Degradation Mechanisms of 4,7-Dihydroxycoumarin Derivatives in Advanced Oxidation Processes: Experimental and Kinetic DFT Study

Abstract

Coumarins represent a broad class of compounds with pronounced pharmacological properties and therapeutic potential. The pursuit of the commercialization of these compounds requires the establishment of controlled and highly efficient degradation processes, such as advanced oxidation processes (AOPs). Application of this methodology necessitates a comprehensive understanding of the degradation mechanisms of these compounds. For this reason, possible reaction routes between HO^• and recently synthesized aminophenol 4,7-dihydroxycoumarin derivatives, as model systems, were examined using electron paramagnetic resonance (EPR) spectroscopy and a quantum mechanical approach (a QM-ORSA methodology) based on density functional theory (DFT). The EPR results indicated that all compounds had significantly reduced amounts of HO^• radicals present in the reaction system under physiological conditions. The kinetic DFT study showed that all investigated compounds reacted with HO^• via HAT/PCET and SPLET mechanisms. The estimated overall rate constants (k_overall) correlated with the EPR results satisfactorily. Unlike HO^• radicals, the newly formed radicals did not show (or showed negligible) activity towards biomolecule models representing biological targets. Inactivation of the formed radical species through the synergistic action of O₂/NO_x or the subsequent reaction with HO^• was thermodynamically favored. The ecotoxicity assessment of the starting compounds and oxidation products, formed in multistage reactions with O₂/NO_x and HO^•, indicated that the formed products showed lower acute and chronic toxicity effects on aquatic organisms than the starting compounds, which is a prerequisite for the application of AOPs procedures in the degradation of compounds.

1. Introduction

The rapid advancement of synthetic organic chemistry has led to the appearance of numerous compounds with remarkable biological properties. Available literature data indicate that various newly synthesized coumarin derivatives have pronounced pharmacological and biological properties, such as anticarcinogenic [1,2], antimicrobial [3,4], antioxidant [5,6], antiviral [7,8], and, especially, anticoagulant activities [9,10]. Coumarin derivatives, such as warfarin and coumatetralyl, are some of the most frequently used anticoagulant agents [11]. On the other hand, the mentioned compounds are also potent rodenticides that act through the same anticoagulant mechanism [12]. Due to their pharmaceutical and industrial applications, significant concentrations of these compounds and their hydroxylated derivatives are present in wastewater treatment plants, from where they often end up in natural receiving waters as part of effluents [13,14]. Due to their stability and persistence, coumarin derivatives reabsorbed in the diets of aquatic organisms can be especially dangerous. Their pronounced biological activity and the potential application of newly synthesized coumarin derivatives in industry have resulted in the need for a specific, highly efficient methodology for the study of their degradation. In recent decades, particular emphasis has been placed on the application of techniques based on advanced oxidation processes (AOPs) [15,16]. The first step in AOPs is the in situ generation of strong oxidants—e.g., through the Fenton reaction or photocatalytic oxidation—capable of oxidizing various compounds [17,18]. However, the application of this methodology requires the development of a strategy and modeling of the reaction process. This necessitates a comprehensive investigation of the mechanisms of the reaction between the highly reactive radical species and the corresponding compound, as well as an assessment of the toxicity of the formed intermediates [19]. Reliable knowledge about the possible mechanisms, intermediates, and final products is crucial for successful modeling of AOPs. Standard experimental techniques are often limited in providing unambiguous identification of mechanisms due to the formation of unstable intermediates that are difficult to detect [20].

For this reason, the degradation mechanisms of previously synthesized aminophenol 4,7-dihydroxycoumarin derivatives (Figure 1) [21] were examined in this study under AOP conditions (HO^•) as examples of stable aromatic compounds utilizing the sophisticated Electron paramagnetic resonance (EPR) spectroscopy experimental technique and a theoretical quantum mechanics-based test for overall radical scavenging activity (the QM-ORSA methodology) [22] based on density functional theory (DFT). The structure of these compounds offers the possibility of analyzing the effect of the substituent (–OH) position on the reaction parameters. A similar methodology has been successfully applied to other coumarin derivatives [23,24].

The applied methodology was based on the calculation of the thermodynamic and kinetic parameters of generally accepted radical scavenging mechanisms, such as hydrogen atom transfer (HAT), single-electron transfer followed by proton transfer (SE−TPT), sequential proton loss followed by electron transfer (SPLET), and radical adduct formation (RAF) [25,26]. In addition, assessment of the reactivity of the newly formed radical species utilizing appropriate models for biomolecular targets was one of the main goals of this work, since one of the prerequisites for AOPs is the lower reactivity of final products. A theoretical prediction of the ecotoxicity of the formed products toward aquatic organisms was also calculated using available software resources. The obtained results for the title compounds, as model systems, represent a basis for future investigations into the degradation processes of different coumarin derivatives.

2. Materials and Methods

2.1. Chemicals and Instrumentations

Chemicals used in the synthesis and spectroscopic EPR measurements were obtained from Merck (Darmstadt, Germany), except for spin-trap DEPMPO, which was purchased from Enzo Life Sciences (Farmingdale, NY, USA).

2.2. EPR Measurement with HO^• Radical

The Bruker EMX Nano X-band (9.65 GHz) spectrometer was used for the EPR measurements, which were conducted at room temperature (293 K) using the following experimental parameters: 10 dB power attenuation; 2 mT modulation amplitude; 100 kHz modulation frequency; and 120 s sweep time. The hydroxyl radical (HO^•) was generated in 100 mM phosphate buffer, pH = 7.4, using the standard Fenton reaction (1 mM H₂O₂ and 0.33 mM FeSO₄) with the addition of 0.1 M 2-diethoxyphosphoryl-2-methyl-1-oxido-3,4-dihydropyrrol-1-ium (DEPMPO) as a spin-trapping agent. Spectra collection started 180 s after the addition of the iron catalyst. Jackson’s procedure for purifying the spin trap was followed [27]. Stock solutions of compounds (15 mM) were prepared in DMSO and diluted to 10 μM with water. The amount of DMSO in the blank sample was the same as in the samples containing the investigated compounds. The final concentration of the examined compounds was 0.75 μM. The average intensity of the two most intense peaks of the DEPMPO–HO^• adduct at the low-field region of the spectrum was used to calculate reactivities to HO^•. Measurement results are expressed as the % of radical reduction = 100 × (I₀ − I_a)/I₀. In the previous equation, I_a and I₀ are the intensities of the peaks of the DEPMPO–HO^• adduct with and without the investigated compounds (A₁–RH–A₃–RH), respectively.

2.3. Computational Methodology

The Gaussian09 program package [28] was used for all the calculations based on density functional theory (DFT). The M06-2X/6-311++G(d,p) theoretical model (with polarization and diffuse functions included) was employed for the optimization of the structures of the coumarin derivatives, as suggested in [29]. The applied theoretical model is suitable for thermodynamic and kinetic analyses of various reactions [23,24,25,30,31]. The conductor-like polarizable continuum model (CPCM, water (ε = 78.36)) was applied to approximate the solvent effect in the experimental environment [32].

The radical mechanisms presented in this study were evaluated based on thermodynamic and kinetic considerations. This was consistent with the quantum mechanics-based test for overall free radical scavenging activity (QM-ORSA) methodology [22], commonly used to determine antiradical activity. After the calculation of the corresponding reaction Gibbs free energies (Δ_rG), kinetic calculations were performed for all exergonic (Δ_rG < 0) and isoergonic (Δ_rG = 0) reaction pathways. The rate constants (k) were calculated using transition state theory (TST) [33] or the Eyring equation, as well as Eckart’s method, which represents the special case of the zero-curvature tunneling approach (ZCT_0) [34]. The first theory is based on the laws of classical kinetics, whereas the second includes quantum effects, such as tunneling (Equation (1)):

$$k_{ZCT\_0}=\sigma \gamma (T)\frac{k_{B}T}{h}\exp \left(\frac{-\Delta G_a^{\ne }}{RT}\right)$$

(1)

where k_B and h are the Boltzmann and Planck constants; T is the temperature in K (298.15 K); ΔG_а^≠ is the activation Gibbs free energy; σ represents the reaction path degeneracy accounting for the number of equivalent reaction paths; and γ(T) is the tunneling correction [35]. For these calculations, TheRate program was used [36].

Evaluation of the overall rate constant (k_overall) in a polar medium offers a comprehensive picture of the reactivity of the investigated compounds. The k_overall is the sum of the products of the molar fractions of acid–base species included in specific reactions and the total rate constant (k_tot). The k_tot comprises the sum of all kinetically favored reaction pathways for a particular species. A detailed explanation of the k_overall estimation, the process of quantifying molar fractions of acid–base species at physiological pH, is given in previous research [23]. Additionally, the equations for the estimation of reactivity towards a specific radical (r^T) relative to the reference standard antioxidant (Trolox), as well as relative amounts of products (%)—i.e., the branching ratios (Г_i)—are integral parts of a previous report [23].

The Ecological Structure–Activity Relationships program (ECOSAR V2.0) [37] was used to evaluate the acute and chronic toxicities (ChV, mg·L⁻¹) of the investigated compounds and their oxidation products towards aquatic organisms: green algae, fish, and daphnia. Acute toxicity was defined using EC₅₀ values (the concentration of the examined compound that affected the growth of 50% of green algae after 96 h of exposure) and LC₅₀ values (the concentration of the investigated compound that caused 50% mortality in fish and daphnia after 96 h) [38,39].

The estimated k_overall values made it possible to determine the stability of the investigated compounds during their degradation initiated by HO^• radicals through the half-life (τ_1/2) using the following equation:

$${\tau }_{1/2}=\ln 2/k_{\mathrm{overall}}\times \left[\mathrm{H}{\mathrm{O}}^{•}\right]$$

(2)

where [HO^•]_aq is the concentration of HO^• in an aqueous solution [40].

To examine the activity of the newly formed radical products (A₁–R^•, A₂–R^•, A₃–R^•) towards biologically essential macromolecules, interactions with three groups of building blocks were considered: model lipids, amino acid residues, and nucleobases, as depicted in Figure 2 [41]. The lipid model (LM) mimics unsaturated fatty acids as essential biomolecules. It is represented as a reduced linoleic acid (LA) model that retains its primary chemical reactivity characteristic: two allylic H atoms. Amino acids, as constituents of proteins, are modeled realistically. This model has been successfully used and is widely accepted as appropriate for investigating protein site reactions. The following residues, being the most susceptible to oxidative damage in proteins, were used in this study: cysteine (Cys), leucine (Leu), tyrosine (Tyr), tryptophan (Trp), methionine (Met), and histidine (His). 2′-Deoxyguanosine (2dG) was selected as a model for oxidative DNA damage because guanine (G) is the most easily oxidized nucleobase. Therefore, when one-electron oxidation of DNA occurs, it is primarily located at G sites. Consequently, if a chemical oxidant (radical species) can oxidize 2dG, it can cause oxidative damage to DNA. In contrast, if there is no potential to oxidize 2dG, the oxidant is considered harmless to DNA.

3. Results and Discussion

3.1. Experimental HO^• Scavenging Activity

EPR spectroscopy was used to trace the reactivity of the obtained compounds toward HO^•. All spectra were collected starting from the same time point—180 s after the reaction beginning. Scavenged HO^• radicals were formed in the Fenton system, and DEPMPO was used as a spin trap to enable the monitoring of the decrease in the HO^• concentration. Figure 3 shows the EPR spectra of DEPMPO–HO^• adducts before and after the addition of A₁–RH to A₃–RH compounds. Signal intensity, proportional to the number of scavenged radical species, was reduced after addition of coumarin derivatives, indicating the reaction between the investigated compounds and HO^•. The reactivity of the investigated compounds towards HO^• was calculated as explained in the Materials and Methods section. The scavenging activities decreased in the following order: A₁–RH (91%) > A₂–RH (88%) > A₃–RH (81%). Differences in these values indicate the variation in the reactivity of the investigated compounds. The studied coumarin derivatives contained the –OH group in various positions relative to the –NH– group and the rest of the molecule, leading to different reactivities. This group made hydrogen atom/proton abstraction possible in the standard examination of the activity towards radicals. The amino group was not considered a potential hydrogen atom/proton donor, as this hydrogen atom encloses a quasi-six-membered ring through a hydrogen bond with the carbonyl group, as previously observed in the crystal structure of similar compounds [42,43,44]. The most reactive compound was A₁–RH, which can be explained by the possible formation of hydrogen bonds between oxygen and the NH group upon the reaction with HO^•. Due to the existence of a negative charge in the aromatic ring, higher reactivity for A₃–RH was expected in comparison to A₂–RH. Radical adduct formation (RAF) is another plausible mechanism, as these compounds contain many unsaturated bonds [45,46]. The following sections include a detailed quantum chemical analysis of the oxidation process, emphasizing the role of acid-base equilibria. Hydrogen atom transfer (HAT), the direct exchange of protons followed by the transfer of electrons from formed anions, and the formation of radical adducts are the most probable reaction pathways for coumarin derivatives [23,24]. These mechanisms play crucial roles in the synergy between the elimination of radical species from wastewater and the production of less harmful oxidation products [47,48,49,50].

3.2. Acid-Base Equilibria

As the acid–base equilibrium determines the relative abundance of protonated/deprotonated forms present in an aqueous solution, it is evident that the pH value of the solution determines the dominant mechanism of free radical scavenging. The degree of deprotonation of a compound, expressed through the corresponding pKa value, determines various physicochemical properties, such as hydrophobicity, lipophilicity, polarizability, etc. Quantifying the molar fractions of acid–base species provides a comprehensive way of examining the mechanisms of radical scavenging action. Therefore, it was necessary to determine the pKa values to obtain the deprotonation route and quantify the molar fractions (f). The ACD/pK_a software package was employed to calculate the pK_a values of studied derivatives [51]. Figure 4 shows their deprotonation routes, as well as the estimated pKa values and molar fraction (f) values under physiological conditions. The pK_a values depend on the position of the –OH group. As there were no additional stabilization effects in the formed anion, the meta-substituted derivative (A₂–R⁻) showed the lowest value (pK_a = 9.64). The A₁–R⁻ anion (pK_a = 9.71) was stabilized by the intramolecular hydrogen bond between the amino group and the oxygen atom. The extended delocalization in the aromatic ring of the formed anion A₃–R⁻ was responsible for the highest pK_a value (pK_a = 10.43). This analysis proves that hydrogen atom/proton donation is only possible from the –OH group.

Based on the obtained pK_a values, neutral species dominate (>99%) at physiological pH. Due to this fact, theoretical investigations were performed on neutral forms: A₁–RH (99.5%), A₂–RH (99.4%), and A₃–RH (99.9%). Their optimized structures, with carbon atom numbering schemes, are shown in Figure 5.

3.3. Reactions of A_n–RH with HO^• Radical—Thermodynamic Approach

The possible reaction centers for the standard mechanisms (HAT/PCET (Equation (3)), SPLET (Equations (4) and (5)), and SETPT (Equations (6) and (7))) of radical action between A₁–RH, A₂–RH, A₃–RH, and HO^• were aromatic –OH groups. For the RAF mechanism, these centers included aromatic carbon atoms (Equation (8)). The calculated values of the reaction Gibbs energies (Δ_rG) for the mentioned mechanisms are listed in

Table 1. Estimated values of reaction Gibbs energies (Δ_rG) in kJ·mol⁻¹ for reactions between coumarin derivatives (A₁–RH, A₂–RH, A₃–RH) and HO^• at 298.15 K.

Species	HO•
	HAT/PCET	SET−PT		SPLET
	ΔrGHAT/PCET	ΔrGSET	ΔrGPT	ΔrGSPL	ΔrGET
A1–RH	−127	139	−266	−115	−13
A2–RH	−124	144	−268	−103	−21
A3–RH	−126	122	−248	−115	−28
Positions	RAF, ΔrGRAF
	A1–RH	A2–RH		A3–RH
C3	−7	−15		−5
C5	−41	−43		−37
C6	−18	−21		−17
C7	−44	−43		−40
C8	−34	−36		−35
C9	−31	−35		−29
C10	2	−4		4
C1′	−27	−27		−24
C1″	−35	−27		−34
C2″	−43	−38		−17
C3″	−30	−34		−31
C4″	−22	−42		−40
C5″	−24	−22		−32
C6″	−31	−21		−30

.

HAT: A_n–RH + HO^• → A_n–R^• + H₂O

(3)

SPL: A_n–RH + HO⁻ → A_n–R⁻ + H₂O

(4)

ET: A_n–R⁻ + HO^• → A_n–R^• + HO⁻

(5)

SET: A_n–RH + HO^• → A_n–RH^•+ + HO⁻

(6)

PT: A_n–RH^•+ + HO⁻ → A_n–R^• + H₂O

(7)

RAF: A_n–RH + HO^• → [HO–A_n–RH]^•

(8)

According to the Δ_rG values shown in Table 1 for the first step of each mechanism, HAT/PCET was thermodynamically favored for all derivatives. The reactivity of the compounds and the stability of the formed radical products increased in the following order: A₂–RH (−124 kJ·mol⁻¹) > A₃–RH (−126 kJ·mol⁻¹) > A₁–RH (−127 kJ·mol⁻¹). This order nicely follows the discussion on the possible stabilization effects of proton removal in acid-base equilibrium processes.

Negative Δ_rG_RAF values made the RAF mechanism thermodynamically spontaneous in almost all the positions of the investigated compounds. The most favored positions for attack by electrophilic HO^• were the C5 (from −43 to −37 kJ·mol⁻¹) and C7 (from −44 to −40 kJ·mol⁻¹) atoms of the aromatic part of the chroman ring, as well as the C1″ to C6″ positions of the aromatic aminophenol rings. As mentioned, the aromatic carbon atoms of both rings were possible reaction sites. It is essential to notice that the values for the chroman part of the molecule did not significantly depend on the position of the substituent (around 5 kJ·mol⁻¹ difference), with the exception of position C3. When aminophenol carbon atoms were involved, noticeable differences were only obtained for the carbon atoms adjacent to the position of the –OH group. However, slightly endergonic values for the C10 position of the A₁–RH (2 kJ·mol⁻¹) and A₃–RH (4 kJ·mol⁻¹) compounds were obtained. In the optimized geometries of radical adducts (Figures S1–S3), the rehybridization of the carbon atom (sp² to sp³) where the HO^• radical was attached occurred, leading to broken aromaticity and planarity in the system. The most thermodynamically favored products were characterized by short interatomic distances in adducts C−2″ (A₁–RH, 1.408 Å), C−3″ (A₂–RH, 1.405 Å), and C−5″ (A₃–RH, 1.405 Å) due to stabilization by intramolecular contacts (Figures S1–S3).

For all the examined compounds, significantly negative Δ_rG_SPL values indicated that the first step of the SPLET mechanism was thermodynamically spontaneous (Table 1). The reactivity of the compounds and the stability of the formed anionic species increased in the following sequence: A₂–RH (−103 kJ·mol⁻¹) > A₁–RH (−115 kJ·mol⁻¹) > A₃–RH (−115 kJ·mol⁻¹), with the same plausible explanation as for the first mechanism. Comparison of Δ_rG_HAT/PCET and Δ_rG_SPL indicated that the hydrogen atom transfer from the –OH group was slightly more favored than the proton transfer. In the second step of the SPLET mechanism—i.e., electron transfer—Δ_rG_ET values decreased in the following sequence: A₁–RH (−13 kJ·mol⁻¹) > A₂–RH (−21 kJ·mol⁻¹) > A₃–RH (−28 kJ·mol⁻¹). These values depended on the spin delocalizations in the formed radicals.

Finally, highly endergonic values (122–144 kJ·mol⁻¹) for the first step of the SET−PT mechanism (Δ_rG_SET) suggested that this mechanism was not thermodynamically probable. Thus, it was not considered in further kinetic studies (Table 1).

3.4. Reactions of A_n–RH with HO^• Radical—Kinetic Approach

Thermodynamically favored reaction pathways (Δ_rG ≤ 0) were subjected to kinetic investigation. After locating the transition state geometries (where possible), the activation Gibbs energies (ΔG_a) were evaluated. Rate constants for reactions involving electron transfer were calculated using Marcus theory (

Table 2. Estimated values of kinetic parameters at 298.15 K: activation Gibbs energy (ΔG_a, kJ·mol⁻¹) and rate constants of the bimolecular chemical reactions (M⁻¹ s⁻¹) between the investigated compounds A₁–RH, A₂–RH, and A₃–RH and HO^• estimated with the Eckart method (k_{ZCT_0}). The k^ET values (M⁻¹ s⁻¹) represent rate constants calculated with Marcus theory.

Species	HAT/PCET		SPLET
	$\mathsf{\Delta }{\mathit{G}}_{\mathit{a}}^{\mathit{H}\mathit{A}\mathit{T}/\mathit{P}\mathit{C}\mathit{E}\mathit{T}}$	${\mathit{k}}_{\mathit{Z}\mathit{C}\mathit{T}\_\mathbf{0}}^{\mathit{H}\mathit{A}\mathit{T}/\mathit{P}\mathit{C}\mathit{E}\mathit{T}}$	$\mathsf{\Delta }{\mathit{G}}_{\mathit{a}}^{\mathit{S}\mathit{P}\mathit{L}}$	${\mathit{k}}^{\mathit{S}\mathit{P}\mathit{L}}$	$\mathsf{\Delta }{\mathit{G}}_{\mathit{a}}^{\mathit{E}\mathit{T}}$	${\mathit{k}}^{\mathit{E}\mathit{T}}$
A1–RH	~0	1.91 × 109	~0	1.91 × 109	2	8.02 × 109
A2–RH					2	8.01 × 109
A3–RH					6	7.90 × 109
Position	A1–RH		A2–RH		A3–RH
	$\mathsf{\Delta }{\mathit{G}}_{\mathit{a}}^{\mathit{R}\mathit{A}\mathit{F}}$	${\mathit{k}}_{\mathit{Z}\mathit{C}\mathit{T}\_\mathbf{0}}^{\mathit{R}\mathit{A}\mathit{F}}$	$\mathsf{\Delta }{\mathit{G}}_{\mathit{a}}^{\mathit{R}\mathit{A}\mathit{F}}$	${\mathit{k}}_{\mathit{Z}\mathit{C}\mathit{T}\_\mathbf{0}}^{\mathit{R}\mathit{A}\mathit{F}}$	$\mathsf{\Delta }{\mathit{G}}_{\mathit{a}}^{\mathit{R}\mathit{A}\mathit{F}}$	${\mathit{k}}_{\mathit{Z}\mathit{C}\mathit{T}\_\mathbf{0}}^{\mathit{R}\mathit{A}\mathit{F}}$
C3	40	1.61 × 107	41	1.48 × 107	47	1.22 × 106
C5	54	7.15 × 104	51	2.77 × 105	53	1.11 × 105
C6	56	3.34 × 104	53	1.35 × 105	55	4.66 × 104
C7	60	7.54 × 103	51	2.80 × 105	63	2.31 × 103
C8	47	1.33 × 106	44	3.46 × 106	53	1.19 × 105
C9	56	3.12 × 104	53	1.35 × 105	57	2.12 × 104
C10	50	4.15 × 105	46	1.85 × 106	52	1.49 × 105
C1′	54	8.03 × 104	50	3.72 × 105	55	4.55 × 104
C1″	41	1.29 × 107	51	2.53 × 105	41	1.34 × 107
C2″	47	1.35 × 106	36	4.46 × 107	49	5.96 × 105
C3″	41	1.20 × 107	48	1.48 × 107	39	2.44 × 107
C4″	48	7.15 × 105	33	1.39 × 108	52	1.46 × 105
C5″	42	7.94 × 106	51	2.78 × 105	39	2.55 × 107
C6″	42	3.34 × 106	32	5.66 × 107	43	5.55 × 106

). The rate constants were estimated using the TST (Table S1) and ZCT_0 (Table 2) methods.

The pronounced exergonic values for hydrogen atom transfer (HAT/PCET) between A_n–RH and HO^• indicate the thermodynamic favorability of this mechanism. However, attempts to find transition state geometries describing these reactions have been unsuccessful. Thus, it is reasonable to assume that these reactions occur in a practically barrier-less manner [25]. To confirm the above assumption, the energy change as a function of the corresponding distance—i.e., HO–H2″ (−OH, Å) (A₁–RH), HO–H3″ (−OH, Å) (A₂–RH), HO–H4″ (−OH, Å) (A₃–RH)—was monitored (Figure S4). Analyzing Figure S4, it was discovered that there was a constant decrease in total energy as a function of distance from −1314.79 to −1314.87 a.u. This means that the reaction takes place without an activation barrier as a diffusion-controlled process with the rate constant, based on available literature data, of 1.91 × 10⁹ M⁻¹·s⁻¹ [52,53,54].

Another plausible mechanistic pathway for the reaction of HO^• with the investigated compounds is the RAF mechanism. The values of the rate constants estimated with the ZCT_0 method (Table 2) correlate with the values estimated with the TST method (Table S1). The rate constants obtained were in the range of 10³ to 10⁷ M⁻¹·s⁻¹. Comparison of thermodynamic and kinetic parameters provided evidence that thermodynamically favored products are not necessarily kinetically preferred. The kinetically most preferred positions for HO^• attack were C1″ (1.29 × 10⁷ M⁻¹·s⁻¹) and C3″ (1.20 × 10⁷ M⁻¹·s⁻¹) for A₁–RH, C2″ (4.46 × 10⁷ M⁻¹·s⁻¹) and C4″ (1.39 × 10⁸ M⁻¹·s⁻¹) for A₂–RH, and C3″ (2.44 × 10⁷ M⁻¹·s⁻¹) and C5″ (2.55 × 10⁷ M⁻¹·s⁻¹) for A₃–RH, with ΔG_a values in the interval from 36 to 41 kJ·mol⁻¹. The optimized geometries of the corresponding transition states are shown in Figure 6, Figures S5 and S6. The transition states of the kinetically most favored products were characterized by larger interatomic distances: C1″ (2.047 Å) and C3″ (2.070 Å) for A₁–RH, C2″ (2.093 Å) and C4″ (2.115 Å) for A₂–RH, and C3″ (2.077 Å) and C5″ (2.088 Å) for A₃–RH. Moreover, the geometries of the mentioned transition states were stabilized by hydrogen bonds between the reactive HO^• particle and the polar functional group.

Analogously to the HAT/PCET mechanism, the geometries of the transition states for the proton transfer reactions (SPL mechanism) have not been found, despite numerous attempts. In this case, the dependence of the total energy (a.u.) on the distance was monitored. The constant decrease in energy indicated that these reactions occurred without an activation barrier as diffusion-controlled processes (Figure S7, 1.91 × 10⁹ M⁻¹·s⁻¹) [52,53,54]. The electron transfer rate constants estimated using Marcus theory decreased in this sequence: A₁–RH (8.02 × 10⁹ M⁻¹·s⁻¹) > A₂–RH (8.01 × 10⁹ M⁻¹·s⁻¹) > A₃–RH (7.90 × 10⁹ M⁻¹·s⁻¹). Based on these results, the formation of A₁−R^• was a kinetically favored process, while A₃−R^• was thermodynamically preferred (Table 2 and

Table 3. Estimated values of reaction Gibbs energies (Δ_rG) in kJ·mol⁻¹ for reactions between the biologically important target molecules and the formed A₁−R^•, A₂−R^•, A₃−R^• radicals at 298.15 K.

Target Molecule	A1–O•	A2–O•	A3–O•	HO•
LM	62	65	63	−190
NF−Leu (γ−site)	−16	−13	−15	−111
NF−Cys (SH site)	18	21	19	−145
NF−Tyr (OH site)	9	12	10	−136
NF−Tyr (SET)	139	148	155	127
NF−Trp (SET)	92	101	108	80
NF−Met (γ−site)	−13	−10	−12	−114
NF−His (SET)	−5	−2	−3	−123
G	17	14	16	−110
2dG	30	27	29	−97

). The stability of A₂−R^• depended on the position of the OH substituent and the delocalization of unpaired electrons through the structure. No additional hydrogen bonds were observed.

Using the individual rate constants, the overall rate constant (k_overall) was determined as a measure of the susceptibility of a compound to the AOPs involving HO^• (Table S2). All investigated compounds showed a high overall rate constant, with a negligible decrease in activity in the following order: A₁–RH (1.21 × 10¹⁰ M⁻¹·s⁻¹) > A₂–RH (1.19 × 10¹⁰ M⁻¹·s^–1) > A₃–RH (1.18 × 10¹⁰ M⁻¹·s⁻¹). This correlated well with the experimental values obtained with EPR spectroscopy. This comparison proved the applicability of the QM-ORSA methodology for the prediction of the capacity and mechanisms of the radical action of the investigated compounds.

To evaluate the relative amounts of products, as well as the influence of individual reaction pathways on the overall capacity, branching ratios (Г_i, %) were estimated (Table S2). The results in Table S2 indicate that HAT and SPLET were the dominant mechanisms in the HO^• removal process. Radicals in the HAT/PCET mechanism and anionic species in the SPL mechanism were formed in significant percentages: 16.06% (A₁–RH), 15.78% (A₂–RH), and 16.20% (A₃–RH). Radicals formed during the electron transfer from the phenoxide anions to HO^• were present in the highest relative percentages: 67.40% (A₁–RH), 66.16% (A₂–RH), and 67.00% (A₃–RH). The difference in the stabilization of anions and radicals overcame the importance of the substitution position in the cases of A₂–RH and A₃–RH, thus leading to the higher experimental and theoretical reactivity of the former towards HO^•.

Finally, based on the k_overall value, it was possible to estimate the half-life (τ_1/2) values of the investigated compounds exposed to HO^• radicals. The τ_1/2 values calculated under physiological conditions and with different concentrations of HO^• are presented in Table S3. In natural water, [HO^•]_aq concentrations ranged from 10⁻¹⁸ or 10⁻¹⁴ M to ca. 10⁻¹⁰ M in the AOP system. Specifically, at very low concentrations of HO^• in the range from approximately 10⁻¹⁸ to 10⁻¹⁶ M, the τ_1/2 for degradation of A₁–RH−A₃–RH was in the range of 679.9–6.6 days. At HO^• concentrations between 10⁻¹⁵ and 10⁻¹⁴ M, the τ_1/2 decreased to 16.8–1.6 h. At the HO^• concentration of 10⁻¹⁰ M, the half−life dropped to ~0.6 s. Thus, the effectiveness of AOP technology was demonstrated, as well as the importance of theoretical investigations and modeling of these processes.

3.5. Damage to a Target Biomolecule

To obtain information about the reactivity of the formed radical species (A₁–O^•, A₂–O^•, and A₃–O^•), interactions with the constituents of essential macromolecules—the phospholipid bilayer, proteins, and nucleic acids—were examined (Table 3). The optimized geometries of the reaction participants, neutral molecular targets, and corresponding radicals/radical cations are shown in Figure S8 and Figure 7. As expected, highly reactive radical species, such as HO^•, interacted spontaneously with all investigated biomolecules (the lipid model (−190 kJ·mol⁻¹), amino acid residues (<−111 kJ·mol⁻¹), and nucleotides (<−97 kJ·mol⁻¹)) except for NF-Trp (80 kJ·mol⁻¹).

The lipid model (LM) is a model of linoleic acid that was employed on the basis of literature data [55]. This unsaturated fatty acid has two allylic H atoms that can react with radical species through the HAT mechanism [56]. Endergonic reactions between the formed radicals and LM (>62 kJ·mol⁻¹) indicated that they do lead to the destruction of the building blocks of the cell membrane of living organisms.

Model compounds were chosen to represent the building blocks of proteins; amino acids have been successfully applied as reactive centers in the study of protein reactions [57]. Available literature data indicate that the selected amino acid residues (leucine (Leu), cysteine (Cys), methionine (Met), tyrosine (Tyr), histidine (His), and tryptophan (Trp)) are susceptible to radical attack [58]. These amino acid residues react with radical species through different mechanisms: SET (Tyr, Trp) and HAT (Cis, Leu, Met, His) [41]. Except for slightly exergonic Δ_rG values with the amino acid residues NF-Leu (γ-site) (<−13 kJ·mol⁻¹), NF-Met (γ-site) (<−10 kJ·mol⁻¹), and NF-His (γ-site) (–2 kJ·mol⁻¹), the newly formed radicals did not interact with the other investigated building blocks of the protein.

2′-Deoxyguanosine (2dG) and guanine (G), which is the most easily oxidized of all nucleobases, were chosen for oxidative DNA damage modeling [41,59]. The newly formed radical species did not interact with the building blocks of DNA molecules (nucleotides (>30 kJ·mol⁻¹)), nor with the corresponding bases (>14 kJ·mol⁻¹), as indicated by the endergonic Δ_rG values.

3.6. Termination of A_n–R^• Reactions by Synergistic Reactions with O₂/NO and HO^•

Although the formed radicals did not show activity towards important constituents of biomolecules, the question of their further fate remained open. Based on available literature data [38], two possible reaction paths comprising radical inactivation and the formation of neutral products were proposed. For A_n–R^• radical species, two carbon atoms located near the oxygen were chosen, and the hydrogen atom/proton abstraction process was modeled. The proposed reaction schemes for the mechanisms are presented in Figure 8, while the corresponding values of the thermodynamic parameters are summarized in

Table 4. Estimated values of reaction Gibbs energies (Δ_rG) in kJ·mol⁻¹ for reactions between the formed radicals A₁−R^•, A₂−R^•, and A₃−R^• and O₂/NO in different sequential reaction pathways (I_a, II_a, III_a, IV_a) or HO^• (I_b, II_b) at 298.15 K.

Radical	Position	Ia	IIa	IIIa	IVa	Ib	IIb
A1–O•	C-3	−98	−32	−15	−416	−207	−101
	C-5	−112	−28	−10	−421	−207	/
A2–O•	C−2	−110	−21	−29	−419	−211	−107
	C-4	−116	−21	−24	−414	−214	−107
A3–O•	C-3	−95	−31	−9	−438	−200	−116
	C-5	−98	−28	−27	−421	−211	−111

.

Available literature data indicate the ability of radicals to react synergistically with O₂/NO and form neutral products (Figure 8 and Figure 9, P2) [38]. A variable concentration of dissolved molecular oxygen (O₂) in water enables the reaction with radical species leading to the formation of a corresponding peroxide adduct (IN1, Ia, Figure S9), which can further react with the NO present in natural and wastewater to form a radical adduct (P1, IIa, Figure S10). The next step involved the spontaneous intramolecular separation of NO₂ molecules (IIIa) with the formation of the intermediate radical adduct IN2 (Figure S11). In this specific context, Δ_rG was exergonic and thermodynamically favored, especially in the case of the addition of molecular oxygen (Table 4). Finally, the action of HO^•, through a highly exergonic mechanism (<−414 kJ·mol⁻¹) that has already been observed in our previous research, was found to result in the intramolecular separation of water molecules (IVa) and the formation of a neutral product (P2, Figure 9).

Another mechanism has also been postulated and discussed in detail in previous work focused on AOP systems [24,24,53]. It involves the reaction of a formed radical with another HO^• radical (Ib), resulting in the formation of a neutral product (P3, Figure S12). In the next step, through keto–enol tautomerism (IIb) in a highly exergonic process (>−101 kJ·mol⁻¹, Table 2), a catechol-type product is formed (P4).

3.7. Ecotoxicological Approach

The resulting stable oxidation products (P2, P4) were subjected to acute and chronic ecotoxicity estimation investigations for aquatic organisms: fish, daphnia, and green algae. The results, obtained as part of the ECOSAR program, together with the reference values published by the European Union (acute toxicity, described in Annex VI of Directive 67/548/EEC) [60] and in the Chinese hazard evaluation guidelines for new chemical substances (chronic toxicity, HJ/T 154-2004) [61], are summarized in

Table 5. Estimated ecotoxicity values of A₁–RH, A₂–RH, and A₃–RH and their oxidation products in relation to aquatic organisms (mg·L⁻¹) at pH = 7.4.

Products	Acute Toxicity *			Chronic Toxicity *
	Fish LC50	Daphnia LC50	Green Algae EC50	Fish ChV	Daphnia ChV	Green Algae ChV
A1–RH	9.40	17.20	6.04	0.60	8.31	2.29
P1-C3/C5	27.40	3.54	2.49	1.24	0.32	0.88
P2-C3	99.6	11.60	10.1	6.28	0.93	3.28
P2-C5	59.1	7.40	5.73	3.30	0.60	1.92
P3-C3	49.8	6.10	4.77	2.67	0.51	1.61
P3-C5	199.00	22.00	21.20	14.80	1.67	6.65
P4-C3	18.7	36.10	13.70	1.21	20.30	4.43
A2–RH	15.10	28.60	10.60	0.95	15.30	3.60
P1-C2/C4	86.70	10.30	8.58	5.15	0.84	2.83
P2-C2/C4	99.60	11.60	10.10	6.28	0.93	3.28
P3-C2/C4	157.00	17.60	16.40	11.10	1.37	5.22
P4-C2	18.70	36.10	13.70	1.21	20.30	4.43
P4-C4	30.00	60.00	24.10	2.10	36.90	6.69
A3–RH	15.10	28.60	10.60	0.95	15.30	3.60
P1-C3/C5	86.70	10.30	8.58	5.15	0.84	2.83
P2-C3/C5	99.6	11.60	10.10	6.28	0.93	3.28
P3-C3/C5	157.00	17.60	16.40	11.10	1.37	5.22
P4-C3/C5	30.00	60.00	24.10	2.10	36.90	6.69

* Reference values [60,61]. Not harmful: log LC₅₀ > 100 or log EC₅₀ > 100. Log ChV > 10. Harmful: 10 < log LC₅₀ < 100 or 10 < log EC₅₀ < 100. 1 < log ChV < 10. Toxic: 1 < log LC₅₀ < 10 or 1 < log EC₅₀ < 10. 0.1 < log ChV < 1. Very toxic: log LC₅₀ < 1 or log EC₅₀ < 1. Log ChV < −0.1.

.

All starting compounds (A₁–RH, A₂–RH, and A₃–RH) showed harmful acute (<15.10 mg·L⁻¹) and chronic toxic effects (<1 mg·L⁻¹) on fish. On the other hand, all oxidation products showed less acute harmful (>18.70 mg·L⁻¹) and chronic (>1.21 mg·L⁻¹) toxicity. In contrast, the oxidative product P3 of all compounds was entirely harmless in terms of acute (>157.00 mg·L⁻¹) and chronic toxicity (>11.10 mg·L⁻¹). In general, oxidation product P4 showed a less acute harmful effect on daphnia (>36.10 mg·L⁻¹) in comparison to neutral compounds, while being utterly harmless in terms of chronic toxicity (>20.30 mg·L⁻¹). Oxidation products P3 and P4 showed fewer harmful effects in terms of acute (>13.10 mg·L⁻¹) and chronic toxicity (>4.43 mg·L⁻¹) in comparison to the neutral starting compounds. A similar trend was observed in the interpretation of the ecotoxicological status of green algae.

4. Conclusions

Application of advanced oxidation processes to stable coumarin derivatives is one way to remove them from wastewater and decrease the toxicity towards aquatic organisms. Three aminophenol derivatives of 4,7–hydroxycoumarin and HO^• were employed for experimental and theoretical examination of the relevant reaction mechanisms. Based on the results of EPR measurements, it can be concluded that the investigated compounds showed high reactivity towards the HO^• radical, with a decrease in reactivity in the following order A₁–RH (91%) > A₂–RH (88%) > A₃–RH (81%). At the physiological pH value, all three compounds presented as neutral species (>99%), followed by the monoanionic forms. Analysis of the thermodynamic and kinetic parameters confirmed that the hydrogen atom transfer (HAT), sequential proton loss followed by electron transfer (SPLET), and radical adduct formation (RAF) mechanisms were the operative reaction pathways in the degradation of the studied compounds induced by the HO^• radical. The hydrogen atom and electron transfers represented diffusion-controlled reactions, while the RAF rate constants were between 10³ and 10⁷ M⁻¹s⁻¹, depending on the reaction site. Estimated overall rate constants (k_overall) decreased slightly in the order: A₁–RH (1.21 × 10¹⁰ M⁻¹·s⁻¹) > A₂–RH (1.19 × 10¹⁰ M⁻¹·s⁻¹) > A₃–RH (1.18 × 10¹⁰ M⁻¹·s⁻¹), as obtained using the QM−ORSA methodology, showing excellent agreement with the reactivity order observed using EPR spectroscopy. The anionic species present greatly influenced the overall rate constant, leading to the obtained order of reactivity. The stability of the formed radical and anionic species resulted from extended delocalization and weak interactions between groups within compounds. The estimated values of the branching ratios (Г_i, %) of products indicated that the degradation of the investigated compounds induced by HO^• mainly occurred via HAT and SPLET mechanisms, with half-life (τ_1/2) values of ca. 0.6 s. The distinctly endergonic Δ_rG values for the reaction of the formed radicals (A₁−R^•, A₂−R^•, and A₃−R^•) and the biomolecule building blocks (linoleic acid, amino acids, and guanine) demonstrated the importance of the lower toxicity of products in AOPs. As expected, the Δ_rG values were more endergonic compared to the interaction of the HO^• radical and the investigated macromolecular targets. The formed radical species could further interact with the O₂/NO and HO^• present in wastewaters to end the cycle and form neutral species. The thermodynamic favorability of these reaction pathways was reflected in the highly exergonic Δ_rG values for the four/two steps of the proposed mechanisms The formed neutral products had lower acute and chronic toxicity than the starting neutral compounds, as estimated in the ECOSAR program, towards daphnia, fish, and green algae. The presented experimental/theoretical results demonstrate the applicability of the proposed mechanisms. They open the way for future analysis and application of the mentioned theoretical approach in developing advanced oxidation processes and highlight the need for reliable determination of toxicity towards aquatic organisms.