bases studied here. Our calculations on this ion (an admittedly unique oxonium compound) confirm '5b that the predicted structure at the 3-21G level has a D symmetry. Much more elaborate calculations are needed 22923u in order to find its 'floppy' (inversion barrier of 1.4-1.5 kcal mol-') pyramidal str~cture.'~~ However in the light of the results obtained for the neutral bases and on account of the fact that the differences between the experimental and calculated bond lengths and bond angles are quite systematic we feel that at least the general structural trends and the comparisons thereof are likely to be correct.These trends are as follows. + For protonated (2) to (7). (i) The average R(H)O-H and C(a)-C(p) bond lengths are respectply equal to 0.974 amp; 0.001 and 1.516 f0.003 A. (ii) The C-OH bond distance steadily increases along the series. C1.532 A for (2),1.589 A for (7). (iii) The average COH bond angle is 120 f 1". + For the protonated ROCH series. (i) The average R(CH3)- 0-H and C(a)-C(p) bond lengths are respectively equal to 0.970s 0.001 and 1.521 f$).004 A. (ii) Along the series the R(H)O-CH3 and CH,(H)O-R bond lengths respectively decrease from 1.504 A (9) to 1.494 A (14)and increase from 1.504 A (9) to 1.557 A (14).(iii) The average COC angle is 123.5 f 1.6" For protonated (22)to (25). In all cases the C(a)O bond is stretched by 0.07-0.08 A while the C(a)-C(p) bonds are shortened by some 0.015 A. The torsional angles of (24)and (25) are little affected by protonation. These results lead to the following conclusions. (a) The OH bond length is essentially the same for protonated alcohols and ethers and is very slightly longer in the protonated than in the + neutral forms. It follows that 0-H bonds are strong and have largely covalent character.' 5b (b) Upon protonation all C-0 bonds are appreciably stretched 5b*23 while all the C(a)-C(p) bonds are shortened. This implies that mesomeric structures (1') (II') and (11") are significant. This contention is supported by the fact that bond stretching increases with the a-hyperconjugative24 ability of R CH C2H5 i-C3H -c t-C,H,.This is related to the finding by Meot-Ner," and Hiraoka and Kebarle,26 that AH for reaction (4) in the gas-phase increases by some 60 kcal mol-' on going amp; + H20-(ROH2)+ (4) from R = CH3 to R = t-C4H9. The same structural criteria indicate that differential o-hyperconjugative effects are much smaller in the neutral forms. (c) When comparing the series ROH and ROCH we found that LCOC is consistently larger than L COH. The same holds for their protonated forms although for the latter both sets of angles are wider i.e. 120"or more possibly as a consequence of enhanced electrostatic repulsions between the substituents on the oxygen.In the case of the protonated cycles (22)to (24) the release of I-strain by this mechanism is severely restricted and this is likely to be one of the reasons for (22) (23) and (24)being respectively less basic than (9) (lo),and (la)." As with acyclic ethers however protonation leads to a considerable stretching of the C-0 bonds. (d) Following protonation the average increase of the R-0 bond length is some 0.03 A larger for the ROH than for the ROCH series. The shortening of the C(a)-C(P) bonds is also more important in the former case. This indicates that relative to hydrogen a methyl group reduces the o-hyperconjugative contribution from R. Although much smaller the alkyl substituent effect on the O-CH distance suggests that the weight of contribution of structure (111') decreases as the bulk of R increases. R6(H)CH3 -ROHeH (111) (111') In general the AM1 method provides a satisfactory description of the geometries of the neutral species.'* Here we find that the C-C and C-0 bond lengths are at most to within 0.02 A of the experimental values and bond angles agree to within 2"or better.29 This method even out-performs the 3-21G model in the calculation of many COH and COC bond angles.The same holds for the C-0 bond length in (23)(calc. 1.436A).Also the most stable conformations of the acyclic molecules are generally well predicted. The main weakness of the method lies in the determination of the torsional angles for (24)and (25);the former is predicted to be planar and while the chair structure of the latter is correctly established the calculated torsional angles (31.9")are too small.For the protonated species significant differences exist between the AM1 and STO 3-21G geometries. Taking as a reference the optimized geometries for CH36Hz and C2H56H2 determined by means of high level ab initio cal~ulations,'~~~~the STO 3-21G results are superior. Nevertheless the AM1 calculations are able to reproduce the main structural features described in the previous section. This lends support to the finding that the But-0 bond lengths in protonated (7) (14) and (21)decrease following the order (7) (14) (21). MNDO tends to overestimate core-core repulsions.' As a consequence we find that for neutral species both the C(a)-C(P) bond lengths and the COC bond angles are too large by ca.0.03 568 J. CHEM. SOC. PERKIN TRANS. 2 1990 Table 3. Influence of the basis set on the calculated Epavalues. Base 3-21Gb 3-21G*b 4-31Gb 4-31G*' 6-31Gb 6-31G*d Epa,exp(l 191.6 182.2 183.2 174.7 182.6 173.7 167.3 204.8 195.0 199.9 190.3 199.2 189.6 182.5 (6)(*) 214.0 203.2 208.9 198.9 208.4 192.0 (9) 213.1 200.5 209.6 199.2 208.8 198.5 191.1 In kcal mol-'. Fully optimized geometries. 4-31G optimized geometries. 6-31G optimized geometries. A0.0-35.0-30.0-25.0 -20.0-15.0 -5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 Figure 1. Experimental Eps,expus. calculated Epa(3-21G) differential proton affinities.Compounds numbered as in Table 1. A C0.l and 0.05 A for (8) and (22). Again (24) is found to be planar; for (25),the bond angles are overestimated by up to 11" and the torsional angles underestimated by up to 47".Even so most of the trends revealed by the other methods can still be recognized and the correct conformation for alkyl alcohols 31 obtained. Proton AfJin it ies Theoretical Calculations.-(a) ab initio. 'Theoretical Epa values at the STO 3-21G level Epa(3-21G)s,are defined by equation (2). Let AEzp AE,, AEHF and AE,,, respectively stand for the difference in zero-point vibrational energy AEzp = EO,vib (BH') -EO,vib (B) the thermal energy correction (AEter),the energy difference at the Hartree-Fock (AEHF) limit and the electron correlation energy (Aamp;,").The Epaat 0 K Epa is given by 23932 equation (5). From previous work on water 32 and alcohols,23 the (AEzp + AE,,,) contribution is estimated at 7.0 kcal mol-'. It follows that the EPa(3-21G)values are some 16 kcal mol-' too large (the uncorrected values being so by an average of 23 kcal mol-I). This difference has three compon- ent~,~~~~~*~~i.e. AE(BSE) AE(BSSE) and AE,,, the first two originating in the basis-set effect and in the basis-set super- position error respectively. A direct evaluation of these terms for all the bases studied herein was not feasible but higher level calculations have been carried out on (l) (2) (6) and (9) (calculations at the 4-3 lG* and 6-3lG* levels respectively). The results are displayed in Table 3.These values show as expected a substantial decrease in the calculated Epavalues with an increase in the size of the basis set the effect being largest for The most remarkable feature is the large effect brought about by the inclusion of the polarization functions. Thus in every case Epa(3-21G*)d Epa(6-31G).In fact if we recall that (Azp + AE,,,) ca. 7.0 kcal mol-' the corrected Epa(4-31G*)values are close within the limits of experimental error to the experi- mental Epavalues. This explains why the difference between Epa(4-31G*)and Epa(6-31G*)is less than 1 kcal mol-'. These results agree with recent findings33 regarding the influence of polarization functions on calculated Epavalues (i) they reduce the size of the BSSE by a factor of 24 and (ii) for systems wherein the basic centre is first-row atom singly polarized basis sets provide a reasonably good description of electron correlation in protonation processes.Recent work 33 on (22) has shown that at the 3-21G level AE(BSSE) is ca. -3.3 kcal mol-'. Hence AE(BSE) + AE,, ca. -13 kcal mol-'. This term is too large for the straightforward use of Epa(3-21G)to be of chemical interest. Fortunately these errors as well as AE, and most of the AEzp term largely cancel out when comparing a series of isodesmic reactions such as reaction (6).34 ROR' + H,O+-RO(H)R'+ + H20 (6) Indeed Figure 1 is a plot of 8Epa,expus. SEpa(3-21G).GEpa= Epa(ROR') -Epa(H20) and it portrays an excellent linear relationship spanning a range of 45 kcal mol-' (equation 7).6Epa(3-21G)= (-0.9 amp; 1.3) + (0.941 amp; 0.050)6Epa,exp(7) {In kcal mol-'; n = 14 excluding (8) (22) and (23)j; r2 = 0.993;sd = 0.9 kcal mol-'}. This equation does not apply to (8) (22) or (23),which reflects the inadequacy of a small basis set for the treatment of small cycles and hydrogen-bonded systems. The E,,(MNDO)s given in Table 1 are seen to be too small (by 7-15 kcal mol-I). A plot of GEpa,expus. GEpa(MNDO) shows that alcohols and aliphatic ethers define two separate parallel lines with very high slopes (ca. 1.77).This is a consequence of the range of variation of the GEpa(MNDO)s being greatly reduced by the overestimated core-core repulsions. This effect together with the poor description of hydrogen-bonding provided by this method' account for the GEpa(MNDO) of (8) being 19.5 kcal mol-' off the line for aliphatic ethers. The results reported in Table 1 indicate that the Epa(AM1) are too low by 3-12 kcal mot'.The plot of 8Epa,expus. GEpa(AM1) (Figure 3) however shows a great improvement with respect to the MNDO results. Thus a single correlation equation applies to both alcohols and ethers equation (S). (1)and (23) are off the line but (8)and (22) GEpa(AMl)= (0.66 f0.23) + (0.960 amp; 0.086)6Epa,exp(8) In kcal mol-'; n = 15 r2 = 0.974; sd = 1.6 kcal mol-'1 are quite well behaved. From equations (7) and (8) a linear relationship between 6Epa(3-21G)and GEpa(AM1)is derived. It allows the estimation J.CHEM. SOC. PERKIN TRANS. 2 1990 40.035.0t 30.0-25.0-20.0-15.0-10.0-5.0-Ool 576.0 1g.O 26.0 25.0 36.0 35.0 46.0 45.0 80 Figure 3. Experimental Epa,expus. calculated GEp,(AM 1) differential proton affinities. Compounds numbered as in Table 1. 0,ROH; W RORrsquo;. 55.0 -50.0 -45.0-t 40.0 -35.0 30.0-25.0-22 20.0 lrsquo; I 0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 Figure 2. Calculated differential energies of the highest-occupied MOs GEHoMo Com-us. experimental differential proton affinities GEpa,exp. pounds numbered as in Table 1. 0 RORrsquo;.ROH; . of 6Epa(3-21G) for (21) at 41.2 kcal mol-rsquo;. This value has been used to obtain the corresponding Epa(3-21G) given in Table 1.Empirical Correlations.-(a) Proton charges. Protonation of an n-base leads to a substantial build-up of positive charge on the hydrogen@) attached to the donor atom. Empirical correlations have been established between the electron populationsrdquo; on these hydrogens qH+ and the Epavalues of the bases.36 We find a reasonable linear correlation between and qH+(3-21G) n = 14 excluding (8) (22) and (23) r2 = 0.968 sd = 2.0 kcal mol-rsquo;. It is remarkable that qH+(3- 21G) is essentially the same within the couples (6)/(7) and (13)/(14).The correlations between the 6Epa,expvalues and the qH+ values determined by the NDDO methods are too crude to be useful.37 (b) Energies of the highest-occupied molecular orbitals (HOMO).The Epavalues of n-bases such as alcohols and ethers can be related to the ionization potential of the lone pairs or the donor atom through equation (9)38where HA(BH+) is the homolytic bond dissociation energy of the 0-H bond.If this term remains constant within these families the Epavalues must then match exactly the adiabatic ionization potentials of the neutral bases. In the absence of all the pertinent experimental data the energies of the HOMOS EHOMO can be used. Figure 2 is a plot Of 6EHOM0 CsEHOMO = EHOMO(B) -EHOMO(H20)16Epa,exp.It shows that a crude linear relationship does indeed exist but its slope (1.6) is much higher than unity. Closer inspection of this plot reveals that two limited correlations pertaining respectively to alcohols excluding (S) and alkyl ethers are generated; their slopes (1.00 f0.34) and (0.82 f 0.43) being much closer to the expected value.These results are consistent with the known sensitivity of these correlations to changes in the hybridization and geometry at the basic ~entre.~~.~rsquo;No useful relationships can be obtained by using the AM1 or MNDO values. 01,Orbital Energies.-It has long been established 40 that within families of bases good linear relationships exist between Epaand the 1s core binding energies of their basic centres. Thus McMahon and Kebarle have recently reported 41 a remarkably good linear relationship between Epmand the experimental (ESCA) 01,binding energies for a variety of oxygen bases with Epavalues spanning a range of 100 kcal mol-rsquo; (from O2 to Me2CO).Since experimental values are lacking for most of the compounds studied herein we have compared the Epawith the 01,orbital energies calculated at the 3-21G level. In a plot of Epa,expus. 6E0,. = Eolt(B) -Eo,s(H20) alcohols excluding (8) and alkyl ethers define separate lines with slopes much higher than that found experimentally. Thus Eel values at the 3-21G level are not sufficiently reliable for these purposes. Correlation Analysis Approach.-This section is restricted to the analysis of Epafor compounds (147) and (9H21). The main structural changes to be expected on going from water to alcohols and then to ethers are those associated with (i) p~larizability,~~(ii) o-hyperconjugation and (iii) re-hybridization of the oxygen atom.Polarizability effects are measured by the oapararneter~.~~ Figure 4 is a plot of 6Epa,expus. Co = o,(R) + o,(Rrsquo;) for compounds having the general formula RORrsquo;. From this plot two highly precise (sd 0.4 kcal mol-rsquo;) linear relationships are obtained pertaining respectively to alcohols A o,(H) = 01 and ethers (B).The corresponding correlation equations 43 are given by equations (10) and (11). The additivity of alkyl 6Epa,exp= (3.0 amp; 2.2) + (36.7 amp; 1.4)Zoa (10) = (6.4 +_ 1.7) + (26.8 +_ 1.5)C0 (11) polarizability effects in the ether series holds all the way from (CH3) to (t-C4Hg)ZO. The slope in equation (10) is smaller than that in equation (11) indicating that Epa(RORrsquo;) Epa(ROH) + E,,(Rrsquo;OH) -Epa(H20).This difference reaches 16.6 kcal mol-rsquo; in the case of (9).It follows that on going from the alcohol to the ether series 50.C 40.O 30.C 20.0 10.0 I 1 1 I 0.50 100 1.50 Figure 4. Experimental differential proton affinities i3Epa,crpus. polariz-ability parameters Zsm.Compounds numbered as in Table 1.0 ROH; m ROR'. Table 4. Differential methyl-cation and proton affinities i3REmcaand amp;REp,for selected aliphatic alcohols in the gas-phase at 298 K. Alcohol 8REpall.b 8REmcal(*b*c (2) (3) (4) 0 5.3 7.1 0 3.8 5.1 (5) 7.7 6.3 (6) 9.5 6.7 (7) 10.9 7.3 a In kcal mol-'. Defined in the text. 'The enthalpies of formation of the neutral species are taken from ref. 44. and along the latter increasing polarizability is counterbalanced by some effects@) varying in a proportional way.Saturation of the o-hyperconjugation fits this requirement (this follows from the discussion in the section Molecular Geometries). Further-more an analysis at the 3-21G level of the positive charge transferred to the R groups in the protonated ROCH series shows it to be smaller than that transferred to the same groups in the protonated alcohol series. Also the charge transferred to the CH group decreases in the order CH C2H i-C3H t-C4H,. The methyl cation affinity of an alcohol Em,,(ROH) is defined as EmCa(ROH) = -AH for reaction (12) in the gas- ROH + CH3+__+ RO(H)CH,+ (12) ROCH + H++ RO(H)CH,+ -Epa(ROCH3) (13) J. CHEM. SOC. PERKIN TRANS. 2 1990 phase.Taking into account reaction (13) it follows that Em,,(ROH) = Ep,(ROCH3) + AHf(R0H) -AHf(ROCH3) + AHf(H+)-AHf(CH3+) Differential structural effects on a property X GR(X) are defined as GR(X) = X(R) -X(CH3) and from which we obtain equation (14). Using the data given in Table 1 the differential methyl-cation affinities collected in Table 4 are obtained. These data also allow the determination (or a very good estimation) of other alkyl affinities. We notice that This indicates that the difference between Em and Epais only determined by the stability of the ionic forms.45 From the results given in Table 3 we obtain equation (15). GREmca(RoH) = (0.0 amp; 0.7) + (0.70 fO.lO)GREpa(ROH) (15) (in kcal mol-' n = 6 r2 = 0.971 sd = 0.4 kcal mol-') It can be shown46 that because of equations (10) and (1 l) all differential alkyl-cation affinities GRE,,,(ROH) are the same irrespective of the size of the alkyl cation (in the absence of appreciable steric effects). This is confirmed and the average ratio SREa,,(ROH)/SREP,(ROH) is found to be equal to 0.73 k0.09.47 The differential But cation affinity for Bu'OH is 3.1 kcal mol-' while the calculated value is 7.5 kcal mol-'.We take this difference as indicating a back-strain effect. Figure 4 shows no abnormal behaviour for Buf20 therefore a strain effect of ca. 4.4/0.73 = 6.0 kcal mol-' is also to be found in the neutral form. Indeed AH = 7.8 kcal mol-' for reaction (16) in the gas phase. t-C,H,OH + t-C4HgOCH3 + (t-C,H,),O + CH30H (16) Finally we notice that differential lithium-cation affinities El are available for a variety of alcohols.48 Their 6Elaand Epa are proportional but the slope of the line is 0.42.In the light of previous analyses,'5b this is related to the 0-Li bond having a smaller covalent character.We have performed calculations at the 4-31G level on the species RO(H)Li+ and CH,O(Li)R+. They show that the stretching of the C-0 bond and the amount of positive charge transferred to the alkyl groups are smaller for these ions than for the corresponding protonated forms.,' Conclusions From a computational point of view to obtain 'absolute' Epa values it is necessary to reach at least the 4-31G*//4-31Glevel. In this case the calculated Epavalues are to within 1 or 2 kcal mol-' of the experimental values (upon the appropriate corrections). ab initio 3-2 1G and semiempirical AM 1 calcul- ations are comparable in providing correct 'differential' Epaand geometries of the neutral forms (in the absence of chelation or severe I-strain).The MNDO method gives less satisfactory results. An important conclusion of this study is that o-hypercon- jugative effects play a significant role in both protonated alcohols and ethers. Regarding structure-reactivity relationships those existing J. CHEM. SOC. PERKIN TRANS. 2 1990 between Epa,and 01,orbital energy or HOMO range from non- existent to poor (3-21G calculations) contrary to literature statements. Within families Epais a linear function of the polarizability of the substituent on the oxygen atom (as measured by the oaparameter).Moreover in the acyclic ether series polarizability effects are additive. Finally this work leads to new insights regarding alkyl-cation affinities of alcohols. References 1 (a) H. E. Schroeder and C. J. Pedersen Pure Appl. Chem. 1988,60 445 and references therein; (b) C. J. Pedersen J. Am. Chem. SOC. 1967,89,7017; (c) C. J. Pedersen J. Am. Chem. SOC.,1967,89,2495; (d) J. R. Damewood W. P. Anderson and J. J. Urban J. Comput. Chem. 1988,9,111 and references therein; (e)J. M. Lehn Pure Appl. Chem. 1980,52 2303 ibid. 1978 50 871; (f)D. J. Cram and J. M. Cram Science 1974 183 801; (g) G. Dotseni Y. Sogal and D. J. Cram J.Am. Chem. SOC.,1975,97,1259;(h)R.C. Hegelson K. Koga J. M. Tinko and D. J. Cram ibid. 1973,95 3021,3023. 2 This is particularly important if uncertainties of up to 1 or 2 kcal mol-rsquo; in the relative proton affinities of two compounds are to be avoided. See e.g. S. G. Lias J. F. Liebman and R.D. Levin J.Phys. Chem. Re$ Data 1984,13,695. 3 (a) J. F. Wolf R.H. Staley I. Koppel M. Taagepera R. T. Molver Jr. J. L. Beauchamp and R.W. Taft J. Am. Chem. SOC.,1977 99 5417. A temperature correction has been applied as given in J. Bromilow J.-L. Abboud C. B. Lebrilla R. W. Taft G. Scorrano and V. Lucchini J. Am. Chem. SOC.,1981 103 5448; (b) For a general description of the experimental technique see e.g.T. A. Lehman and M. Bursey lsquo;Ion Cyclotron Resonance Spectrometry,rsquo; Wiley New York 1976; R. T.McIver Jr. Rev. Sci. Instrum. 1978 49 111; (c) R. W. Taft M. Taagepera J.-L. M. Abboud J. F. Wolf D. J. De Fress W. J. Hehre J. E. Bartmess and R.T. McIver Jr. J.Am. Chem. SOC.,1978,100,7765. 4 J. S. Binkley J. A. Pople and W. J. Hehre J. Am. Chem. SOC.,1980 102,939. 5 D. Ditchfield W. J. Hehre and J. A. Pople J. Chem. Phys. 1971 56,5255. 6 MONSTERGAUSS 80; M. R. Patersson and R. A. Poirier Department of Chemistry University of Toronto Ontario Canada. 7 J. A. Pople D. P. Santry and G. A. Segal J. Chem. Phys. 1965,43 S 129. 8 M. J. S. Dewar and W. Thiel J. Am. Chem. SOC.,1977,99,4899. 9 M. J. S. Dewar E. G. Zoebish E. F. Healy and J. J. B. Stewart J.Am. Chem. SOC.,1985,107,3902. 10 W. Thiel in lsquo;Quantum Chemistry Program Exchange Catalog,rsquo; Indiana University Bloomington Indiana 1978 QCPE program 353.11 M. J. S. Dewarrsquo;s Research Group and J. J. P. Stewart QCPE Bull. 1986,6,24; QCPE program 506. 12 (a) S. Olivella F. Urpi and J. Vilarrasa J. Comput. Chem. 1984 5 230; (b)G. P. and J. D. Scribner ibid. 1983,4,594;(c) M. J. S. Dewar and K. M. Dieter J. Am. Chem. SOC.,1986,108,8075. 13 (a)M. J. S. Dewar J.Phys. Chem. 1985,89,2145; (b)J. A. Del Bene J. Am. Chem. SOC.,1978,100,1673;(c)J. A. Del Bene and A. Vaccaro ibid. 1976,98 7526. 14 (a) M. C. L. Gerry R. M. Lees and G. Winnewisser J. Mol. Spectrosc. 1976 61 231; (6) M. Hayashi and K. Kuwada J. Mol. Struct. 1975,28 147. 15 (a)C. Glidewell and C. Thomson J. Comput. Chem. 1982,3,495;(b) S.F. Smith J. Chandrasekhar and W. L. Jorgensen J. Phys. Chem. 1982,82,3308. 16 P. J. Krueger and H. D. Mettee Can.J. Chem. 1964,42,340. 17 J. Murto M. Rasanen A. Aspiala and T. Lotta J. Mol. Struct. (Theochem),1984,10,99. 18 (a)H. J. Geise W. J. Adams and L. S. Bartell Tetrahedron 1969,25 3045; (b)H. M. Almenningen R.Seip and T. Willadsen Acta Chem. Scand. 1969 23 2748; (c) Gas-phase data suggest almost free pseudorotation but in the crystal (at -170 and -125 OC the molecule has a single structure with C symmetry P. Luger and J. Buschman Angew. Chem. Znt. Ed. Engl. 1983 5 410); (d) H. E. 57 1 Breedm G. Gundersen and R. Seip Acta Chem. Scand. Ser. A 1979,33,225. 19 D. Cremer and J. A. Pople J.Am. Chem. SOC.,1975,97,1358. 20 0.0.MO J.L. G. de Paz and M. Yaiiez J. Phys. Chem. 1987,91 6484. 21 P. Luger and J. Buschmann J.Am. Chem. SOC.,1984,106.71 19. 22 (a)W. I. Ferguson and N. C. Handy Chem. Phys. Lett. 1980,71;(b) R. Ahlrichs F. Driessler H. Lischka V. Stammler and W. Kutzelnigg J. Chem. Phys. 1975,62 1225. 23 (a) H. Huber and Vogt J. Chem. Phys. 1982,62 399; (b)gas-phase microwave studies of hydrogen-bond complexes between HF and oxygen bases (l),(22) and (23) show a pyramidal arrangement of bonds at the oxygen. (See e.g. C. Legon Chem. SOC.Rev. 1987,16 467). 24 e.g.,Y. K. Sirkin and M. E. Dyatkina lsquo;Structure of Molecules and the Chemical Bond,rsquo; Butterworths London 1950. ch. 6. 25 M. Meot-Ner (Mautner) M. M. Ross and J. E. Campana J. Am. Chem. SOC.,1985,107,4839.26 K. Hiraoka and P. Kebarle J. Am. Chem. SOC.,1977,99,360. 27 Differences in polarizability may also be important (J. Gasteiger and M. J. Hutchings J. Am. Chem. SOC.,1984,106,6489). 28 e.g. M. Masamura J. Mol. Struct. (Theochem) 1988 164 299 and references therein. 29 For comparison the average errors in equilibrium bond lengths and bond angles determined by ab initio calculations at the 4-31G level are 0.02 A and 5O S. Iwata lsquo;Reliability of ab initio Calculationsrsquo; in lsquo;Quantum Chemistry Literature for 1978-1980,rsquo; eds. K. Ohno and K. Morokuma Elsevier Amsterdam 1982 p. 427. 30 DZP + electronic correlation. 31 S. Romanowski T. M. Pietrzak L. Wojtczak and S. Tariwska-Osinska J. Mol. Struct. (Theochem) 1986 137 217. This reference also provides a wealth of information on the structures of aliphatic alcohols.32 J. E. Del Bene H. D. Mettee M. J. Frisch B. T. Luke and J. A. Pople J. Phys. Chem. 1983,87,3279. 33 0.MO J. L. G. de Paz and M. Yaiiez Theor. Chim. Acta 1988,73 307. 34 I. A. Koppel U. H. Molder and V. A. Palm Org. React. (Tartu) 1985,22,3. 35 R. S. Mulliken J. Chem. Phys. 1955,23,1833,1841,2338 and 2343. 36 W. J. Hehre M. Taagepera R. W. Taft and R. D. Topsom J. Am. Chem. SOC.,1981,103,1344. 37 qH+(3-21G)and q,+(NDDO) values cannot be directly compared see ref. 12(b). 38 D. H. Aue and M. T. Bowers in lsquo;Gas-phase Ion Chemistry,rsquo; ed. M. T. Bowers Academic Press New York 1978 ch. 2. 39 (a) J. Catalan 0.MO J. L. G. de Paz P. PCrez M. Yaiiez and J. Elguero J.Org.Chem. 1984,49,4379;(b)D. Christen J. H. Griffiths and J. Sheridan 2. Naturforsch. Teil A 1982,37 1378. 40 (a)R.L. Martin-and D. A. Shirley,J.Am. Chem. SOC.,1974, 5299; (b)D. W. Davis and J. W. Rabalais J.Am. Chem. SOC.,1974, 5305. 41 (a) T. B. McMahon and P. Kebarle J. Am. Chem. SOC.,1985 107 2612; (b)T. X. Carrol S. R. Smith and T. D. Thomas J.Am. Chem. SOC.,1975 97,659. 42 R. W. Taft and R. D. Topsom Prog. Phys. Org. Chem. 1987 16 1 and references therein. 43 The value for (7) has not been included in the correlation. 44 J. B. Pedley R.D. Naylor and S. P. Kirby lsquo;Thermochemical Data of Organic Compounds,rsquo; 2nd edn. Chapman and Hall London 1986. 45 J. I. Brauman and C. Chan J.Am. Chem. SOC.,1988,110,5611. 46 J.-L. M. Abboud R. W. Taft and J. Elguero manuscript in prepara- tion. 47 T. B. Mc Mahon T. Heinis G. Nicol J. K. Hovey and P. Kebarle J. Am. Chem. SOC.,1988,110,7591. 48 R. W. Taft F. Anvia J.-F. Gal S. Walsh M. Capon M. C. Holmes K. Hosn G. Oloumi R. Vasanwala and S. Yazdani Pure Appl. Chem. in the press. 49 J.-L. M. Abboud J. Elguero M. El Mouhtadi M. Essefar D. Liotard R.W. Taft M. Yafiez manuscript in preparation. Paper 9/034 13G Received 10th August 1989 Accepted 31st October 1989