Mechanism of Hydroxyl Radical Addition to Imidazole and Subsequent

5598

J. Phys. Chem. B 1999, 103, 5598-5607

Mechanism of Hydroxyl Radical Addition to Imidazole and Subsequent Water Elimination Jorge Llano†,‡ and Leif A. Eriksson*,‡ Laboratorio de Quı´mica Computacional y Teo´ rica, Departamento de Quı´mica Fı´sica, Facultad de Quı´mica, UniVersidad de La Habana, La Habana 10400, Cuba, and Department of Quantum Chemistry, Uppsala UniVersity, Box 518, S-751 20 Uppsala, Sweden ReceiVed: January 25, 1999

The addition reaction of the hydroxyl radical to imidazole and subsequent elimination of water to form the 1-dehydroimidazolyl radical is investigated using MP2 and B3LYP methods, including large basis sets and SCI-PCM modeling of solvent effects. It is found that the barrier to addition of the hydroxyl radical at the 5-position is energetically favored over addition to the 2- or 4-positions by 2-3 kcal/mol at the SCI-PCM/ MP2/6-311G(2df,p)//MP2/6-31G(d,p) level, whereas the corresponding B3LYP calculations yield a barrierfree addition at the 5-position. The lower barrier and NBO analysis explain the experimentally observed specificity for the 5-hydroxylation of imidazole and histidine, albeit the 2-adduct is about 4 kcal/mol more stable than the 5-adduct. The NBO energetic analysis shows that the exoanomeric effect stabilizes the transition state at the 5-position about 0.3 kcal/mol more than that at the 2-position. Moreover, the π-interaction between the attacking nonbonding spin orbital of the hydroxyl radical and the π-cloud of imidazole is the least for the transition state at the 5-position, favoring the σC5-O bond formation. The 5-hydroxyimidazolyl radical undergoes a slow elimination of water (the added OH group and the hydrogen at the N1 position) to yield the 1-dehydroimidazolyl radical. The base-catalyzed dehydration profile was modeled in two steps at the B3LYP/ 6-311G(2df,p)//6-31G(d,p) level. The PES for the dehydration reaction seems rather flat. The first step is a barrier-free loss of the proton at N1 induced by the hydroxide ion to yield the 1-dehydro-5-hydroxyimidazolyl radical anion. In the second step, the hydroxide ion is regenerated from the intermediate to yield the final product with a barrier of 2.7 kcal/mol. The calculated hyperfine structures in the presence of the continuum solvent model for the 5-hydroxyimidazolyl and 1-dehydroimidazolyl radicals are in close agreement with the experimental ones recorded in aqueous solution.

Introduction The aromatic heterocycle imidazole is widespread in organic compounds. In biochemical processes, for instance, imidazole plays an important role because of its special acid-base characteristics. The side chain of histidine contains a weakly basic imidazole group that is a versatile catalyst; it is a strong Lewis base, besides a nucleophile, and it is a Brønsted acid in its protonated form. Accordingly, some histidine residues are essential for the activity of proteins such as cytochrome c, hemoglobin, carbonic anhydrase, adenosine deaminase, triose phosphate isomerase, serine proteases, chymotrypsin, etc. Moreover, two nitrogenous bases found in nucleotides, adenine and guanine, are derivatives of purine, a heterocycle consisting of fused pyrimidine and imidazole rings. Nucleotides are building blocks of nucleic acids and coenzymes with diverse functions.1 It is well-known that the reactions of the hydroxyl radical (•OH) with aromatic and heterocyclic compounds are very favored.2 Hence, compounds containing these functional groups can be suspected to be more sensitive to the damaging effects of the ionizing radiation in aqueous solution. In particular, the •OH attack to histidine could modify the performance of several proteins in metabolism. Experimental evidence demonstrates that * To whom correspondence [email protected]. † Universidad de La Habana. ‡ Uppsala University.

should

be

addressed.

E-mail:

•OH reacts with pyrroles and imidazoles by addition at a carbon adjacent to the nitrogen.3,4 More specifically, the reaction of imidazole (I) with •OH could yield three possible adducts, i.e., the 2-, 4-, and 5-hydroxyimidazolyl radicals (I2OH•, I4OH•, and I5OH•). However, both experimental and electron spin resonance (ESR, EPR) measurements as well as theoretical studies have shown that in neutral and alkaline (pH ) 9-10) aqueous solution, •OH specifically adds to the 5-position of imidazole (Scheme 1) and, in acidic media (pH ) 2), to the same position in the side chain of histidine leading to the 5-adduct.3-5 The site specificity is despite the fact that I2OH• is energetically more favored by about 4 kcal/mol with respect to I5OH•. The 5-radical adduct undergoes slow elimination of water (the added OH group and the hydrogen at the N1 position), which can be base-catalyzed, to yield the 1-dehydroimidazolyl radical. It appears that the elimination reaction is favored with increasing pH, since the 5-hydroxyimidazolyl and 1-dehydroimidazolyl radicals are estimated to exist at similar concentrations at pH ) 10, but only the latter is observed at pH ) 12.3 The EPR studies suggest a two-step mechanism for the overall reaction of •OH with imidazole, the first of which is the •OH addition. This is, however, a specific addition to the 5-position. If the 4- and 5-positions in imidazole were regarded as equivalent in solution, because of rapid tautomeric shifts of hydrogen from one nitrogen to the other, •OH could also add to the 4-position. Experimental hyperfine coupling constants (HFCC) recorded at pH 9-10 demonstrate, however, that the

10.1021/jp9902957 CCC: $18.00 © 1999 American Chemical Society Published on Web 06/11/1999

•OH

Addition and H2O Elimination

SCHEME 1: Hydroxylation of Imidazole and Subsequent Base-Catalyzed Dehydration to Yield the 1-Dehydroimidazolyl Radical

nitrogens are not equivalent in I5OH•. This suggests differences in the •OH addition energy profiles at the 2-, 4-, and 5-positions of imidazole. A detailed inspection of the EPR spectrum of I5OH• recorded in solution with steady-state in situ irradiation at pH 9-10 shows that H5 has a hyperfine coupling constant of 26.37 G, which is larger than the expected for a typical aromatic or aliphatic proton.3 Likewise, the EPR spectra of the 5-hydroxyhistidinyl radical cation generated with a Ti3+ Fenton reagent at pH 2 in a steady-state flow system provided a hyperfine coupling constant of 30.2 G for H5.4 Upon addition, the spin density is primarily localized on the planar fragment of the ring and also interacts with the proton bonded to the tetrahedral center C5. The interaction of the π-electron singly occupied molecular orbital (SOMO) with H5 can be rationalized in terms of hyperconjugation.6 Two stereoelectronic effects are present in the hydroxyimidazolyl radicals: conjugation and generalized anomeric effect. For instance, in I5OH•, conjugation is associated with the N1C2-N3-C4 fragment while the generalized anomeric effect is related to the C2-N1-C5-OH moiety. Accordingly, the •OH addition to the 2-, 4-, or 5-positions in imidazole should be ruled by the generalized anomeric effect and the influence of the conjugated fragment thereon. The generalized anomeric effect (An) is the preference for the synclinal (sc) or gauche arrangement over the antiperiplanar (ap) or trans arrangement in cyclic or aliphatic compounds containing the R-X-T-Y moiety.7-12 R can be H or C, X can be a nonmetallic element or a metalloid that binds, leaving lone electron pairs (X ) N, O, S, Se, or Te), T is a tetrahedral center of intermediate electronegativity (T ) C, Si, P), and Y denotes a more electronegative element than T (Y ) N, O, S, Se, Te, F, Cl, or Br). Moreover, if Y is also bonded to a substituent R′ (R′ ) H, C), the anomeric effect in the fragment R-X-T-Y-R′ becomes the contribution of two components: the endoanomeric effect (endo-An), connected with the R-X-T-Y fragment, and the exoanomeric effect (exo-An) related to the X-T-Y-R′ fragment. The generalized anomeric effect has been rationalized in terms of electrostatic7b,8-10,13 and hyperconjugative9,11,13-17 interactions. According to the hyperconjugative hypothesis, the anomeric effect could be qualitatively explained as an nX f σ*T-Y overlap, which is the strongest interaction among other stabilizing hyperconjugative ones. In the presence of a continuum solvent model, the nX f σ*T-Y interaction should weaken with respect to that in the gas phase to reproduce the experimental evidence that the anomeric effect is reduced as the solvent polarity increases.13,18 This study is aimed at explaining the specificity of the •OH addition to imidazole in aqueous solution using accurate quantum methods, as outlined below. We also outline the subsequent base-catalyzed water elimination reaction and report on the effects of the solvent on the calculated radical HFCCs. Through the NBO analyses, the present study also provides insight into the localized molecular orbital interactions as a means to rationalize the calculated hydroxylation mechanisms.

J. Phys. Chem. B, Vol. 103, No. 26, 1999 5599 Methods The reaction profiles of the •OH addition were calculated for the 2-, 4-, and 5-positions of imidazole. The adducts are denoted I2OH•, I4OH•, and I5OH•. Fully optimized geometries, harmonic vibrational frequencies, and zero-point energies of reactants, transition structures, and adducts were calculated at both the MP219 and the hybrid Hartree-Fock/density functional theory (HF/DFT) B3LYP level20 using the 6-31G(d,p) basis set. In the case of the 5-addition, the PES was also scanned at the B3LYP/6-31+G(d) level. The reaction path was followed along the intrinsic reaction coordinate (IRC)21 from the transition states to the reactant complex to confirm that the former are connected to the latter. Restricted and unrestricted formalisms were utilized for closed-shell and open-shell systems, respectively. All calculations were carried out with the Gaussian 94 program.22 Previous studies indicate that Møller-Plesset perturbation theory successfully describes the reaction profiles of the •OH addition and abstraction reactions.23-29 Since transition structures calculated at the UHF level are affected by considerable spin contamination,30 the reaction barriers can be overestimated by up to 10 kcal/mol when correlation corrections are calculated by the unrestricted Møller-Plesset perturbation theory.26 Accordingly, all reactions investigated at the unrestricted MP2 (UMP2) level included spin projection techniques (PMP2// UMP2).31 At the MP2 level, the expectation values of S2 were less than 0.900 and 0.800 for the transition states and adducts. After the spin projection, however, the expectation values of S2 were less than 0.800 and 0.760, respectively. Furthermore, as the system size increases, MP2 calculations become computationally too expensive to be practical. Hybrid HF-DFT methods, such as the B3LYP functional, have also proven to provide accurate results, but at a lower computational cost. A well-known artifact with the present-day DFT methods is the too low transition barriers. This is in part corrected for through the addition of a HF component as in, for example, the B3LYP functional, although we may still expect the barriers for the •OH addition to be lower than at the PMP2 level.32 Single-point calculations were performed on the optimized MP2 and B3LYP geometries with the 6-311G(2df,p) basis set to evaluate energies, HFCCs, and delocalization effects, both in the gas phase and including the isodensity polarized continuum model (SCI-PCM).33-35 The convergence criterion in the direct SCF single-point calculations was set to 10-6. Delocalization effects were estimated through the natural bond orbital (NBO) analyses36 at the HF/6-31G(d,p)//MP2/6-31G(d,p) level. The HFCCs are part of the spin Hamiltonian and arise from the interaction between the unpaired electrons and the magnetic nuclei in the sample. The isotropic component of the 3 × 3 hyperfine interaction tensor is related to the spin density at the position of the nucleus and can be calculated using the expression

Aiso,N )

4π g β g β 〈S 〉-1F(R BN) 3 e e N N z

In this equation, ge and βe are the electronic g factor (taken as the free electron value, 2.0023) and Bohr magneton, respectively, gN and βN are the corresponding nuclear terms, 〈Sz〉 is the value of the spin angular momentum, e.g., 1/2 for radicals, and F(R BN) is the unpaired spin density at the position of the nucleus N. Since all available experimental data are obtained in aqueous solution in which any anisotropic contributions cancel through tumbling motion, we here only report the

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Llano and Eriksson

Figure 1. Components of the generalized anomeric effect in I50H•.

calculated isotropic HFCC’s. For more detailed outlines on HFCC calculations, we refer to ref 37. Solvent effects were estimated using the self-consistent isodensity polarized continuum model (SCI-PCM). This model describes the solvent surrounding the solute by a dielectric continuum of uniform dielectric constant . Since the solvent effects are taken into account as a solute-solvent interaction potential in the molecular Hamiltonian of the solute, a cavity in the continuum solvent (where the solute is placed) should be defined to solve the corresponding Schro¨dinger equation. The SCI-PCM defines the cavity in terms of an isodensity surface that, in principle, is related to the molecular size and shape depending on the value of the isosurface. The cavity relaxes during the geometry optimization as a result of the interaction of the solute charge distribution with the polarizable medium. In this work, the bulk dielectric constant of water at 298 K was set to 78.39. The 0.0004 au isosurface was chosen, since it has been shown that the molar volumes defined by this isodensity surface are in good agreement with the experimentally measured liquid molar volumes.33 Delocalization effects were evaluated through the NBO analyses36 of the unrestricted wave functions at the HF//MP2/ 6-31G(d,p) level, both in the gas phase and in the presence of the SCI-PCM. The natural bond spin orbital (NBSO) set forms a complete orthonormal set of one-electron functions for expanding the delocalized molecular spin orbitals and have optimal convergence properties for describing the R- and β-electron densities. In cases where the R- and β-spin density matrices are different, two different NBSO sets describe R- and β-electron densities. Hence, two different Lewis structures arise, one for each spin.36f In the restricted formalism, a hypothetical Lewis structure consists of strictly localized one-center (core and lone pairs) and two-center (bonds) doubly occupied spatial orbitals. Likewise, the R- and β-spin Lewis structures in the unrestricted formalism may be defined in terms of spin orbitals, keeping in mind that there are core spin orbitals, nonbonding spin orbitals (instead of lone pairs), and bonding spin orbitals. Since the Fock matrix is only diagonal in the canonical molecular orbital basis, off-diagonal elements arise in the Fock

matrix in the NBO basis. Those off-diagonal elements represent delocalization interactions between the occupied orbitals and the antibonds. The energy stabilization of a delocalization interaction may be calculated as the difference between the total energy and the energy calculated by removing the off-diagonal element corresponding to the interaction in question. This is termed deletion in the NBO procedure. The anion-like and cation-like Lewis structures were chosen for the R- and β-electrons of I2OH•, I4OH•, and I5OH•, respectively, as well as for their transition states. These Lewis structures consist of more than 97% of the R- and β-electron densities. As depicted in Figure 1, the energy stabilization due to the generalized anomeric effect can be split into three components for a cyclic compound: the exoanomeric effect and the two components of the endoanomeric effect, i.e., the axial (a-endoAn) and equatorial (e-endo-An) contributions. The anomeric stabilization can thus be written in short as

An ) endo-An + exo-An ) (a-endo-An + e-endo-An) + exo-An The axial endoanomeric contribution consists of delocalizations from the axial p and π spin orbitals to the axial σ*C-O and σ*C-H spin antibonds in the tetrahedral carbon. The equatorial endoanomeric contribution consists of delocalizations from the equatorial sp2N3, σN1-H, and σC-H spin orbitals to the equatorial σ*C-N and σ*C-C spin antibonds. The exoanomeric contribution, finally, consists of delocalizations from the pO, hybrid spnO, and σOH spin orbitals to the σ* spin antibonds at the tetrahedral carbon. A gross estimation of the endoanomeric effect exerted by the X atom, abbreviated (endo-An)X, has been calculated considering all the interactions involving bonding and nonbonding spin orbitals lying on this atom. The dehydration profile of I5OH• was subsequently modeled by including a hydroxide ion and a water molecule. Fully optimized geometries, harmonic vibrational frequencies, and zero-point energies of reactants, transition structures, intermediate, and product were calculated at the B3LYP/6-31G(d,p) level.

•OH

Addition and H2O Elimination

J. Phys. Chem. B, Vol. 103, No. 26, 1999 5601

TABLE 1: Isotropic Hyperfine Coupling Constants (Aiso in G) and Total Atomic Spin Densities (Spin)a for the Hydroxyimidazolyl Radicals Calculated at the (g) B3LYP/6-311G(2df,p) and (aq) SCI-PCM/B3LYP/6-311G(2df,p) Levels I2OH•

I4OH•

atom

Aiso (g)

Aiso (aq)

spin (g)

spin (aq)

Aiso (g)

Aiso (aq)

N1 H (N1-H) C2 H (C2-H) N3 C4 H (C4-H) C5 H (C5-H) O H (O-H)

5.95 -0.70 -4.10 25.51 4.79 -9.04 -0.15 9.81 -11.28 -12.83 -1.09

5.98 -1.07 -3.72 25.50 4.51 -7.68 -1.07 8.71 -10.85 -13.51 -0.98

0.194

0.200

0.17 -3.66 -2.23 -1.07 1.62 -3.67 28.93 34.43 -14.64 -25.80 2.23

0.09 -3.53 -1.56 -1.57 1.58 -3.00 28.26 33.62 -14.72 -27.26 2.33

0.371

0.357

0.437

0.415

I5OH• spin (g)

spin (aq)

0.113

0.110

0.765

0.754

Aiso (g)

Aiso (aq)

3.10 -0.25 13.11 -11.67 -2.35 19.27 -14.95 -3.70 22.84 -25.49 2.01

3.14 -0.41 12.47 -11.39 -2.34 19.30 -15.12 -3.19 24.30 -24.32 1.88

a

spin (g)

spin (aq)

a (G) exptlb 1.43 0.35

0.395

0.376

-0.108 0.602

-0.100 0.612

9.85 2.63 16.30 26.37 1.43

b

Only absolute values of the total atomic spin densities greater than 0.100 are included in the table. Reference 3. Note that experimentally only absolute values are observed.

TABLE 2: Isotropic Hyperfine Coupling Constants (Aiso in G) and Total Atomic Spin Densities (Spin)a for the 1-Dehydroimidazolyl Radical Isolated (C2W Symmetry) and in the Product Complex (C1 Symmetry), Calculated at the (g) B3LYP/6-311G(2df,p) and (aq) SCI-PCM/B3LYP/6-311G(2df,p) Levels product complexb

isolated atom N1 C2 H (C2-H) N3 C4 H (C4-H) C5 H (C5-H) O

Aiso (g)

Aiso (aq)

-1.34

-1.36

-13.06 -1.34

-13.00 -1.36

-9.46

-9.58

-9.46

-9.58

spin (g)

spin (aq)

0.489

0.483

0.352

0.355

0.352

0.355

Aiso (g)

Aiso (aq)

-0.78

-0.93

-5.00 -0.88

-5.93 -1.06

-1.82

-2.69

-4.16

-4.98

spin (g)

spin (aq)

0.194

0.219

0.151

0.174

0.173

0.196

0.601

0.543

charge (g)

charge (aq)

a (G) exptlc

-0.400

-0.422

2.00

-0.404

-0.427

13.62 2.00 10.55

-0.584

-0.631

10.55

a Only absolute values of the total atomic spin densities greater than 0.100 are included in the table. b Structure of product complex (P) in Figure 6. Total atomic charges (charge) are included. c Reference 3. Note that experimentally only absolute values are observed.

Energy calculations were performed on the optimized structures at the B3LYP/6-311G(2df,p) level. Results and Discussion I. Hyperfine Structure of the Isotropic ESR Spectra for the Imidazolyl Radicals. The ESR spectra of I5OH• at pH 9-10 and of the 5-hydroxyhistidinyl radical cation at pH 2 have three hyperfine splittings that appear to be the fingerprint of the 5-hydroxyimidazolyl radicals. In the cases of I5OH• and the 5-hydroxyhistidinyl radical cation, the observed HFCCs are 1.43/1.4 G for N1, 2.63/2.7 G for N3, and 26.37/30.2 G for H5, respectively.3,4 These values for the imidazole ring seem to be rather independent of pH and of the β-alanyl substituent, whereas the hyperfine splitting for the anomeric proton seems to be dependent on the charge in the ring and/or hydrogen bonding to the solvent. As can be seen in Table 1, the calculated HFCCs for I2OH• and I4OH• do not match the experimental ones. Only the calculated HFCCs for I5OH•, both in the gas phase and in the presence of the continuum solvent model, are consistent with all observed nuclei. This fact confirms previous results according to which •OH adds only to the 5-position of the imidazole ring in histidine.4,5 We also note that the continuum solvent model improves the calculated values of the splittings of H4, H5, and the hydrogen from the OH group. A detailed inspection of the hyperfine structure for I5OH• suggests that the spin densities of N1 and C4 are increased by both the conjugation and generalized anomeric effects. As a result, they show positive HFCCs. It is worth noting that the

radical character is chiefly located on C2 and C4 according to the atomic spin densities. Regarding H5, the NBO energetic R , analysis reveals that the delocalizations from pRN1, pRC4, σN1-H R R R R R β β β σC4-H, pO, spO, and σOH to σ*C5-H; and πN1-C2, πN3-C4, σN1-H , β β , pβO, spβO, and σβOH to σ*C5-H contribute 13.36 kcal/mol in σC4-H the gas phase and 13.05 kcal/mol in aqueous solution to the anomeric stabilization. This accounts for the high HFCC of H5. The calculated hyperfine structures for I2OH• and I4OH• follow the same pattern as that for I5OH•: large positive HFCCs for the hydrogen at the anomeric carbon and high positive spin densities at the centers adjacent to the anomeric carbon. In both cases, the radical character is mainly borne on N3 and C5. Table 2 provides the calculated and experimental hyperfine structure for the 1-dehydroimidazolyl radical. The calculated spectra in the gas phase and aqueous solution for the C2V structure of this radical are again in close accord with the experimental results. In this case, the solvent does not appear to have significant effect on the hyperfine structure. II. Hydroxylation Profiles. Table 3 summarizes the hydroxylation profiles of imidazole at various levels of theory. Figure 2 shows the optimized structures of the reactant complex (RC), transition states (TS), and adducts (P). The hydroxylation mechanism of imidazole and histidine does not appear to be under thermodynamic control, since the order of stability of the adducts is I2OH• > I5OH• > I4OH•, but the addition is specific to the 5-position of the ring. In the gas phase at the PMP2/6-311G(2df,p) level, I2OH• is 4.1 and 9.3 kcal/ mol more stable than I5OH• and I4OH•, respectively (5.0 and 10.4 kcal/mol, respectively, at the B3LYP/6-311G(2df,p) level).

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TABLE 3: Relative ZPE-Corrected Total Energies with Respect to the Isolated Reactants (∆E in kcal/mol) for the Hydroxylation of Imidazole Calculated at Different Levels of Theorya level of theory

∆E(RC) I- - -•OH

MP2/6-31G(d,p) PMP2/6-31G(d,p)//MP2/6-31G(d,p) MP2/6-311G(2df,p)//6-31G(d,p) PMP2/6-311G(2df,p)//MP2/6-31G(d,p) SCI-PCM/MP2/6-311G(2df,p)//MP2/6-31G(d,p) SCI-PCM/PMP2/6-311G(2df,p)//MP2/6-31G(d,p) B3LYP/6-31G(d,p) B3LYP/6-311G(2df,p)//6-31G(d,p) SCI-PCM/B3LYP/6-311G(2df,p)//B3LYP/6-31G(d,p) B3LYP/6-311G(2df,p)//MP2/6-31G(d,p) SCI-PCM/B3LYP/6-311G(2df,p)//MP2/6-31G(d,p)

-7.7 -7.7 -7.4 -7.4 -5.8 -5.7 -7.8 -7.3 -6.1 -7.2 -5.8

a

RC stands for reactant complex, TS for transition state, and P for product. 6-31+G(d) levels.

I2OH•

∆E(TS) I4OH•

15.4 3.3 13.2 1.0 15.0 3.7 -5.2 -5.0 -3.0

15.8 8.5 12.3 5.2 10.8 5.0 -2.6 -2.6 -2.5

I5OH•

I2OH•

∆E(P) I4OH•

12.2 1.7 9.9 -0.5 11.3 1.6 b b b -5.2 -3.4

-14.4 -20.1 -17.5 -23.0 -14.0 -19.0 -28.3 -27.0 -23.2

-10.8 -11.7 -12.8 -13.7 -9.5 -10.1 -17.5 -16.6 -13.9

I5OH• -10.3 -17.0 -12.5 -18.9 -10.7 -16.5 -23.2 -22.0 -19.6 -20.7 -18.4

b•

OH addition without barrier at the B3LYP/6-31G(d,p) and B3LYP/

Figure 3. Hydroxylation profile of imidazole calculated at the SCIPCM/PMP2/6-311G(2df,p)//MP2/6-31G(d,p) level, with relative ZPEcorrected total energies with respect to the isolated reactants (R). RC stands for reactant complex, TS for transition state, and P for product.

Figure 4. Hydroxylation profile of imidazole calculated at the SCIPCM/B3LYP/6-311G(2df,p)//B3LYP/6-31G(d,p) level, with relative ZPE-corrected total energies with respect to the isolated reactants (R). RC stands for reactant complex, TS for transition state, and P for product. Figure 2. MP2/6-31G(d,p) optimized structures for the hydroxylation of imidazole. Significant bond lengths (in Å) are given for MP2/631G(d,p) geometries and, in parentheses, the corresponding B3LYP/ 6-31G(d,p) ones.

In the presence of the SCI-PCM, the three adducts are destabilized at the (P)MP2 and B3LYP levels with respect to the isolated reactants (cf. Figures 3 and 4). In solution, I2OH• is 2.5 and 8.9 kcal/mol more stable than I5OH• and I4OH•, respectively (3.6 and 9.3 kcal/mol, respectively, at the B3LYP/ 6-311G(2df,p) level). The relative stability of the adducts can be explained through the NBO energetic analysis. Tables 4-9 record the energetic

contributions to each component of the anomeric effect for the adducts and transition states. The contributions of the individual hyperconjugative interactions taken into account for each component are listed for R- and β-electrons and were calculated by zeroing the off-diagonal Fock matrix elements connecting the X nonbonding and bonding spin orbitals with the T-Y spin antibonds. When the superscript Rβ appears in one interaction, R Rβ R β f σ*T-Y and nβX f σ*T-Y i.e., nRβ X f σ*T-Y, both nX interactions have been zeroed simultaneously in the unrestricted Fock matrices because R- and β-NBSO have spatial bond orbitals of the same symmetry about the internuclear axis. As

•OH

Addition and H2O Elimination

J. Phys. Chem. B, Vol. 103, No. 26, 1999 5603

TABLE 4: Contributions (in kcal/mol) of Hyperconjugative Interactions to the Generalized Anomeric Effect in I2OH•, Calculated at the (g) HF//MP2/6-31G(d,p) and (aq) SCI-PCM/HF//MP2/6-31G(d,p) Levels / del(nXfσT-Y )

contribution An endo-An a-endo-An R pRN1 f σ*C2-O R pRN3 f σ*C2-O R R pN1 f σ*C2-H R pRN3 f σ*C2-H β β πN1-C5 f σ*C2-O β β πN3-C4 f σ*C2-O β β πN1-C5 f σ*C2-H β β πN3-C4 f σ*C2-H e-endo-An Rβ Rβ σN1-H f σ*C2-N3 Rβ f σ* sp2Rβ N3 N1-C2 exo-An Rβ Rβ pO f σ*N1-C2 Rβ spRβ O f σ*C2-N3 Rβ σRβ f σ* OH C2-H (endo-An)N1 (endo-An)N3

(g)

(aq)

4.59 6.20 2.27 2.49 3.61 2.20 2.00 1.21

4.68 6.26 2.29 2.48 3.65 2.40 2.02 1.29

1.30 6.48

1.35 6.31

12.41 3.54 2.79

12.20 3.53 2.73

/ del(nXfσT-Y )

del (g)

(aq)

contribution

53.39 34.40 26.33

53.47 34.72 26.78

An endo-An a-endo-An R pRN1 f σ*C5-O R pRC4 f σ*C5-O R pRN1 f σ*C5-H R pRC4 f σ*C5-H β β πN1-C2 f σ*C5-O β β πN3-C4 f σ*C5-O β β πN1-C2 f σ*C5-H β β πN3-C4 f σ*C5-H e-endo-An Rβ Rβ σN1-H f σ*C4-C5 Rβ Rβ f σ*N1-C4 σC4-H exo-An Rβ pRβ O f σ*N1-C5 Rβ Rβ spO f σ*C5-H Rβ σRβ f σ* OH C4-C5 (endo-An)N1 (endo-An)C4

7.74

7.62

19.10

18.78

14.03 18.89

14.20 18.99

TABLE 5: Contributions (in kcal/mol) of Hyperconjugative Interactions to the Generalized Anomeric Effect in I4OH•, Calculated at the (g) HF//MP2/6-31G(d,p) and (aq) SCI-PCM/HF//MP2/6-31G(d,p) Levels / del(nXfσT-Y )

contribution An endo-An a-endo-An R R πC2-N3 f σ*C4-O R R pC5 f σ*C4-O R R f σ*C4-H πC2-N3 R R pC5 f σ*C4-H β β f σ*C4-O πN1-C5 β β πC2-N3 f σ*C4-O β β πN1-C5 f σ*C4-H β β f σ*C4-H πC2-N3 e-endo-An Rβ sp2Rβ N3 f σ*C4-C5 Rβ Rβ σC5-H f σ*N3-C4 exo-An Rβ pRβ O f σ*N3-C4 Rβ f σ* spRβ O C4-H Rβ Rβ σOH f σ*C4-C5 (endo-An)N3 (endo-An)C5

(g)

(aq)

5.09 6.90 1.55 2.35 0.52 3.97 0.32 1.29

5.23 7.03 1.44 2.37 0.54 4.26 0.34 1.31

4.57 1.50

4.46 1.54

7.75 2.32 3.73

TABLE 6. Contributions (in kcal/mol) of Hyperconjugative Interactions to the Generalized Anomeric Effect in I5OH•, Calculated at the (g) HF//MP2/6-31G(d,p) and (aq) SCI-PCM/HF//MP2/6-31G(d,p) Levels (g)

(aq)

5.76 7.79 2.28 2.96 5.07 0.49 0.30 2.23

5.77 7.75 2.21 2.85 5.06 0.47 0.29 2.16

1.02 1.31

1.04 1.28

12.43 3.34 2.98

12.35 3.32 2.96

del (g)

(aq)

50.15 31.53 29.06

49.69 31.12 28.68

2.33

2.32

19.06

18.90

16.56 12.74

16.38 12.53

TABLE 7: Contributions (in kcal/mol) of Hyperconjugative Interactions to the Generalized Anomeric Effect in the Transition State of I2OH•, Calculated at the (g) HF//MP2/ 6-31G(d,p) and (aq) SCI-PCM/HF//MP2/6-31G(d,p) Levels / del(nXfσT-Y )

del (g)

(aq)

contribution

42.39 28.56 22.31

42.62 29.03 22.84

An endo-An a-endo-An β β πN1-C5 f σ*C2-O β β πN3-C4 f σ*C2-O e-endo-An Rβ Rβ σN1-H f σ*C2-N3 Rβ f σ* sp2Rβ N3 N1-C2 exo-An R R pO f σ*N1-C2 R spRO f σ*C2-N3 β pβO f σ*N1-C2 β sp0.35β f σ*C2-N3 O (endo-An)N1 (endo-An)N3 R sp2.54R f π*C2-N3 O

6.03

5.98

14.01

13.72

16.67 11.57

16.88 11.78

7.64 2.28 3.62

an example, in the case of I5OH•, the delocalization interactions considered in Table 6 are illustrated in Figure 1. As can be seen in Tables 4-9, the relative stability of the adducts is in line with the stabilization provided by the generalized anomeric effect. Both in the gas phase and solution, the anomeric effect decreases in the order I2OH• > I5OH• > I4OH•. In solution, the anomeric effect for I5OH• drops by 0.46 kcal/mol with respect to the gas phase. In contrast, the anomeric effect slightly increases in solution by 0.08 and 0.23 kcal/mol in I2OH• and I4OH•, respectively. In solution, the anomeric effect contributes 53.47 kcal/mol in I2OH•, 49.69 kcal/mol in I5OH•, and 42.62 kcal/mol in I4OH•. The relative anomeric contributions provide a better idea of the hyperconjugative stabilization: I5OH• and I4OH• are 3.78 and 10.85 kcal/mol

(g)

(aq)

3.75 1.65

4.08 1.92

2.10 8.68

2.18 8.45

0.58 0.12 0.60 0.10

0.57 0.12 0.60 0.10

24.09

del (g)

(aq)

17.47 16.05 5.28

17.92 16.51 5.87

10.74

10.59

1.40

1.40

5.86 10.34

6.27 10.37

23.55

less favored by the anomeric effect than I2OH• in aqueous solution. These results are in quantitative agreement with the relative stabilities of the adducts: I5OH• and I4OH• are 2.5 and 8.9 kcal/mol less stable than I2OH•. Although the axial endoanomeric contribution in I5OH• is about 2 kcal/mol greater Rβ than in I2OH•, the equatorial sp2Rβ N3 f σ*N1-C2 interactions • strongly favor I2OH by about 5 kcal/mol, yielding nearly equal exoanomeric effects for both radicals. As in I2OH•, the Rβ • equatorial sp2Rβ N3 f σ*C4-C5 interactions stabilize I4OH , but the axial endoanomeric and the exoanomeric contributions favor I4OH• less than I2OH• and I5OH•. The calculated hydroxylation barriers (Table 3) decrease in the following order at the PMP2 level: I5OH• < I2OH• < I4OH•, both in the gas phase and in solution (cf. Figures 3 and 4). In contrast, the hydroxylation at the 5-position is barrierfree at the B3LYP/6-31G(d,p) and B3LYP/6-31+G(d) levels. The B3LYP hydroxylation barriers for the 2- and 4-positions

5604 J. Phys. Chem. B, Vol. 103, No. 26, 1999

Llano and Eriksson

TABLE 8: Contributions (in kcal/mol) of Hyperconjugative Interactions to the Generalized Anomeric Effect in the Transition State of I4OH•, Calculated at the (g) HF//MP2/ 6-31G(d,p) and (aq) SCI-PCM/HF//MP2/6-31G(d,p) Levels / del(nX f σT-Y )

contribution An endo-An a-endo-An β β πN1-C5 f σ*C4-O β β πC2-N3 f σ*C4-O e-endo-An Rβ sp2Rβ N3 f σ*C4-C5 Rβ Rβ σC5-H f σ*N3-C4 exo-An R sp2.13R f σ*N3-C4 O R f σ* sp2.76R O C4-C5 0.38β β spO f σ*N3-C4 β pβO f σ*C4-C5 (endo-An)N3 (endo-An)C5 R sp4R O f π*C4-C5

(g)

(aq)

0.28 4.92

0.35 6.40

5.78 1.84

5.73 1.92

0.24 0.09 0.60 0.02

0.27 0.10 0.60 0.02

21.51

del (g)

(aq)

13.64 12.70 5.05

15.25 14.28 6.59

7.59

7.62

0.95

0.99

10.75 2.13

12.19 2.27

20.28

TABLE 9: Contributions (in kcal/mol) of Hyperconjugative Interactions to the Generalized Anomeric Effect in the Transition State of I5OH•, Calculated at the (g) HF//MP2/ 6-31G(d,p) and (aq) SCI-PCM/HF//MP2/6-31G(d,p) Levels / del(nXfσT-Y )

contribution An endo-An a-endo-An β β πN1-C2 f σ*C5-O β β πN3-C4 f σ*C5-O e-endo-An Rβ Rβ σN1-H f σ*C4-C5 Rβ Rβ σC4-H f σ*N1-C5 exo-An R pRO f σ*N1-C5 R spRO f σ*C4-C5 6.08β β spO f σ*N1-C5 0.64β β spO f σ*C4-C5 (endo-An)N1 (endo-An)C4 R sp2R O f π*C4-C5

(g)

(aq)

4.25 0.57

4.68 0.61

1.38 2.13

1.42 2.09

0.75 0.05 0.71 0.16

0.74 0.05 0.69 0.16

19.05

del (g)

(aq)

9.85 8.20 4.69

10.30 8.67 5.15

3.50

3.50

1.67

1.65

5.64 2.71

6.11 2.71

18.70

are lower than those at the PMP2 level, but the transition state at the 4-position remains the larger one. The decreasing order in the hydroxylation barriers, i.e., I5OH• < I2OH• < I4OH•, indicates that I5OH• would be kinetically favored. The gas-phase calculated barriers for I5OH•, I2OH•, and I4OH• are 6.9, 8.4, and 12.6 kcal/mol at the PMP2/6-311G(2df,p) level (6.2, 7.7, and 11.9 kcal/mol, including thermal corrections). At the B3LYP/6-311G(2df,p) level, the 2- and 4-additions have 2.3 and 4.7 kcal/mol barriers, respectively. Although the 5-hydroxylation is barrier-free at the B3LYP/631G(d,p) and B3LYP/6-31+G(d) levels, it shows a 2.0 kcal/ mol barrier at the B3LYP/6-311G(2df,p)//MP2/6-31G(d,p) level. The calculated barriers in solution for I5OH•, I2OH•, and I4OH• are 7.3, 9.4, and 10.7 kcal/mol at the SCI-PCM/PMP2/6-311G(2df,p) level (6.6, 8.7, and 10.0 kcal/mol, including thermal corrections). At the SCI-PCM/B3LYP/6-311G(2df,p) level, the 2- and 4-additions have 3.1 and 3.6 kcal/mol barriers, whereas the 5-addition has a 2.4 kcal/mol barrier at the SCI-PCM/ B3LYP/6-311G(2df,p)//MP2/6-31G(d,p) level. Hence, in the gas phase at the PMP2 level, the transition states at the 2- and 4-positions are 1.5 and 5.7 kcal/mol higher in energy than the transition state at the 5-position. Likewise in solution, the

transition states at the 2- and 4-positions are 2.0 and 3.4 kcal/ mol higher in energy than the transition state at the 5-position. It is worth noting that in the presence of the SCI-PCM, the barriers for the 2- and 5-hydroxylations rise with respect to those at the gas phase, while they drop for the 4-hydroxylation (cf. Figures 3 and 4). The calculated SCI-PCM/PMP2/6-311G(2df,p)//MP2/6-31G(d,p) solvation energies of •OH, imidazole, and the transition states at the 2-, 4-, and 5-positions are -3.8, -6.7, -8.7, -12.0, -9.1 kcal/mol, respectively. Hence, in terms of solvation stabilization, the transition states at the 2- and 5positions are 1.8 and 1.4 kcal/mol less stable than the isolated reactants, while the transition state at the 4-position is 1.5 kcal/ mol more stable. Moreover, smaller barriers could be expected in the real solution because it is more likely that •OH and imidazole are hydrogen-bonded to the solvating water molecules rather than to one another, as in the reactant complex obtained with the current model (Figure 2). Water molecules of the solvation shells could help to create a cage effect stabilizing a π-like reactant complex closer in energy to the transition states. This would be expected to reduce the hydroxylation barriers. These results, however, do not explain completely the specificity of the 5-addition, inasmuch as the difference in the 2- and 5-hydroxylation barriers is only about 2 kcal/mol. Since I2OH• is 2.5 kcal/mol more stable than I5OH•, one would expect to see a mixture of I2OH• and I5OH• in solution. The outcome of the NBO energetic analysis shown in Tables 7-9 gives some insight into the molecular orbital interactions in the transition states. It should be noted that the anomeric effect is weaker in the transition states than in the adducts. The transition states are mostly stabilized by the endoanomeric effect, whose equatorial component favors I2OH• and I4OH•. However, the full anomeric stabilization does not account for the observed trends in the barriers. It appears that the transition state stabilization is particularly sensitive to the exoanomeric effect. The exoanomeric stabilization decreases in the following order: I5OH• > I2OH• > I4OH•. This suggests that •OH polarizes the π-cloud, and its four nonbonding spin orbitals parallel to the ring interact with the spin antibonds at the carbon with different strengths, as can be seen in Tables 7-9. The most stabilizing exoanomeric interactions are attained at the 5-position, even though the C-O distance is longer at the 5-position than at the 2-position. There is another factor that appears to make the 5-addition specific: the interaction of the attacking nonbonding spin orbital of •OH with the π-cloud. To form the C-O bond, the attacking nonbonding spin orbital of •OH should interact with the Rydberg orbitals at carbon. However, this interaction could be affected by the strong interaction of the attacking nonbonding spin orbital with the π-cloud, since the former should enter parallel to the latter to interact with the Rydberg orbitals at carbon. The NBO R analysis shows that the sp2R O f π*C4-C5 interaction of the 2R • attacking spO orbital in I5OH is less stabilizing than the R R • f π*C2-N3 and sp4R sp2.54R O O f π*C4-C5 interactions in I2OH • and I4OH . It appears also that the increasing s-character of the attacking spnO spin orbital favors more the π-interaction than the σC-O spin orbital formation. As a result, the •OH attack follows more effectively to the 5-position than to the other two. Geometries. Figure 2 summarizes the significant distances for the hydroxyl adducts and the corresponding transition states. There is good agreement between the MP2 and the B3LYP geometries except for that of the transition state at the 2-position in which the C2-O bond distance is 2.518 Å at the B3LYP level. This long bond distance is due to stronger nonbonding

•OH

Addition and H2O Elimination

Figure 5. Base-catalyzed dehydration profile of I50H• calculated at the B3LYP level, with relative energies with respect to the isolated reactants, i.e., I50H•, OH-, and H2O. RC stands for reactant complex, TS for transition state, I for intermediate, and P for product.

interactions at the B3LYP level than at the MP2 level, which favor a stronger attraction between •OH and the lone pair at N3. The adducts show gauche conformations about the C-O bond in the anomeric fragment consistent with the generalized anomeric effect. At the MP2 (B3LYP) levels, significant conformations are φ(N1-C2-O-H) ) 92.0° (90.3°) for I2OH•, φ(N3-C4-O-H) ) -49.5° (-50.3°) for I4OH•, and φ(N1C5-O-H) ) 96.9° (98.7°) for I5OH•. The C-O lengths in the transition states at the MP2 level decreases in the order I5OH• > I2OH• > I4OH•. It seems that the dipole-dipole interactions between •OH and the π-cloud rule the conformation about the C-O line inasmuch as •OH is oriented parallel to the ring plane and eclipses one bond in the way that the dipole-dipole interaction is the most favored. III. Dehydration Profile. Figure 5 contains the basecatalyzed dehydration profile of I5OH• at the B3LYP level. Figure 6 shows the optimized structures of the reactant complexes (RC1 and RC2), transition states (TS1 and TS2), intermediate (I), and product (P). Two possible reactant complexes are considered in this model, taking into account the rapid proton shift from water to OH-. Accordingly, the B3LYP/6-311G(2df,p)/6-31G(d,p) results including ZPE corrections indicate a barrier-free proton migration from water to OH- in the first reactant complex (RC1) to

J. Phys. Chem. B, Vol. 103, No. 26, 1999 5605 provide a 0.4 kcal/mol (0.2 kcal/mol at the B3LYP/6-31G(d,p) level without including ZPE) less stable reactant complex (RC2). In RC2 OH- is directly hydrogen-bonding the proton attached to N1. Thereafter, OH- induces the proton loss from I5OH• to yield the 1-dehydro-5-hydroxyimidazolyl radical anion. The proton loss is barrier-free, both at the B3LYP/6-311G(2df,p)/ 6-31G(d,p) and B3LYP/6-31G(d,p) levels including ZPE, although it has an insignificant barrier of 0.07 kcal/mol at the B3LYP/6-31G(d,p) level without ZPE. At the ZPE-corrected B3LYP/6-311G(2df,p)/6-31G(d,p) level, the intermediary cluster (I), i.e., the one that contains the 1-dehydro-5-hydroxyimidazolyl radical anion, is only 1.2 kcal/mol more stable than the first reactant complex. The 1-dehydro-5-hydroxyimidazolyl radical anion then loses OH- to yield the 1-dehydro-imidazolyl radical with a barrier of 2.7 kcal/mol. According to this model, the overall reaction appears to be thermoneutral and the PES quite flat. This suggests that the energetics under the standard conditions of temperature, pressure, and composition are not the driving forces of the basecatalyzed dehydration but rather the effect of pH. It is also noteworthy that the intermediate complex (I) is slightly more stable than the product complex (P) in the modeled dehydration profile, although the 1-dehydro-5-hydroxyimidazolyl radical has not been experimentally recorded.3,4 At the ZPE-corrected B3LYP/6-311G(2df,p)/6-31G(d,p) level, the proton affinity of 356.8 kcal/mol for the 1-dehydro-5-hydroxyimidazolyl radical anion is comparable to that of 356.6 kcal/ mol for the imidazolyl anion. As a result, the calculated proton affinities do not account for differences in acidity between the imidazolyl anion and the 1-dehydro-5-hydroxyimidazolyl radical anion. On the other hand, the higher stability of the intermediate cluster with respect to the product cluster is probably an artifact of the small model utilized. The intermediate complex (I) consists of the 1-dehydro-5-hydroxyimidazolyl radical hydrogenbonded to two water molecules. This configuration is more stable than a structure with hydrogen bonds arranged like in the reactant complexes (RC), given that each O-H‚‚‚N hydrogen bond stabilizes the structure about 7 kcal/mol whereas each O-H‚‚‚O hydrogen bond stabilizes about 5 kcal/mol. Furthermore, the intermediate complex (I) is connected to the second reactant complex (RC2) through the first transition state (TS1) in the proton loss reaction path. Likewise, the product complex (P) is connected to the intermediate complex (I) through the second transition state (TS2) in the OH- regeneration reaction

Figure 6. B3LYP/6-31G(d,p) optimized cluster structures for the base-catalyzed dehydration of I50H•. Significant bond lengths (in Å) are provided.

5606 J. Phys. Chem. B, Vol. 103, No. 26, 1999 path. However, the hydrogen bond arrangement is not the most favorable one in this cluster (P) because the oxygen at the leaving OH- accepts only one hydrogen bond, and hence, the charge is not so efficiently delocalized as in the reactant complexes in which oxygen at OH- acts as a double acceptor in the bifurcated hydrogen bond. While the calculated charge and spin distributions in the reactant and intermediary complexes are correctly located on the different centers, they are not in the product complex; the leaving hydroxide ion carries high spin density and the nitrogens have considerable negative charge, as can be seen in Table 2. As a result, the hyperfine structure of the 1-hydroxyimidazolyl radical in the product complex does not match the experimental or the calculated structure for the isolated radical, even though the charge and spin distributions in the product complex were computed from a wave function that is stable at the B3LYP/ 6-311G(2df,p)//6-31G(d,p) level. This suggests that the dispersion of the negative charge over the neighboring solvating water molecules is a significant thermodynamic factor driving the OHregeneration. Conclusions The calculated hyperfine structures of the isotropic ESR spectra for the imidazolyl radicals are in close agreement with the experimental ones, especially when the SCI-PCM is included. For the three possible hydroxyimidazolyl radical adducts, the experimental and computed HFCCs in solution at the protons attached to the tetrahedral carbon, some conformational features at their calculated geometries, and the decreasing order of stability I2OH• > I5OH• > I4OH• have been accounted for in terms of the generalized anomeric effect. In contrast, the stability of the adducts cannot explain the experimentally observed specificity of 5-hydroxylation of imidazole and histidine. On the other hand, the calculated barriers increase in the order I5OH• < I2OH• < I4OH•, indicating that I5OH• is kinetically favored. The kinetic preference can be rationalized from the mechanistic standpoint as the contribution of two factors. First, the transition state at the 5-position is the most favored by the exoanomeric interaction among the nonbonding spin orbitals of •OH and the spin antibonds at C5 in imidazole. The exoanomeric interaction decreases in the order I5OH• > I2OH• > I4OH• for the transition states. Second, the interaction of the attacking spnO nonbonding spin orbital of •OH with the π-cloud is the lowest at the 5-position; hence, the interaction with the Rydberg orbitals at carbon to form the σC-O spin orbital would be less hindered. Although B3LYP/6-31G(d,p) geometries are close to MP2/6-31G(d,p) ones, the hydroxylation energetics are quite different. The barriers for hydroxylation are smaller at the B3LYP level than at the MP2 level, but the same trends are observed for both methods. The 5-hydroxylation is even barrierfree at the B3LYP/6-31G(d,p) and B3LYP/6-31+G(d) levels. Some observed differences in geometries at the B3LYP and MP2 levels seem to be due to stronger nonbonding interactions at the former. The model used to study the two-step base-catalyzed dehydration of the 5-hydroxyimidazolyl radical suggests that the potential energy surface is very flat, and hence, the reaction kinetics appears to be dominated by the effect of pH rather than by the calculated energy profile. High pH drives the proton loss at the N1 position, whereupon the regeneration of the hydroxide ion proceeds to form the 1-dehydroimidazolyl radical favored by the solvating effect of the water molecules over the leaving hydroxide ion.

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•OH

Addition and H2O Elimination

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