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 (
link)]. The applied theoretical model is suitable for thermodynamic and kinetic analyses of various reactions [23 (
link),24 (
link),25 (
link),30 (
link),31 (
link)]. The conductor-like polarizable continuum model (CPCM, water (
ε = 78.36)) was applied to approximate the solvent effect in the experimental environment [32 (
link)].
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 (
link)], 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 (
link)] or the Eyring equation, as well as Eckart’s method, which represents the special case of the zero-curvature tunneling approach (ZCT_0) [34 (
link)]. The first theory is based on the laws of classical kinetics, whereas the second includes quantum effects, such as tunneling (Equation (1)):
where
kB and
h are the Boltzmann and Planck constants;
T is the temperature in K (298.15 K); Δ
Gа≠ 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 (
link)]. For these calculations,
TheRate program was used [36 (
link)].
Evaluation of the overall rate constant (
koverall) in a polar medium offers a comprehensive picture of the reactivity of the investigated compounds. The
koverall is the sum of the products of the molar fractions of acid–base species included in specific reactions and the total rate constant (
ktot). The
ktot comprises the sum of all kinetically favored reaction pathways for a particular species. A detailed explanation of the
koverall estimation, the process of quantifying molar fractions of acid–base species at physiological pH, is given in previous research [23 (
link)]. Additionally, the equations for the estimation of reactivity towards a specific radical (
rT) relative to the reference standard antioxidant (Trolox), as well as relative amounts of products (%)—i.e., the branching ratios (
Гi)—are integral parts of a previous report [23 (
link)].
The Ecological Structure–Activity Relationships program (ECOSAR V2.0) [37 (
link)] 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 EC
50 values (the concentration of the examined compound that affected the growth of 50% of green algae after 96 h of exposure) and LC
50 values (the concentration of the investigated compound that caused 50% mortality in fish and daphnia after 96 h) [38 (
link),39 (
link)].
The estimated
koverall values made it possible to determine the stability of the investigated compounds during their degradation initiated by HO
• radicals through the half-life (
τ1/2) using the following equation:
where [HO
•]
aq is the concentration of HO
• in an aqueous solution [40 (
link)].
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 (
link)]. 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.
Milanović Ž., Dimić D., Klein E., Biela M., Lukeš V., Žižić M., Avdović E., Bešlo D., Vojinović R., Dimitrić Marković J, & Marković Z. (2023). Degradation Mechanisms of 4,7-Dihydroxycoumarin Derivatives in Advanced Oxidation Processes: Experimental and Kinetic DFT Study. International Journal of Environmental Research and Public Health, 20(3), 2046.