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Why are carboxylic acids stronger acids than alcohols? The electrostatic theory of Siggel–Thomas revisited
Journal of Molecular Structure (Theochem) 505 (2000) 161±167
www.elsevier.nl/locate/theochem
Why are carboxylic acids stronger acids than alcohols? The electrostatic theory of Siggel±Thomas revisited P. Burk a,b,*, P. von Rague Schleyer a a
Institute of Organic Chemistry, University of Erlangen-NuÈrnberg, Henkestr. 42, D-91054 Erlangen, Germany b Institute of Chemical Physics, Tartu University, Jakobi 2, 51014 Tartu, Estonia Received 30 August 1999; accepted 16 September 1999
Abstract The electrostatic explanation of Siggel and Thomas for the acidity differences between series of acids was investigated critically. Acidities and electrostatic potentials at the protons of XOH, XNH2, and XCH3 derivatives X H; CH3, HCO, NO2, and F) were calculated at the Becke3LYP/6-3111G pp level. Final state (anion) relaxation energies were obtained as proposed by Siggel and Thomas. Examination of initial and ®nal state contributions revealed de®ciencies in the Siggel±Thomas method as the ®nal-state (relaxation) energies still retain contributions from the electronic structure of the initial state. Hence, this relaxation energy is not reliable as a measure of resonance stabilisation in anion. The application of Siggel±Thomas approach in two opposite directionsÐdissociation of neutral acid and protonation of an anionÐleads to contradictory conclusions about whether the acidity difference between methanol and formic acid is determined by the neutral acid or anion. Hence, this scheme cannot be used to determine the initial state (neutral acid) and ®nal state (anion) contributions to acidity as proposed by Siggel and Thomas. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Acidity; Resonance; Electrostatics
1. Introduction Acidity is a basic molecular property. The strength of a BroÈnsted acid in the gas phase is given quantitatively by DE, DH or DG for proton removal (Eq. (1)). Stronger acids have lower values of DE, DH or DG. Acidity is determined by the stability of both the neutral acid AH and its conjugate anion, A 2, Eq. (2) AH O A2 1 H21
1
DE E A2 1 E H1 2 E AH
2
extents. Although possible electrostatic contributions were recognized by Wheland [1], the greater acidity of carboxylic acids compared to aliphatic alcohols traditionally has been attributed to the enhanced stability of carboxylate anions (usually assumed to be due to p electron delocalisation, i.e. resonance, 1 $ 2 [2].
Resonance, hyperconjugation, ®eld/inductive effects, etc. can stabilize AH and A 2 to different * Corresponding author.
This resonance-based explanation of higher acidity
0166-1280/00/$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0166-128 0(99)00357-7
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P. Burk, P. von Rague Schleyer / Journal of Molecular Structure (Theochem) 505 (2000) 161±167
of carboxylic acids over alcohols was ®rst challenged by Siggel and Thomas 14 years ago [3]. They concluded that resonance delocalisation ªplays only a minor roleº and attributed that greater acidity of carboxylic acids compared to aliphatic alcohols primarily due to electrostatic interactions, which are present already in the neutral acid, due to the polarization of carbonyl group. An analysis based on simple two step thermodynamic cycle for proton removal from acid was proposed. In the ®rst formal step a proton is removed from the acid without any change in the electron distribution or geometry relaxation. The energy of such a hypothetical proton removal process (2V) is given by the negative of the electrostatic potential at the site of the acidic proton in the neutral acid. In the second formal step, the hypothetical anion relaxes into its most stable form. R is the corresponding relaxation energy, which bene®ts from electron delocalization in the anion, and also all other electronic and geometric reorganizations. Hence, the energy of reaction (1), DE is divided into two components, V and R DE 2V 2 R
3
Theoretical evaluations of R and V were based on ab initio computations of DE and V, 1 R was obtained by difference from Eq. (3). While absolute values of V and R are not amenable to experimental evaluation, the difference in deprotonation energy, DDE, between two acids, for instance, formic acid and methanol, can be expressed by Eq. (4): DDE 2DV 2 DR
4
Hence, Siggel and Thomas evaluated DV and DR from experimental measurements of gas-phase acidities and O±H oxygen 1s electron ionisation energies in neutral acids (Eqs. (6) and (7)). DR
2DI 2 DDE 2
6
DV
DI 2 DDE 2
7
by assuming that V and R in Eqs. (3) and (4) are essentially the same quantities (as both DE and I correspond to the removal of a unit charge, positive or negative, from close regions of space). As an example, the values of DV and DR for the methanol and formic acid, derived from experiment and from ab initio calculations, are given in Table 1. According to the Siggel±Thomas interpretation, V measures the initial state (primarily inductive) contribution to the acidity, while R is determined by the ®nal state contribution (mainly charge delocalization, accompanying proton removal). Comparing the values of DR and DV of alcohols and carboxylic acids led to the revolutionary conclusion that the greater acidity of carboxylic acids relative to aliphatic alcohols is primarily determined by differences in the initial states, e.g. the neutral acids. The values of DR were small (see Table 1) both by experimental (DR and DV calculated from experimental acidities and O± H oxygen core-ionisation energies) and theoretical data (DR and DV calculated from ab initio acidities
A similar expression (5) was proposed earlier [4] for O±H oxygen core-ionisation energies (i.e. the energy needed for removing an oxygen 1s electron) differences (DI) in neutral acids
Table 1 Acidity (DE), O±H oxygen 1s electron ionisation energy (I), electrostatic potential (V, at acidic proton), and relaxation energy (R) differences for methanol and formic acid (all values in kcal/mol). Experimental DV and DR were calculated from Eqs. (6) and (7). R for ab initio results was obtained from Eq. (3) using literature data
DI DV 2 DR
Experimental
5
1
The electrostatic potential V is calculated as Z f f X X ZA m n Pmn 2 dr 0 V ur 2 r 0 u mn A ur 2 RA u Pmn refers to a particular density matrix element of the wavefunction for the molecule as obtained from the SCF-MO calculation; f m and f n are the atomic basis wavefunctions. The ®rst term is summed over all nuclei (except the nucleus at which site the potential is evaluated), and the second term is summed over all electrons in molecule.
DE [27]
I [28]
V
CH3OH 372.9 297.3 ± HCOOH 334.0 261.1 ± D 38.9 236.2 237.6 Ab initio (6-3111G(2d,p)/6-31111G(2d,p) [29] DE I V CH3OH 399.2 ± 2634.4 HCOOH 357.2 ± 2592.4 D 42.0 ± 242.0
R ± ± 21.35 R 235.2 235.2 0.0
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and electrostatic potentials on acidic proton using Eq. (4)). This interpretation, not in keeping with the traditional view that the differences in acidities between carboxylic acids and alcohols are due to the extra resonance stabilization of the carboxylate anions, has received both criticism [5±9] and support [10± 17]. Using Bader's topological charge density analysis [18] Thomas et al. [10] and Siggel et al. [11] supported their analysis further by examining the charge distributions in formic acid, ethanol and vinyl alcohol as well as the charge ¯ow when the hydroxylic proton is removed from these molecules. They concluded that the carbonyl bond is strongly polarized already in the neutral formic acid. This charge distribution in the anion changed little. Hence, the leading resonance structure for formiate anion should be 3. They concluded that the higher acidity of carboxylic acids relative to aliphatic alcohols is due mainly (ca. 85%) to carbonyl inductive effects. Based on their method of analysis Siggel and Thomas also concluded, that the anomalously high acidity of formic acid compared to other aliphatic carboxylic acids [13] was due to the result of higher electrostatic potential at the acidic proton in formic acid. Dewar and Krull [8] argued that enhanced acidities of vinylogues of formic acid and vinyl alcohol relative to aliphatic alcohols are due to resonance stabilization of the conjugate anions. This was refuted subsequently by Thomas [15]: the acidity of vinylogues of formic acid and vinyl alcohol relative to aliphatic alcohols also was found to be determined by initial state contributions (mainly inductive effects). The origin of the carboxylic acid acidity was attributed recently by Wiberg et al. [16] to the stabilization of the anion by the carbonyl group accepting some p electron density (ca. 0.1e) and by stabilizing electrostatic interaction between the positively charged carbonyl carbon and the adjacent negatively charged atom. Part of the negative charge arising from deprotonation of the acid appears at the hydrogens in the nodal plane of the p system. Based on correlation analysis of the gas phase acidities of O±H acids, Taft et al. [6] agreed with the conclusion of Siggel and Thomas that the acidity of formic acid relative to acetic acid is due primarily to
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inductive effects, but also indicated that the acidities of carboxylic acids relative to aliphatic alcohols are determined both by resonance and by inductive effects to comparable extents. The 36 kcal/mol acidity difference between methanol and formic acid was ascribed to resonance (13 kcal/mol) and to inductive effects (23 kcal/mol). Similar conclusions were reached more recently by Hiberty and Byrman [7] as well as by de Mota and Nascimento [19]. Their valence bond calculations on formic acid, vinyl alcohol and ethanol indicated that about half of the acidity difference between ethanol and formic acid was determined by the extra resonance interaction in anion. The use of Bader electronic populations to support the Siggel±Thomas model of acidifying effects [10,11] was criticized by Perrin [9] and Jug et al. [20]. They argued that the Bader populations on more electronegative atoms are exaggerated since the location of the zero-¯ux surface depends on the atomic size. However, other authors have discounted these criticisms [21,22]. Exner [5] used simple thermodynamical considerations to support that carboxylate anions are stabilized by resonance. However, Siggel and Thomas [12] refuted Exner's analysis by arguing that his isodesmic reactions would not separate the contributions of inductive and resonance effects. Speers et al.'s [14] recent investigation of the relative acidities of CH3SCH3, CH3SOCH3, and CH3SO2CH3, also used Bader's topological charge density analysis [18] to partition the total energies into the atomic energies, and concluded that the contribution from relaxation in the anion is unimportant energetically. A similar conclusion was reached by Laidig and Streitwieser [17], who investigated the origins of relative acidities in ®rst and second period hydrides. On the contrary, Wiberg and Castejon's study of the acidities of dimethyl sul®de, dimethyl ether [23], and substituted methanes [24] indicated that intramolecular charge relaxation in anions resulted in considerable energetic effects. Since the origin of the higher acidity of carboxylic acids relative to alcohols is not settled, we have carried out ab initio calculations on various O±H, N±H and C±H acids, to test the electrostatic theory of Siggel and Thomas on a wider class of compounds.
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Table 2 298 Calculated (B3LYP/6-3111G pp) electrostatic potential V on acidic protons, calculated (DE 1, DH0298 ; and DG298 0 and experimental [27] DH0 and DG298 acidities (all in kcal/mol) 0
H2O CH3OH HCOOH HNO3 FOH NH3 CH3NH2 H2NCHO H2NNO2 FNH2 F2NH CH4 CH3CH3 CH3CHO CH3NO2 CH3F CH2F2 CHF3 a
V
DE a (calc.)
DH0298 (calc.)
DG298 (calc.) 0
DH0298 (exp.)
DG298 (exp.) 0
2623.8 2630.0 2589.9 2573.0 2585.8 2665.1 2670.9 2624.5 2607.7 2636.7 2608.5 2704.9 2710.2 2678.5 2659.2 2688.5 2671.7 2650.8
396.0 388.4 348.3 326.9 361.5 412.6 411.8 367.1 346.2 388.4 363.8 425.3 428.6 371.9 360.9 416.4 402.8 382.1
389.2 379.4 341.0 320.4 355.1 404.2 402.2 360.0 339.3 380.2 355.9 416.8 419.4 364.6 353.3 407.7 394.8 373.7
382.2 372.5 333.5 313.7 348.2 396.9 394.3 352.6 331.5 372.1 347.9 408.3 410.2 357.2 347.0 398.6 386.0 365.2
390.8 380.4 345.1 324.6
384.1 374.0 338.2 317.9
403.7 403.2 359.9
396.0 395.8 352.8
359.0 416.9 420.9 365.9 355.4
352.1 408.7 412.3 359.0 349.7
386.7 376.9
379.1 369.3
DE is calculated from electronic energies of acid and conjugated anion without any corrections.
2. Methods Table 3 Calculated (B3LYP/6-3111G pp) relative acidities (DDE), electrostatic potentials (DV) at acidic proton in neutral acid, and relaxation energies (DR) of O±H, N±H and C±H acids relative to H2O, NH3, and CH4, respectively (in kcal/mol)
H2O CH3OH HCOOH HNO3 FOH NH3 CH3NH2 H2NCHO H2NNO2 FNH2 F2NH CH4 CH3CH3 CH3CHO CH3NO2 CH3F CH2F2 CHF3
DDE
DV
DR
0.0 27.6 247.7 269.1 234.5 0.0 20.8 245.5 266.4 224.2 248.8 0.0 3.1 253.4 264.4 28.9 222.5 243.2
0.0 26.2 33.9 50.8 38.0 0.0 25.8 40.6 57.4 28.4 56.6 0.0 25.3 26.4 45.7 16.4 33.2 54.1
0.0 13.8 13.8 18.3 23.5 0.0 6.6 4.9 9.0 24.2 27.8 0.0 2.2 27.0 18.7 27.5 210.7 210.9
Density functional calculations were performed at Becke3LYP/6-3111G pp using the gaussian 94 program [25]. Geometries of the neutral acids and of the corresponding anions were fully optimized and harmonic frequencies calculated. Acidities E were calculated as the differences in total energies of the parent acid DH and the conjugated anion, A 2. DH 298 and DG 298 were calculated for comparison with experiment using thermochemical corrections from frequency calculations [26]. Electrostatic potentials at the sites of all nuclei were computed as implemented in the gaussian 94 program. These data are presented in Table 2 along with the experimentally determined values. In Table 3 DE, DV, and DR (calculated from data in Table 2 using Eq. (4)) are given for the O±H, N±H and C±H acids relative to H2O, NH3, and CH4, respectively. 3. Results and discussion The results in Table 2 show that the B3LYP/6-311G pp level (with ZPE and thermal corrections)
P. Burk, P. von Rague Schleyer / Journal of Molecular Structure (Theochem) 505 (2000) 161±167
reproduces the experimental acidities [27] with the average unsigned error of 2.5 kcal/mol. The relative values of DV and DR given in Table 3 for methanol and formic acid agree with Siggel and Thomas that DV is the predominant term in Eq. (4), i.e. it can be said (based on their methodology) that the acidity difference of methanol and formic acid are usually determined by the electron distribution in the neutral acid. However, DR is generally not smallÐin three cases is DR larger than DV and for seven more cases in Table 3 over 20% of DV. The negative relaxation energies of the ¯uorosubstituted derivatives relative to H2O, NH3, and CH4, evidently result from the high electronegativity of ¯uorine. The ¯uorines have large negative charges in the neutral acid so that further negative charge increase at ¯uorine in anion is not favorable energetically. However, R, calculated from Eq. (3), does not correspond to the ªresonance energyº or to the ªdelocalization energyº as usually understood by organic chemists. The crucial difference between relaxation energy of Siggel±Thomas and conventional resonance energy lies in the reference state used to deduce the energy of the real, fully relaxed anion. The Siggel±Thomas relaxation energy (R) is calculated as the energy difference between a real anion and a hypothetical anion (formed as a result of the ®rst step of deprotonation) with the electron distribution of the neutral. The resonance energy is traditionally understood as the difference between the energy of a real anion and a hypothetical anion with a Lewis structure where all electron pairs are completely localized either in bonds or on atoms (core electrons, lone pairs). Clearly, these two reference states (the hypothetical anion with the geometry and electronic structure of the neutral species, and the real anion with completely localized Lewis structure) are not equivalent. The 44.1 and 41.7 kcal/mol rotational barriers around the C±C or C±N bonds, respectively, in the CH2CHO 2 and in the CH2 NO2 2 anions, provide rough estimates of the resonance (®nal state) stabilisation in these anions, but are quite different from the relaxation energies obtained from Eq. (4) (27.0 and 18.7 kcal/mol, respectively). Furthermore, the relaxation energy R of CH3OH is much larger than that of H2O and only fortuitously similar to HCOOH (Table 3).
165
These differences support our criticism that the relaxation energy R, calculated from Eq. (3), does not correspond to the ªresonance energyº or to the ªdelocalization energyº as usually understood by organic chemists. The relaxation energy (R) is the energy difference between the real anion and a hypothetical anion with the electron distribution of the neutral acid. Hence, the relaxation energy R still depends on the initial state (via electron distribution in neutral acid) and does not characterize the stabilization of anion by charge delocalisation unambiguously. The energy-partitioning scheme presented by Siggel and Thomas [3] (Eqs. (3)±(7)) can be applied also in reverse direction (on the reaction of the protonation of anion (8)) A2 1 H1 O AH
8
The energy of such reaction, 2DE, is the negative of the acidity (DE) of acid AH, and can be analyzed based on a three step thermodynamic cycle of the proton addition to the anion. In the ®rst formal step the geometry of anion is rearranged into that of neutral acid. The energy of this step, Rrg ; can be easily calculated as the difference of energies of anion at the neutral acids geometry and at the optimized geometry. We note that Rrg ; corresponds to the energy of geometry relaxation in the second step of the thermodynamic cycle proposed by Siggel and Thomas. In the second formal step proton is added to the anion (at the geometry of neutral acid) without any change in the electron distribution. The energy of such hypothetical proton addition (V r) is given by the electrostatic potential in the anion at the position, where the proton should be placed. In the ®nal step, the hypothetical neutral acid with the electron distribution of anion relaxes into its most stable electronic state. Rrel is the corresponding relaxation energy. Hence, the energy of reaction (8) is divided into three components Rrg ; V r ; and Rrel 2DE Rrg 1 V r 1 Rrel
9
As 2DE; Rrg ; and V r can be easily calculated, Rrel can be obtained as Rrel 2DE 2 Rrg 2 V r
10
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166
Table 4 Results of the Siggel±Thomas analysis on the reactions of protonation of formiate and methoxy anions (Eqs. (9) and (10)): acidity (DE), energy of the rearrangement of anions geometry into that of neutral acid Rrg ; electrostatic potential in the anion at the position, where the proton should be placed (V r), the energy of electronic relaxation in neutral acid after proton addition Rrel for methanol and formic acid, and corresponding relative values (DDE, DRrg ; DV r, and DRrel for formic acid relative to methanol (all values in kcal/ mol, calculated at B3LYP/6-3111G pp level of theory)
CH3OH HCOOH D
DE
Vr
Rrel
Rrg
388.4 348.3 40.1
2215.5 2188.1 227.4
2177.7 2168.0 29.7
4.8 7.8 23.0
In Table 4 are presented the results of such energy partitioning for methanol and formic acid as well as the relative values DDE; DRrg ; DV r ; and DRrel for formic acid relative to methanol. Here again the acidity difference is predominantly due to differences in electrostatic potential in initial state, but in this case the initial state is anion. The energies of ®nal state (neutral acid) relaxation contribute only one quarter of the acidity difference between methanol and formic acid. Should one, in analogy with original Siggel± Thomas approach, draw the conclusion that DE (and hence the acidity) is determined mainly by electron distribution in anion? As shown, the application of Siggel±Thomas approach in two opposite directionsÐdissociation of neutral acid and protonation of an anionÐof the acid±base equilibria reaction leads to contradictory conclusions about whether the acidity difference between methanol and formic acid is determined by the neutral acid or anion. Hence, this scheme (Eqs. (3)±(7)) cannot be used to determine the initial state (neutral acid) and the ®nal state (anion) contributions to acidity as proposed by Siggel and Thomas [3]. Besides this energy separation scheme presented by Siggel and Thomas [3] (Eqs. (3)±(7)), and its reversed version presented by us (Eqs. (8)±(10)), another scheme based on a thermodynamic proton transfer cycle may be employed (Eqs. (11) and (12)). E BDE A 2 H 2 EA Az 1 IP H
11
E BDE A 2 H 2 IP A2 1 IP H
12
BDE (A±H) is the homolytic dissociation energy of
the A±H bond in AH, EA(A z ) is the electron af®nity of the A z radical, IP(A 2) is the ionisation potential of the anion A 2 and IP(H) is the hydrogen atom ionisation potential (313.6 kcal/mol). This energy-partitioning scheme has the virtue that all energy components in Eq. (11) or Eq. (12) can in principle be measured independently experimentally. Eq. (12) can be simpli®ed further to Eq. (13) E 2IP A2 1 const:
13
since IP(H) is constant and BDE(O±H) is also nearly constant for aliphatic alcohols and carboxylic acids [27]. Hence, the ionisation potential of the anion is the only variable determining acidity differences between alcohols and carboxylic acids. This statement holds perfectly for the comparison of acidities of methanol and formic acidÐthe 38.9 kcal/mol difference of experimental acidities (372.9 and 334.0 kcal/ mol, respectively [27]), matches the 39.0 kcal/mol difference of electron af®nities (1.57 and 3.26 eV, respectively [27]) of corresponding RO z radicals. Indeed, when a larger range of XOH acids are considered, the BDE(O±H) variation can be quite large. However, such interpretation also is not universal since IP A2 E Az 2 E A2
14
where E(A z ) and E(A 2) are the energies of a radical and its corresponding anion. Hence, the ionisation potential (and the acidity) still depend not only on the energy of the anion, but also on that of the corresponding radical. 4. Conclusions The relaxation energy (R) obtained by means of Siggel±Thomas scheme (Eqs. (3)±(7)) does not correspond to the ªresonance energyº or to the ªdelocalization energyº as usually understood by organic chemists. Also, R cannot be used as a measure of the ®nal state (anion) contribution to acidity as proposed by Siggel and Thomas [3], since R also depends on the initial state (neutral acid). Moreover, the application of Siggel±Thomas approach in two opposite directionsÐdissociation of neutral acid and protonation of an anion leads to contradictory conclusions about whether the acidity difference between
P. Burk, P. von Rague Schleyer / Journal of Molecular Structure (Theochem) 505 (2000) 161±167
methanol and formic acid is determined by the neutral acid or anion. Hence, this scheme (Eqs. (3)±(7)) cannot be used to determine the initial state (neutral acid) and the ®nal state (anion) contributions to acidity as proposed by Siggel and Thomas [3]. Acknowledgements Fonds der Chemischen Industrie, der Deutchen Forschungsgemeinschaft, der Stiftung Volkswagenwerk and the Convex Computer Corporation are acknowledged for support. PB thanks the Alexander von Humboldt Stiftung for a post-doctoral fellowship. References [1] G.W. Wheland, Resonance in Organic Chemistry, Wiley, New York, 1955. [2] J. March, Advanced Organic Chemistry, 3, Wiley, New York, 1985. [3] M.R.F. Siggel, T.D. Thomas, J. Am. Chem. Soc. 108 (1986) 4360. [4] D.A. Shirley, Phys. Rev. A 7 (1973) 1520. [5] O. Exner, J. Org. Chem. 53 (1988) 1810. [6] R.W. Taft, I.A. Koppel, R.D. Topsom, F. Anvia, J. Am. Chem. Soc. 112 (1990) 2047. [7] P.C. Hiberty, C.P. Byrman, J. Am. Chem. Soc. 117 (1995) 9870. [8] M.J. Dewar, K.L. Krull, J. Chem. Soc. Chem. Commun. (1990) 333. [9] C.L. Perrin, J. Am. Chem. Soc. 113 (1991) 2865. [10] T.D. Thomas, M.R.F. Siggel, A. Streitwieser Jr., J. Mol. Struct. (Theochem) 165 (1988) 309. [11] M.R.F. Siggel, A. Streitwieser Jr., T.D. Thomas, J. Am. Chem. Soc. 110 (1988) 8022.
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[12] T.D. Thomas, T.X. Carroll, M.R.F. Siggel, J. Org. Chem. 53 (1988) 1812. [13] M.R.F. Siggel, T.D. Thomas, J. Am. Chem. Soc. 114 (1992) 5795. [14] P. Speers, K.E. Laidig, A. Streitwieser, J. Am. Chem. Soc. 116 (1994) 9257. [15] T.D. Thomas, J. Chem. Soc. Perkin Trans. 2 (1994) 1945. [16] K.B. Wiberg, J. Ochterski, A. Streitwieser, J. Am. Chem. Soc. 118 (1996) 8291. [17] K.E. Laidig, A. Streitwieser, J. Comp. Chem. 17 (1996) 1771. [18] R.F.W. Bader, Atoms in Molecules: A Quantum Theory, Oxford University, Oxford, 1990. [19] J.D. da Motta, M.A.C. Nascimento, J. Phys. Chem. 100 (1995) 15 105. [20] K. Jug, E. Fasold, M.S. Gopinathan, J. Comp. Chem. 10 (1989) 965. [21] K.E. Laidig, J. Am. Chem. Soc. 114 (1992) 7912. [22] C. Gatti, P. Fantucci, J. Phys. Chem. 97 (1993) 11 677. [23] K.B. Wiberg, H. Castejon, J. Am. Chem. Soc. 116 (1994) 10 489. [24] K.B. Wiberg, H. Castejon, J. Org. Chem. 60 (1995) 6327. [25] M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. Al-Laham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.P. Stewart, M. Head-Gordon, C. Gonzalez, J.A. Pople, gaussian 94, Revision D.3, Gaussian, Inc., Pittsburgh, PA, 1995. [26] J.B. Foresman, A. Frisch, Exploring Chemistry with Electronic Structure Methods: A Guide to Using Gaussian, Gaussian Inc., Pittsburgh, PA, 1993. [27] S.G. Lias, J.E. Bartmess, J.F. Liebman, J.L. Holmes, R.D. Levin, W.G. Mallard, J. Phys. Chem. Ref. Data (Suppl. 1) (1988). [28] B.E. Mills, R.L. Martin, D.A. Shirley, J. Am. Chem. Soc. 98 (1976) 2380. [29] D. Ji, T.D. Thomas, J. Phys. Chem. 98 (1994) 4301.
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Why are carboxylic acids stronger acids than alcohols? The electrostatic theory of Siggel±Thomas revisited P. Burk a,b,*, P. von Rague Schleyer a a
Institute of Organic Chemistry, University of Erlangen-NuÈrnberg, Henkestr. 42, D-91054 Erlangen, Germany b Institute of Chemical Physics, Tartu University, Jakobi 2, 51014 Tartu, Estonia Received 30 August 1999; accepted 16 September 1999
Abstract The electrostatic explanation of Siggel and Thomas for the acidity differences between series of acids was investigated critically. Acidities and electrostatic potentials at the protons of XOH, XNH2, and XCH3 derivatives X H; CH3, HCO, NO2, and F) were calculated at the Becke3LYP/6-3111G pp level. Final state (anion) relaxation energies were obtained as proposed by Siggel and Thomas. Examination of initial and ®nal state contributions revealed de®ciencies in the Siggel±Thomas method as the ®nal-state (relaxation) energies still retain contributions from the electronic structure of the initial state. Hence, this relaxation energy is not reliable as a measure of resonance stabilisation in anion. The application of Siggel±Thomas approach in two opposite directionsÐdissociation of neutral acid and protonation of an anionÐleads to contradictory conclusions about whether the acidity difference between methanol and formic acid is determined by the neutral acid or anion. Hence, this scheme cannot be used to determine the initial state (neutral acid) and ®nal state (anion) contributions to acidity as proposed by Siggel and Thomas. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Acidity; Resonance; Electrostatics
1. Introduction Acidity is a basic molecular property. The strength of a BroÈnsted acid in the gas phase is given quantitatively by DE, DH or DG for proton removal (Eq. (1)). Stronger acids have lower values of DE, DH or DG. Acidity is determined by the stability of both the neutral acid AH and its conjugate anion, A 2, Eq. (2) AH O A2 1 H21
1
DE E A2 1 E H1 2 E AH
2
extents. Although possible electrostatic contributions were recognized by Wheland [1], the greater acidity of carboxylic acids compared to aliphatic alcohols traditionally has been attributed to the enhanced stability of carboxylate anions (usually assumed to be due to p electron delocalisation, i.e. resonance, 1 $ 2 [2].
Resonance, hyperconjugation, ®eld/inductive effects, etc. can stabilize AH and A 2 to different * Corresponding author.
This resonance-based explanation of higher acidity
0166-1280/00/$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0166-128 0(99)00357-7
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of carboxylic acids over alcohols was ®rst challenged by Siggel and Thomas 14 years ago [3]. They concluded that resonance delocalisation ªplays only a minor roleº and attributed that greater acidity of carboxylic acids compared to aliphatic alcohols primarily due to electrostatic interactions, which are present already in the neutral acid, due to the polarization of carbonyl group. An analysis based on simple two step thermodynamic cycle for proton removal from acid was proposed. In the ®rst formal step a proton is removed from the acid without any change in the electron distribution or geometry relaxation. The energy of such a hypothetical proton removal process (2V) is given by the negative of the electrostatic potential at the site of the acidic proton in the neutral acid. In the second formal step, the hypothetical anion relaxes into its most stable form. R is the corresponding relaxation energy, which bene®ts from electron delocalization in the anion, and also all other electronic and geometric reorganizations. Hence, the energy of reaction (1), DE is divided into two components, V and R DE 2V 2 R
3
Theoretical evaluations of R and V were based on ab initio computations of DE and V, 1 R was obtained by difference from Eq. (3). While absolute values of V and R are not amenable to experimental evaluation, the difference in deprotonation energy, DDE, between two acids, for instance, formic acid and methanol, can be expressed by Eq. (4): DDE 2DV 2 DR
4
Hence, Siggel and Thomas evaluated DV and DR from experimental measurements of gas-phase acidities and O±H oxygen 1s electron ionisation energies in neutral acids (Eqs. (6) and (7)). DR
2DI 2 DDE 2
6
DV
DI 2 DDE 2
7
by assuming that V and R in Eqs. (3) and (4) are essentially the same quantities (as both DE and I correspond to the removal of a unit charge, positive or negative, from close regions of space). As an example, the values of DV and DR for the methanol and formic acid, derived from experiment and from ab initio calculations, are given in Table 1. According to the Siggel±Thomas interpretation, V measures the initial state (primarily inductive) contribution to the acidity, while R is determined by the ®nal state contribution (mainly charge delocalization, accompanying proton removal). Comparing the values of DR and DV of alcohols and carboxylic acids led to the revolutionary conclusion that the greater acidity of carboxylic acids relative to aliphatic alcohols is primarily determined by differences in the initial states, e.g. the neutral acids. The values of DR were small (see Table 1) both by experimental (DR and DV calculated from experimental acidities and O± H oxygen core-ionisation energies) and theoretical data (DR and DV calculated from ab initio acidities
A similar expression (5) was proposed earlier [4] for O±H oxygen core-ionisation energies (i.e. the energy needed for removing an oxygen 1s electron) differences (DI) in neutral acids
Table 1 Acidity (DE), O±H oxygen 1s electron ionisation energy (I), electrostatic potential (V, at acidic proton), and relaxation energy (R) differences for methanol and formic acid (all values in kcal/mol). Experimental DV and DR were calculated from Eqs. (6) and (7). R for ab initio results was obtained from Eq. (3) using literature data
DI DV 2 DR
Experimental
5
1
The electrostatic potential V is calculated as Z f f X X ZA m n Pmn 2 dr 0 V ur 2 r 0 u mn A ur 2 RA u Pmn refers to a particular density matrix element of the wavefunction for the molecule as obtained from the SCF-MO calculation; f m and f n are the atomic basis wavefunctions. The ®rst term is summed over all nuclei (except the nucleus at which site the potential is evaluated), and the second term is summed over all electrons in molecule.
DE [27]
I [28]
V
CH3OH 372.9 297.3 ± HCOOH 334.0 261.1 ± D 38.9 236.2 237.6 Ab initio (6-3111G(2d,p)/6-31111G(2d,p) [29] DE I V CH3OH 399.2 ± 2634.4 HCOOH 357.2 ± 2592.4 D 42.0 ± 242.0
R ± ± 21.35 R 235.2 235.2 0.0
P. Burk, P. von Rague Schleyer / Journal of Molecular Structure (Theochem) 505 (2000) 161±167
and electrostatic potentials on acidic proton using Eq. (4)). This interpretation, not in keeping with the traditional view that the differences in acidities between carboxylic acids and alcohols are due to the extra resonance stabilization of the carboxylate anions, has received both criticism [5±9] and support [10± 17]. Using Bader's topological charge density analysis [18] Thomas et al. [10] and Siggel et al. [11] supported their analysis further by examining the charge distributions in formic acid, ethanol and vinyl alcohol as well as the charge ¯ow when the hydroxylic proton is removed from these molecules. They concluded that the carbonyl bond is strongly polarized already in the neutral formic acid. This charge distribution in the anion changed little. Hence, the leading resonance structure for formiate anion should be 3. They concluded that the higher acidity of carboxylic acids relative to aliphatic alcohols is due mainly (ca. 85%) to carbonyl inductive effects. Based on their method of analysis Siggel and Thomas also concluded, that the anomalously high acidity of formic acid compared to other aliphatic carboxylic acids [13] was due to the result of higher electrostatic potential at the acidic proton in formic acid. Dewar and Krull [8] argued that enhanced acidities of vinylogues of formic acid and vinyl alcohol relative to aliphatic alcohols are due to resonance stabilization of the conjugate anions. This was refuted subsequently by Thomas [15]: the acidity of vinylogues of formic acid and vinyl alcohol relative to aliphatic alcohols also was found to be determined by initial state contributions (mainly inductive effects). The origin of the carboxylic acid acidity was attributed recently by Wiberg et al. [16] to the stabilization of the anion by the carbonyl group accepting some p electron density (ca. 0.1e) and by stabilizing electrostatic interaction between the positively charged carbonyl carbon and the adjacent negatively charged atom. Part of the negative charge arising from deprotonation of the acid appears at the hydrogens in the nodal plane of the p system. Based on correlation analysis of the gas phase acidities of O±H acids, Taft et al. [6] agreed with the conclusion of Siggel and Thomas that the acidity of formic acid relative to acetic acid is due primarily to
163
inductive effects, but also indicated that the acidities of carboxylic acids relative to aliphatic alcohols are determined both by resonance and by inductive effects to comparable extents. The 36 kcal/mol acidity difference between methanol and formic acid was ascribed to resonance (13 kcal/mol) and to inductive effects (23 kcal/mol). Similar conclusions were reached more recently by Hiberty and Byrman [7] as well as by de Mota and Nascimento [19]. Their valence bond calculations on formic acid, vinyl alcohol and ethanol indicated that about half of the acidity difference between ethanol and formic acid was determined by the extra resonance interaction in anion. The use of Bader electronic populations to support the Siggel±Thomas model of acidifying effects [10,11] was criticized by Perrin [9] and Jug et al. [20]. They argued that the Bader populations on more electronegative atoms are exaggerated since the location of the zero-¯ux surface depends on the atomic size. However, other authors have discounted these criticisms [21,22]. Exner [5] used simple thermodynamical considerations to support that carboxylate anions are stabilized by resonance. However, Siggel and Thomas [12] refuted Exner's analysis by arguing that his isodesmic reactions would not separate the contributions of inductive and resonance effects. Speers et al.'s [14] recent investigation of the relative acidities of CH3SCH3, CH3SOCH3, and CH3SO2CH3, also used Bader's topological charge density analysis [18] to partition the total energies into the atomic energies, and concluded that the contribution from relaxation in the anion is unimportant energetically. A similar conclusion was reached by Laidig and Streitwieser [17], who investigated the origins of relative acidities in ®rst and second period hydrides. On the contrary, Wiberg and Castejon's study of the acidities of dimethyl sul®de, dimethyl ether [23], and substituted methanes [24] indicated that intramolecular charge relaxation in anions resulted in considerable energetic effects. Since the origin of the higher acidity of carboxylic acids relative to alcohols is not settled, we have carried out ab initio calculations on various O±H, N±H and C±H acids, to test the electrostatic theory of Siggel and Thomas on a wider class of compounds.
P. Burk, P. von Rague Schleyer / Journal of Molecular Structure (Theochem) 505 (2000) 161±167
164
Table 2 298 Calculated (B3LYP/6-3111G pp) electrostatic potential V on acidic protons, calculated (DE 1, DH0298 ; and DG298 0 and experimental [27] DH0 and DG298 acidities (all in kcal/mol) 0
H2O CH3OH HCOOH HNO3 FOH NH3 CH3NH2 H2NCHO H2NNO2 FNH2 F2NH CH4 CH3CH3 CH3CHO CH3NO2 CH3F CH2F2 CHF3 a
V
DE a (calc.)
DH0298 (calc.)
DG298 (calc.) 0
DH0298 (exp.)
DG298 (exp.) 0
2623.8 2630.0 2589.9 2573.0 2585.8 2665.1 2670.9 2624.5 2607.7 2636.7 2608.5 2704.9 2710.2 2678.5 2659.2 2688.5 2671.7 2650.8
396.0 388.4 348.3 326.9 361.5 412.6 411.8 367.1 346.2 388.4 363.8 425.3 428.6 371.9 360.9 416.4 402.8 382.1
389.2 379.4 341.0 320.4 355.1 404.2 402.2 360.0 339.3 380.2 355.9 416.8 419.4 364.6 353.3 407.7 394.8 373.7
382.2 372.5 333.5 313.7 348.2 396.9 394.3 352.6 331.5 372.1 347.9 408.3 410.2 357.2 347.0 398.6 386.0 365.2
390.8 380.4 345.1 324.6
384.1 374.0 338.2 317.9
403.7 403.2 359.9
396.0 395.8 352.8
359.0 416.9 420.9 365.9 355.4
352.1 408.7 412.3 359.0 349.7
386.7 376.9
379.1 369.3
DE is calculated from electronic energies of acid and conjugated anion without any corrections.
2. Methods Table 3 Calculated (B3LYP/6-3111G pp) relative acidities (DDE), electrostatic potentials (DV) at acidic proton in neutral acid, and relaxation energies (DR) of O±H, N±H and C±H acids relative to H2O, NH3, and CH4, respectively (in kcal/mol)
H2O CH3OH HCOOH HNO3 FOH NH3 CH3NH2 H2NCHO H2NNO2 FNH2 F2NH CH4 CH3CH3 CH3CHO CH3NO2 CH3F CH2F2 CHF3
DDE
DV
DR
0.0 27.6 247.7 269.1 234.5 0.0 20.8 245.5 266.4 224.2 248.8 0.0 3.1 253.4 264.4 28.9 222.5 243.2
0.0 26.2 33.9 50.8 38.0 0.0 25.8 40.6 57.4 28.4 56.6 0.0 25.3 26.4 45.7 16.4 33.2 54.1
0.0 13.8 13.8 18.3 23.5 0.0 6.6 4.9 9.0 24.2 27.8 0.0 2.2 27.0 18.7 27.5 210.7 210.9
Density functional calculations were performed at Becke3LYP/6-3111G pp using the gaussian 94 program [25]. Geometries of the neutral acids and of the corresponding anions were fully optimized and harmonic frequencies calculated. Acidities E were calculated as the differences in total energies of the parent acid DH and the conjugated anion, A 2. DH 298 and DG 298 were calculated for comparison with experiment using thermochemical corrections from frequency calculations [26]. Electrostatic potentials at the sites of all nuclei were computed as implemented in the gaussian 94 program. These data are presented in Table 2 along with the experimentally determined values. In Table 3 DE, DV, and DR (calculated from data in Table 2 using Eq. (4)) are given for the O±H, N±H and C±H acids relative to H2O, NH3, and CH4, respectively. 3. Results and discussion The results in Table 2 show that the B3LYP/6-311G pp level (with ZPE and thermal corrections)
P. Burk, P. von Rague Schleyer / Journal of Molecular Structure (Theochem) 505 (2000) 161±167
reproduces the experimental acidities [27] with the average unsigned error of 2.5 kcal/mol. The relative values of DV and DR given in Table 3 for methanol and formic acid agree with Siggel and Thomas that DV is the predominant term in Eq. (4), i.e. it can be said (based on their methodology) that the acidity difference of methanol and formic acid are usually determined by the electron distribution in the neutral acid. However, DR is generally not smallÐin three cases is DR larger than DV and for seven more cases in Table 3 over 20% of DV. The negative relaxation energies of the ¯uorosubstituted derivatives relative to H2O, NH3, and CH4, evidently result from the high electronegativity of ¯uorine. The ¯uorines have large negative charges in the neutral acid so that further negative charge increase at ¯uorine in anion is not favorable energetically. However, R, calculated from Eq. (3), does not correspond to the ªresonance energyº or to the ªdelocalization energyº as usually understood by organic chemists. The crucial difference between relaxation energy of Siggel±Thomas and conventional resonance energy lies in the reference state used to deduce the energy of the real, fully relaxed anion. The Siggel±Thomas relaxation energy (R) is calculated as the energy difference between a real anion and a hypothetical anion (formed as a result of the ®rst step of deprotonation) with the electron distribution of the neutral. The resonance energy is traditionally understood as the difference between the energy of a real anion and a hypothetical anion with a Lewis structure where all electron pairs are completely localized either in bonds or on atoms (core electrons, lone pairs). Clearly, these two reference states (the hypothetical anion with the geometry and electronic structure of the neutral species, and the real anion with completely localized Lewis structure) are not equivalent. The 44.1 and 41.7 kcal/mol rotational barriers around the C±C or C±N bonds, respectively, in the CH2CHO 2 and in the CH2 NO2 2 anions, provide rough estimates of the resonance (®nal state) stabilisation in these anions, but are quite different from the relaxation energies obtained from Eq. (4) (27.0 and 18.7 kcal/mol, respectively). Furthermore, the relaxation energy R of CH3OH is much larger than that of H2O and only fortuitously similar to HCOOH (Table 3).
165
These differences support our criticism that the relaxation energy R, calculated from Eq. (3), does not correspond to the ªresonance energyº or to the ªdelocalization energyº as usually understood by organic chemists. The relaxation energy (R) is the energy difference between the real anion and a hypothetical anion with the electron distribution of the neutral acid. Hence, the relaxation energy R still depends on the initial state (via electron distribution in neutral acid) and does not characterize the stabilization of anion by charge delocalisation unambiguously. The energy-partitioning scheme presented by Siggel and Thomas [3] (Eqs. (3)±(7)) can be applied also in reverse direction (on the reaction of the protonation of anion (8)) A2 1 H1 O AH
8
The energy of such reaction, 2DE, is the negative of the acidity (DE) of acid AH, and can be analyzed based on a three step thermodynamic cycle of the proton addition to the anion. In the ®rst formal step the geometry of anion is rearranged into that of neutral acid. The energy of this step, Rrg ; can be easily calculated as the difference of energies of anion at the neutral acids geometry and at the optimized geometry. We note that Rrg ; corresponds to the energy of geometry relaxation in the second step of the thermodynamic cycle proposed by Siggel and Thomas. In the second formal step proton is added to the anion (at the geometry of neutral acid) without any change in the electron distribution. The energy of such hypothetical proton addition (V r) is given by the electrostatic potential in the anion at the position, where the proton should be placed. In the ®nal step, the hypothetical neutral acid with the electron distribution of anion relaxes into its most stable electronic state. Rrel is the corresponding relaxation energy. Hence, the energy of reaction (8) is divided into three components Rrg ; V r ; and Rrel 2DE Rrg 1 V r 1 Rrel
9
As 2DE; Rrg ; and V r can be easily calculated, Rrel can be obtained as Rrel 2DE 2 Rrg 2 V r
10
P. Burk, P. von Rague Schleyer / Journal of Molecular Structure (Theochem) 505 (2000) 161±167
166
Table 4 Results of the Siggel±Thomas analysis on the reactions of protonation of formiate and methoxy anions (Eqs. (9) and (10)): acidity (DE), energy of the rearrangement of anions geometry into that of neutral acid Rrg ; electrostatic potential in the anion at the position, where the proton should be placed (V r), the energy of electronic relaxation in neutral acid after proton addition Rrel for methanol and formic acid, and corresponding relative values (DDE, DRrg ; DV r, and DRrel for formic acid relative to methanol (all values in kcal/ mol, calculated at B3LYP/6-3111G pp level of theory)
CH3OH HCOOH D
DE
Vr
Rrel
Rrg
388.4 348.3 40.1
2215.5 2188.1 227.4
2177.7 2168.0 29.7
4.8 7.8 23.0
In Table 4 are presented the results of such energy partitioning for methanol and formic acid as well as the relative values DDE; DRrg ; DV r ; and DRrel for formic acid relative to methanol. Here again the acidity difference is predominantly due to differences in electrostatic potential in initial state, but in this case the initial state is anion. The energies of ®nal state (neutral acid) relaxation contribute only one quarter of the acidity difference between methanol and formic acid. Should one, in analogy with original Siggel± Thomas approach, draw the conclusion that DE (and hence the acidity) is determined mainly by electron distribution in anion? As shown, the application of Siggel±Thomas approach in two opposite directionsÐdissociation of neutral acid and protonation of an anionÐof the acid±base equilibria reaction leads to contradictory conclusions about whether the acidity difference between methanol and formic acid is determined by the neutral acid or anion. Hence, this scheme (Eqs. (3)±(7)) cannot be used to determine the initial state (neutral acid) and the ®nal state (anion) contributions to acidity as proposed by Siggel and Thomas [3]. Besides this energy separation scheme presented by Siggel and Thomas [3] (Eqs. (3)±(7)), and its reversed version presented by us (Eqs. (8)±(10)), another scheme based on a thermodynamic proton transfer cycle may be employed (Eqs. (11) and (12)). E BDE A 2 H 2 EA Az 1 IP H
11
E BDE A 2 H 2 IP A2 1 IP H
12
BDE (A±H) is the homolytic dissociation energy of
the A±H bond in AH, EA(A z ) is the electron af®nity of the A z radical, IP(A 2) is the ionisation potential of the anion A 2 and IP(H) is the hydrogen atom ionisation potential (313.6 kcal/mol). This energy-partitioning scheme has the virtue that all energy components in Eq. (11) or Eq. (12) can in principle be measured independently experimentally. Eq. (12) can be simpli®ed further to Eq. (13) E 2IP A2 1 const:
13
since IP(H) is constant and BDE(O±H) is also nearly constant for aliphatic alcohols and carboxylic acids [27]. Hence, the ionisation potential of the anion is the only variable determining acidity differences between alcohols and carboxylic acids. This statement holds perfectly for the comparison of acidities of methanol and formic acidÐthe 38.9 kcal/mol difference of experimental acidities (372.9 and 334.0 kcal/ mol, respectively [27]), matches the 39.0 kcal/mol difference of electron af®nities (1.57 and 3.26 eV, respectively [27]) of corresponding RO z radicals. Indeed, when a larger range of XOH acids are considered, the BDE(O±H) variation can be quite large. However, such interpretation also is not universal since IP A2 E Az 2 E A2
14
where E(A z ) and E(A 2) are the energies of a radical and its corresponding anion. Hence, the ionisation potential (and the acidity) still depend not only on the energy of the anion, but also on that of the corresponding radical. 4. Conclusions The relaxation energy (R) obtained by means of Siggel±Thomas scheme (Eqs. (3)±(7)) does not correspond to the ªresonance energyº or to the ªdelocalization energyº as usually understood by organic chemists. Also, R cannot be used as a measure of the ®nal state (anion) contribution to acidity as proposed by Siggel and Thomas [3], since R also depends on the initial state (neutral acid). Moreover, the application of Siggel±Thomas approach in two opposite directionsÐdissociation of neutral acid and protonation of an anion leads to contradictory conclusions about whether the acidity difference between
P. Burk, P. von Rague Schleyer / Journal of Molecular Structure (Theochem) 505 (2000) 161±167
methanol and formic acid is determined by the neutral acid or anion. Hence, this scheme (Eqs. (3)±(7)) cannot be used to determine the initial state (neutral acid) and the ®nal state (anion) contributions to acidity as proposed by Siggel and Thomas [3]. Acknowledgements Fonds der Chemischen Industrie, der Deutchen Forschungsgemeinschaft, der Stiftung Volkswagenwerk and the Convex Computer Corporation are acknowledged for support. PB thanks the Alexander von Humboldt Stiftung for a post-doctoral fellowship. References [1] G.W. Wheland, Resonance in Organic Chemistry, Wiley, New York, 1955. [2] J. March, Advanced Organic Chemistry, 3, Wiley, New York, 1985. [3] M.R.F. Siggel, T.D. Thomas, J. Am. Chem. Soc. 108 (1986) 4360. [4] D.A. Shirley, Phys. Rev. A 7 (1973) 1520. [5] O. Exner, J. Org. Chem. 53 (1988) 1810. [6] R.W. Taft, I.A. Koppel, R.D. Topsom, F. Anvia, J. Am. Chem. Soc. 112 (1990) 2047. [7] P.C. Hiberty, C.P. Byrman, J. Am. Chem. Soc. 117 (1995) 9870. [8] M.J. Dewar, K.L. Krull, J. Chem. Soc. Chem. Commun. (1990) 333. [9] C.L. Perrin, J. Am. Chem. Soc. 113 (1991) 2865. [10] T.D. Thomas, M.R.F. Siggel, A. Streitwieser Jr., J. Mol. Struct. (Theochem) 165 (1988) 309. [11] M.R.F. Siggel, A. Streitwieser Jr., T.D. Thomas, J. Am. Chem. Soc. 110 (1988) 8022.
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