A DFT study on the deprotonation antioxidant mechanistic step of ortho-substituted phenolic cation radicals

Chemical Physics 316 (2005) 195–204 www.elsevier.com/locate/chemphys

A DFT study on the deprotonation antioxidant mechanistic step of ortho-substituted phenolic cation radicals Anastasios P. Vafiadis, Evangelos G. Bakalbassis

*

Laboratory of Applied Quantum Chemistry, Department of Chemistry, Aristotle University of Thessaloniki, 541 24 Thessaloniki, Greece Received 25 March 2005; accepted 11 May 2005 Available online 28 June 2005

Abstract The conformers of the 2-, 3- and 4-substituted phenolic cation radicals, 2-X-, 3-X- and 4-X-ArOH
+, and the respective phenoxyl radicals, ArO
, the intramolecular hydrogen bond strength (DHintra) estimate along with the electronic effects of five electron withdrawing (EWG) and eight electron donating groups (EDG) on the gas-phase O–H proton dissociation enthalpies, (PDEs), of the short-lived, 2-X-ArOH
+, (involved in the single-electron transfer antioxidant mechanism), are studied at the DFT/B3LYP level of theory. EWG result to smaller PDEs, hence to stronger acidity; EDG to weaker acidity. The deprotonation antioxidant mechanistic step is not a rate-controlling step for 2-X-ArOH to scavenge free radicals. Approximate estimations of the DPDEs (hence acidities as well) can be derived from calculated structural and/or vibrational frequency values. DHintras correlate reasonably with geometrical parameters for the closed-shell, neutral counterparts, in contrast with previous estimates. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Density functional theory; Phenolic cation radicals; Proton dissociation enthalpy; Hydrogen bonding; Electronic effect; Antioxidant mechanism

1. Introduction Antioxidants (ArOH) intercept and react with free radicals, through two major mechanisms [1], namely, the H-atom transfer, (hereafter denoted as HAT) and the single-electron transfer (SET). Despite the two different intermediate reaction schemes involved, being RO
þ ArOH ! ROOH þ ArO
ð1Þ 2

and þ
RO2
þ ArOH ! RO
2 þ ArOH

ð2:1Þ

ArOHþ
! ArO
þ Hþ

ð2:2Þ

þ RO
2 þ H ! ROOH

ð2:3Þ

*

Corresponding author. Tel.: +30 2310 997695; fax: +30 2310 997738. E-mail address: [email protected] (E.G. Bakalbassis). 0301-0104/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2005.05.015

respectively, the net result is the same in both cases, namely, ð3Þ RO
2 þ ArOH ! ROOH þ ArO

where, RO and ROOH are a peroxy radical and a lipid 2

hydroperoxide, respectively. All these may also be rationalized by assuming the formation of a cationic intermediate as the initial step in the reaction, in contrast to a direct abstraction of a hydrogen (see Scheme 1). As a consequence, O–H bond dissociation enthalpy (BDE) of ArOH is the parameter determining to a certain extend the HAT, ionization potential (IP) along with the O–H proton dissociation enthalpy [1b], (PDE) of ArOH
+ determine SET [2]. To our knowledge, a few attempts have only been made to study the above transient species, ArOH
+, either experimentally [3] and/or theoretically [1b,1c]. In particular, the electronic effects on the PDEs of 3-Xand 4-X-ArOH
+ [1b] and that of catecholic cation radicals [1c] in the gas-phase have only been calculated.

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A.P. Vafiadis, E.G. Bakalbassis / Chemical Physics 316 (2005) 195–204

X

OH

- e(IP)

-H X

OH

(BDE)

- H+ (PDE) X

O

Scheme 1.

Neither the structure of the ArOH
+ and ArO
conformers nor those used in the determination of the PDEs were reported in these studies. More interestingly, possibly due to the intramolecular hydrogen bond (HB) formation in some of the 2-X-ArOH
+, these latter have not been studied so far. Hence, the goal of this study is fivefold, namely, the structural study of the conformers of the 2-X-, 3-Xand 4-X-ArOH
+ species and the respective phenoxyl radicals, ArO
, the intramolecular HB strength (DHintra, hereafter denoting either the intramolecular HB strength and/or the intramolecular HB enthalpy) estimate for the 2-X-ArOH
+ species, the electronic effects of a series of five electron withdrawing (EWG) (–NO2, –CF3, –CN, –CHO, –COOH) and eight electron donating (EDG) (–F, –Cl, –Br, – CH3, –OH, –OCH3, –NH2, –N(CH3)2) groups on the PDEs, the investigation of the deprotonation antioxidant mechanistic step for the 2-X-ArOH to scavenge free radicals, and the establishment of possible correlations between the calculated and experimental and/or theoretical molecular descriptors. In recent studies [4], we have examined the structure-activity relationships on phenolic antioxidants. Moreover, accurate gas-phase absolute and relative BDEs were determined for the 2-X- and 2,6-X-ArOH, using DFT/B3LYP [5]. Our simple theoretical methodology is applied herein on the gas-phase PDE calculation of a series of 2-substituted phenolic cation radicals, ArOH
+, in an attempt to check its general applicability.

2. Computational details Details on the systematic evaluation of the optimum basis set were given in a recent paper [5]. Hence, a few details of our methodology along with those needed to obtain the PDE, are only given here.

All calculations reported in the present study were carried out using the density functional theory [6], as implemented in the GAUSSIAN 98 program suite [7]. BeckeÕs 3-Parameter hybrid functional combined with the Lee–Yang–Parr correlation functional, abbreviated as B3LYP level of density functional theory [8], with the 6-31+G(,3pd) basis set [5], were used. UB3LYP was used for the geometry and vibrational frequency calculations of the ArOH
+, the phenoxyl radicals, and the H atom. B3LYP was used for the closed-shell, neutral counterparts and the proton. All possible conformers for the ArOH
+ and the respective ArO
were investigated in our calculations and are given as Supplementary data in Fig. S1. Consequently, a total of 126 structures were considered, involving only uncharged groups as 2-, 3- and 4-substituents, in which full geometry optimization was performed, with tight convergence criteria, on each species. In all computations no constrains were imposed on the geometry. All structures were true minima on the calculated potential surface, verified by final frequency calculations that provide energy minima with certainty. Alike BDE computation, PDE values are the algebraic sum of enthalpies (Eq. (4)). Hence, it seems reasonable to apply our simple theoretical methodology [5] on the gas-phase PDE calculation of a series of 2-X-, 3-Xand 4-X-ArOH
+. On the other hand, as it was shown in a recent paper [1c], the basis set dependence of O–H PDE is negligible. According to its definition [1c], O–H PDE is given by the equation, PDE ¼ H r þ H p
H c ;

ð4Þ

where, Hr is the enthalpy of the phenoxyl radical generated after proton dissociation, Hp is the enthalpy for proton, 0.00236 hartree, and Hc is the enthalpy of the phenolic cation radical. Since the relative PDE, (DPDE ¼ PDEArOH
þ
PDEPhOH
þ ) is determined by both the stabilization/ destabilization of the phenoxyl radical (SPR) and that of the phenolic cation radical effect (SPC), namely DPDE = SPR
SPC, [1b], nine isodesmic reactions (three for each one of the three possible substitution positions) should be constructed to characterize them, as demonstrated by the studies of electronic effects on DBDE [9]. In the present study a scale factor of 0.9610 for the theoretical harmonic vibrational frequencies was used [5]. However, for the reasons described in that paper, both ZPE and Hvib values were used unscaled. The intramolecular HB enthalpy, DHintra of the 2-substituted phenols, was derived [10] by comparing the DFT enthalpies at 298 K for the intra-HB conformer and the lowest-energy, fully-optimized conformer, in

A.P. Vafiadis, E.G. Bakalbassis / Chemical Physics 316 (2005) 195–204

197

which the hydroxyl group is pointing away from the substituent. For the non-HB 2-X-ArOH
+, Brown parameter rþ o value determination could be based upon the equation [11],

3. Results and discussion

þ rþ o ¼ 0.66rp

The gas-phase structures of both phenol and phenoxyl radical have been reported [5,14,15]. To the best of our knowledge, experimental and/or theoretical structural data has not been published for the ArOH
+ so far. Hence, selected, optimized structural parameters of the latter are compared to those of phenol and phenoxyl radical [5], in Table S2 (Supplementary data). An inspection of this data clearly shows that contrary to the parent phenol, that of its two radicals indicate a quinoid structure, evidenced by the significant lengthening of C1–C2, C3–C4, C4–C5 and C1–C6 bonds, compared to those of C2–C3 and C5–C6 (C1 is the ipso C atom). Another point to emerge from the same table is ˚ ) of the phenolic O–H bond a lengthening (ca. 0.01 A
+ length in ArOH , relative to that of phenol, followed ˚ ) of the C– by (i) a concomitant shortening (ca. 0.06 A O bond length and (ii) a significant increasing (ca. 4.8°), of the phenolic C–O–H bond angle in ArOH
+; C–O bond length is found to be intermediate between those of the phenol and the phenoxyl radical. Very good correlations were derived between R(O–H) and m(O–H), for the 2-X-, 3-X- and 4-X-ArOH
+. Corresponding data (for n = 14) are [m(O–H) =
12 732 R (O–H) + 15 989 with a correlation coefficient, r value of 0.9961 (r2 = 0.9922)], [m(O–H) =
12 399R(O–H) + 15666 with r = 0.9987 (r2 = 0.9974)] and [m(O–H) =
12 385R(O–H) + 15 653 with r = 0.9995 (r2 = 0.9990)], respectively, (see Figs. S2–S4). Hence, by applying the computational fast, geometry optimization procedure, the R(O–H) could be used as an universal molecular descriptor for the determination of the m(O–H) for a short-lived 2-X-, 3-X- and/or 4-X-ArOH
+ and viceversa.

ð5Þ

On the other hand, the rþ p is related to the field/inductive, F, and resonance component, R+, values for the 4substituents, by the relation [12a], þ rþ p ¼ F þR

ð6Þ

In order to check whether the methodology used for calculating the PDE is acceptable, correlation coefficients between the calculated relative PDEs and experimental [3b] pKa and/or lifetime (sexp) values [3a] are determined, because both pKa and the lifetimes (sexp) values for ArOH
+ relate to the calculated PDEs. Unlike the 4-X- and 3-X-ArOH
+, for which enough experimental pKa values exist, there are only four experimental pKa values for the 2-substituted ones [3b], affording a correlation coefficient, r value of 0.8335, between the experimental pKa values and the calculated relative PDEs. Nevertheless, our coefficient for the 3- and 4-substituted ones is identical with that of the literature [1b], (0.9777 compared to 0.9754). This is also the case with the correlation coefficients derived between the calculated relative PDEs and log(1/sexp), Brown parameter [12] rþ p , field/inductive, F, and/or resonance component, R+ parameter values for the 4-substituents [1b], (
0.8849,
0.9753,
0.6469 and
0.9385 compared to 0.8892, 0.9510, 0.6259 and 0.9095, respectively). Moreover, for comparison and uniformity reasons to our previous work [5], quite analogous to the DBDEs, relative PDEs, DPDEs value-differences are used throughout, leading to DPDEs bearing an opposite sign, in regard to those of the literature [1b]. The same holds true for the SPC and SPR values. The PDE value for the PhOH
+ was calculated to be 208.43 kcal/mol. The values of the spin operator hS2i for the 2-X-, 3-X- and 4-X-ArOH
+ range between 0.76 and 0.78, those of the respective ArO
between 0.77 and 0.79, (a full list of the hS2i values is summarized in the Supplementary data (Table S1)). Hence, they are all found to be very close to the expected value for a pure doublet wave function, 0.75. Moreover, since both the ArOH
+ and its respective ArO
are calculated at the same level of theory, they are not expected to introduce any systematic error in the PDEs. Hence, calculated PDEs should be accurate because our DFT calculations are both less affected by spin contamination, and fully consistent [13]. Consequently, the method and the calculated results in this study are acceptable and applicable in the following discussion.

3.1. Equilibrium geometries of the ArOH
+ and vibrational frequencies

3.2. Intramolecular hydrogen bonds and conformers As it will be discussed later in this and the next sections, most of the global energy conformers of the phenoxyl radicals, involved in the calculation of the PDE in the 2-X-ArOH
+, possess an intramolecular HB. In order to calculate only the electronic effect on the PDE this additional enthalpic contribution has to be removed. On the other hand, attempts have also been made [10] to correlate the intramolecular HB enthalpy, DHintra with structural parameters in the neutral counterparts of the 2-X-ArOH
+ under study. Hence, DHintra deserves to be studied as a prerequisite for a complete theoretical investigation. In Table 1 the HB enthalpy, DHintra of the hydrogenbonded 2-X-ArOH
+ are tabulated along with selected structural parameters of the corresponding conformers.

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A.P. Vafiadis, E.G. Bakalbassis / Chemical Physics 316 (2005) 195–204

Table 1 Hydrogen bond enthalpies, DHintra, selected calculated structural data, and O–H stretching frequencies of the optimized geometries of the 2-XArOH
+, and their corresponding closed-shell neutral counterparts 2-X-Phenola

H NO2(6)b CN(5) CF3(6) CHO(6) CO2H(6) Br(5) Cl(5) F(5) CH3(5) OCH3(5) OH(5) N(CH3)2(5) a b c d e f g

Phenolic cation radicalsb

Closed-shell neutral counterparts

DHintrac

R(O–H)d

R(OH  A)

\(C–O–H)e

m(O–H)f

DHintra

DHintrag

R(O–H)

R(OH  A)

\(C–O–H)

m(O–H)


12.5
1.1
3.3
11.4
14.8
1.0
1.7
2.7 1.1
3.2
3.0 6.6

0.9745 1.0232 0.9789 0.9818 1.0270 1.0266 0.9797 0.9791 0.9782 0.9737 0.9765 0.9769 0.9660

1.5780 2.4294 1.8831 1.5852 1.5774 2.5416 2.4783 2.2972 2.4751 2.1680 2.2002 2.4491

115.5 108.1 115.9 115.1 108.9 109.0 113.7 114.0 114.7 115.1 112.3 113.4 114.8

3584.0 2728.6 3510.3 3457.7 2642.0 2659.0 3474.9 3497.9 3532.9 3589.0 3545.8 3544.0 3683.7


12.0
2.1
2.5
8.0
11.7
3.5
3.5
3.7 0.4
5.8
5.1
3.7


11.9
2.6
2.4
9.2
11.4
3.9
3.0
3.0 0.5
4.4
4.1
4.8

0.9657 0.9882 0.9690 0.9680 0.9895 0.9859 0.9702 0.9694 0.9685 0.9651 0.9704 0.9692 0.9803

1.6918 2.4004 1.9744 1.7397 1.7493 2.5261 2.4623 2.2714 2.4365 2.1105 2.1742 2.0794

110.7 107.7 111.8 112.2 108.3 108.7 109.9 110.0 109.9 111.0 107.9 108.9 104.4

3690.1 3264.1 3640.1 3655.5 3235.8 3307.5 3607.1 3628.4 3656.2 3698.3 3624.3 3644.2 3442.5

The hydrogen bond accepting atom of the substituent is given in bold italics. (5) and (6) imply the five- and six-membered hydrogen-bonded rings, respectively. DHintra in kcal/mol. ˚. All bond lengths in A All bond angles in degrees. Vibrational frequencies in cm
1. From [10].

Since the correctness of the calculated DHintra value depends upon the conformational arrangement adopted by the away and toward cation radical conformers [10], DHintra values in the table refer to the lowest-energy conformer of the non-hydrogen-bonded species. For comparison, our calculated gas-phase corresponding data of the closed-shell, neutral counterparts along with literature data is also summarized. Table 1 shows that in both the neutral species and the ArOH
+, DHintras vary in the same way. Moreover, in the latter species, the relative strength of the intramolecular HB decreases relative to the former one, accounting that five-membered HB rings are formed, possibly due to the reduced electronic charge on the HB in the ArOH
+. Vedernikova et al. [16] reached similar results for the 2-OH-ArOH
+ and its neutral counterpart; still, the corresponding HB strength difference, DDHintra was calculated to be very close to ours (2.1 compared to 2.2 kcal/mol). It is worth mentioning here that the six-membered HB rings, in the ArOH
+, correspond to stronger HB than the five-membered ones, possibly due to less steric hindrances. Moreover, the former rings exhibit stronger HB in the ArOH
+ than in the neutral counterparts. In the case of the neutral, closed-shell molecules, upon the formation of the HB, the hydroxyl group \C–O–H bond angles, R(O–H), m(O–H), HB length, R(OH  A), and the DHintra values of the present study, vary in the same way as the literature values [12]. It should be stressed out that, despite the different basis set used in the two studies, both afforded very similar DHintras. Nevertheless, unlike the work by Korth et al.

[10] reasonable correlations are derived between the DHintra and the R(O–H), R(OH  A) and the m(O–H) values (r = 0.8491, 0.8185 and 0.8470, respectively), while that between DHintra and \C–O–H is very poor (r = 0.4493). It is also seen that all 2-groups in 2-X-ArOH
+, except 2-N(CH3)2, present higher R(O–H)s, lower m(O– H) values and higher \C–O–H values than their closed-shell, neutral counterparts. Moreover, as expected, the long R(O–H)s are followed by concomitant short R(OH  A)s in the six-membered HB rings. The correlations derived between the DHintra and the R(O– H), R(OH  A), m(O–H) and \C–O–H values appear better in the 2-X-ArOH
+, (r = 0.9438, 0.8940, 0.9317 and 0.8800, respectively) than in their neutral counterparts. For most of the 2-substituents studied viz. F, Cl, Br, CN, OH, CH3, OCH3, COOH and NO2, calculations show that the conformation in the HB form is retained in the lowest-energy non-HB form upon rotation of the phenolic OH group into the away position. This holds true for both the neutral and the cation radical conformers, because conformational changes are insignificant. The only exceptions are (i) the away conformer of the CHO substituent, in which there is a rotation of the group by 180°, with respect to the toward one, in both the 2-CHO-ArOH
+ and the 2-CHO-ArO
species, and (ii) the N(CH3)2 and CF3 groups, in which some distortions are observed (see also Scheme SI). The opposite sign derived for the DHintra, of the 2-N(CH3)2 substituent, is due to the away form lying lower in energy by ca. 6.6 kcal/mol than the toward one. For 2-NH2, to-

A.P. Vafiadis, E.G. Bakalbassis / Chemical Physics 316 (2005) 195–204

ward conformer in the ArOH
+ species, cannot be detected neither as a global nor as a local minimum, hence, a DHintra cannot be derived. Nevertheless, contrary to Korth et al. [10] who, in the case of the neutral counterpart, failed to calculate a DHintra (because, according to DFT, the non-HB conformer existed only as a rotational transition state), we reached a global minimum, affording a DHintra value of 1.7 kcal/mol. It is worth pointing out that, strictly speaking, the only possible conformation for a hydrogen bonding in the 2-CH3 substituent could be a ‘‘reverse’’ one between a H of the CH3 group and the phenolic O atom. However, in the neutral counterpart [10], DHintra refers to an enthalpic contribution not associated with the pure donor–acceptor HB interaction. In particular, the H atom of the hydroxyl group in this case is oriented either away or toward, relative to the two H atoms of the CH3 group. This is also the case with the cation counterpart studied herein, in which the away conformer is found more stable, by ca. 1.1 kcal/mol than the toward one, due to steric effects. 3.3. Proton dissociation enthalpies for 2-, 3- and 4-X-ArOH
+ Computed DPDEs to phenol, for the 2-X-ArOH
+ species have been computed and are summarized in Table 2, along with the DPDEs values for 3-X- and 4-XArOH
+, for comparison. In the 2-substitution, alike DHintra, PDE is calculated using the lowest-energy non-HB conformer for both the ArOH
+ and its corresponding radical (see also Fig. S1); hence conformational changes are incorporated. For some of the 2-substituents, viz., OH and COOH, the global energy conformer of the phenoxyl radical in-

199

volves an intramolecular HB (see Fig. 1) between a H atom of the substituent and the phenolic O. In an attempt to calculate only the electronic effect on the PDE, this additional enthalpic contribution has to be removed. A lowest-energy non-HB radical could be computed for the 2-OH (less stable by 8.7 kcal/mol than the global one) and 2-COOH (less stable by 7.2 kcal/mol) substituents. These two conformers were used in the calculation of the corresponding PDEs in Table 2, presented in the form of the relative PDEs, DPDEs. Moreover, for comparison, DPDEs derived from the most stable (global minimum) conformers (mainly corresponding to HB-ones) are given in parentheses. No experimental and/or theoretical PDEs exist for the 2-X-ArOH
+ for comparison to be made. However, calculated DPDEs correlate well with the rþ o values, estimated by using Eq. (5). Corresponding correlation is fairly good (r =
0.9700, see also Table 3) for the away conformer, but worse (r =
0.8036) for the toward one, in which an intramolecular HB exists. The coefficient of the 2-away-conformers is almost identical to that (r =
0.9753) of the 4-substituted ones (vide infra). The reasonable correlation found, could justify the correctness of our choice to use Eq. (5) for the calculation þ of the rþ o values. Hence, the series of the calculated ro values could be considered as reasonable, despite the fact that Eq. (5) has been initially proposed for only three 2-X-substituents [11]. Moreover, the negative value of r suggests that EDG groups raise the PDE, while EWG groups present an opposite effect. Both 3-X- and 4-X-ArOH
+ exhibited identical [1b] effects to those of the 2-species. For the 3-X- and 4-X-ArOH
+, the corresponding to the ortho-lowest energy non-HB parent/radical conformer pairs were considered in the calculation of the

Table 2 + B3LYP/6-31+(,3dp) calculated DPDE, SPC, SPR, S(O)c, S(O)r and DQ for 2-X-ArOH
+ as well as Brown parameters rþ o , F, R and experimental
+ pKa parameter values, along with DPDEs for 3- and 4-X-ArOH Substituent

DPDEa (2-X)

SPCa

SPRa

S(O)c

S(O)r

DQ

r+b

H NO2 CN CF3 CHO COOH Br Cl F CH3 OCH3 OH NH2 N(CH3)2

0.00
14.9 (
2.4)d
10.4 (
9.2)
11.9 (
8.6)
8.7 (2.7)
4.3 (3.4)
1.0 (0.0)
3.7 (
1.9)
7.0 (
4.3) 4.3 (4.3) 11.8 (12.4) 5.6 (
0.2) 15.7 (
) 25.6 (19.0)

0.0 25.1 13.3 17.5 10.4 12.4 2.8 6.6 11.0
6.4
11.5
4.3
25.6
32.8

0.0 10.2 2.9 5.6 1.7 8.1 1.8 2.9 4.0
2.1 0.3 1.3
9.9
7.2

0.2150 0.2096 0.2044 0.2257 0.2055 0.2273 0.1625 0.1822 0.2087 0.1888 0.1421 0.1640 0.0830 0.0691

0.5179 0.5156 0.5004 0.5177 0.4925 0.5117 0.4899 0.4954 0.5151 0.4875 0.4701 0.4876 0.3887 0.3655

0.188 0.129 0.159 0.163 0.158 0.158 0.133 0.146 0.161 0.164 0.118 0.144 0.088 0.057

0.00 0.52 0.44 0.40 0.31 0.28 0.10 0.07
0.05
0.20
0.51
0.51
0.86
1.12

a b c d

DPDE, SPC and SPR in kcal/mol; PDE value for phenol was calculated to be 208.43 kcal/mol. Calculated from Eq. (5). From [3b]. Values given in parentheses correspond to the most stable (global minimum) conformers.

pKac
8.1


13
9.3
6.4

DPDEa (3-X)

DPDEa (4-X)

0.00
15.1 (
14.9)
10.8 (
10.4)
11.8
7.1
5.2 (
5.0)
2.5 (
1.7)
4.8 (
4.1)
7.3 (
6.6) 4.5 (5.1) 9.7 (10.9) 3.9 (4.8) 20.4 (20.8) 31.4

0.0
15.5
8.4
12.5
6.5
5.7 (
5.5) 1.7
1.1
4.5 6.8 13.7 7.7 21.0 30.0

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A.P. Vafiadis, E.G. Bakalbassis / Chemical Physics 316 (2005) 195–204

Fig. 1. DFT energy scheme for 2-OH, and 2-COOH-phenolic cation radicals (PCR and PR stand for the phenolic cation radicals and the respective phenoxyl radical, respectively).

PDEs, for consistency. PDEs of the most stable parent/ radical conformer pairs are also given in parentheses. It should be mentioned that, with the exception of the 3-CF3, 3-N(CH3)2 and 3-CHO groups, in which the away conformer was lying lower in energy than the toward one, this latter was the global minimum in all other groups [17], (toward is the conformer in which the phenolic H atom is pointing toward the 3-substituent). It is also seen that most of our DPDEs for the 3-X- and 4-X-ArOH
+, are in close agreement with the literature values [1b], derived at the same level of theory, by using a different basis set (Tables S3 and S4). 3.4. Electronic effects on the acidities of 2-, 3- and 4-X-ArOH
+ and mechanism The origin of differences, between the PDEs of the 2-, 3- and 4-X-ArOH
+, is examined through their relative, DPDEs, (electronic effect). These value-differences are shown in Fig. 2, in which both EDG and EWG are arranged according to their Brown parameter rþ p values. Since the higher the PDE, the more difficult for the proton is to dissociate, positive DPDEs imply a difficult proton dissociation from the 2-X-, 3-X- and 4-X-ArOH
+, relative to the unsubstituted phenolic species; negative values are in line with an easy dissociation. Fig. 2 shows that the three series of the 2-X-, 3-Xand 4-X-ArOH
+ appear similar electronic effects. In particular, they present positive DPDEs, in the case of the five out of the eight EDG studied, (left-hand side of Fig. 2); negative values appear in the case of the rest three EDG, (halogens), and in the five EWG. This is not an unexpected result, because the three halogens are usually considered as borderline groups (vide infra).

Therefore, EDG decrease the acidity of the ArOH
+, while EWG have an opposite effect, in all three substitution positions. The very few experimental pKa data, existing for the 2-X-ArOH
+, show that both 2-CH3- and 2-Cl-ArOH
+ should present an easier tendency for a proton dissociation, relative to the unsubstituted phenolic one (see also Table 2); 2-OCH3-ArOH
+ should exhibit a harder tendency. Our theoretical findings are in line with those for 2-Cl- and 2-OCH3-ArOH
+, and in contrast to that of the 2-CH3 species. However, CH3 is also an EDG, hence, it should exhibit a quite analogous behavior to that of OCH3. Consequently, an equal to or lower pKa value should be also calculated for the latter, compared to that of the CH3 species. Moreover, a pKa value lower than –8.1 (being the value of the unsubstituted phenolic species) should be expected, for the Cl (EWG), too. Actually, based upon their rþ p values [18], F (-0.07), Cl (0.11) and Br (0.15) should be considered as borderline groups, the former located in the EDG, the two latter in the EWG, respectively. Moreover, due to their Hammett parameter rm values, F (0.34), Cl (0.37) and Br (0.37) substituents should be considered as EWG [18]. All these are in close agreement with our theoretical results, showing that, with the exception of the 4-Br, all three halogens should be classified as weak to moderate EWG, (because they present low negative DPDEs in the 2-, 3- and 4-substitution). This behavior appears stronger in the case of the F substituent, weaker for Br. Our results on the 3- and 4-substitution are in close agreement with those of the literature [1b], however, Br was not considered in that study. Fig. 2 also shows that electronic effects appear stronger in the 3-X- and 4-X-ArOH
+ species, involving the five stronger EDG,

c

DPDE SPC SPR 4-X

b

0.9758 0.9213


0.6469 0.6450 0.6337 DPDE SPC SPR 3-X

S(O)c and S(O)r stand for the calculated atomic spin densities at the phenolic O of the phenolic cation radicals and/or phenoxyl radicals, respectively. Qc and Qr stand for the calculated charge at the OH group of the phenolic cation radicals, and the phenolic O radical of the phenoxyl radicals, respectively. DQ stands for the calculated change of charge between the phenolic cation radical and its neutral counterpart.


0.9858 0.9844
0.9704 0.9708
0.8936 0.8943 0.9720
0.9753 0.9784 0.9849


0.9385 0.9425 0.9534

0.9838
0.8784 0.8974 0.9554


0.8849


0.9206 0.9221


0.8977


0.9548
0.9568


0.9669

0.8912 0.8999

0.8335
0.9700 0.9635 0.8512 DPDE SPC SPR 2-X

a


0.9853 0.9783
0.9393 0.9293
0.9281 0.9122
0.9369 0.9238


0.8949


0.9341 0.9270


0.8424

0.8809 0.8537

201

than those of the 2-substituted ones. In all other cases, the acidities of the 2-X-, 3-X- and 4-X-ArOH
+ species are of almost equal intensity. It is also well known that EDG enhance the radical scavenging activity of phenolic antioxidants. Consequently, since in all substituent positions, EDG increase PDEs, deprotonation is not a rate-controlling step to scavenge free radicals.

0.9697
0.9702

0.9456
0.9350

0.9164
0.9261

\(C–O–H)


0.9222 0.8642

R(O–H)


0.9337 0.9322
0.7389 0.7134
0.8725
0.8485 0.8667
0.8746
0.9017 0.9120

DQc Qrb Qcb S(O)ra S(O)ca log (1/sexp) pKa R+ F r+

Table 3 Correlation coefficients, r, between DPDEs, SPC and/or SPR, and experimental and/or theoretical parameters of the 2-, 3- and 4-substituted radicals

m(O–H)

A.P. Vafiadis, E.G. Bakalbassis / Chemical Physics 316 (2005) 195–204

3.5. Electronic effects on the stabilities of 2-, 3- and 4-X-ArOH
+ and ArO
The stability differences between the 2-X-, 3-X- and 4-X-ArOH
+ as well as those between their respective ArO
species, are examined through their SPR and SPC values, respectively, summarized in Tables S2, S3 and S4. It is seen that EWG destabilize more the ArOH
+ (positive SPC) than their respective ArO
species (positive SPR). In addition, EDG stabilize more the ArOH
+ (negative SPC) than their respective ArO
species (negative SPR). As a result, larger PDEs are derived for the latter groups than those of the former ones. Scheme 2 shows this in a qualitative way. It is noteworthy that this scheme is different than that derived for the neutral counterparts [9a]. This is because in the neutral species, the EWG stabilize the ground state, while the EDG destabilize it, which account well for the smaller BDEs corresponding to the EDG than those of the EWG, whereas the opposite holds true for the corresponding PDEs. In the 4-X- and 3-X-ArOH
+ [1b], as well as in the 2-X- ones, PDEs are mainly determined by SPC, in contrast with BDEs which are mainly determined by SPR [9,13,14,19]. SPC and SPR values for the 2-X-ArOH
+, are given for the first time. Moreover, alike with their DPDEs, all three halogens, except 4-Br substituent, should be classified as weak EWG, since they present positive SPC and SPR values in the 2-, 3and 4-substitution. A quantitative correlation between the SPC and SPR in the DPDE, can be derived, based upon the criterion established by Pratt et al. [12b,20] In particular, the slope q+ for the linear correlation of SPC and SPR with r of the substituent, (Fig. 3) are 29.5 and 8.4, 47.6 and 5.4, and 19.7 and 4.0 kcal/mol, for the 2-X-, 3-X- and 4-X-ArOH
+, respectively. Hence, the SPC makes a 3.5-, 8.8- and 4.9-fold greater contribution to the DPDE than do SPR, for the corresponding species, respectively, being in close agreement with the qualitative correlations found above. Moreover, our results support the argument by Bordwell et al. [3b] that 4-N(CH3)2 and 4-NH2 groups are best at stabilizing both ArOH
+ and ArO
. In particular, our theoretical results (see also Tables 2, S3 and S4) also show that (i) these two groups are best at stabilizing ArOH
+ as well as ArO
either as 2-, 3- and/ or 4-substitutent, and not as a 4-substituent only,

202

A.P. Vafiadis, E.G. Bakalbassis / Chemical Physics 316 (2005) 195–204

Fig. 2. Electronic effect on the acidities of 2- (grey bar), 3- (open bar) and 4-substituted (solid bar) phenolic cation radicals.

W

.

O

.

O ∆ HW < ∆ HH

OH

.

O

W

.+

D

SPR ∆HH SPC

∆ HD > ∆ HH

.+

OH D

.+

D = electron-donating group W = electron-withdrawing group

OH

Scheme 2.

however, (ii) they are best at stabilizing the ArOH
+ than the ArO
(iii) N(CH3)2 stabilize better the ArOH
+ than the NH2 group, since the former presents larger SPCs than the latter, (iv) the five EWG and the three halogens provide a stronger destabilization to the ArOH
+, (higher positive SPCs), than those of 3- and 4-substituted, and this is also the case with their respective ArO
species, (higher positive SPRs), however, (v) the five EDG [N(CH3)2 through CH3] at the 4-position, provide stronger stabilization (higher negative SPCs), than those of 3- and 2-substituted, and this is also the case with most of their respective ArO
species, (higher negative SPRs). Calculations also show that the 4-N(CH3)2-ArO
is more stable than the unsubstituted phenolic one by nearly 7.6 kcal/mol, in good agreement with the experimental value (9.6 kcal/mol) [3b], and this is also the case

with our destabilization value for the ArO
, due to the 4NO2 group (ca. 3.6 kcal/mol compared to ca. 4.8 kcal/ mol). However, our theoretical value (19.1 kcal/mol) for the destabilization of the ArOH
+, due to the 4NO2 group, is in better agreement with the available theoretical [1b] (17.6 kcal/mol) than the experimental value of
9.4 kcal/mol. 3.6. Correlation of the molecular descriptors Table 3 shows additional correlations derived between the calculated DPDEs, SPC, and SPR with a series of both theoretical molecular descriptors, and experimental [3b] ones, being, pKa and [11] log(1/sexp) values, as well as Hammett/Brown parameter values [14], of the 4-X-, 3-X- and 2-X-ArOH
+, where available.

A.P. Vafiadis, E.G. Bakalbassis / Chemical Physics 316 (2005) 195–204

40

E (kcal/mol)

20

0

-20

-40 -1.5

-1.0

-0.5

a

0.0 σo+

0.5

1.0

40

E (kcal/mol)

20

0

-20

-40 -0.5

0

b

σm

0.5

1

40

E (kcal/mol)

20

0

-20

-40 -2 c

-1.5

-1

-0.5 σp +

0

0.5

1

Fig. 3. Correlation of DPDE (j), SPC (d) and SPR (m) with r parameters for 2-X- (a), 3-X- (b) and 4-X-substituents (c).

Deprotonation of the radical cations appears via the phenolic OH group, hence, it is worth considering the atomic spin densities on the O atom, S(O)c, and the charge distributions at the phenolic OH group. Unlike the former, being an exact quantum chemical value, charge distribution depends upon the approximation applied. Mulliken orbital theory provides a reasonable representation of the charge distribution within a molecule. Consequently, by using Mulliken charges, the differences in charges between ground state and radical cation are well comparable. Unlike 4-X-ArOH
+ species, there is a lack of experimental lifetimes for the 2-X- and 3-X-

203

ones. Reasonable correlations are found for the former, between the S(O)c and changes of the Mulliken charge at the OH group atom, DQ with the lifetimes (sexp) (0.7897 and 0.7899, respectively, not shown in Table 3). It can be seen that the larger the S(O)c and the change of the DQ, the shorter the lifetimes, hence, the higher the reactivity. Hermann et al. [3a] also reached analogous conclusions. Correlation coefficient, r values derived between the DPDE and the phenolic structural, [R(O–H) and \(C– O–H)] and/or frequency, m(O–H) parameters are fairly good, (ca. |0.92| for the 2-X-ArOH
+, between |0.94| and |0.99|, for the 3- and 4-species), allowing for an approximate estimation of the DPDE values (hence acidity as well) from either one of the three calculated R(O–H), m(O–H), and/or \(C–O–H) values. It is worth also mentioning that (i) unlike the 2-substitution [21], DPDE/\(C–O–H) correlations for the 3- and 4- species, are the best derived among all calculated ones, and (ii) for the latter species, all correlation coefficients exhibited by the DPDEs and SPCs are of the same order of magnitude. Reasonably well overall correlations appear between DPDE and the experimental pKa values, especially in the case of 4-X- and 3-X-ArOH
+. Consequently, DPDE (hence acidity, too) could be predicted from their pKa values and vice versa. Moreover, correlations derived between the DPDE and the rþ o;p and/or rm values appear quite good for the two former cation radicals and of minor quality for the latter one. Finally, correlations derived for the 2-substituted species, between the DPDE, SPC, SPR, and the DQ and/or S(O)c, S(O)r, Qc, Qr values, show that they are not appropriate for DPDE, SPC and SPR predictions. Nevertheless, due to the reasonably well correlations, derived for the 3-X- and especially for the 4-X-species, an approximate estimation of the DPDE values (hence acidity as well) could be based upon (a) the spin density values on the phenolic oxygen atom, S(O)c of the cation radicals, (b) the charge on the OH group of the phenolic cation radicals, Qc, (3- and 4-substitution) as well as (c) that of phenolic radical, Qr (4-substitution). Correlation values in Table 3 also show that SPC values for the 3- and 4-substituted species could be approximately estimated by the S(O)c (3-substitution) and Qc (3- and 4-substitution). Analogous correlations are estimated between SPR and Qr (4-substitution).

4. Conclusions It can be concluded that, contrarily to the neutral counterparts, EWG destabilize more the ArOH
+ than the ArO
, resulting to smaller PDEs for 2-X-ArOH
+, hence to stronger acidity; EDG to weaker acidity. According to the PDE values, deprotonation is not a

204

A.P. Vafiadis, E.G. Bakalbassis / Chemical Physics 316 (2005) 195–204

rate-controlling step in all substituent positions, to scavenge free radicals. Approximate estimations of the DPDEs (hence acidities as well) can be derived from calculated structural and/or vibrational frequency values. Very good correlations are derived between the computed R(O–H) and m(O–H) values, showing that the former can be used as an universal molecular descriptor for the latter and vice-versa. Moreover, (a) the correlation of the DHintra with geometrical parameters appears reasonable for the closed-shell, neutral counterparts, (in contrast with previous estimates), better in the ArOH
+, and, (b) DHintra-value variation in the ArOH
+, relative to the neutral counterparts, depends upon the size of the intramolecular HB ring formed.

Appendix A. Supplementary data Four tables, one scheme and four figures with additional information on structures, conformers, correlations and energetics are available. Supplementary data associated with this article can be found, in the online version at doi:10.1016/j.chemphys.2005.05.015.

[4]

[5] [6] [7] [8]

[9]

[10] [11] [12]

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(f) O. Brede, R. Hermann, W. Naumann, S. Naumov, J. Phys. Chem. 106 (2002) 1398. (a) E.G. Bakalbassis, A. Chatzopoulou, V.S. Melissas, M. Tsimidou, M. Tsolaki, A. Vafiadis, Lipids 36 (2001) 181; (b) E.G. Bakalbassis, N. Nenadis, M. Tsimidou, J. Am. Oil Chem. Soc. 80 (2003) 459; (c) A.P. Vafiadis, E.G. Bakalbassis, J. Am. Oil Chem. Soc. 80 (2003) 1217; (d) A.T. Lithoxoidou, E.G. Bakalbassis, J. Am. Oil Chem. Soc. 81 (2004) 799. E.G. Bakalbassis, A.T. Lithoxoidou, A.P. Vafiadis, J. Phys. Chem. 107 (2003) 8594. R.G. Parr, W. Yang, Density Functional Theory of Atoms and Molecules, Oxford University press, New York, 1989. M.J. Frisch et al., Gaussian 98 Revision A.11, Gaussian Inc., Pittsburgh, PA, 2001. (a) C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785; (b) A.D. Becke, J. Chem. Phys. 98 (1993) 1372; (c) P.J. Stevens, F.J. Devlin, C.F. Chabalowski, M.J. Frisch, J. Phys. Chem. 98 (1994) 11623. (a) Y.D. Wu, D.K.W. Lai, J. Org. Chem. 61 (1996) 7904; (b) H.-Y. Zhang, Y.M. Sun, D.Z. Chen, Quant. Struct. Act. Relat. 20 (2001) 148. H.G. Korth, M.I. de Heer, P. Mulder, J. Phys. Chem. 106 (2002) 8779. M. Jonsson, J. Lind, T.E. Eriksen, G. Mere´nyi, J. Chem. Soc., Perkin Trans. II (1993) 1567. (a) For all substituents, values are taken from C. Hansch, A. Leo, R.W. Taft, Chem. Rev. 91 (1991) 165, for rþ p ðOHÞ ¼
0.78. The originally proposed value of
0.92 is almost certainly too large to be applicable with the calculated, gas-phase DPDEs, see:; (b) D.A. Pratt, M.I. de Heer, P. Mulder, K.U. Ingold, J. Am. Chem. Soc. 123 (2001) 5518, for rþ p ðCHOÞ ¼
0.47 see:; (c) C.D. Selassie, A.J. Shuterman, S. Kapur, R.P. Verma, L. Zhang, C. Hanch, Chem. Soc., Perkin Trans. II (1999) 2729. T. Brinck, M. Haeberline, M. Jonsson, J. Am. Chem. Soc. 119 (1997) 4239. J.S. Wright, D.J. Carpenter, D.J. Mckay, K.U. Ingold, J. Am. Chem. Soc. 119 (1997) 4245. N.W. Larsen, J. Mol. Struct. 51 (1979) 175. I. Vedernikova, E. Proynov, D. Salahub, A. Haemers, Int. J. Quantum Chem. 77 (2000) 161. In the global minimum conformer of the 3-OH group, the substituent H atom is pointing toward the phenolic H atom; in the 3-COOH one, the phenolic H atom is pointing toward the OH moiety of COOH. N.S. Isaacs, Physical Organic Chemistry, Wiley and Sons, New York, 1995. (a) F.G. Bordwell, X.-M. Zhang, A.V. Satish, J.P. Cheng, J. Am. Chem. Soc. 116 (1994) 6605; (b) G.A. DiLabio, D.A. Pratt, A.D. LoFaro, J.S. Wright, J. Phys. Chem. A 103 (1999) 1653; (c) T. Brinck, H.N. Lee, M. Jonsson, J. Phys. Chem. A 103 (1999) 7094. D.A. Pratt, G.A. Dilabio, P. Mulder, K.U. Ingold, Acc. Chem. Res. 37 (2004) 334. The non-HB phenoxyl radical for the 2-NH2 does not exist. By omitting the 2-NH2 DPDE from the correlation, the corresponding coefficient is increased to
0.9625.