There are five possible sites for OH addition, i.e. carbonyl, ipso, ortho, meta and para carbons of benzoate anion. The optimized structures of benzoate anion and addition products for the addition reaction are shown in Figure 1. For the carbonyl, ipso, meta and para addition products, respectively two minima were found on the CCOH torsion potentials, where the O-H bonds point toward or away from the ring. For the ortho addition product, two conformers are present, where the O-H bond points toward the ring or toward the COO group to form the H-bond. Some optimized geometrical parameters are also given in Figure 1.

Table 1 lists the relative electronic energies, including the zero-point vibrational energies (Δ_rE), relative enthalpies at 298 K (Δ_rH) and relative Gibbs energies at 298 K (Δ_rG). The Δ_rG for the carbonyl addition reactions are calculated to be positive while others to be negative. The spin density of the carbonyl addition product is localized on the oxygen atoms of the OH added COO group, whereas those of the other products are delocalized to gain the resonance stabilization energies. The ortho₁ addition product was calculated to be the thermodynamiccally most stable one due to an intramolecular hydrogen bond with CO···HO distances in the range of 1.707 (UmPW1PW91) to 1.826 (UM06-2X) Å. The ipso₁ addition product also forms an intramolecular hydrogen bond with CO···HO distances in the range of 1.758 (UmPW1PW91) to 1.816 (UM06-2X) Å.

Optimized structures of the transition states for the OH

addition reactions and complexes calculated at the UB3LYP/6-311++G(2d,2p) level of theory are shown in Figure 2. Transition states TS_carbonyl1, TS_carbonyl2, TS_ipso1, TS_ipso2, TS_ortho1, TS_ortho2, TS_meta and TS_para correspond to the formation of addition products carbonyl₁, carbonyl₂, ipso₁, ipso₂, ortho₁, ortho₂, meta₁ and para₁, respectively. IRC calculations revealed that transition states TS_ortho1 and TS_ipso1 are connected with complex₁, and TS_ortho2, TS_meta and TS_para are connected with complex₂, complex₃ and complex₄, respectively.

The imaginary frequencies and relative energies of the transition states and distance ratios of r_C···OH/r_C–OH are summarized in Table 2. The C···OH distances in the transition states for the ipso, ortho, meta and para addition reactions are elongated by over 40% as compared with those of the addition products, indicative of an early transition state. On the contrary, in the transition states

Table 1. Thermochemical parameters (kcal∙mol⁻¹) of addition products.

for the carbonyl addition reaction, the C···OH distances are approximately 20% longer than the equilibrium distances in the addition products, indicative of a late transition state. The ΔG^≠ value for the addition of OH to carbonyl carbon is found to be much higher than those of others. The ΔG^≠ values for the formation of ortho₁ and para₁ are comparable and the lowest, though it depends on the functionals. Therefore, ortho and para positions should be the kinetically most favored sites for addition of OH radical. In complex₁, the O-H bond length is elongated by 4.0% (UB3LYP) to 4.6% (UM06-2X) as compared with that of the bare OH radical. The CO bond interacting with the OH radical is also elongated while the other CO bond is contracted as compared with that of the benzoate anion. The Δ_rG values for the formation of the complex₁ are calculated to a range from −1.3 (UM06-2X)

Table 2. Calculated imaginary frequencies, CO distance ratios and thermochemical parameters (kcal∙mol⁻¹) of the transition states and rate constants for addition reactions.

to −0.4 kcal∙mol⁻¹ (UB3LYP). The Δ_rH values for the formation of the complex₂, complex₃ and complex₄ are calculated to be negative while Δ_rG values to be positive. Therefore, at 298 K the formation of complex₂, complex₃ and complex₄ are negligible. Complex₃ was unable to be located on the potential energy surfaces at the UM06-2X level.

The functional dependence of Δ_rG shows a similar trend for each stationary point. The value of Δ_rG increases in the order of UmPW1PW91 ≈ UM06-2X ≈ UCAM-B3LYP < UB3LYP for the products and ΔG^≠, in the order of UB3LYP < UmPW1PW91 ≈ UCAMB3LYP < UM06-2X.

The calculated rate constants for OH addition to the carbonyl, ipso, ortho, meta and para carbons are listed in Table 2. The rate constants for the carbonyl addition are much lower than those for others owing to a large barrier height. Total rate constants for the addi tion reaction were obtained to be 5.2 × 10⁻¹², 1.1 × 10⁻¹², 7.3 × 10⁻¹³ and 3.2 × 10^{−14 cm3}∙mol⁻¹∙s⁻¹ using UB3LYP, UmPW1- PW91, UCAM-B3LYP and UM06-2X functionals, respectively. The UB3LYP value is slightly smaller than the experimental one, 9.8 × 10⁻¹² cm³∙mol⁻¹∙s⁻¹ [14].

Optimized structures of the relevant stationary points for H-atom abstraction from the benzoate anion by the OH radical calculated at the UB3LYP/6-311++G(2d, 2p) level of theory are shown in Figure 3. Table 3 lists the ΔE^≠, ΔH^≠ and ΔG^≠ values for the H-atom abstraction reactions. For H-atom abstractions from the ortho and meta positions, the transition states were optimized by starting from the three initial geometries where the OH molecular axis was perpendicular to the molecular plane of the benzoate anion or the OH molecular axis was in the plane of the benzoate anion with either the H-atom or O-atom of the OH radical pointing to the carbonyl oxygen atom. For H-atom abstraction from the para position, the calculation was started from the two initial geometries where the OH molecular axis was perpendicular to or in the molecular plane of the benzoate anion. TS_{ab_ortho1} was calculated to be planar with the OH···OC distance in the range from 1.650 (mPW1PW91) to 1.704 (B3LYP) Å. TS_{ab_ortho2} was calculated to be nonplanar with the O-H bond pointing away from the carbonyl group. In the TS structures for the meta and para H-atom abstraction reactions, the OH molecular axis was perpendicular to the molecular plane of the benzoate anion. The breaking C-H bonds are elongated by about 17, 14, 12 and 13% as compared with the equilibrium C-H bond of the benzoate anion while the forming O-H bonds are elongated by about 28, 35, 37 and 35% as compared with the O-H bond length of H₂O for TS_{ab_ortho1}, TS_{ab_ortho2}, TS_{ab_meta} and TS_{ab_para}, respectively for the UB3LYP calculation. The reactant-like geometry is characteristic of an early transition state. The ΔG^≠ values of TS_{ab_ortho1} are smaller than those of TS_{ab_ortho2} owing to hydrogen bonding stabilization.

The calculated rate constants for H-atom abstraction are listed in Table 3. The rate constant for the abstraction reaction via TS_{ab_ortho1} is one to three orders of magnitude larger than those for the other abstraction reactions. Total rate constants for the abstraction reaction were obtained to be 7.0 × 10⁻¹², 4.0 × 10⁻¹², 1.4 × 10⁻¹² and 1.3 × 10^{−13 cm3} mol⁻¹ s⁻¹ using UB3LYP, UmPW1- PW91, UCAM-B3LYP and UM06-2X functionals, respectively. Figure 4 gives the potential energy profile for the reaction pathway. The product distribution was obtained for the UB3LYP calculations as follows: carbonyladdition:ipso-addi-tion:ortho-addition:meta-addition:para-addition:ortho-abstraction:meta-abstraction:para-abstraction = 0.0:0.4:19.9:8.6: 13.7:50.7:4.7:2.1. Comparing the rate constants for the addition reactions versus the abstraction reaction, it can be concluded that the latter is the slightly favored reaction channel for the reaction of OH radical with the benzoate anion.

Table 3. Calculated imaginary frequencies, ratios of HO and CH distances, and thermochemical parameters (kcal∙mol⁻¹) of the transition states and rate constants for abstraction reactions.