1938
J. Phys. Chem. B 1998, 102, 1938-1944
Ab Initio Quantum Chemical Studies of the pKa’s of Hydroxybenzoic Acids in Aqueous Solution with Special Reference to the Hydrophobicity of Hydroxybenzoates and Their Binding to Surfactants Warwick A. Shapley, George B. Bacskay,* and Gregory G. Warr School of Chemistry, UniVersity of Sydney, NSW, 2006, Australia ReceiVed: October 22, 1997; In Final Form: January 5, 1998
Using quantum chemical methods, the thermodynamic stabilities of benzoic, o-, m-, and p-hydroxybenzoic, and acetic acids and their conjugate bases were studied in both gas phase and aqueous solution, enabling the computation of the pKa’s of the above acids. The electronic structure calculations were carried out at the Hartree-Fock SCF and MP2 levels of theory, using 6-31G(d,p) and 6-311+G(2d,p) basis sets. Solvation energies were calculated using two dielectric continuum methods: SCIPCM and PCM. o-Hydroxybenzoic acid and its anion were found to possess intramolecular hydrogen bonds, which in the case of the anion are so strong as to result in a “bridged” structure in the gas phase with the proton effectively midway between the oxygens of the carboxylic and hydroxide groups. As a consequence of this strong hydrogen bond, the ortho anion appears to have the lowest solvation energy, lower (in magnitude) by ∼8-10 kcal/mol than that of benzoate itself, despite the presence of a potentially hydrophilic hydroxy group. The trends in the calculated solvation energies of the anions provide an explanation for the unusual binding strength of o-hydroxybenzoate to surfactant films. The computed pKa’s of the acids were analyzed in terms of the contributing energetics, and while these calculations have not yielded quantitatively accurate predictions of the pKa’s, they do exhibit the correct qualitative trend among the acids studied.
Introduction Salicylate (o-hydroxybenzoate) occupies a unique place among counterions for surfactant self-assembly. Its strong binding to cationic micelles and screening of repulsions between surfactant headgroups induce the formation of wormlike micelles just above the critical micelle concentration.1 This behavior contrasts markedly with conventional counterions such as bromide or chloride, in which spherical micelles exist at concentrations of added anion of up to 0.1 M or even higher.2 Many benzoate and benzenesulfonate derivatives associate strongly with surfactant aggregates and adsorbed films. In most cases the strength of counterion binding is directly related to the hydrophobicity of the ion. The phenyl moiety itself is hydrophobic and is known to intercalate between cationic surfactant headgroups in micelles and adsorbed films. Increasing the hydrophobicity by substitution of a methyl or chloro group3,4 or decreasing hydrophobicity by m- or p-hydroxy substitution5 causes a corresponding change in the degree of counterion binding. Salicylate was one of the first counterions discovered that induce viscoelasticity and is certainly the most extensively studied.6 More than this, salicylate binds more strongly than it should. It binds more strongly than both m- and p-hydroxybenzoates, but more strikingly it binds to cationic surfactant films more strongly than benzoate itself. A recent measurement of the selective uptake of benzoate and salicylate yielded ion exchange equilibrium constants for benzoate and salicylate over bromide of 14 and 50, respectively.7 This, despite the presence of the hydrophilic hydroxyl group, which should decrease association with the hydrophobic micelle. There has also been a great deal of conjecture about the existence of 1:1 association complexes between quaternary
ammonium headgroups and salicylate anions.8-10 Although careful examination of the evidence does not support any such specific association, this does underscore the strength of the binding of salicylate to micelles and surfactant films.11 In an effort to determine what gives rise to the unique behavior of salicylate we have used ab initio quantum chemical techniques to examine the electronic structures of benzoate and of the three isomers of hydroxybenzoate in vacuo and in aqueous solution, using two different dielectric continuum solvent models. The free energy of solvation so calculated provides a measure of the hydrophobicity/hydrophilicity of each species and could thus be used to rationalize the observed trends in the binding of these anions to surfactants. Further, by extending the calculations to the conjugate acids, their pKa’s could also be evaluated and compared with experiment. As well as being a check on the accuracy of the calculations, the pKa’s are of interest in the context of the current problem, since it has been noted that the degree of binding of a given benzoate correlates with the acid-dissociation constant of the conjugate acid, which in turn suggests that the latter may correlate with the hydrophobicity. Given that solvation is just one contributing factor to the pKa, it is of interest to study the acidities in some detail, so as to quantify all major contributions to it, in particular the importance of the intrinsic electronic stability. It has been noted7 that salicylate may possess a strong intramolecular hydrogen bond and that this may be connected with its unusual behavior in some way. Therefore, the characterization of the hydrogen bonds in both salicylic acid and salicylate, and their effects on the thermodynamic stabilities in the gas phase and solution, is an important aspect of this work.
S1089-5647(97)03417-2 CCC: $15.00 © 1998 American Chemical Society Published on Web 02/20/1998
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Theory and Computational Methods The acid-dissociation constant Ka of a given acid HA in aqueous solution is related to the standard Gibbs free energy change of the appropriate reaction by the standard thermodynamic relationship
-RT ln Ka ) ∆G°aq ) G°aq(H+) + G°aq(A-) - G°aq(HA) (1) where the standard free energies apply to the solvated species. At a given temperature T the pKa is then simply
pKa ) ∆G°aq/2.303RT
(2)
The ab initio prediction of a pKa therefore requires the computation of Gibbs free energies in solution. In this work this was carried out by calculating as accurately as practicable the electronic energies of the acid HA and its conjugate base A-, followed by the calculation of their entropies, enthalpies, and free energies in the gas phase and finally by computation of their solvation energies. The free energy of H+ in solution is simply its translational free energy plus its solvation energy, and for the latter the experimental value12 of -259.5 kcal/mol has been used in the calculation of the pKa’s. The gas-phase molecular geometries and electronic energies were computed using Hartree-Fock (HF) plus second-order Møller-Plesset perturbation theory (MP2) in conjunction with the 6-31G(d,p) basis sets. In selected cases improved estimates of the electronic energies (at the MP2/6-31G(d,p) geometries) were obtained at the MP2 level using the significantly larger 6-311+G(2d,p) basis set. This will be referred to as the extended basis in this work. In the MP2 calculations the 1s core electrons of C and O were treated as frozen. The rotational constants and (harmonic) vibrational frequencies were calculated at the HF/6-31G(d,p) level (at the appropriate HF geometries). Using these data, the partition functions and hence the thermal corrections to the internal energy as well as the entropies were obtained utilizing the standard equations for classical translation, rotation, and quantized harmonic vibrations. Combined with the electronic energies, these then yield the gas-phase free energies at temperatures of 0 and 298.15 K. Given the high computational cost of calculating frequencies at the MP2 level and noting that the thermal corrections were found to make relatively small contributions to the relative stabilities of the systems studied, the use of SCF frequencies is justified as well as prudent. In the case of rotational constants, the differences between the MP2 and SCF values were found to be negligibly small, since the respective geometries are in close agreement. The free energies of solvation of the various acids and their anions were computed by the self-consistent isodensity polarized continuum model (SCIPCM)13 at the HF/6-31G(d,p) level at the MP2 optimized geometries, using the value14 of 80.20 as the dielectric constant of water. The total free energy of a given species is thus the sum of the gas-phase electronic and thermal contributions, plus the solvation energy, viz.,
G°aq ) Eelec + ∆Gtherm(T) + ∆Gsolv
(3)
where Eelec is the total electronic energy, ∆Gtherm is the thermal correction to the free energy at the given temperature T, and ∆Gsolv is the free energy of solvation. As a check, the solvation energies were also calculated by Tomasi’s polarized continuum model (PCM),15,16 using the recommended atomic radii of Stefanovich and Truong.17 These authors criticized the accuracy of the SCIPCM model in the case of ionic systems and
recommended instead the PCM method with atomic radii that reflect the chemical environment, viz., orbital hybridization of a given atom. Since these dielectric continuum methods require that a cavity within the dielectric be specified, which can be reasonably well accomplished on the basis of the electronic charge distribution, such methods are inapplicable to the study of the solvation of a proton. Therefore, we chose to use the experimental solvation energy for H+. In the case of the salicylate anion, where an intramolecular hydrogen bond exists between the oxygens of the hydroxy and carboxyl groups, the vibrational motion of the bridging proton was investigated in some detail, computing its frequency in an effective one-dimensional double-well potential. These calculations were carried out in a basis of sinusoidal functions, using the generalized finite element method (GFEM).18 The quantum chemical calculations were carried out using the Gaussian 94 system of programs.13 All computations were performed on the DEC alpha 600/5/333 workstations of the Theoretical Chemistry group at Sydney University. Results and Discussion Geometries and Thermodynamic Stabilities. The various isomers and conformers of hydroxybenzoic acids and their anions, as well as of the parent, unsubstituted systems, that were studied in this work, are shown in Figure 1. In the geometry optimizations all species were assumed to be planar. This assumption was validated, at least at the SCF level, inasmuch as all the vibrational frequencies were computed to be real, with the obvious exceptions of 5a, 9a, and 11a, which correspond to saddle points on the molecular potential energy surfaces of 5, 9, and 11. With regard to the choice of other conformations, the alternatives are not expected to have very different stabilities from those chosen for this study. All the species studied have closed shell configurations, and thus the electronic states are all 1A′. In previous work on o- and p-hydroxybenzoic acids, Nagy et al.19 also found 1 and 3 to be the most stable conformations. The presence of H-bonding in o-hydroxybenzoic acid and its anion is clearly manifested in their geometric parameters, the most relevant of which in the context of H-bonding are defined in Figure 2 and summarized in Table 1. The OH bond in the hydroxy groups is uniformly ∼0.965 Å in all species except in the ortho isomers 1 and 5, where it is considerably longer. In these systems, concomitant with the presence of H-bonds, the CO distances in the carboxylate and hydroxy groups are longer and shorter, respectively, as expected on the basis of a partial proton transfer. In the case of o-hydroxybenzoate the strong H-bond is further manifested in a distortion of the heavy atom skeleton, with a decrease in the O-O distance. In this system the phenoxy, viz., acid form of salicylate (7), has stability comparable to the “normal” isomer (5). The two structures, which are local minima on the MP2 potential energy surface, are connected by a transition state, viz., a “bridged” structure (6) where the proton is equally shared by two oxygens. By contrast, in 1a and 5a, where H-bonding is not present, the analogous bond distances are effectively the same as in the meta and para isomers. The computed MP2 energies of the above 16 species, along with the zero-point corrections, thermal corrections, and solvation energies, are given in Table 2. Among the hydroxybenzoic acids, purely on the basis of electronic energy, the ortho isomer (1) is more stable by ∼5 kcal/mol than the meta and para forms, which in turn are essentially isoenergetic. The difference in stabilities can be interpreted as a measure of the
1940 J. Phys. Chem. B, Vol. 102, No. 11, 1998
Shapley et al.
Figure 1. Structures of (hydroxy) benzoic acids and benzoates studied.
TABLE 1: Selected MP2/6-31G** Geometrical Parameters of Hydroxybenzoic Acids and Hydroxybenzoate Anionsa HOh
Figure 2. Definition of salient geometric parameters of hydroxybenzoates with reference to intramolecular hydrogen bonding.
strength of the intramolecular H-bond. Interestingly, the alternative ortho conformer 1a is predicted to be destabilized by an additional ∼5.5 kcal/mol, probably as a result of nonbonded O‚‚‚O repulsion. The gas-phase thermodynamic stabilities of these isomers follow the basic pattern of the electronic energies, since the zero-point energies as well as the thermal corrections to the free energies vary little. Similar observations can be made for the anions, inasmuch as the ortho forms 5, 6, and 7 are ∼18 kcal/mol more stable than the meta and para isomers; that is, a much stronger H-bond is evident than in the parent acid, as noted already on the basis of geometries. The stronger H-bond in the anionic salicylate is of course consistent with the increased electrostatic interaction between the protonic hydrogen and an oxygen atom with a higher negative charge than in salicylic acid. Comparing the two ortho conformers, we find that 5a is ∼28 kcal/mol less
o-hydroxybenzoic acid o-hydroxybenzoic acid m-hydroxybenzoic acid p-hydroxybenzoic acid o-hydroxybenzoate bridged o-hydroxybenzoate (acid) o-hydroxybenzoateb m-hydroxybenzoate m-hydroxybenzoate (acid) m-hydroxybenzoate (acid)b p-hydroxybenzoate p-hydroxybenzoate (acid) p-hydroxybenzoate (acid)b
(1) (1a) (2) (3) (5) (6) (7) (5a) (8) (9) (9a) (10) (11) (11a)
HOc
OhOc ChOh CcOc
0.979 0.967 0.966 0.966 1.056 1.209 1.419 0.967 0.965
1.776 2.646 1.353 1.235 2.680 1.364 1.219 1.369 1.222 1.369 1.222 1.431 2.449 1.346 1.294 1.199 2.384 1.324 1.314 1.059 2.448 1.304 1.335 2.722 1.380 1.256 1.390 1.264 0.970 1.270 1.377 0.967 1.269 1.374 0.965 1.393 1.263 0.969 1.265 1.392 0.965 1.265 1.390
a
Planar geometries; all distances in Å. b Possesses one imaginary a′′ HF frequency.
stable than 5, in line with the observation above concerning the existence of an O‚‚‚O repulsion, but which is considerably larger than in the parent acid. This effect is also mirrored by the trends in the O‚‚‚O distances. In the gas phase the stabilities of the acid, or phenoxy, forms of the hydroxybenzoate anions appear to be comparable with the corresponding normal forms. Their interconversion, with the exception of salicylate, is indirect, in that it must occur via the formation of the parent acid. In the case of the salicylate anion, where the standard hydroxy form is in effect isoenergetic with the acid form, interconversion is possible by direct proton migration. The computed barrier to this is only ∼0.5 kcal/mol,
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J. Phys. Chem. B, Vol. 102, No. 11, 1998 1941
TABLE 2: Electronic Energies and Zero-Point and Thermal Free Energy Corrections and Solvation Energies of (Hydroxy) Benzoic Acids, Acetic Acid, and Their Anions at 0 and 298.15 K Eelec (Eh)a o-hydroxybenzoic acid o-hydroxybenzoic acid m-hydroxybenzoic acid p-hydroxybenzoic acid o-hydroxybenzoate bridgedc o-hydroxybenzoate (acid) o-hydroxybenzoated m-hydroxybenzoate m-hydroxybenzoate (acid) m-hydroxybenzoate (acid)d p-hydroxybenzoate p-hydroxybenzoate (acid) p-hydroxybenzoate (acid)d benzoic acid benzoate acetic acid acetatef
(1) (1a) (2) (3) (5) (6) (7) (5a) (8) (9) (9a) (10) (11) (11a) (4) (12)
-494.652 110 -494.634 758 -494.643 350 -494.643 436 -494.100 246 -494.099 422 -494.100 067 -494.055 144 -494.072 479 -494.066 690 -494.065 030 -494.068 840 -494.078 021 -494.071 589 -419.605 575 -419.031 972 -228.469 334e -227.879 224e
Eelec(ext)b (Eh) -494.975 487 -494.967 341 -494.967 576 -494.446 700 -494.445 985 -494.446 146 -494.421 185 -494.417 754 -419.867 190 -419.318 563 -228.616 131 -228.054 624
∆EZPE ∆Etherm(298) ∆Gtherm(298) ∆Gsolv (SCIPCM) ∆Gsolv (PCM) (kcal/mol) (kcal/mol) (kcal/mol) (kcal/mol) (kcal/mol) 81.8 81.1 81.1 81.2 72.4 70.3 72.4 71.7 72.0 71.9 71.6 71.9 72.2 71.7 78.1 68.9 41.9 32.5
86.4 86.0 86.0 86.1 76.8 74.5 76.8 76.0 76.8 76.6 75.9 76.8 76.8 76.0 82.3 73.0 44.6 35.2
61.4 59.8 60.3 60.5 52.2 51.1 52.3 51.8 51.3 51.1 51.7 51.2 51.6 51.7 58.2 49.5 25.0 15.0
-6.8 -11.6 -9.6 -10.1 -52.5 -51.0 -49.8 -64.6 -58.6 -53.4 -51.2 -60.7 -50.3 -51.5 -6.5 -57.9 -6.4 -63.3
-12.5 -17.1 -17.4 -77.3 -74.4 -72.5 -86.6 -87.7 -12.1 -86.1 -12.5 -86.8
a MP2/6-31G(d,p) energies. b MP2/6-311+G(2d,p) energies. c Thermal corrections include the vibrational energy of the proton involved in the intramolecular H-bond. d Possesses one imaginary a′′ HF frequency. e Includes correlation of core electrons. f Possesses one imaginary a′′ MP2 frequency.
Figure 3. One-dimensional potential, vibrational energy levels, and wave functions for proton and deuterium transfer in salicylate.
which we thought could be low enough to lie below the zeropoint energy of the proton-transfer mode. To address this problem, the appropriate one-dimensional double-well potential was computed at the MP2/6-31G(d,p) level, where the molecular geometries corresponding to a particular Oh-H distance were obtained by interpolation between the computed equilibrium and saddle point structures (and extrapolation for Oh-H or H-Oc distances that are smaller than their equilibrium values). The one-dimensional Schro¨dinger equation was then solved by the GFEM method18 for a proton as well as a deuterium. The potential and the computed lowest energy levels and wave functions are shown in Figure 3. Clearly, the zero-point energies are well above the central barrier to yield delocalized wave functions, and hence the vibrationally averaged (gas-phase) geometries in effect correspond to “bridged” structures. In contrast with the observed trends in the gas-phase thermodynamic stabilities, the solvation energies, displayed in Table 2, are such that they tend to reverse this trend. In the case of the acids the meta and para isomers (2, 3) have larger (in the absolute sense) solvation energies than the ortho form (1); that is, the latter is less efficiently solvated. Similarly, the
calculated solvation energies for o-hydroxybenzoate (5, 6, 7) are uniformly smaller in magnitude than those for the hydroxy forms of the meta and para isomers. This is readily understood by noting that the intramolecular H-bond in the ortho forms effectively reduces the number of sites to which water as solvent could hydrogen-bond or, in terms of the continuum model, that a smaller surface area is presented to the solvent than in the meta or para forms, thereby reducing the solute-solvent interactions. Thus, as may be expected, the solvation energies of the ortho rotomers 1a and 5a, where no intramolecular H-bond is possible, are comparable with those calculated for the meta and para isomers. It is also interesting to note that while a lower solvation energy is computed for benzoic acid than for the m- and p-hydroxybenzoic acids, as may be expected, given the presence of a hydrophilic OH group in the latter, in the case of the anions their solvation energies are quite similar. The two different models of solvation used yield quite different results in that the PCM solvation energies are uniformly larger (in magnitude) than those obtained by the SCIPCM method. However the trends are qualitatively the same, irrespective of the solvation model used. The trends noted above are more obvious if the energetics are examined in a relative sense. Table 3 contains such relative energies, showing clearly the effects of basis set expansion, zeropoint and thermal corrections, and solvation. Thus, in the case of the acids, despite the higher stability of the ortho form, the final free energies (that include solvation) are effectively the same. These results are also shown in Figure 4, where the relative importance of electronic and solvation energetics can be clearly seen. The analogous results for the anions, in Table 3 and Figure 5, show a qualitatively similar trend, with an important difference: the ortho forms of the anion that possess an intramolecular H-bond are so much more stable at the electronic level that despite the lower solvation energy, the o-hydroxybenzoate anion is predicted to be significantly more stable in solution (as well as in the gas phase) than the meta and para isomers. (Note that in some cases the electronic energy of a given anion and its free energy in solution at 298 K are accidentally almost the same.) The relative stabilities are dependent on the solvation model used, but at a qualitative level the SCIPCM and PCM predictions are in good agreement.
1942 J. Phys. Chem. B, Vol. 102, No. 11, 1998
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TABLE 3: Relative Energiesa,b (in kcal/mol) of (Hydroxy) Benzoic Acids, Acetic Acid, and Their Anions at 0 and 298.15 K in Gaseous and Aqueous Phases
o-hydroxybenzoic acid o-hydroxybenzoic acid m-hydroxybenzoic acid p-hydroxybenzoic acid o-hydroxybenzoate bridged o-hydroxybenzoate (acid) o-hydroxybenzoate m-hydroxybenzoate m-hydroxybenzoate (acid) m-hydroxybenzoate (acid) p-hydroxybenzoate p-hydroxybenzoate (acid) p-hydroxybenzoate (acid) benzoic acid benzoate acetic acid acetate
(1) (1a) (2) (3) (5) (6) (7) (5a) (8) (9) (9a) (10) (11) (11a) (4) (12)
Eelec
∆Eelec
G°0(g)
G°298(g)
G°298(aq) (SCIPCM)
G°298(aq) (SCIPCM) (ext)c
0.0 10.9 5.5 5.4 0.0 0.5 0.1 28.3 17.4 21.1 22.1 19.7 13.9 18.0 0.0 0.0 0.0 0.0
-202.9
81.8 92.0 86.6 86.6 72.4 70.8 72.5 100.0 89.4 93.0 93.7 91.6 86.1 89.7 78.1 68.9 41.9 32.5
61.4 70.7 65.8 65.9 52.2 51.6 52.4 80.1 68.7 72.2 73.8 71.0 65.6 69.7 58.2 49.5 25.0 15.0
54.6 59.1 56.2 55.8 -0.3 0.5 2.5 15.6 10.2 18.8 22.6 10.2 15.2 18.2 51.7 -8.4 18.7 -48.3
-148.3
48.9
-154.0
-147.1 -147.6 -217.7 -217.0 -214.7
48.7 48.5 -25.1 -22.9 -20.1
-154.6 -154.9 -242.5 -240.4 -237.3
-208.6
-17.8
-236.6
-208.7
-16.7
-235.6
-112.5 -188.2 -73.5 -158.3
46.1 -36.6 12.5 -71.8
-118.1 -216.4 -79.6 -181.9
-203.3 -203.4 -217.4 -217.5 -217.2 -218.8 -218.9 -164.2 -179.8 -92.1 -110.1
G°298(aq) (PCM)
G°298(aq) (PCM) (ext)c
a Energies of hydroxybenzoic acids and hydroxybenzoates relative to respective ortho isomers (1) and (5). b Using 6-31G(d,p) basis (except where indicated otherwise). c Based on MP2/6-311+G(2d,p) electronic energies.
Figure 4. Relative free energies of hydroxybenzoic acids (using SCIPCM solvation model).
(Since the acid forms of the meta and para anions appear to be considerably less stable in solution than the parent molecules, their energies were not computed at the MP2/6-311+G(2d,p) level.) The use of a dielectric continuum method for the calculation of solvation energies is undoubtedly the weakest point in our study, especially in the case of the anions. The simplest improvement in the treatment of solvation would be to include a small number of water molecules, ∼6-8, in the quantum chemical calculations, so that at least the strongest H-bonds to the carboxylic and hydroxy oxygens would be described on the molecular level, while the long-range effects of solvation could be modeled by immersing the resulting cluster in a dielectric continuum. Such hybrid techniques have been found to be quite successful in modeling the solvation of both H+ 20 and OH-.21 Acidity Constants. From the data in Tables 2 and 3 the free energy changes associated with the dissociation (ionization) of the (hydroxy) benzoic acids, in the gas phase and in aqueous solution, as well as their pKa’s were computed. The results are
Figure 5. Relative free energies of hydroxybenzoates (using SCIPCM solvation model).
summarized in Table 4, where the computed pKa’s are also compared with the experimental values,22 and in Figure 6. In the gas phase the free energies of ionization for m- and p-hydroxybenzoic acids, as well as benzoic acid itself, appear to be within ∼2 kcal/mol of each other, but ∼12 kcal/mol higher than for the ortho isomer. This pattern is effectively preserved when solvation is allowed for, but the difference between the ortho isomer and the rest is reduced to ∼6-8 kcal/mol, the actual value depending on the solvation model used. The trend in the predicted pKa’s agrees with experiment in a very qualitative sense, but as the results show, the discrepancies in the absolute values are rather large, up to 10 pKa units. The SCIPCM and PCM pKa’s (in conjunction with the extended basis results) actually appear to bracket the experimental values. The variation in computed pKa’s among benzoic acid and its hydroxy-substituted forms is also significantly larger than observed, although salicylic acid is predicted to have the lowest pKa, in qualitative agreement with experiment.
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J. Phys. Chem. B, Vol. 102, No. 11, 1998 1943
TABLE 4: Free Energies of Dissociationa (in kcal/mol) and pKa’s of (Hydroxy) Benzoic Acids and Acetic Acid
∆G°298(g) o-hydroxy benzoic acidd m-hydroxy benzoic acidf p-hydroxy benzoic acid benzoic acid acetic acid
∆G°298(g) ∆G°298(aq)c (ext)b (SCIPCM)
∆G°298(aq)c (SCIPCM) (ext)b
pKa(calc) (SCIPCM)
pKa(calc) (SCIPCM) (ext)b
∆G°298(aq)c (PCM)
∆G°298(aq)c (PCM) pKa(calc) (ext)b (PCM)
pKa(calc) (PCM) (ext)b
pKa (ext)e
329.8
315.2
25.2
10.7
18.47
7.86
6.1
-8.4
4.50
-6.13
2.97
339.4
327.0
34.0
18.5
24.91
13.55
13.5
-2.0
9.93
-1.44
4.06
344.6
329.1
34.5
19.0
25.26
13.88
14.8
-0.7
10.88
-0.48
4.48
344.5 353.6
328.9 335.6
33.7 37.2
18.0 19.2
24.65 27.25
13.17 14.09
11.0 19.8
-4.6 1.8
8.09 14.51
-3.34 1.31
4.19 4.75
a Using 6-31G(d,p) basis (except where indicated otherwise). b Based on MP2/6-311+G(2d,p) electronic energies. c Using experimental proton solvation energy of -259.5 kcal/mol (ref 12). d Lowest energy salicylate structure used; i.e. bridged structure in gas phase, hydroxy structure in aqueous phase. e Experimental values from ref 22 (o-, m- and p-hydroxybenzoic acid pKa’s at 292.15 K). f Using most stable form of anion in each phase.
continuum theories. Free energy perturbation theory,26,27 employing good quality potentials for solute/solvent and solvent/ solvent interactions, appears to hold much promise for such problems, as demonstrated for example in the recent work of Balbuena et al.28 An alternative approach to the calculation of pKa’s, which eliminates the need to explicitly consider the solvation of H+, is to make use of a suitable isodesmic type reaction,
HA + B- h HB + A-
(4)
Using the computed equilibrium constant KAB of this reaction and the experimental pKa of HB, the pKa of A is then simply
pKa(HA) ) pKa(HB) - log KAB
Figure 6. Dissociation energies of hydroxybenzoic, benzoic, and acetic acids (using SCIPCM solvation model).
As a test of the computational methodology used in this work, we also carried out an analogous series of calculations for acetic acid and the acetate anion, since in the case of this smaller system it is possible to carry out higher level ab initio calculations than for hydroxybenzoic acids and their anions. The results are summarized in Tables 2, 3, and 4. We note that our computed (extended basis) energy change of the ionization reaction in the gas phase at 0 K, viz., 343.0 kcal/mol, compares well with the value of 345.7 kcal/mol, computed using Gaussian-2 theory,23 as well as with the experimental value24 of 347.3 ( 3.0 kcal/mol. The computed SCIPCM solvation energy of acetic acid, -6.4 kcal/mol, is in good agreement with the experimental value of -6.7 kcal/mol; however, for the anion the discrepancy between SCIPCM and experiment25 is ∼12 kcal/ mol. It appears that PCM tends to overestimate the solvation energies by nearly as much, in the case of acetate, as SCIPCM underestimates it. Consequently, depending on the solvation model, our computed pKa’s for acetic acid bracket the experimental value by fairly large margins. Interestingly, if we use the experimental solvation energies in conjunction with our computed free energy changes at 298 K, we obtain a pKa of 5.3 for acetic acid, which agrees reasonably well with the experimental value of 4.76. Clearly, the quantitative prediction of acidity constants requires a more sophisticated treatment of ion solvation than currently possible by simple dielectric
(5)
The potential accuracy of this scheme also relies on the partial cancellation of errors in the computed solvation energies of the species on the two sides of eq 4. Choosing benzoic acid as HB and the PCM model of solvation, the resulting pKa’s of o-, m-, and p-hydroxybenzoic acids are computed as 1.40, 6.09, and 7.05, respectively. In an absolute sense these are clearly in much closer agreement with the experimental pKa’s than those quoted in Table 4, but of course the relative pKa’s are unchanged. Although not quantitative, our results provide an explanation for the high acidity of o-hydroxybenzoic acid. According to our calculations, the dissociation energy of this acid in the gas phase is significantly lower than for the other acids; this is a direct consequence of the intramolecular H-bond in the ortho anion that confers a high degree of electronic stability on this ion. Solvation has a very large effect on the computed dissociation energies, but without altering their gas-phase ordering. As a result, the pKa differences between the acids reflect primarily the differences in electronic stabilities rather than trends in the solvation energies. Behavior of Anions as Counterions. In the study by Thalody and Warr7 the binding strength of the anions to surfactant surfaces at the air/solution interface was found to decrease in the order o-hydroxybenzoate > m-hydroxybenzoate > benzoate > p-hydroxybenzoate and noted that this is the same as the order for the acidities of the conjugate acids. Since the binding of counterions such as these is driven by their hydrophobicity, it was thought that the apparently anomalous binding strength of the ortho anion might be associated with the presence of an intramolecular hydrogen bond (which is absent from the other anions). Our results demonstrate that a strong hydrogen bond is indeed present in salicylate and confers a high degree of (electronic) stability to this ion, but which, at
1944 J. Phys. Chem. B, Vol. 102, No. 11, 1998 the same time, is responsible for its low solvation energy, this being the smallest among all the anions studied (not considering the thermodynamically unstable acid forms of the meta and para isomers), by ∼8-10 kcal/mol. Salicylate is therefore the least hydrophilic of the anions, which concurs with its observed position in the sequence of binding strengths to the air/solution interface, as discussed in the Introduction. On the basis of the calculated solvation energies, benzoate would precede mhydroxybenzoate in the order above. However, hydrophobicity is but one (albeit important) factor determining binding strength, and benzoate and m- and p-hydroxybenzoate have solvation energies within a few kcal/mol of each other, thus rendering it difficult to obtain the exact order for these three species by comparing solvation energies alone. Since the solvation energy of salicylate is considerably less than that of the others, it may be safely concluded that this anion would exhibit the strongest binding of all. The high acidity of salicylic acid is due to the high electronic stability of the anion, which, of course, is a manifestation of the strong intramolecular hydrogen bond. This stability is so great that it overcomes the countereffect of the (relatively) low anion solvation energy so that salicylic acid has the smallest free energy of dissociation in solution. With regard to the other three (hydroxy) benzoic acids, the electronic components in their dissociation energies are much larger (since the anions are not stabilized by an internal H-bond) so that even though these anions are better solvated than salicylate, the net effect is that in solution the dissociation of these acids is associated with larger (positive) ∆G° values. When present, the intramolecular hydrogen bond has a complementary effect on the electronic stability and the solvation energy (for the species studied). The binding strength of the anions (to surfactants) depends on their solvation free energies and not on the dissociation energy of the parent acid, i.e., its pKa. Consequently, the apparent correlation between the binding strengths of these counterions and the pKa’s of their conjugate acids is coincidental. Conclusion The quantum chemical calculations performed on the most stable conformations of benzoic and o-, m-, and p-hydroxybenzoic acids and their anions demonstrate that strong intramolecular hydrogen bonds exist in o-hydroxybenzoic acid and its anion (structures 1, 5, 6, and 7). This hydrogen bond is especially strong in the anion, so that its structure is best described as a “bridged” one whereby the hydroxy proton is found midway between the hydroxy and carboxyl oxygens. This point corresponds to a transition state on the electronic potential energy surface but to a minimum once the zero-point energy is taken into account. The presence of this H-bond results in a substantially lower energy for these species in comparison with other conformers/isomers (without such a H-bond). With respect to the solvation of the acids and their anions it was found that the ortho isomers (with intramolecular H-bonds) had significantly smaller (less negative) solvation energies than the other isomers and that in fact o-hydroxybenzoate has a lower solvation energy than benzoate; this, despite the extra hydrophilic hydroxy group in the former. This is rationalized by noting that the geometric structure of salicylate is such that the surrounding solvent is partially excluded and is unable to interact with the hydroxy and carboxyl groups to as great an extent as
Shapley et al. it otherwise would, as in the other isomers. Alternatively, in terms of a discrete solvation model, the strong intramolecular H-bond reduces the interaction of salicylate with the solvent molecules and partially blocks certain solute/solvent interactions. Since the ability of counterions such as salicylate to bind to surfactant surfaces correlates with their hydrophobicity, the seemingly unusual behavior of salicylate is simply a reflection of its high hydrophobicity. The computed pKa’s of the acids are found to exhibit the correct qualitative trend, although quantitative agreement with experiment is certainly not achieved. The relatively low pKa of salicylic acid that was computed (in agreement with experiment) is attributable to the greater electronic stability of the salicylate anion, despite its low solvation energy, when compared with the benzoate or m- or p-hydroxybenzoate anions. The apparent correlation between pKa’s of the acids and binding strengths of the anions is thus seen as accidental. Acknowledgment. The award of a Sydney University Postgraduate Scholarship to W.A.S. is gratefully acknowledged. References and Notes (1) Rehage, H.; Hoffmann, H. Faraday Discuss. Chem. Soc. 1983, 76, 363. (2) Quirion, F.; Magid, L. J. J. Phys. Chem. 1986, 90, 5435. (3) Carver, M.; Smith, T. L.; Gee, J. C.; Delishere, A.; Caponetti, E.; Magid, L. J. Langmuir 1996, 12, 691. (4) Soltero, J. F. A.; Puig, J. E.; Manero, O. Langmuir 1996, 12, 2654. (5) Underwood, A. L.; Anacker, E. W. J. Phys. Chem. 1984, 88, 2390. (6) Ulmius, J.; Wennerstro¨m, H.; Johansson, B.-A.; Lindblom, G.; Gravsholt, S. J. Phys. Chem. 1979, 83, 2232. (7) Thalody, B. P.; Warr, G. G. J. Colloid Interface Sci. 1995, 175, 297. (8) Bachofer, S. J.; Turbitt, R. M. J. Colloid Interface Sci. 1990, 135, 325. (9) Nemoto, N.; Kuwahara, M. Langmuir 1983, 9, 419. (10) Shikata, T.; Hirata, H.; Kotaka, T. Langmuir 1988, 4, 354. (11) Cassidy, M. A.; Warr, G. G. J. Phys. Chem. 1996, 100, 3237. (12) Lim, C.; Bashford, D.; Karplus, M. J. Phys. Chem. 1991, 95, 5610. (13) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; HeadGordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 94 (Revision B.3); Gaussian, Inc.: Pittsburgh, PA, 1995. (14) Lide, D. R., Ed. Handbook of Chemistry and Physics, 72nd ed.; CRC Press: Boca Raton, FL, 1991; Section 6. (15) Miertus, S.; Tomasi, J. Chem. Phys. 1982, 65, 239. (16) Miertus, S.; Scrocco, E.; Tomasi, J. Chem. Phys. 1981, 55, 117. (17) Stefanovich, E.; Truong, T. Chem. Phys. Lett. 1995, 244, 65. (18) Nordholm, S.; Bacskay, G. Chem. Phys. Lett. 1976, 42, 253. (19) Nagy, P.; Dunn, W., III; Alagona, G.; Ghio, C. J. Phys. Chem. 1993, 97, 4628. (20) Tun˜on, I.; Silla, E.; Bertra´n, J. J. Phys. Chem. 1993, 97, 5547. (21) Grimm, A. R.; Bacskay, G. B.; Haymet, A. D. J. Mol. Phys. 1995, 86, 369. (22) Lide, D. R., Ed. Handbook of Chemistry and Physics, 72nd ed.; CRC Press: Boca Raton, FL, 1991; Section 8. (23) Curtiss, L.; Raghavachari, K.; Trucks, G.; Pople, J. J. Chem. Phys. 1991, 94, 7221. (24) Ochterski, J.; Petersson, G.; Wiberg, K. J. Am. Chem. Soc. 1995, 117, 11299 and references therein. (25) Pearson, R. J. Am. Chem. Soc. 1986, 108, 6109. (26) Brooks, C. L., III In Theoretical Models of Chemical Bonding Vol. 4: Theoretical Treatment of Large Molecules and their Interactions; Maksic, Z. B., Ed.; Springer-Verlag: Berlin, 1991; p 51. (27) Jorgensen, W. L.; Buckner, J. K. J. Phys. Chem. 1987, 91, 6083 and references therein. (28) Balbuena, P. B.; Johnston, K. P.; Rossky, P. J. J. Phys. Chem. 1996, 100, 2716.
