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Theoretical Prediction of pKa Values of Seleninic, Selenenic, Sulfinic, and Carboxylic Acids by Quantum-Chemical Methods S. Tahir Ali,† Sajjad Karamat,†,| Juraj Ko´nˇa,‡ and Walter M. F. Fabian*,† Institut fu¨r Chemie, Karl Franzens UniVersita¨t Graz, Heinrichstrasse 28, A-8010 Graz, Austria, and Institute of Chemistry, Center for Glycomics, SloVak Academy of Sciences, 845 38 BratislaVa, SloVak Republic ReceiVed: March 12, 2010; ReVised Manuscript ReceiVed: October 9, 2010
Aqueous acid dissociation constants of substituted areneseleninic, areneselenenic, arenesulfinic, and benzoic acids are calculated by ab initio (MP2) and DFT (B3LYP) methods in combination with bulk solvation models (IEFPCM, CRSrad) from appropriate thermodynamic cycles. Mean absolute deviations (MAD) between experimental and calculated pKa values are quite large for basis sets without diffuse functions; however, trends are reasonably well described. Best agreement with experiment as described by MAD as well as correlation coefficient and slope of the correlation equation pKa ) a*∆Gcalc/RT ln(10) + b is obtained with the CPCM solvation model using the defaults optimized within COSMO-RS (CRSrad; MAD ) 1.54, R2 ) 0.94, a ) 0.83). Sulfenic (selenenic) acid tautomers are significantly more stable than the corresponding sulfoxide (selenoxide) forms. SCHEME 1
Introduction Areneseleninic acids, ArSeO2H, are moderately strong oxidants that can be reduced to diselenides by a number of reagents.1–3 Consequently, they have found widespread application as catalysts in oxidation reactions including bromination,4 especially with hydrogen peroxide.5,6 Most importantly, the antioxidant activity of selenium compounds is exploited for the protection of cells against oxidative stress,7 especially as glutathione peroxidase (GPx) mimics, e.g., the anti-inflammatory compound ebselen.8,9 Seleninic acids had been assumed not to be directly involved in the catalytic cycle but rather be formed by overoxidation and, thus, disrupting the main catalytic pathway.10 However, recently a revised mechanism for the GPxlike activity of ebselen, involving reversible cyclizations to seleninic and selenenic acids has been proposed, indicating a seleninic acid as the only stable and isolable product in the oxidation of ebselen by peroxides.11 Moreover, seleninic acids are considered the “storage” form of chemically modified enzymes, e.g., selenosubtilisin (a peroxidase transformed protease).12,13 The kinetics and mechanism of the redox reaction of seleninic acids with thiols, used as the model system for the glutathione peroxidase catalytic cycle, strongly depend on the pH and, thus, on the ionization state of the involved organoselenium species, seleninic and selenenic acids, selenol, and thiol/ thiolate.3 With few exceptions,14,15 modeling studies on GPxlike activities of organoselenium compounds have been done on the neutral undissociated species;10,11,16–18 in some cases solvent-assisted proton exchange has been taken into account.16,19 Experimentally, selenolate rather than selenol (pKa(selenocysteine) ) 5.2 compared with pKa (cysteine) ) 8.3) has been suggested as the actual species.20 Seleninic acids are also weak acids21,22 with pKa values comparable to those of benzoic acids;23 in contrast, selenenic acids are considerably less acidic, pKa ) * To whom all correspondence should be addressed. Tel: +43-316-3808636. Fax: +43-316-380-9840. E-mail:
[email protected]. † Karl Franzens Universita¨t Graz. E-mail: S.T.A., ali.syed-tahir@ edu.unigraz.at. ‡ Slovak Academy of Sciences. E-mail: J.K.,
[email protected]. | Deceased July 16, 2008.
10-11.24 Consequently, proper treatment of the ionization state of those species, i.e., estimation of their pKa values, is essential in modeling GPx-like activity of organoselenium compounds.17b Here we present a computational approach to calculate the pKa values of a series of meta- and para-substituted benzene seleninic, selenenic, and sulfinic acids by ab initio and density functional methods. Literature data for the latter compounds differ quite significantly.25–28 We show that computed pKa values might be used to resolve such discrepancies. Finally, comparison will also be made to similarly substituted benzoic acids.23,29b–d The data set, thus, contains acids derived from first, second, and third row elements, spanning a pKa range from ∼1 to ∼12. Conceptual density functional theory30 is used to rationalize the difference in acidity between areneseleninic and arenesulfinic acids compared with areneselenenic acids. Computational Details. Ab initio calculations of pKa values usually employ some thermodynamic cycle.31–34 Here we apply the following cycle (Scheme 1 and eqs 1 and 2).31
pKa ) ∆G/2.303RT
(1)
∆G ) ∆Ggas + ∆Gsolv(A-) + ∆Gsolv(H+) - ∆Gsolv(HA) (2) The Gibbs free energy of the gas phase proton was taken from the Sackur-Tetrode equation as Ggas(H+) ) -6.28 kcal mol-1;35 for the Gibbs free energy of hydration of the proton the
10.1021/jp102266v 2010 American Chemical Society Published on Web 11/05/2010
Seleninic, Selenenic, Sulfinic, and Carboxylic Acids
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SCHEME 2
Results and Discussion
experimental value,36 ∆Gsolv(H+) ) -264.0 kcal mol-1, was used. This value has also been suggested by Namazian et al.29a in their thorough study of the pKa value of trifluoroacetic acid. The usual correction term of 1.9 kcal mol-1 was applied for standard state conversion between 1 atm in gas phase and 1 mol L-1 in aqueous solution.31 In a variation of this approach, experimental data for both the gas phase acidity, ∆Ggas, and the aqueous solvation free energy ∆Gsolv(HA) of neutral molecules, have been used to obtain pKa values.32 Alternatively, an isodesmic reaction together with the experimental dissociation constant of acetic acid (pKa ) 4.76, ∆G1 ) 6.48 kcal mol-1) has also been used (Scheme 2 and eqs 3 and 4).29b
∆G2 ) ∆Ggas + ∆Gsolv(A-) + ∆Gsolv(CH3COOH) ∆Gsolv(HA) - ∆Gsolv(CH3COO-) pKa ) (∆G1 + ∆G2)/2.303RT
(3)
(4)
Ab initio (MP237) and density functional theory (B3LYP38,39) methods combined with the 6-31G(d,p),40 6-31+G(d,p)41 [for selenium this basis set corresponds to the Binning-Curtiss SVP basis42,43 augmented by a diffuse sp shell (R ) 0.03)], and augcc-pVDZ and aug-cc-pVTZ44 basis sets, are used for the calculation of ∆Ggas. In addition, calculations of seleninic and selenenic acids were also done with the Binning-Curtiss TZVP basis set42,43 for the selenium atom combined with the 6-31+G(d,p) basis set for C, H, and O.45 Zero point energy and thermal corrections to Gibbs free energies are unscaled. Aqueous solvation energies were obtained by single point calculations on gas phase geometries using bulk solvation models, IEFPCM,46 using UA0 as well as UFF radii, CPCM,47–49 and a CPCM variant using COSMO-RS radii50 (keyword COSMORS with the default settings of the Gaussian 03 program package51). To distinguish this procedure from “true” COSMORS calculations,52 in the following we will use the abbreviation CRSrad for this solvent model. Because of the lack of selenium parameters for the calculation of cavitation/dispersion/repulsion contributions, only the electrostatic component of the solvation energy was taken into account. To assess the effect of higherlevel correlation contributions to the gas phase acidity, a composite approach was applied
EC ) E(MP2/aug-cc-pVTZ) + E[CCSD(T)/6-31G(d)] E[MP2/6-31G(d)] + ∆Gtherm[MP2/aug-cc-pVDZ] (5) For selenium and bromine, the SDB-aug-cc-pVTZ53 and 6-311G(d) basis sets were used for the MP2 and CCSD(T) calculations, respectively. The coupled-cluster calculations54 were done with NWChem 5.1.1.55
Computational procedures for the proper treatment of organoselenium compounds have been evaluated previously.56,57 Bachrach and Jiang,56 using the Binning-Curtiss basis set for Se, have found little difference between HF, MP2, B3LYP, and B3PW91 geometries; Pearson et al.57 recommend for the prediction of geometries and energetics of organoselenium compounds use of the B3PW91 density functional38,58 and the 6-311G(2df,p)59,60 basis set. To test the reliability of our approaches, we commence with a comparison of the calculated structures of benzeneseleninic and -sulfinic acid [B3LYP/631+G(d,p), MP2/6-31+G(d,p)] with the corresponding X-ray data from a CSD61 search (PhSeO2H, BENSEA;62 PhSO2H, ZYYOH63). For PhSeO2H comparison is also made with B3LYP and B3PW91 calculations using the 6-311G(2df,p) and Binning-Curtiss TZVP basis sets. Pertinent structural parameters are presented in Table 1. In both acids the configuration at the selenium or sulfur atom is pyramidal62,63 as evidenced by the height h of these atoms above the C1sO8sO9 plane and the sum ΣR of the bond angles around X7 (Table 1). According to these geometric criteria the amount of the calculated pyramidalization equals that found experimentally. Agreement between experimental and calculated bond lengths and bond and torsional angles is also quite satisfactory with little difference between B3LYP, B3PW91, and MP2 results (this also holds for the MP2/ aug-cc-pVDZ geometry of PhSeO2H). Consistently, the calculated aryl-chalcogen and X7dO8 bond lengths are too long compared with the X-ray data; in contrast, the X7sO9 single bonds are too short, especially for the seleninic acid. It should be noted, however, that in the crystal, benzeneseleninic acid forms infinite chains that are held together by strong intermolecular hydrogen bonds,62 which might explain the deviation between experimental and calculated bond lengths. Irrespective of the computational procedure and basis set used, the mean absolute deviation of the bond lengths involving the Se or S atom is 0.05-0.06 (PhSeO2H) and 0.04-0.05 Å (PhSO2H). Calculated valence bond angles deviate by e3° from the X-ray data. The X7dO double bond is only slightly twisted out of the phenyl plane. Experimental pKa values of meta- and para-substituted benzeneseleninic acids (R ) CH3, CH3O, NO2, F, Cl, and Br)21,22 and those obtained by various computational models (B3LYP, MP2), basis sets, and solvation models (IEFPCM, CRSrad) are summarized in Table 2. From these data several points can be made: (i) Mean absolute deviations (MAD) between experimental and calculated pKa values are very large (>20 pKa units) for the 6-31G(d,p) basis set; thus diffuse functions are absolutely necessary for reasonable MADs. (ii) The CPCM variant of the polarizable continuum model virtually results in identical calculated pKa values as when IEFPCM is used (Table S1 of the Supporting Information). In contrast, substantially lower MADs are obtained with the CRSrad solvation model, especially when the Binning-Curtiss basis set is used for the selenium atom. Taking into account higher-level correlation contributions by a composite approach (eq 5, see above) does not significantly change the deviation between the experimental and calculated pKa values. (iii) The considerably more time-consuming MP2 procedure does not provide a substantial improvement over B3LYPcalculated pKa values. (iv) In contrast to mean absolute deviations (MAD), the experimentally observed trend of the effect of substituents on the acidity of benezeneseleninic acids is reasonably well reproduced by all computational ap-
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Ali et al. calculated17b and experimental pKa values24 of benzeneselenenic acids (unsubstituted parent acid and 4-R-2-nitro derivatives, R ) H, Cl, CH3, CH3O) is provided in Table S2 of the Supporting Information. Similar to the case for benzeneseleninic acids, MP2/aug-cc-pVTZ calculations or the composite energy approach do not lead to improved results (Table S2). A detailed investigation concerning computational procedure and basis set, including the effect of different optimized geometries on the calculated pKa value of trifluoroacetic acid, has been described earlier.29a The level of geometry optimization apparently had little effect. In Table S3 we present an analogous analysis on gas phase acidities and solvation energies. Gas phase acidities, -∆Ggas, obtained with the 6-31G(d,p) basis set (MP2 and B3LYP) are too low by up to 20 kcal mol-1 compared with those resulting when diffuse functions are added. Since Gibbs free energies of solvation, ∆Gsolv(HA) and ∆Gsolv(A-), show much less basis set dependence, pKa values calculated by MP2/6-31G(d,p) and B3LYP/6-31G(d,p) are considerably too high. B3LYP/ 6-31+G(d,p) calculations consistently result in larger values
SCHEME 3: Atomic Numbering of Benezeneseleninic Acid (X ) Se) and Benzenesulfinic Acid (X ) S)
proaches; see the correlation coefficient R2 of the respective correlation equation, eq 6 (Table 2)
pKa ) a*∆Gcalc /RT ln(10) + b
(6)
(v) Calculation of acid dissociation constants using eqs 3 and 4 slightly reduces the mean absolute deviation but otherwise has little influence. (vi) Completely analogous results with respect to the effect of the basis set as well as the solvation model are obtained for benzeneselenenic, benzenesulfinic, and benzoic acids. A comparison of
TABLE 1: Pertinent Experimental and Calculateda Geometrical Parameters of Benzeneseleninic (X ) Se) and Benzenesulfinic (X ) S) Acidb benzeneseleninic acid C1-X7 X7-O8 X7-O9 C1-X7-O8 C1-X7-O9 O8-X7-O9 C2-C1-X7-O9 C2-C1-X7-O8 h ΣR
benzenesulfinic acid
I
II
III
IV
V
MP2
X-ray62
I
MP2
X-ray63
1.945 1.648 1.841 102.2 96.9 106.2 73.8 -177.9 0.80 305.3
1.960 1.639 1.821 102.1 96.8 106.6 66.5 175.2 0.79 305.5
1.960 1.629 1.811 102.0 96.5 107.0 66.7 175.7 0.79 305.5
1.947 1.632 1.807 102.0 96.7 106.6 66.7 175.3 0.79 305.3
1.947 1.623 1.798 101.9 96.5 106.9 67.2 176.1 0.78 305.3
1.930 1.641 1.835 102.2 94.8 107.3 71.3 -179.8 0.80 305.3
1.903 1.706 1.763 99.1 98.6 103.7 -61.7 -167.2 0.82 304.4
1.827 1.496 1.688 104.9 97.5 109.8 61.6 174.5 0.68 312.2
1.805 1.497 1.686 104.8 96.1 110.5 56.2 169.3 0.68 311.4
1.802 1.506 1.575 103.1 101.0 108.4 50.4 162.5 0.66 311.5
a I: B3LYP/6-31+G(d,p). II: B3LYP with Binning-Curtiss TZVP for Se and 6-31+G(d,p) for C,H,O. III: B3LYP/6-311G(2df,p). IV: B3PW91 with Binning-Curtiss TZVP for Se and 6-31+G(d,p) for C,H,O. V: B3PW91/6-311G(2df,p), and MP2/6-31+G(d,p). b h: height of X7 above the C1-O8-O9 plane. ΣR: sum of angles around X7. Distances and h are in Å, angles and ΣR are in degrees; for atom numbering, see Scheme 3.
TABLE 2: Experimental and Calculateda pKa Values of Substituted Benzeneseleninic Acids (IEFPCM and CRSrad Solvation Models) 6-31G(d,p)
aug-cc-pVDZ
6-31+G(d,p)
aug-cc-pVTZ
R
exp21,22
B3LYP
MP2
B3LYP
MP2
B3LYPb
MP2
6-31+G(d,p) B3LYPc
B3LYPd
MP2e
ECe
H 4-CH3 3-CH3 4-CH3O 3-CH3O 4-NO2 3-NO2 4-F 3-F 4-Cl 3-Cl 4-Br 3-Br MAD R2 slope intercept
4.79 4.88 4.80 5.05 4.65 4.00 4.07 4.50 4.34 4.48 4.47 4.50 4.43
24.10 24.38 24.49 25.99 23.99 21.49 21.32 23.68 23.11 23.12 22.47 23.11 22.45 18.83 0.87 0.22 -0.70
23.76 24.04 24.00 24.91 23.59 21.91 21.35 23.27 22.73 22.95 22.43 22.82 22.33 18.55 0.78 0.24 -1.14
12.42 12.66 12.82 14.13 12.70 10.40 10.66 12.00 11.58 11.79 11.34 11.75 11.47 7.44 0.83 0.27 1.29
10.14 10.20 10.25 11.41 10.23 8.89 8.52 9.76 9.35 9.62 9.21 9.60 9.20 5.19 0.87 0.38 0.85
12.53 (10.89) 14.35 (11.80) 12.89 (10.29) 13.14 (10.64) 12.90 (10.33) 10.47 (7.85) 10.68 (8.08) 12.06 (9.46) 11.50 (8.86) 11.85 (9.23) 11.70 (9.00) 11.94 (9.32) 11.73 (9.04) 7.60 (5.06) 0.84 (0.86) 0.27 (0.25) 1.31 (2.16)
11.19 11.38 11.56 11.34 11.21 9.76 9.59 10.73 10.20 10.67 10.50 10.63 10.42 6.17 0.91 0.46 -0.44
8.68 (6.74) 9.63 (7.33) 8.18 (7.30) 8.62 (7.75) 7.96 (7.34) 6.17 (5.28) 6.38 (5.46) 7.56 (6.58) 6.94 (6.24) 7.28 (6.38) 7.07 (5.92) 7.32 (6.32) 7.03 (6.24) 3.07 (1.99) 0.85 (0.89) 0.28 (0.38) 2.38 (2.05)
5.78 6.36 6.33 6.79 6.38 4.32 4.49 5.61 5.28 5.42 4.96 5.35 5.28 1.03 0.89 0.38 2.42
5.65 (5.24) 5.80 (5.36) 5.87 (5.37) 7.74 (6.19) 5.99 (5.57) 4.75 (5.28) 4.35 (4.82) 5.62 (5.32) 5.21 (4.93) 5.37 (5.03) 4.99 (4.76) 5.36 (5.08) 4.96 (4.81) 1.01 (0.70) 0.73 (0.44) 0.31 (0.52) 2.80 (1.85)
7.16 (6.76) 7.36 (6.91) 7.32 (6.82) 9.24 (7.70) 7.30 (6.88) 6.13 (6.67) 6.10 (6.57) 7.15 (6.85) 6.66 (6.37) 6.94 (6.60) 6.57 (6.35) 6.97 (6.69) 6.59 (6.44) 3.19 (2.89) 0.74 (0.46) 0.33 (0.59) -2.21 (0.54)
a pKa calculated according to eqs 1 and 2. b Values in parentheses obtained with UFF radii. c CRSrad solvation model. Values in parentheses: Binning-Curtiss basis set for Se; 6-31+G(d,p) for other elements. d pKa calculated according to eqs 3 and 4; Binning-Curtiss basis set for Se; 6-31+G(d,p) for other elements. e MP2/aug-cc-pVDZ CRSrad solvation energies; pKa values in parentheses were obtained using B3LYP CRSrad solvation energies with the Binning-Curtiss basis set for Se and 6-31+G(d,p) for other elements.
Seleninic, Selenenic, Sulfinic, and Carboxylic Acids
Figure 1. Plot of MP2/aug-cc-pVTZ (squares) and B3LYP/631+G(d,p) (triangles) gas phase acidities vs those calculated by the composite energy approach. Open symbols indicate substituted benzeneselenenic acids.
of ∆Ggas (1-2 kcal mol-1) than MP2 in benzeneseleninic acids, Table S3. In contrast, for benzeneselenenic acids, MP2derived ∆Ggas values are higher by the same amount. MP2/ aug-cc-pVTZ//MP2/aug-cc-pVDZ single point calculations only slightly affect ∆Ggas, usually increasing it. This is even more the case with the composite energy approach EC (eq 5). For benzoic acids, B3LYP/6-31+G(d,p) gas phase acidities closely correspond to those derived from EC. Overall, the trend of B3LYP/6-31+G(d,p) gas phase acidities closely follows that resulting from the composite energy approach (Figure 1). Larger deviations are only found for substituted benzene selenenic acids (for the unsubstituted PheSeOH, ∆Ggas ) 344.0 (EC) and 343.2 kcal mol-1 [B3LYP/631+G(d,p)], Table S3, Supporting Information). Note that these are the only compounds in the whole series bearing an ortho substituent (NO2). Irrespective of basis set and computational procedure used, the CRSrad solvation model results in less stabilization of the acid [∆Gsolv(HA) less negative] and greater stabilization of the anion [∆Gsolv(A-) more negative] by aqueous solution than IEFPCM or CPCM. Hence, using CRSrad yields smaller pKa values than the two other solvent models. Actually, the big differences in pKa values between IEFPCM and CRSrad have little to do with
J. Phys. Chem. A, Vol. 114, No. 47, 2010 12473 the underlying solvation models themselves. Instead, they are mostly due to different radii used to construct the cavities. Considerably smaller MADs are obtained with IEFPCM when UFF is used instead of UA0 radii, 5.06, 4.92, 1.46, 2.55 vs 7.70, 6.92, 4.35, 5.38 for ArSeOOH, ArSeOH, ArSOOH, and ArCOOH, respectively, with B3LYP/6-31+G(d,p). Consequently, as a compromise between computational efficiency and reliability with respect to both mean absolute deviation and the correlation coefficient R2, in the following CRSrad/B3LYP/6-31+G(d,p) calculations will be used. However, one additional aspect needs to be discussed. The resulting slopes of the correlation eq 6 (Table 2) are significantly lower than the expected value a ) 1. Such discrepancies have been found previously.32,33,64,66 They have first been discussed in great detail by Klamt et al.66 and later also by Kelly et al.32 In particular, although implicit solvent models without considering explicit water molecules frequently can lead to quite good predictions of pKa values, the usually found small slopes apparently indicate some systematic errors. For the present molecules, these small slopes can be attributed at least partly to the limited spread of the pKa values within each individual series of compounds, benzeneseleninic acids, benzeneselenenic acids, benzenesulfinic acids, and benzoic acids (see below). Another possibility to increase the slopes consists in adding explicit solvent molecules. For instance, Adam33d successively has added water molecules to the anions of phenols and carboxylic acids to obtain slopes of ∼0.9. Along similar lines, Kelly et al.32 suggested to add a single water molecule to any anion with e3 atoms or those containing oxygen atoms with more negative partial atomic charges than in water (according to this heuristic approach, in contrast to Adam,33d no explicit water molecules were added to phenols by Kelly et al.32). Since among the present molecules, the oxygen atom in the conjugate bases of benzeneselenenic acids bear the most negative partial charge [q(B3LYP/6-31+G(d,p)) ) 0.65-0.71 compared with q ) 0.71 for the oxygen atom in H2O], one explicit water molecule was added to these anions. In line with our previous findings,17b no significant change in slopes (0.30-0.50) or MAD’s (∼8 for IEFPCM and ∼4 for CRSrad) was obtained (Table S4 in the Supporting Information). Available experimental pKa values of benzenesulfinic acids25–28 differ to some extent (Table 3). Essentially no correlation at all exists between the calculated pKa values [CRSrad B3LYP/631+G(d,p)] and those quoted in refs 25 and 27 (R2 ) 0, a ) 0, Table 3). The influence of the solvation model on calculated pKa values of benzenesulfinic acids using the composite energy gas phase acidities is provided in Table S5.
TABLE 3: Comparison of Experimental and Calculated pKa Values of Benzenesulfinic Acids
a
R
exp25
H 3-Cl 4-Cl 3-NO2 4-NO2 4-Br 4-OCH3 4-CH3 MAD R2 slope intercept
2.76 2.68 2.76 2.81 2.77 3.08 2.72 2.80 0.67 (1.27) 0.00 (0.01) -0.01 (-0.02) 2.86 (2.82)
exp26
exp27
exp28
1.45
1.84
1.21
1.15 0.55
1.81 1.88 1.86 1.89
0.48 0.64 1.09
1.99 0.70 (0.59) 0.11 (0.04) 0.03 (0.02) 1.81 (1.85)
1.24 1.41 (0.51) 0.91 (0.91) 0.44 (0.44) -0.09 (0.33)
1.09 1.70 1.55 1.52 (0.56) 0.94 (0.94) 0.55 (0.55) -0.28 (0.25)
calca 2.97 (2.00) 2.26 (1.29) 2.51 (1.55) 1.67 (0.70) 1.43 (0.46) 2.51 (1.55) 3.84 (2.88) 3.12 (2.15)
B3LYP/6-31+G(d,p); CRSrad solvation model; calculation of pKa according to eqs 1 and 2; values derived from eqs 3 and 4 in parentheses.
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TABLE 4: Comparison of Experimental and Calculateda pKa Values of Benzoic Acids this work R H 4-CH3 3-CH3 4-OCH3 3-OCH3 4-NO2 3-NO2 4-F 3-F 4-Cl 3-Cl 4-Br 3-Br MAD R2 slope intercept
23
exp
4.20 4.37 4.25 4.50 4.10 3.43 3.46 4.15 3.86 4.00 3.84 3.96 3.81
IEFPCM
b
10.07 (9.20) 10.42 (9.32) 9.95 (9.42) 10.83 (9.71) 9.93 (9.16) 7.56 (7.58) 7.72 (7.05) 9.66 (9.00) 8.99 (8.44) 9.35 (8.64) 8.91 (8.20) 9.42 (8.56) 8.99 (8.16) 5.38 (4.65) 0.97 (0.95) 0.33 (0.40) 0.90 (0.50)
CRSrad
previous work b
5.17 (4.46) 5.65 (4.69) 5.20 (4.83) 6.25 (5.25) 5.33 (4.71) 3.16 (3.27) 3.36 (2.75) 5.06 (4.56) 4.40 (4.01) 4.69 (4.10) 4.28 (3.69) 4.70 (3.97) 4.30 (3.59) 0.80 (0.34) 0.98 (0.92) 0.37 (0.44) 2.26 (2.18)
CRSrad
c
4.21 4.68 4.24 5.92 4.37 2.19 2.39 4.10 3.44 3.72 3.31 3.73 3.34 0.49 0.94 0.32 2.78
PCM
MP229c
B3LYPd
3.30 3.44
2.90 3.19
3.99 (3.49) 3.45 (4.25) (3.51)
3.63
3.67
3.38
3.50 3.65
3.13 2.72
3.06 (3.69) 3.72
0.54
0.94
0.45
MP3
3.65 3.53 4.34 4.68 3.14 3.53 2.68 3.37 3.82 2.96 3.47 2.94 2.94 0.59 0.35 0.33 2.85
29b
a B3LYP/6-31+G(d,p) results using eqs 1 and 2. b MP2/aug-cc-pVTZ results in parentheses. c CRSrad results using eqs 3 and 4. d Reference 29d. Values in parentheses form ref 33a.
pKa values of carboxylic acids, including several substituted benzoic acids, have been calculated previously by DFT (B3LYP)33a and perturbation theory procedures (MP2, MP3).29b–d Results obtained by these latter authors are included in Table 4. Surprisingly, these authors found considerably smaller differences between experimental23 and calculated pKa values of benzoic acids than we obtain when using the IEFPCM variant of the polarizable continuum model. Results obtained with the “original” Gaussian98-PCM combined with the thermodynamic cycle used here (eqs 1 and 2) are also presented in Table 4. Indeed, this solvation model results in a significantly lower MAD; however, the correlation coefficient is rather poor. Thus, despite the larger MAD the IEFPCM variant or, preferentially, CRSrad should be used. To the best of our knowledge, experimental gas phase acidities, ∆Ggas, are only available for benzoic acids.65 Previous DFT (B3LYP)33a calculations on the pKa values of a heterogeneous group of organic compounds, including some benzoic acids (R ) H, 4-CH3, 3-CH3, 4-Cl), have shown good agreement with B3LYP calculated and experimental ∆Ggas values. Our calculated [EC, MP2/aug-ccpVTZ, B3LYP/6-31+G(d,p)] gas phase acidities of benzoic acids are compared with the corresponding experimental values65 in Table 5. Agreement between experimental and calculated data is quite good, mean absolute deviation MAD ) 0.6 (EC), 2.9 (MP2/aug-cc-pVTZ), and 2.0 [B3LYP/6-31+G(d,p)]; R2 ) 0.996, 0.994, and 0.995 (Figure S1, Supporting Information). This indicates that ∆Ggas obtained from B3LYP/6-31+G(d,p) calculations should be sufficiently accurate. Irrespective of the computational procedure (basis set, solvation model, thermodynamic cycle) the slopes of the respective correlation equations (eq 4) are again quite small, a ) 0.3-0.4 (Table 4). Moreover, using MP2/aug-cc-pVTZ//MP2-aug-cc-pVDZ gas phase acidities and solvation energies, does not improve the results, Table 4. A more detailed statistical analysis using different methods, basis sets, and solvation models, as well as calculated pKa values of benzoic acids is provided in Table S6 (Supporting Information). Some representative MADs, correlation coefficients, and slopes: 0.80, 0.98, 0.37 [B3LYP/6-31+G(d,p)]; 0.34, 0.92, 0.44 (MP2/aug-cc-pVTZ); and 1.93, 0.98, 0.49 (EC, MP2/aug-ccpVTZ solvation energies). A possible reason for these low values of the slopes is the small spread of pKa values within each series of compounds.
TABLE 5: Comparison of Experimentala and Calculated Gas Phase Acidities of Benzoic Acids R
exp
EC
H 4-Me 3-Me 4-MeO 3-MeO 4-NO2 3-NO2 4-F 3-F 4-Cl 3-Cl
333.0 334.0 333.6 333.8 332.4 321.1 322.0 330.0 329.1 328.5 328.2
332.2 333.1 332.9 333.6 331.5 321.4 322.0 329.4 328.4 327.9 327.4
MP2b aug-ccpVTZ B3LYPc 6-31+G(d,p) 329.8 (331.2) 330.6 (332.3) 330.7 331.3 329.4 319.1 (318.1) 319.3 327.0 326.1 325.4 (326.5) 324.8 (325.8)
331.2 (334.1) 332.5 (334.6) 331.6 (333.9) 333.2 330.7 318.1 319.6 328.1 326.9 326.5 (329.9) 325.8
a Experimental gas phas acidities from ref 65. b MP3 results of ref 29b in parentheses. c B3LYP/cc-pVQZ results of ref 33a in parentheses; a correction of -7.76 kcal mol-1 has been applied to convert to Gibbs free energies.
TABLE 6: Statistical Results for the Whole Set of Compounds Obtained by B3LYP/6-31+G(d,p) CRSrad Calculations (Binning-Curtiss Basis for Se)a MAD R2 slope intercept
I
II
III
IV
1.37 (0.94) 2.41 (1.52)b 0.92 (0.92) 0.96 (0.97)b 0.71 (0.71) 0.51 (0.49)b 0.55 (1.24) 1.25 (2.14)b
1.54 (0.81) 2.62 (1.23)b 0.94 (0.94) 0.97 (0.96)b 0.83 (0.82) 0.57 (0.56)b -0.45 (0.34) 0.53 (1.52)b
1.40 (0.81) 2.54 (1.35)b 0.94 (0.94) 0.98 (0.97)b 0.77 (0.77) 0.54 (0.53)b 0.05 (0.79) 0.83 (1.77)b
1.53 (0.81) 2.68 (1.23)b 0.94 (0.94) 0.96 (0.96)b 0.82 (0.82) 0.57 (0.56)b -0.40 (0.39) 0.48 (1.47)b
a Experimental pKa values of benzenesulfinic acids from ref 25 (I), ref 26 (II), ref 27 (III), and ref 28 (IV). Calculated pKa values are derived from eqs 1 and 2; those resulting from eqs 3 and 4 are given in parentheses. b EC gas phase acidities combined with B3LYP/6-31+G(d,p) CRSrad solvation energies (Binning-Curtiss basis for Se); MP2/aug-cc-pVTZ gas phase acidities combined with B3LYP/6-31+G(d,p) CRSrad solvation energies (Binning-Curtiss basis for Se) in parentheses.
Indeed, combining all investigated acids into one data set results in significantly larger slopes, a ) 0.7-0.8 (Table 6). For instance, using the experimental data for benzenesulfinic acids from ref 26, B3LYP/6-31+G(d,p) CRSrad calculations in
Seleninic, Selenenic, Sulfinic, and Carboxylic Acids
J. Phys. Chem. A, Vol. 114, No. 47, 2010 12475 TABLE 7: Gas Phase Acidities, ∆Ggas, Difference in Solvation Energies between Anions and Neutral Acids, ∆∆Gsolv, Global Hardness, η, and Electronic Chemical Potential, µa PhSeO2H PhSO2H PhSeOH PhSOH PhCO2H
∆Ggas
∆∆Gsolv
η
µ
332.12 325.16 342.23 338.10 331.22
-56.29 -57.12 -56.31 -56.93 -60.17
0.0991 (0.0725) 0.1034 (0.0665) 0.0813 (0.0511) 0.0886 (0.0514) 0.1034 (0.0800)
-0.1682 (0.0247) -0.1627 (0.0323) -0.1504 (0.0547) -0.1384 (0.0576) -0.1689 (0.0218)
∆Ggas and ∆∆Gsolv in kcal mol-1; η and µ in au; values for anions in parentheses. a
combination with eqs 1 and 2 result in the following correlation equation (Table 6, Figure 2):
observed variation of pKa values, PhSeOH > PhSOH > PhSeO2H > PhCO2H > PhSO2H. Conceptual density functional theory30 is a powerful approach to rationalize chemical reactivity, including gas phase acidity.71,72 Specifically, chemical hardness η and electronic chemical potential µ,73 defined by the difference between electron affinity A and ionization potential I, and the arithmetic mean of these two quantities, η ) 1/2(I - A) and µ ) -1/2(I + A) or η ) 1 /2(εLUMO - εHOMO), and µ ) 1/2(εLUMO + εHOMO), have been used as global reactivity descriptors for gas phase acidities of a variety of hydrides, e.g., CH4, NH3, H2O, HF, and HCl.71 In the resulting correlation equation for gas phase acidities,
pKa ) 0.83*∆Gcalc /RT ln(10) - 0.45
∆Ggas ) a + b*χ + c*η
Figure 2. Plot of experimental pKa values vs those calculated by eq 7: ArSeO2H (squares), ArSeOH (circles), ArSO2H (triangles), ArCO2H (diamonds).
(7)
CRSrad B3LYP/6-31+G(d,p) calculations result in a pKa ) 12.6 (eqs 1 and 2) and 11.6 (eqs 3 and 4) for benzenesulfenic acid C6H5SOH. Using the composite energy approach, eq 5, results in virtually the same acidity, pKa ) 12.41. Applying eq 7 to this “raw” pKa [or its equivalent for pKa values derived via eqs 3 and 4, pKa ) 0.82*pKa(calc) + 0.34] gives pKa ) 10.0 and pKa ) 9.9. These values deviate substantially from the experimental ones, although quite approximate, aqueous acid dissociation constant, pKa ) 5.67 However, the predicted pKa given by Chemical Abstracts, pKa ) 10.41 ( 0.53,68 is much closer to our values. Consequently, we propose that pKa ≈ 10.0 for benzenesulfenic acid. In deriving this value, we have assumed the O-protonated form PheSOH of the sulfenic acid. MP2/6311+G(d,p) calculations69 on the sulfoxide/sulfenic acid tautomerism of a series of simple sulfenic acids R-SOH indicate that this latter tautomeric form is more stable by >10 kcal mol-1. Low-temperature infrared spectra of transient benzenesulfenic acid generated by flash vacuum pyrolysis indicate the possibility for coexistence between the two tautomeric forms, at least below -50 °C.70 With the composite energy approach, eq 5, at room temperature we obtain ∆G > 17 kcal mol-1 (gas phase) and ∆G > 14 kcal mol-1 (aqueous solution) in favor of the sulfenic acid. This preference is even more pronounced in the case of the benzeneselenenic acid a hydroseleninylbenzene tautomeric equilibrium, ∆G > 29 kcal mol-1 (gas phase) and ∆G > 23 kcal mol-1 (aqueous solution). Finally, an attempt to rationalize the quite differing pKa values of the investigated acids, ca. 4-5 (ArSeO2H), 1-3 (ArSO2H), 10-12 (ArSeOH), and 4 (ArCO2H), will be made. Gas phase acidities, ∆Ggas, and difference in solvation energies between anions and neutral acids, ∆∆Gsolv, for the unsubstituted parent acids are listed in Table 7. Except for benzoic acid, where ∆∆Gsolv is especially large, leading to smaller pKa values, this quantity shows only little variation. Thus, the difference in acidity will largely be determined by ∆Ggas, which follows the
(8)
group hardness η and group electronegativity χ ) -µ had opposite signs with η dominating. Using η of the neutrals and µ of the conjugate bases (Table 7), we obtain in line with these previous findings a ) 422.8, b ) 156.5, c ) -872.7; R2 ) 0.92. Thus, a higher electronic chemical potential µ (lower group electronegativity χ) of the anion (b > 0) as well as a higher hardness η of the acid (c < 0) indicates a greater acidity. Conclusions Aqueous dissociation constants (pKa values) for a series of benzeneseleninic, -selenenic, and -sulfinic acids as well as benzoic acids were calculated by ab initio (MP2) and DFT (B3LYP) methods using several basis sets [6-31G(d,p), 6-31+G(d,p), aug-cc-pVDZ] and solvation models (IEFPCM, CPCM, CRSrad). Two different thermodynamic cycles (Scheme 1 and eqs 1 and 2 vs Scheme 2 and eqs 3 and 4) were used. The latter one, based on the experimental pKa of acetic acid as reference, yields substantially smaller mean absolute deviations between experimental and calculated data, especially if the whole series of compounds is considered. MADs are very large for 6-31G(d,p) calculations; adding diffuse functions significantly improves the results. Moreover, the CRSrad solvation model generally yields much smaller MADs than those obtained with IEFPCM. The slopes of the correlation equation pKa ) a*∆Gcalc/RT ln(10) + b significantly deviate from the expected value, a ) 1, for each individual series of compounds. Despite the fact that about the same small slopes are found for each subset, the small spread of data within each of the four series of acids reduces its significance. Combining all compounds into one data set results in quite reasonable slopes, a g 0.8. For benzenesulfenic acid, pKa ≈ 10.0 is suggested. Calculated structural parameters of benzeneseleninic acid and benzenesulfinic acid agree well with X-ray data. With respect to the possible benzene sulfenic/selenic acid a sulfinyl (seleninyl)
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benzene tautomerism, PheSOH (PheSeOH) a PheSHdO (PheSeHdO), a strong preference for the O-protonated form is obtained. Acknowledgment. S.T.A. thanks the Higher Education Commission of Pakistan for the scholarship. J.K. acknowledges financial support from the Scientific Grant Agency of the Ministry of Education of Slovak Republic and Slovak Academy of Sciences, VEGA grant 2/0176/09. NWChem Version 5.1.1, as developed and distributed by Pacific Northwest National Laboratory, P.O. Box 999, Richland, WA 99352 U.S., and funded by the U.S. Department of Energy, was used to obtain some of these results. Supporting Information Available: CPCM results for benzeneseleninic acids (Table S1); experimental and calculated pKa values of areneselenenic acids without (Table S2) and with one water molecule added to anions (Table S4); gas phase acidities and solvation energies (Table S3); calculated pKa values of benzenesulfinic and benzoic acids including statistical analysis for different computational procedures (Tables S5 and S6). Plot of experimental vs calculated gas phase acidities of benzoic acids (Figure S1). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Rheinboldt, H.; Giesbrecht, E. Selenenic Acids. I. Preparation of Selenenic Acids by Reduction of Seleninic Acids with Hydrazine. Chem. Ber. 1955, 88, 666–678. (2) Ferranti, F.; De Filippo, D. Benzeneseleninic Acids. Kinetics of Reduction by Iodide Ion. J. Chem. Soc. B 1971, 1925–1927. (3) Kice, J. L.; Lee, T. W. S. Oxidation - Reduction Reactions of Organoselenium Compounds. 1. Mechanism of the Reaction between Seleninic Acids and Thiols. J. Am. Chem. Soc. 1978, 100, 5094–5102. (4) Drake, M. D.; Bateman, M. A.; Detty, M. R. Substituent Effects in Arylseleninic Acid-Catalyzed Bromination of Organic Substrates with Sodium Bromide and Hydrogen Peroxide. Organometallics 2003, 22, 4158– 4162. (5) (a) Reich, H. J.; Chow, F.; Peake, S. L. Seleninic Acids as Catalysts for Oxidations of Olefins and Sulfides using Hydrogen Peroxide. Synthesis 1978, 299–301. (b) Fragale, G.; Ha¨uptli, S.; Leuenberger, M.; Wirth, T. In Bioorganic Chemistry: Selenium Compounds in Chemical and Biochemical Oxidation Reactions; Diechrisen, U., Lindhorst, T. K., Westermann, B. Wessjohann, L. A., Eds.; Wiley VCH: Weinheim, Germany, 1998; pp 4852; (c) Wirth, T. Stereoselective Oxidation Reactions. Chimia 1999, 53, 230–231. (d) Freudendahl, D. M.; Shahzad, S. A.; Wirth, T. Recent Advances in Organoselenium Chemistry. Eur. J. Org. Chem. 2009, 1649– 1664. (6) Back, T. G. Benzeneseleninic Acid. e-EROS Encycl. Reagents Org. Synth. 2001, John Wiley & Sons, Ltd.: New York, NY, U.S., 2007; DOI: 10.1002/047084289X.rb016.pub2. (7) Sagher, D.; Brunell, D. J.; Weissbach, H. Metallothionein-based Protection against OxidatiVe Damage in Cells. WO 2007130575 A2 20071115. (8) Reich, H. J.; Jasperse, C. P. Organoselenium Chemistry. Redox Chemistry of Selenocysteine Model Systems. J. Am. Chem. Soc. 1987, 109, 5549–5551. (9) (a) Mugesh, G.; du Wont, W.-W.; Sies, H. Chemistry of Biologically Important Synthetic Organoselenium Compounds. Chem. ReV. 2001, 101, 2125–2180. (b) Sarma, B. K.; Mugesh, G. Glutathione Peroxidase (GPx)Like Antioxidant Activity of the Organoselenium Drug Ebselen: Unexpected Complications with Thiol Exchange Reactions. J. Am. Chem. Soc. 2005, 127, 11477–11485. (c) Mugesh, G.; Panda, A.; Singh, H. B.; Punekar, N. S.; Butcher, R. J. Glutathione Peroxidase-Like Antioxidant Activity of Diaryldiselenides: A Mechanistic Study. J. Am. Chem. Soc. 2001, 123, 839– 850. (d) Mugesh, G.; Singh, H. B. Synthetic Organoselenium Compounds as Antioxidants: Glutathioneperoxidase Activity. Chem. Soc. ReV. 2000, 29, 347–357. (10) Bhabak, K. P.; Mugesh, G. A Simple and Efficient Strategy to Enhance the Antioxidant Activities of Amino-Substituted Glutathione Peroxidase Mimics. Chem.sEur. J. 2008, 14, 8640–8651. (11) Sarma, B. K.; Mugesh, G. Antioxidant Activity of the AntiInflammatory Compound Ebselen: A Reversible Cyclization Pathway Via Selenenic and Seleninic Acid Intermediates. Chem.sEur. J. 2008, 14, 10603–10614.
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