Revealing the Antioxidant Properties of Alkyl Gallates: A Novel Approach through Quantum Chemical Calculations and Molecular Docking

doi:10.21203/rs.3.rs-4984177/v1

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Revealing the Antioxidant Properties of Alkyl Gallates: A Novel Approach through Quantum Chemical Calculations and Molecular Docking

https://doi.org/10.21203/rs.3.rs-4984177/v1

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This study investigates the antioxidant properties of alkyl gallates (C1-C10) through quantum chemical calculations and molecular docking methods. Density functional theory (DFT) was employed to calculate key thermochemical parameters such as bond dissociation enthalpy (BDE), ionization potential (IP), proton dissociation enthalpy (PDE), proton affinity (PA), and electron transfer enthalpy (ETE) in both gas and solvent phases (benzene, ethanol, and water). The results indicate that the alkyl chain length and the solvent environment significantly influence the antioxidant activity of alkyl gallates. BDE values demonstrate that the hydrogen atom transfer (HAT) mechanism is preferred in the gas phase due to its relatively consistent BDE values and strong correlation with spin density distributions. Conversely, the SET-PT and SPLET mechanisms are more efficient in polar solvents, as indicated by significant reductions in IP, PDE, PA, and ETE values. Molecular docking studies with Tyrosine kinase Hck, Heme Oxygenase, and Human Serum Albumin reveal how structural changes in the alkyl chain influence binding interactions, guiding the synthesis of new compounds with enhanced antioxidant activity. The computational findings, which align well with experimental data, underscore the importance of considering both molecular structure and solvent effects in evaluating the antioxidant potential of alkyl gallates. This integrated approach highlights the critical interplay between computational predictions and experimental validations in advancing antioxidant research.

Antioxidant Activity

Alkyl Gallates

Density Functional Theory (DFT)

Molecular Docking

Thermochemical Parameters

The human body is constantly attacked by reactive species, which cause oxidative stress and damage essential biomolecules. This can lead to serious diseases such as cancer, cardiovascular diseases, and diabetes [1–7]. Natural antioxidants are crucial in neutralizing these reactive species, making understanding their effectiveness vital in disease prevention [8–12]. Due to their potent properties, research has been focused on developing new phenolic compounds (PCs), abundant in plants, for their potential to prevent these diseases [15–18]. Alkyl gallates are natural antioxidants with exceptional antioxidant properties due to their hydroxyl groups [19–21]. Their alkyl chain length influences their lipophilicity and ability to cross cell membranes, making them effective at neutralizing free radicals within cells [22–25]. Their amphiphilic structure, consisting of polar and nonpolar components, also classifies them as lipophilic phenolic compounds (Lipo-PCs) [26–29]. This amphiphilic nature is crucial in food science as it allows alkyl gallates to interact with the food matrix, influencing properties like taste and odor while preventing lipid oxidation [30, 31]. Their ability to function in water- and fat-soluble media makes them essential in health and food sciences [32, 33].

Lipophenols' antioxidant behavior is parabolic, with the length of alkyl chains playing a crucial role, a phenomenon known as the "cut-off effect" [34, 35]. While longer chains initially enhance lipophenols' ability to reach intracellular targets, excessively long chains can reduce their bioavailability due to decreased water solubility [36]. The optimal chain length depends on various factors, including the food matrix and biological environment [37]. Thus, strategic adjustment is necessary to maximize antioxidant potential [38–42]. Several factors may explain the cut-off effect, including steric hindrance from long chains impeding interaction with free radicals [43–45], disruption of the optimal balance between hydrophilic and hydrophobic components [46], and the formation of micelles at high concentrations [47, 48].

In experimental studies, the potential antioxidant activities of alkyl gallates were determined using the widely used 1,1-diphenyl-2-picrylhydrazyl (DPPH) and 2,2'-azinobis (3-ethylbenzothiazoline-6-sulfonic acid) (ABTS) methods. These methods are preferred because they are fast, simple, and sensitive [49–53]. In a notable study by Reeves et al., the antioxidant properties of alkyl gallates were thoroughly investigated. Reeves used DPPH radical scavenging assays to determine the average EC₅₀ values for each alkyl gallate, showcasing their potent antioxidant potential as alternatives to traditional antioxidants. Notably, methyl gallate exhibited a higher antiradical power (ARP) than other gallate esters, suggesting it may be a more effective antioxidant. Additionally, cyclic voltammetry (CV) analysis revealed that gallate esters undergo two stable and irreversible one-electron oxidations, further supporting their ability to scavenge and stabilize free radicals [54]. Kubo et al. also explored the antioxidant properties of alkyl gallates, focusing on their ability to inhibit lipid peroxidation. The research found that alkyl gallates effectively inhibited linoleic acid peroxidation catalyzed by soybean lipoxygenase-1, with tetradecanyl gallate (C14) demonstrating the most potent inhibition. The inhibition kinetics revealed a competitive and slow-binding inhibition mechanism, suggesting that alkyl gallates interact with the enzyme's active site and hydrophobic domain [55]. Both studies highlight the significant antioxidant potential of alkyl gallates, supporting their potential use as effective alternatives to traditional antioxidants in various applications, including food preservation and cosmetics.

In recent computational studies, the antioxidant activity of numerous phenolic compounds (PCs) has been determined, often using density functional theory (DFT) to calculate physicochemical parameters such as bond dissociation enthalpy (BDE), proton dissociation enthalpy (PDE), proton affinity (PA), ionization potential (IP), and electron transfer enthalpy (ETE) [56–59]. These parameters play a crucial role in understanding and evaluating antioxidant activity. Gallic acid (GA) and its derivatives have been a central focus in both computational and experimental studies, with their radical scavenging activity being examined through quantum chemical calculations [60–62]. However, while experimental studies on the antioxidant activity of alkyl gallates exist, only a limited number specifically focus on those with (C1-C10) alkyl chains.

Molecular docking, which is used to predict the binding mode of a small molecule against a target molecule, predicts structural changes of a ligand that may affect its binding properties and thus guides the synthesis of new compounds with more favorable pharmacological properties [63, 64]. Additionally, docking techniques help to understand the details of biological processes. In a molecular docking study by Sutomo and Pratama, the interactions of methyl gallate with various antioxidant receptors and its antioxidant potential were investigated compared to gallic acid. The study determined that methyl gallate has a better antioxidant potential than gallic acid in the xanthine oxidase pathway and may be a potential alternative compound in treating hyperuricemia [65].

This study aims to investigate the free radical mechanisms that play an important role in determining the antioxidant activity of alkyl gallates and to evaluate the thermodynamics by calculating the physicochemical parameters and the effect of solvent polarity on the activity. The computational results obtained in this study are focused on elucidating the mechanisms of alkyl gallates' antioxidant activity and the literature's uncertainties regarding the factors affecting these mechanisms. Benzene, ethanol, and water were chosen as solvents. However, this study evaluated the compatibility of both results by comparing them with the calculation results based on experimental data by Kubo. Additionally, molecular docking methods used Tyrosine kinase Hck, Heme Oxygenase, and Human Serum Albumin to get insight into the molecules' interactions. The molecular structures of the studied alkyl gallates and gallic acid as a reference compound are shown in Fig. 1.

All calculations were done using the Gaussian 16 software package [66]. The structures of the investigated molecules were drawn using Gaussview 6.0.8 graphical user interface [67]. Density functional theory (DFT) was chosen because the determination of antioxidant activity is based on electron density and has successfully resulted in radical scavenging activity studies. Geometry optimization, calculation of harmonic vibrational frequencies, and calculations of antioxidant parameters BDE, IP, PDE, PA, and ETE were performed using the 6-311G (d, p) basis set with the B3LYP (Becke's exchange function in combination with Lee-Yang-Parr [68] correlation functional. B3LYP is a trendy DFT hybrid function used in computational chemistry because it has a low computational cost and more accuracy and is compatible with experimental results. To calculate these parameters, geometry optimization of the ground state neutral, radical, anion, and radical cation structures of each molecule studied was determined in the gas and solvent phases. The self-consistent reaction field (SCRF) method via the integral equation formalism polarized continuum model (IEF-PCM) was used to determine solvent effects [69]. It should be noted that the basis set used does not include diffuse functions, which may be insufficient for accurately modeling anions. This limitation could introduce bias in the results, particularly in calculations involving anionic species. Future studies may consider including diffuse functions to enhance accuracy.

The literature describes three basic mechanisms used to study PCs' free radical scavenging effect and determine their protection in the oxidative process. All of these mechanisms involve the transfer of a hydrogen atom to free radicals. These mechanisms are widely used to analyze PCs' antioxidant activity. As the literature states, phenolic antioxidants play a protective role in the oxidative process through three basic mechanisms. The first is HAT, which involves a one-step transfer from the antioxidant compound (ArOH) to the radical (R.). The other two mechanisms are two-step reactions: single electron transfer followed by proton transfer (SET-PT, Eq. (2)) and sequential proton loss electron transfer (SPLET, Eq. (3)).

$$\:\text{A}\text{r}\text{O}\text{H}\:+\:\:{\text{R}}^{.}\to\:\:\:{\text{A}\text{r}\text{O}}^{.\:\:\:}+\:\:\text{R}\text{H}$$

$$\:\text{A}\text{r}\text{O}\text{H}\:+\:\:{\text{R}}^{.}\to\:{\text{A}\text{r}\text{O}\text{H}}^{+.}\:+{\text{R}}^{-}\to\:\text{R}\text{H}\:+\:{\text{A}\text{r}\text{O}}^{.}$$

$$\:\text{A}\text{r}\text{O}\text{H}\:\to\:\:\:{\text{A}\text{r}\text{O}}^{-}+\:\:{\text{H}}^{+};\:{\text{A}\text{r}\text{O}}^{-\:}+\:\:{\text{R}}^{.}\to\:{\text{A}\text{r}\text{O}}^{.}+\:\:{\text{R}}^{-};\:{\text{R}}^{-}+\:\:{\text{H}}^{+\:}\to\:\text{R}\text{H}$$

For the applicability of these mechanisms, thermodynamic parameters such as bond dissociation enthalpy (BDE), ionization potential (IP), proton dissociation enthalpy (PDE), proton affinity (PA) and electron transfer enthalpy (ETE) of PCs should be calculated according to the following equations. In other words, the enthalpy changes of the above mechanisms are used to derive thermodynamic parameters. A schematic representation of each stage of these three basic mechanisms is shown in Fig. 2. The enthalpies of H(H.), H(H+), and H(e-) in the gas phase, which are taken from the literature, are − 1306 kJ/mol, 6.197 kJ/mol, and 3.1351 kJ/mol, respectively. The enthalpies of H(H.), H(H+), and H(e-) in the solvent phase have been calculated using the following equation based on the experimental solvation corrections, ΔsolvH, and the enthalpy values in the gas patient's intelligent reaction to the therapist's commentary phase. Specifically, for benzene, the solvation corrections ΔsolvH are − 894 kJ/mol for H(H.), 6.4 kJ/mol for H(H+), and − 7 kJ/mol for H(e-), respectively; for ethanol, these corrections are − 1045 kJ/mol for H(H.), 3.7 kJ/mol for H(H+), and − 76 kJ/mol for H(e-), respectively; and for water, the corrections are − 1090 kJ/mol for H(H.), − 4.0 kJ/mol for H(H+), and − 105 kJ/mol for H(e-), respectively. These values have been utilized to accurately compute the enthalpies in each solvent environment [70–73].

$$\:{\text{H}}_{\text{s}\text{o}\text{l}\text{v}\text{e}\text{n}\text{t}}={\text{H}}_{\text{g}\text{a}\text{s}}+{\varDelta\:}_{\text{s}\text{o}\text{l}\text{v}}\text{H}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(4\right)$$

$$\:\text{B}\text{D}\text{E}=\text{H}\left({\text{A}\text{r}\text{O}}^{.}\right)+\text{H}\left({\text{H}}^{.}\right)-\text{H}\left(\text{A}\text{r}\text{O}\text{H}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(5\right)$$

$$\:\text{I}\text{P}=\text{H}\left({\text{A}\text{r}\text{O}\text{H}}^{.+}\right)+\text{H}\left({\text{e}}^{-}\right)-\text{H}\left(\text{A}\text{r}\text{O}\text{H}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(6\right)$$

$$\:\text{P}\text{D}\text{E}=\text{H}\left({\text{A}\text{r}\text{O}}^{.}\right)+\text{H}\left({\text{H}}^{+}\right)-\:\text{H}\left({\text{A}\text{r}\text{O}\text{H}}^{.+}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(7\right)$$

$$\:\text{P}\text{A}=\text{H}\left({\text{A}\text{r}\text{O}}^{-}\right)+\text{H}\left({\text{H}}^{+}\right)-\:\text{H}\left(\text{A}\text{r}\text{O}\text{H}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(8\right)\:$$

$$\:\text{E}\text{T}\text{E}=\text{H}\left({\text{A}\text{r}\text{O}}^{.}\right)+\text{H}\left({\text{e}}^{-}\right)-\:\text{H}\left({\text{A}\text{r}\text{O}}^{-}\:\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(9\right)\:\:\:\:\:\:$$

In addition to these calculations, boundary molecular orbital analysis calculations were performed using Koopmans' Theorem since HOMO/LUMO energies and band gap energies (△E) play an important role in explaining HOMO/LUMO interactions in all phases and determining the antiradical properties of all molecules studied [74]. With the help of these energy values, electronegativity (χ), electron affinity (EA), ionization potential (lP), chemical hardness (η), chemical softness (σ), and electrophilicity index (ω) parameters known as global reactivity indices were calculated to determine the chemical reactivity of a molecular system which is related to its antioxidant activity [75]. Furthermore, two parameters, generally representing the nucleophilic (electron donor power, ω⁻) and electrophilic (electron acceptor power, ω⁺) reactivities of a molecule as defined by Gazquez et al. [76], were also calculated. The mathematical expressions of the relevant equations used in these calculations are shown below.

$$\:\varDelta\:E={E}_{HOMO}-{E}_{LUMO}$$

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:IP=-{E}_{HOMO}$$

$$\:EA={-E}_{LUMO}$$

$$\:{\eta\:}=\left(\frac{\text{I}\text{P}-\text{E}\text{A}}{2}\right)$$

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{\sigma\:}=1/{\eta\:}$$

$$\:\:\mu\:=-\:{\chi\:}=\left(\frac{IP+EA}{2}\right)$$

$$\:{{\omega\:}}^{-}=\frac{(3\text{I}\text{P}+\text{E}\text{A}{)}^{2}}{\left(16\right(\text{I}\text{P}-\text{E}\text{A}\left)\right)}$$

$$\:{{\omega\:}}^{+}=\frac{(\text{I}\text{P}+3\text{E}\text{A}{)}^{2}}{\left(16\right(\text{I}\text{P}-\text{E}\text{A}\left)\right)}$$

Martinez introduces the electron acceptance index, Ra, and the electron donation index, Rd, to quantify a molecule's ability to accept and donate electrons, respectively. Ra compares a molecule's electron-accepting capacity to the strong electron-acceptor fluorine, while Rd compares its electron-donating capacity to sodium, known for its robust electron-donating properties. These indices standardize the assessment of electron-accepting and donating capabilities across different molecules, providing valuable insights into their chemical behavior [77]. These indices are calculated as follows:

$$\:Ra=\frac{{\:\omega\:}_{L}^{+}}{\:{\:\omega\:}_{F}^{+}}$$

where $\:{\:\omega\:}_{L}^{+}$is the electron-accepting power of the molecule, and $\:{\:\omega\:}_{F}^{+}$is that of fluorine.

$$\:Rd=\frac{{\:\omega\:}_{L}^{-}}{\:{\:\omega\:}_{Na}^{+}}$$

where $\:{\:\omega\:}_{L}^{-}$is the electron-donating power of the molecule, and $\:{\:\omega\:}_{Na}^{+}$is that of sodium.

L represents the molecule studied in these equations, which could be any radical scavenger. This classification of substances in terms of electron acceptance and donation is grounded in their ionization potential (IP) and electron affinity (EA). Fluorine has an IP_F = 17.42282 eV and EA_F =3.4011898 eV, and sodium has IP_Na =5.1391 eV and EA_Na=0.547926 eV. By employing these indices, the analysis enhances understanding of how a molecule initially responds to electron transfer within the SET-PT mechanism for radical scavenging, effectively outlining its antiradical capacities. This insight is crucial for evaluating the potential antioxidant behavior of substances in various environments.

The determination and analysis of these parameters are used to determine how effectively a molecule can neutralize radicals as they provide important information about its potential antioxidant activity. Since (ArOH), which represents the neutral phenolic compound in each mechanism described above, interacts with the radical species indicated by (R) and is transformed into the ordinary free phenoxide radical (ArO.), which is more stable and less reactive than these radicals, the spin density distribution was calculated and evaluated for the phenoxide radical. The spin densities for each atom in the phenoxide radicals (U)B3LYP/6-311G (d, p) were obtained by NBO version 3.1 calculations at the same level of Theory [78]. Molecular Electrostatic Potential (MEP) maps are an essential tool in determining the potential antioxidant activity of antioxidant molecules in the electron transfer process, as they decide which sites are most favorable for electron exchange [79]. Therefore, MEP maps of each molecule analyzed were created and evaluated.

In addition to these analyses, molecular docking was performed to determine the antioxidant properties of the C1-C10 series of alkyl gallates. The crystal structures of tyrosine kinase Hck (PDB ID: 2hck) [80], Heme Oxygenase (PDB ID: 5kzl) [81], and Human Serum Albumin (PDB ID: 7qfe) [82] were downloaded from RCSB protein data bank (https://www.rcsb.org/) on 27 August 2023. All molecular docking calculations were conducted using AutoDockTools 4.2 [83]. Polar hydrogens were included in the docking simulations with Kollman charges. All water molecules were removed before recording the structures in pdbqt format. The Lamarckian genetic algorithm was employed, assessing 150 populations [84]. Ligands were prepared with Gasteiger charges and initiated from randomized positions [85]. The results were visualized using the Discovery Studio 2019 Client (https://discover.3ds.com/discovery-studio-visualizer-download).

3.1. Frontier molecular orbitals (FMOs) analysis.

The HOMO and LUMO electron density distribution in alkyl gallates (C1-C10) reveals that HOMO orbitals are concentrated on the phenolic hydroxyl (OH) groups, which are responsible for antioxidant properties. Alkyl groups, being apolar, do not contribute to these orbitals and thus play no significant role in antioxidant activity. LUMO distribution, on the other hand, occurs along the carbons in the phenol ring and alkoxy group. The calculated band gap values (∆E) for all alkyl gallates are similar, indicating comparable stability, while gallic acid (GA) shows lower stability [86–88]. Although band gap values provide insights into chemical reactivity and kinetic stability, a comprehensive determination of antioxidant activity requires evaluating additional quantum chemical descriptors beyond FMO analysis. The values in Fig. 3, known as band gap (∆E) or energy gap, provide information about each alkyl gallate's chemical reactivity and kinetic stability. It is seen that these calculated values (approx. 4.978 eV-4.992 eV) are almost the same from methyl gallate to dodecyl gallate. This result indicates that all alkyl gallates studied show the same stability. It is seen that the band gap value of gallic acid (GA) is lower than the alkyl gallates examined, i.e., unstable (4.94 eV). As it is known, the interaction of antioxidants with free radicals is related to the ability of radicals to " capture " an electron. The band gap value can determine the amount of energy required for this "electron capture " process, so a molecule with a lower band gap value can theoretically be considered a more powerful antioxidant, but this is not certain. However, since the band gap value only determines the direction of these interactions, quantum chemical descriptors need to be calculated and evaluated to determine the antioxidant activity fully. Therefore, more than Frontier Molecular Orbital (FMO) analysis is required to determine antioxidant activity, and more parameters must be calculated and evaluated. The evaluation of the relevant parameters is made below.

3.2. Molecular electrostatic potential (MEP) analysis.

Molecular Electrostatic Potential (MEP) maps serve as a crucial tool for visualizing the charge distribution within molecules. In these maps, red regions indicate areas rich in electrons (electron-rich), while blue regions signify areas deficient in electrons (electron-poor). This visualization identifies sites within the molecule likely to interact with electrophilic or nucleophilic agents. For alkyl gallates, the MEP analysis reveals that the electron-rich regions are primarily located around the carbonyl oxygen atoms, phenolic OH groups, and certain π electrons within the phenyl ring. These regions are crucial as they represent the most likely sites for interaction with free radicals, which are inherently electron-deficient. However, clarifying the relationship between these electron-rich and electron-poor regions and their interaction with free radicals is important. While free radicals typically attack electron-poor regions, in the case of alkyl gallates, the antioxidant activity is driven by the ability of electron-rich regions to donate electrons and neutralize free radicals. This is because the antioxidant activity is primarily driven by the ability of these regions to donate electrons to neutralize free radicals. The MEP analysis of alkyl gallates, illustrated in Fig. 4, further shows that shorter alkyl chains are associated with higher charge density in the electron-rich regions, enhancing their antioxidant activity. However, this relationship is not strictly linear, as factors such as steric hindrance and the overall molecular conformation can influence the accessibility of these sites to free radicals [89–102].

3.3. Global Reactivity Descriptors (GRDs).

Since antioxidant chemistry is complex, a quantitative analysis of the molecular reactivity of the investigated alkyl gallates requires calculating GRD values, which have an important role in predicting antioxidant activity. Table 1 presents the global reactivity descriptors (GRDs) of alkyl gallates in both gas and solvent phases. These descriptors are pivotal for quantifying molecules' electron-donating and accepting abilities, a fundamental aspect of antioxidant research. The antioxidant activity of alkyl gallates is discernibly influenced by the solvent's polarity and the length of the alkyl chain. In polar environments such as ethanol and water, the observed decrease in Ra values suggests an enhanced electron-donating ability due to better stabilization of radical forms by the solvent. In contrast, in non-polar solvents like benzene, the higher Ra values indicate a diminished electron-donating capacity because of the solvent's limited stabilization of charged species. Rd values also demonstrate dependency on the solvent, with increased values in polar solvents indicating a greater capacity to accept electrons integral to effective antioxidant action. The interplay between lower Ra and higher Rd in these environments underscores the augmented antioxidant properties. Furthermore, the alkyl chain length significantly modulates these properties. Shorter chains (C1-C4) enhance electron-donating and accepting abilities, reflected by lower IP values and higher ω- values, indicating robust electron-donating capabilities. In contrast, higher EA and ω + values suggest effective electron-accepting properties.

Table 1

Calculated Global Reactivity Descriptors (GDRs) in Gas and Solvent Phases for Studied Alkyl Gallates (in eV).
	Gas
	GA	MG	EG	PG	BG	PNG	HG	HPG	OG	DG	DOG
IP	6.23772	6.14982	6.13159	6.12751	6.12343	6.12152	6.12016	6.11934	6.11880	6.11853	6.11826
EA	1.29690	1.17146	1.14425	1.13881	1.13364	1.13064	1.12901	1.12792	1.12765	1.12710	1.12683
ΔE	4.94082	4.97836	4.98734	4.98870	4.98979	4.99088	4.99115	4.99142	4.99115	4.99142	4.99142
η	2.47041	2.48918	2.49367	2.49435	2.49490	2.49544	2.49558	2.49571	2.49558	2.49571	2.49571
σ	0.40479	0.40174	0.40102	0.40091	0.40082	0.40073	0.40071	0.40069	0.40071	0.40069	0.40069
χ	3.76731	3.66064	3.63792	3.63316	3.62853	3.62608	3.62459	3.62363	3.62322	3.62282	3.62254
µ	-3.76731	-3.66064	-3.63792	-3.63316	-3.62853	-3.62608	-3.62459	-3.62363	-3.62322	-3.62282	-3.62254
ω	2.87253	2.69171	2.65361	2.64594	2.63863	2.63450	2.63218	2.63066	2.63021	2.62947	2.62907
ε	0.34813	0.37151	0.37685	0.37794	0.37898	0.37958	0.37991	0.38013	0.38020	0.38030	0.38036
ω+	1.29768	1.17253	1.14636	1.14116	1.13623	1.13339	1.13184	1.13080	1.13054	1.13003	1.12977
ω-	5.06499	4.83317	4.78428	4.77432	4.76476	4.75947	4.75842	4.75444	4.75377	4.75284	4.75231
Ra	0.38167	0.34486	0.33716	0.33564	0.33419	0.33335	0.33289	0.33259	0.33251	0.33236	0.33228
Rd	1.56520	1.49356	1.47845	1.47538	1.47242	1.47079	1.46985	1.46923	1.46903	1.46874	1.46858
	Benzene
IP	6.24588	6.18792	6.17241	6.17214	6.17540	6.17431	6.16887	6.16805	6.16669	6.16588	6.16479
EA	1.34398	1.24684	1.22262	1.22316	1.22534	1.22316	1.21745	1.21636	1.21554	1.21500	1.21391
ΔE	4.90190	4.94108	4.94979	4.94897	4.95006	4.95115	4.95142	4.95169	4.95115	4.95088	4.95088
η	2.45095	2.47054	2.47490	2.47449	2.47503	2.47558	2.47571	2.47585	2.47558	2.47544	2.47544
σ	0.40801	0.40477	0.40406	0.40412	0.40404	0.40395	0.40392	0.40390	0.40395	0.40397	0.40397
χ	3.79493	3.71738	3.69751	3.69765	3.70037	3.69874	3.69316	3.69211	3.69112	3.69044	3.68935
µ	-3.79493	-3.71738	-3.69751	-3.69765	-3.70037	-3.69874	-3.69316	-3.69211	-3.69112	-3.69044	-3.68935
ω	2.93794	2.79673	2.76206	2.76271	2.76617	2.76313	2.75465	2.75307	2.75175	2.75089	2.74927
ε	0.34037	0.35756	0.36205	0.36196	0.36151	0.36191	0.36302	0.36323	0.36340	0.36352	0.36373
ω+	1.34685	1.24686	1.22266	1.22320	1.22537	1.22320	1.21753	1.21645	1.21564	1.21510	1.21402
ω-	5.14178	4.96424	4.92017	4.92085	4.92574	4.92194	4.91069	4.90866	4.90676	4.90554	4.90337
Ra	0.39613	0.36672	0.35961	0.35977	0.36040	0.35977	0.35810	0.35778	0.35754	0.35738	0.35707
Rd	1.58893	1.53407	1.52045	1.52066	1.52217	1.52100	1.51752	1.51689	1.51630	1.51593	1.51526
	Ethanol
IP	6.27826	6.24016	6.23282	6.23282	6.23472	6.23391	6.23227	6.23200	6.23091	6.23118	6.23091
EA	1.42235	1.34888	1.33418	1.33718	1.33745	1.33636	1.33364	1.33337	1.33364	1.33310	1.33310
ΔE	4.85591	4.89129	4.89863	4.89564	4.89727	4.89754	4.89863	4.89863	4.89727	4.89809	4.89782
η	2.42796	2.44564	2.44932	2.44782	2.44864	2.44877	2.44932	2.44932	2.44864	2.44904	2.44891
σ	0.41187	0.40889	0.40828	0.40853	0.40839	0.40837	0.40828	0.40828	0.40839	0.40832	0.40835
χ	3.85031	3.79452	3.78350	3.78500	3.78609	3.78513	3.78296	3.78268	3.78228	3.78214	3.78200
µ	-3.85031	-3.79452	-3.78350	-3.78500	-3.78609	-3.78513	-3.78296	-3.78268	-3.78228	-3.78214	-3.78200
ω	3.05295	2.94368	2.92222	2.92632	2.92703	2.92539	2.92138	2.92096	2.92114	2.92044	2.92039
ε	0.32755	0.33971	0.34221	0.34173	0.34164	0.34183	0.34230	0.34235	0.34233	0.34241	0.34242
ω+	1.43129	1.35213	1.33663	1.33980	1.34006	1.33892	1.33607	1.33578	1.33608	1.33550	1.33551
ω-	5.28160	5.14665	5.12013	5.12480	5.12615	5.12406	5.11902	5.11847	5.11836	5.11764	5.11751
Ra	0.42097	0.39768	0.39313	0.39406	0.39414	0.39380	0.39296	0.39288	0.39296	0.39280	0.39280
Rd	1.63214	1.59044	1.58224	1.58368	1.58410	1.58345	1.58190	1.58173	1.58169	1.58147	1.58143

Table 1

(Continued)
	Water
	GA	MG	EG	PG	BG	PNG	HG	HPG	OG	DG	DOG
IP	6.28180	6.24506	6.23772	6.23853	6.24016	6.23989	6.23826	6.23799	6.23690	6.23717	6.23717
EA	1.43024	1.35868	1.34480	1.34806	1.34779	1.34643	1.34453	1.34425	1.34480	1.34453	1.34453
ΔE	4.85156	4.88639	4.89292	4.89047	4.89237	4.89346	4.89373	4.89373	4.89210	4.89265	4.89265
η	2.42578	2.44319	2.44646	2.44523	2.44619	2.44673	2.44687	2.44687	2.44605	2.44632	2.44632
σ	0.41224	0.40930	0.40875	0.40896	0.40880	0.40871	0.40869	0.40869	0.40882	0.40878	0.40878
χ	3.85602	3.80187	3.79126	3.79330	3.79398	3.79316	3.79139	3.79112	3.79085	3.79085	3.79085
µ	-3.85602	-3.80187	-3.79126	-3.79330	-3.79398	-3.79316	-3.79139	-3.79112	-3.79085	-3.79085	-3.79085
ω	3.06477	2.95806	2.93764	2.94227	2.94218	2.94026	2.93736	2.93694	2.93750	2.93717	2.93717
ε	0.32629	0.33806	0.34041	0.33987	0.33988	0.34011	0.34044	0.34049	0.34043	0.34046	0.34046
ω+	1.43998	1.36252	1.34782	1.35128	1.35097	1.34952	1.34752	1.34724	1.34783	1.34754	1.34754
ω-	5.29600	5.16439	5.13907	5.14458	5.14495	5.14269	5.13891	5.13836	5.13868	5.13838	5.13838
Ra	0.42352	0.40074	0.39642	0.39744	0.39734	0.39692	0.39633	0.39625	0.39642	0.39633	0.39633
Rd	1.63659	1.59592	1.58809	1.58980	1.58991	1.58921	1.58805	1.58787	1.58797	1.58788	1.58788

However, discovering a cutoff effect with longer chains (C9-C10) is a significant finding. It demonstrates that the benefits of extending the alkyl chain do not continue indefinitely and may even diminish due to steric hindrance, increased hydrophobicity, and decreased solubility in polar environments. This cutoff effect underscores the importance of optimizing the alkyl chain length to balance solubility and steric considerations for peak antioxidant efficacy. The optimal antioxidant activity is thus achieved with shorter alkyl chains in polar solvents, guiding the design of more efficacious antioxidants. These findings underscore the need for precision in molecular design and provide clear directives for future research in antioxidant development, emphasizing the role of molecular structure and environmental context. Moreover, the novel insights from this study, including the detailed profiling of GRDs across different phases, not only shed light on the antioxidant behavior of alkyl gallates but also underscore the study's practical implications. Fundamental results, such as the decreasing trend of IP with increasing alkyl chain length across all solvents, suggest that longer chains enhance electron density, easing electron removal and potentially augmenting antioxidant activity. Similarly, the trend of increasing EA with the alkyl chain length in solvents, except in the gas phase, suggests improved electron stabilization capabilities, facilitating electron uptake. These trends, along with solvent-dependent variations in ω- and ω + values, indicate the significant influence of the environment on antioxidant behavior, adding depth to the understanding of these compounds' reactivity and their practical applications across various industries. The investigation of GRDs indicates how the antioxidant properties of alkyl gallates are determined by the interplay of solvent polarity and alkyl chain length, showing the design of molecular advancements for various applications.

3.4. Analysis of spin density distribution.

Spin density (SD) is an essential parameter in antioxidant activity studies as it often determines the radical character of a molecule. Unpaired electron delocalization in radicals is usually characterized based on the spin density distribution, and electron delocalization gives important information about the stability of radicals. Therefore, SD is widely used to determine the strength of radical species. It also determines which atoms or groups an electron is distributed or localized to. SD varies depending on the structure of the molecule, its environment, other chemical properties, and the resonance structure of the radical involved. The resonance structures of two different phenoxide radicals formed from the studied gallic acid (GA) and alkyl gallates (C1-C10) by homolytic cleavage of the O-H bond of hydroxyl groups at the meta and para positions of the carbonyl (C = O) group are shown in Fig. 5 (a). NBO spin density distributions are shown in Fig. 5. Due to these two different resonance structures, the spin density distributions of the phenoxide radicals formed are expected to differ.

In phenolic compounds, it is a known fact that structural factors such as the number and position of the hydroxyl group, the presence of other functional groups and their position relative to the hydroxyl group, and intramolecular hydrogen bonding affect antioxidant and antiradical activity. Therefore, depending on the nature (electron-withdrawing and --releasing properties) and position of the groups attached to the phenyl ring significantly affect the activity of phenolic compounds. There are two main reasons for the different stability of these radicals. The first is that the strength of the phenoxy radical increases as the number of resonance structures is formed by the delocalization of the unpaired electron on the oxygen atom of the phenoxide radical with the help of π electrons, which are displaced between the carbon atoms in the ring. Looking at Fig. 5, since there are four resonance structures in the meta position and six resonance structures in the para position, the resonance structure of the para position is more stable. In addition, when the resonance structure of the para position is examined, the high spin density at carbon number one, to which the electron-withdrawing carbonyl group (C = O) is attached, gives the radical additional stability (III-IV resonance structures). These results indicate that the unpaired electron in the radical at the para position is more efficiently distributed throughout the ring length than at the meta position, resulting in extra stability.

The second is the intramolecular hydrogen bonds formed between the unpaired electron-containing oxygen atom of the phenoxide radical in the para position and the hydrogen atoms of two -OH groups attached to neighboring carbons, as shown in Fig. 5 (b). This provides extra stability to the phenoxide radical in the para position. Furthermore, the positions of different groups in a radical and their electron-withdrawing or --donating effects significantly alter its stability by affecting the electron distribution and spin density of the radical. This special effect affecting the strength of radicals is known as the captodative or push-pull effect [103–106]. In this effect, the stability of multiple phenoxide radicals formed depending on the positions is determined, and the radical is assumed to be "trapped" between the electron donors (-OH) and acceptor group (-COOR), as shown in Fig. 5 (c). The captodative or push-pull effect in alkyl gallates occurs when two OH groups in the ortho position relative to the phenoxide oxygen in the phenyl ring give electrons to the ring by resonance effect. In contrast, the ester group (-COOR) in the para position withdraws electrons from the ring by inductive effect. Since the number of -OH groups is higher, electron donation is more dominant. As a result, the ester group only affects the electron properties of the phenoxide radical. In contrast, the main factor affecting the stability of this radical is the OH groups that cause the resonance effect.

A close relationship exists between the stability of phenoxide radicals formed from phenolic antioxidants such as gallic acid (GA) and alkyl gallates (C1-C10) and antioxidant activity. The higher the stability of the phenoxide radical, the higher the ability of the phenolic antioxidant to neutralize free radicals. This is an indication of its antioxidant activity and its power to prevent cellular damage. Furthermore, the COOH in gallic acid adds to the stability of the phenoxy radicals formed since the COOR groups in alkyl gallates have different electron-withdrawing abilities. The -COOH group has more electron-withdrawing ability than the COOR group. As the electron-withdrawing ability increases, the stability increases as the unpaired electron in the phenoxide radical will spread over a larger area on the ring. In light of the evaluations on the stability of the phenoxide radical, radicals formed from gallic acid are more stable.

Depending on the structural factors mentioned above, there is a close relationship between the different stability of phenoxide radicals and the spin density of the atoms of these radicals. The relationship between radical stability and spin density is crucial for understanding and evaluating the chemical behavior of radical species and determining antioxidant activity the calculated spin density values of phenoxide radicals in Fig. 5 support the above evaluations. When the resonance structures of phenoxide radicals are examined, it is seen that the unpaired electron in the meta position is located on carbons 2, 4, and 6 of the phenyl ring, and the electron in the para position is situated on carbons 1, 3 and 5 of the phenyl ring. The spin density distributions of gallic acid and alkyl gallates in Fig. 6 are consistent with the above considerations regarding the stability of phenoxide radicals. In particular, due to the resonance stability and the higher electron-withdrawing ability of the carboxyl group (-COOH) compared to the ester group (-COOR), the spin density on the phenolic oxygen atom at the para position in gallic acid is lower than at the meta position and higher at the carbonyl oxygen.

The pronounced change in spin density is on the oxygen atoms of the phenoxide radicals. The spin density on the oxygen atom of the phenoxide radical in the meta position, consisting of both gallic acid and alkyl gallates, is 0.388 and 0.384, respectively. In contrast, it is 0.332 and 0.333 in the para position, respectively. The decrease in the spin density at the para position is because the resonance structure of the corresponding position is more stable than the meta position, and the unpaired electron on the oxygen has a wider spread over the ring. The spin density of the carbon atoms in the phenyl ring does not change much. Similar trends are observed in alkyl gallates, and the length of the alkyl chain does not affect the spin density. The more stable the phenoxide radical, the higher the ability of the phenolic compound to neutralize radicals and prevent harmful oxidative stress. The stability of the phenoxide radical of a phenolic compound is often an indicator of its antioxidant activity. After all, gallic acid has higher antioxidant activity than alkyl gallates.

3.5. Evaluation of Thermochemical Parameters and Antioxidant Mechanisms

Previous discussions focused on quantum chemical parameters, spin density distributions, FMO diagrams, and MEP maps of alkyl gallates. This section expands the analysis by evaluating thermochemical parameters related to alkyl gallate interactions with free radicals and quantifying their antiradical activity. Antioxidant capacities of gallic acid and alkyl gallates are assessed through computational chemistry techniques, utilizing specific thermochemical parameters and three main mechanisms (HAT, SET-PT, and SPLET). The preferred mechanism, determined by the lowest numerical value of the thermochemical parameter, is usually the most thermodynamically favored pathway for free radical scavenging. This evaluation, initially conducted in the gas phase, compares the effects of alkyl gallates with gallic acid. Further analysis examines the influence of solvents with varying polarities on antioxidant activity [107].

3.5.1.Hydrogen Atom Transfer Mechanism (HAT)

This study investigates the free radical mechanisms that play an essential role in determining the antioxidant activity of alkyl gallates, evaluates the thermodynamics by calculating key parameters, and examines the effect of solvent polarity on this activity. The calculated thermochemical parameters (BDE) and IC50 values of gallic acid (GA) and alkyl gallates (C1-C10) in the gas phase and various solvents (benzene, ethanol, and water) are presented in Table 2. The HAT mechanism involves the homolytic cleavage of the O-H bond, and lower BDE values indicate more effective antioxidant properties. GA shows BDE values of 78.52 kcal/mol (OH_meta) and 77.36 kcal/mol (OH_para) in the gas phase. Alkyl gallates follow a similar trend with slight variations. For example, DOG has BDE values of 85.05 kcal/mol (OH_meta) and 76.71 kcal/mol (OH_para), suggesting that longer alkyl chains can influence BDE. The lower BDE values in the para position are due to resonance stabilization and lower spin density of phenoxide oxygen. However, the calculated BDEs are considerably lower than the experimental value for the OH bond of phenol (typically around 86.5 kcal/mol), which is the expected result [108].

The influence of polar solvents on the BDE values of alkyl gallates is a significant aspect of the research. BDE values generally increase in polar solvents like ethanol and water, indicating higher energy requirements for homolytic cleavage. For instance, GA in water shows BDE values of 78.81 kcal/mol (OH_meta) and 85.26 kcal/mol (OH_para). DOG shows similar patterns, with BDE values in water being 81.90 kcal/mol (OH_meta) and 75.33 kcal/mol (OH_para). A key research finding is the correlation between alkyl chain length and antioxidant activity. The IC₅₀ values further validate this, with GA at 6.51 ± 0.30 µg/ml, while DOG shows 6.02 ± 0.18 µg/ml. This suggests that longer alkyl chains enhance antioxidant activity. The computational results align well with experimental data, underscoring the reliability of using BDE and spin density (SD) values to predict antioxidant properties. The study indicates that the resonance stabilization and captodative effect significantly enhance the radical scavenging abilities of alkyl gallates. The observed cut-off effect suggests that there is an optimal alkyl chain length that maximizes antioxidant activity. These findings highlight the importance of considering both molecular structure and solvent environment in evaluating the antioxidant potential of alkyl gallates.

Table 2

The calculated thermochemical parameters (BDE) of gallic acid (GA) and alkyl gallates (C1-C10) in the gas phase and solvents. The experimental IC₅₀ is also included for comparison.
Alkyl Gallates		BDE (kcal/mol)				IC₅₀ (lg/ml)*
Alkyl Gallates		Gas	Benzene	Ethanol	Water	IC₅₀ (lg/ml)*
GA	OH_meta	78.52	80.56	80.57	78.81	6.51 ± 0.30
GA	OH_para	77.36	78.71	77.75	85.26	6.51 ± 0.30
MG	OH_meta OH_para	78.17 71.08	83.01 75.92	86.59	78.50	6.34 ± 0.12
MG	OH_meta OH_para	78.17 71.08	83.01 75.92	79.51	72.29	6.34 ± 0.12
EG	OH_meta	78.12	82.97	86.61	78.44
EG	OH_para	71.01	75.86	79.51	72.27
PG	OH_meta	78.11	82.95	86.59	78.39	6.02 ± 0.17
PG	OH_para	71.00	75.84	79.48	72.24	6.02 ± 0.17
BG	OH_meta	78.09	83.05	86.72	78.48
BG	OH_para	70.99	75.94	79.61	72.30
PNG	OH_meta	78.09	83.08	86.77	78.47
PNG	OH_para	76.88	81.87	85.56	72.28
HG	OH_meta	78.09	83.04	86.76	78.41	5.74 ± 0.22
HG	OH_para	70.98	75.93	79.65	72.23	5.74 ± 0.22
HPG	OH_meta	78.09	83.05	86.80	78.39
HPG	OH_para	70.97	75.94	79.69	75.50
OG	OH_meta	85.21	84.44	83.70	82.03	6.09 ± 0.14
OG	OH_para	76.87	77.91	77.10	75.51	6.09 ± 0.14
DG	OH_meta	85.21	85.43	83.70	82.02	5.84 ± 0.17
DG	OH_para	76.87	77.90	77.10	75.50	5.84 ± 0.17
DOG	OH_meta	85.05	85.43	83.71	82.03	6.02 ± 0.18
DOG	OH_para	76.71	77.88	77.05	75.46	6.02 ± 0.18
*IC₅₀ ((lg/ml) values are from reference 55

3.5.2. Single Electron Transfer Followed by Proton Transfer Mechanism (SET-PT)

Unlike the HAT mechanism, this is a two-step process in which the antioxidant molecule transfers an electron to the free radical, and then the cationic radical loses a proton. The thermochemical parameter of the first step of this mechanism is the ionization potential (IP), and the second is the proton dissociation enthalpy (PDE). The calculated thermochemical parameters (IP and PDE) of gallic acid (GA) and its alkyl derivatives (C1-C10) in the gas phase and various solvents (benzene, ethanol, and water) are presented in Table 3. Gallic acid (GA) serves as a reference compound, providing a benchmark for the alkyl derivatives in this study. In the gas phase, the IP values generally decrease with the lengthening of the alkyl chain. For example, GA has an IP of 184.36 kcal/mol, while DOG has a lower IP of 179.98 kcal/mol. This trend suggests that longer alkyl chains reduce the energy required to remove an electron from the molecule, making the first step of the mechanism more favorable. In solvents, the IP values further decrease compared to the gas phase. In water, for instance, the IP of GA drops to 115.06 kcal/mol and that of DOG to 111.73 kcal/mol. This significant reduction in polar solvents like water indicates that these environments stabilize the cationic form of the molecule, making it easier for the molecule to lose an electron, thus lowering the IP values.

Regarding the PDE values, GA has a PDE of 210.88 kcal/mol in the gas phase, and DOG has a similar PDE of 211.21 kcal/mol. The PDE values do not show a consistent trend with the alkyl chain length in the gas phase, suggesting that the alkyl chain length less influences the proton loss step. However, the PDE values significantly decrease in polar solvents such as ethanol and water. For example, GA has a PDE of 1.72 kcal/mol in ethanol, while DOG has a PDE of 0.53 kcal/mol. This substantial reduction in PDE in polar solvents indicates that these environments considerably stabilize the protonated form, thus facilitating the proton dissociation step. In conclusion, the thermochemical parameters reveal that alkyl gallates' antioxidant efficiency is influenced by the length of the alkyl chain and the solvent environment. Longer alkyl chains generally decrease the ionization potential, making the electron transfer step more favorable. Moreover, polar solvents significantly lower both IP and PDE values, enhancing the antioxidant potential by facilitating electron transfer and proton dissociation. As the reference compound, gallic acid (GA) exhibits higher IP and PDE values than its alkyl derivatives, indicating that modifications in the alkyl chain can enhance the antioxidant properties of these compounds. A robust correlation exists between the IP and PDE values associated with the SET-PT mechanism and the Rd and Ra indices. This correlation aids in understanding molecular reactions in solvent environments and their impact on antioxidant activities. It acts as a crucial indicator, especially when assessing molecules' electron-accepting and donating capacities, allowing the use of these values in molecular design and optimization of antioxidant properties.

Table 3

The calculated thermochemical parameters (IP and PDE) of gallic acid (GA) and alkyl gallates (C1-C10) in the gas phase and solvents.
Alkyl Gallates		IP (kcal/mol)				PDE (kcal/mol)
Alkyl Gallates		Gas	Benzene	Ethanol	Water	Gas		Benzene	Ethanol	Water
GA	OH_meta	184.36	157.62	123.35	115.06	208.55	20.38		1.72	9.44
GA	OH_para	184.36	157.62	123.35	115.06	207.38	18.54		-1.10	15.89
MG	OH_meta OH_para	181.63	154.97	122.18	114.10	210.88	25.80		9.09	10.14
MG	OH_meta OH_para	181.63	154.97	122.18	114.10	203.79	18.72		2.00	3.94
EG	OH_meta	180.75	154.86	121.53	113.43	211.71	25.88		9.76	10.75
EG	OH_para	180.75	154.86	121.53	113.43	204.61	18.77		2.66	4.58
PG	OH_meta	180.49	154.50	121.47	113.40	211.97	26.22		9.81	10.74
PG	OH_para	180.49	154.50	121.47	113.40	204.86	19.11		2.69	4.59
BG	OH_meta	180.29	154.74	121.50	113.41	212.15	26.08		9.90	10.82
BG	OH_para	180.29	154.74	121.50	113.41	205.04	18.97		2.79	4.63
PNG	OH_meta	180.17	155.31	122.13	113.36	212.26	25.54		9.32	10.85
PNG	OH_para	180.17	155.31	122.13	113.36	211.05	18.73		2.84	4.67
HG	OH_meta	180.10	155.10	121.45	113.97	212.33	25.71		9.98	10.19
HG	OH_para	180.10	155.10	121.45	113.97	205.22	18.59		2.87	4.00
HPG	OH_meta	180.06	155.11	122.10	114.02	212.37	25.71		9.38	10.12
HPG	OH_para	180.06	155.11	122.10	114.02	205.26	18.60		2.26	7.23
OG	OH_meta	180.02	155.23	122.20	114.11	219.53	27.97		6.18	13.66
OG	OH_para	180.02	155.23	122.20	114.11	211.19	20.44		-0.42	7.15
DG	OH_meta	180.00	155.30	122.18	115.68	219.55	27.90		6.20	12.09
DG	OH_para	180.00	155.30	122.18	115.68	211.21	20.37		-0.41	5.57
DOG	OH_meta	179.98	155.29	122.14	115.64	219.57	27.90		6.24	12.13
DOG	OH_para	179.98	155.29	122.14	115.64	211.23	20.35		-0.41	5.57

3.5.3. Sequential Proton Loss Electron Transfer Mechanism (SPLET)

This mechanism involves a two-step process in which antioxidants interact with free radicals. The antioxidant molecule loses a proton in the first step, with proton affinity (PA) being a critical thermochemical parameter. The resulting form undergoes electron transfer in the second step, where electron transfer enthalpy (ETE) is crucial. The calculated thermochemical parameters (PA and ETE) of gallic acid (GA) and alkyl gallates (C1-C10) in the gas phase and various solvents (benzene, ethanol, and water) are presented in Table 4. In the gas phase, the PA values for gallic acid (GA) are 335.36 kcal/mol (OH_meta) and 335.30 kcal/mol (OH_para). For the alkyl gallates (C1-C10), the PA values are generally around 336.35 kcal/mol, showing minimal variation. However, the PA value for dodecyl gallate (DOG) at OHmeta is significantly higher at 350.81 kcal/mol, suggesting that longer alkyl chains can increase proton affinity in the gas phase.

When considering solvents, the PA values decrease significantly compared to the gas phase. In benzene, GA shows PA values of 96.89 kcal/mol (OH_meta) and 96.42 kcal/mol (OH_para). The alkyl gallates display slightly higher PA values in benzene, around 126.30 kcal/mol. In ethanol and water, the PA values for GA drop further to approximately 42.18–47.32 kcal/mol, while the alkyl gallates follow a similar trend. Notably, DOG exhibits higher PA values in ethanol (51.13 kcal/mol OH_meta) and water (55.87 kcal/mol OH_meta), highlighting the influence of longer alkyl chains. For ETE values, GA shows 57.55 kcal/mol (OH_meta) and 56.44 kcal/mol (OH_para) in the gas phase. The ETE values for alkyl gallates are generally consistent, with slight variations. Notably, DOG shows ETE values of 48.75 kcal/mol (OH_meta) and 54.97 kcal/mol (OH_para) in the gas phase, significantly higher in solvents like ethanol and water. For OG (Octyl Gallate), the PA value in the gas phase is considerably higher at 350.82 kcal/mol (OH_meta) compared to other alkyl gallates, indicating a strong influence of longer alkyl chains on proton affinity. This PA value decreases to 126.35 kcal/mol in benzene, 51.11 kcal/mol in ethanol, and 55.85 kcal/mol in water. The ETE values are relatively high in benzene at 78.12 kcal/mol (OH_meta). Still, they decrease in more polar solvents like ethanol (77.27 kcal/mol OH_meta) and water (71.92 kcal/mol OH_meta), suggesting better stabilization in polar environments.

For DG, the PA value in the gas phase is 350.81 kcal/mol (OH_meta), similar to OG. However, the PA values decrease in solvents: 110.15 kcal/mol in benzene, 51.11 kcal/mol in ethanol, and 55.85 kcal/mol in water. The ETE values for DG follow a decreasing trend from the gas phase (48.75 kcal/mol OH_meta) to benzene (73.05 kcal/mol OH_meta), ethanol (72.27 kcal/mol OH_meta), and water (71.92 kcal/mol OH_meta), indicating efficient electron transfer in polar solvents. For DOG, the highest PA value is observed in the gas phase at 350.81 kcal/mol (OH_meta), which significantly decreases in solvents: 110.14 kcal/mol in benzene, 51.13 kcal/mol in ethanol, and 55.87 kcal/mol in water. The ETE values for DOG show similar trends to DG and OG, with values decreasing from the gas phase (48.75 kcal/mol OH_meta) to solvents: 73.06 kcal/mol (OH_meta) in benzene, 77.26 kcal/mol (OH_meta) in ethanol, and 71.91 kcal/mol (OH_meta) in water. These observations highlight the significant influence of alkyl chain length and solvent environment on alkyl gallates' proton affinity and electron transfer enthalpy. The stabilizing effects of polar solvents are particularly evident, affecting the antioxidant activity of these compounds.

The thermochemical parameters reveal that the antioxidant activity of alkyl gallates is influenced by both the alkyl chain length and the solvent environment. Specifically, the significantly higher PA values in the gas phase for OG, DG, and DOG suggest that longer alkyl chains enhance proton affinity. In contrast, the significant decrease in PA and ETE values in polar solvents indicates that these environments stabilize the protonated and radical forms, making the antioxidant mechanisms more efficient. The HAT mechanism is preferred in the gas phase due to relatively consistent BDE values and a strong correlation with spin density distributions. Conversely, the SET-PT and SPLET mechanisms are more efficient in polar solvents, as indicated by significant reductions in IP, PDE, PA, and ETE values. These results underscore the importance of considering both molecular structure and solvent effects when evaluating the antioxidant potential of alkyl gallates. The observed cut-off effect, particularly in the case of OG, DG, and DOG, suggests that there is an optimal alkyl chain length that maximizes antioxidant activity, beyond which further lengthening does not significantly enhance the activity. The computational findings, which align well with experimental data, confirm the reliability of using thermochemical parameters to predict the antioxidant properties of alkyl gallates. The values have been rechecked to ensure logical consistency, particularly in solvents where deviations were noted.

Table 4

The calculated thermochemical parameters (PA and ETE) of gallic acid (GA) and alkyl gallates (C1-C10) in the gas phase and solvents.
Alkyl Gallates		PA				ETE
Alkyl Gallates		Gas	Benzene	Ethanol	Water	Gas		Benzene	Ethanol		Water
GA	OH_meta	335.36	96.89	42.18	47.32	57.55	81.12		82.88	77.18
GA	OH_para	335.30	96.42	40.74	45.80	56.44	79.74		81.50	85.14
MG	OH_meta OH_para	336.35	126.30	93.30	47.75	56.16	54.48		37.97	76.49
MG	OH_meta OH_para	336.41	89.78	93.36	46.46	49.01	83.91		30.83	71.58
EG	OH_meta	336.43	126.39	93.45	47.86	56.03	54.35		37.84	76.33
EG	OH_para	336.45	89.37	93.47	46.63	48.90	84.25		30.72	71.39
PG	OH_meta	336.35	126.29	93.35	47.82	56.11	54.43		37.92	76.32
PG	OH_para	336.34	89.99	93.34	46.51	49.01	83.61		30.82	71.47
BG	OH_meta	336.33	126.32	93.49	47.89	56.10	54.44		37.91	76.33
BG	OH_para	336.31	89.45	93.46	46.61	49.02	84.26		30.83	71.43
PNG	OH_meta	336.32	126.41	93.52	47.89	56.12	54.44		37.93	76.32
PNG	OH_para	336.29	89.46	93.49	46.61	54.93	90.17		30.84	71.42
HG	OH_meta	336.30	126.36	93.49	47.19	56.13	54.45		37.94	76.97
HG	OH_para	336.27	90.08	93.46	45.93	49.05	83.61		30.86	72.04
HPG	OH_meta	336.29	126.36	93.53	47.18	56.14	54.46		37.95	76.96
HPG	OH_para	336.26	90.05	93.49	45.92	49.06	83.65		30.88	75.32
OG	OH_meta	350.82	126.35	51.11	55.85	48.74	78.12		77.27	71.92
OG	OH_para	336.25	97.56	40.93	45.93	54.96	83.69		80.86	75.33
DG	OH_meta	350.81	110.15	51.11	55.85	48.75	73.05		72.27	71.92
DG	OH_para	336.24	97.55	41.51	46.52	54.97	78.12		80.26	74.73
DOG	OH_meta	350.81	110.14	51.13	55.87	48.75	73.06		77.26	71.91
DOG	OH_para	336.24	97.52	41.51	46.51	54.97	78.13		80.23	74.69

The antioxidant mechanism of alkyl gallates is highly dependent on both alkyl chain length and solvent polarity. Short chains (C1-C4) favor the HAT mechanism in the gas phase, while medium chains (C5-C8) transition towards the SET-PT mechanism in polar solvents. Long chains (C9-C10) predominantly adopt the SPLET mechanism in highly polar environments like water. These findings underscore the importance of considering molecular structure and solvent effects to predict and optimize antioxidant properties accurately. These results open new pathways for understanding and controlling the reaction mechanisms of alkyl gallates' antioxidant potential in solvents of varying polarity. This knowledge can facilitate the design of more effective antioxidants to extend shelf life in the food industry, reduce oxidative stress in biological systems, and even prevent diseases.

3.6. Molecular Docking Analysis

Molecular docking is a computational technique used to predict the binding mode of a small molecule against a target molecule. These studies indicate that structural changes in a ligand may affect its binding properties, thus guiding the synthesis of new compounds with more favorable pharmacological properties [109, 110]. Additionally, docking techniques help to understand the details of biological processes. The method also saves time, labor, and budget by narrowing down the candidate molecules for experimental tests [111]. In this context, molecular docking was performed to determine the antioxidant properties of the C1-C10 series of alkyl gallates. This analysis aims to identify how variations in the alkyl chain length influence the binding interactions with target proteins. The results from the docking studies will guide the synthesis of new alkyl gallates with enhanced antioxidant activity, optimizing their potential therapeutic benefits.

Tyrosine kinases are enzymes that regulate various cellular processes. Hck (Hematopoietic cell kinase) is a member of the Src family of protein tyrosine kinases, which play an important role in signal transduction and controlling cell proliferation differentiation [112]. Activation of Hck is also associated with response to oxidative stress signaling pathways. Although Hck is not an antioxidant enzyme, its activity may influence the cellular response to oxidative stress [113].

Reddy et al. studied a new series of 1-(2,3-dihydro-1H-indan-1-yl)-3-aryl urea/thiourea derivatives and confirmed the results by molecular docking methods. They are interested in hydrogen bonds with Arg160 residue of protein tyrosine kinase enzyme for potential antioxidant activity as excitatory arginine receptor antagonist [114]. Moon and Alam used molecular docking techniques to find out the binding modes and interaction profile of steroidal oxazolidinethiones and recorded various interactions with Arg380, Asn381, Tyr382, Ile383, and Arg385 of the tyrosine kinase [115]. In another study, Festus et al. analyzed Mn(II), Co(II), Ni(II), and Cu(II) complexes with novel pyrimidine-based Schiff base ligands. They used Hck to get detailed insight into the antioxidant activity of the molecules. They recorded hydrogen bonding interactions between the molecules and Asp404, Leu393, Asn391, and Gly274 of the target [116]. In this study, all the molecules interacted with the same residue of the target molecule with different orientations. Many H-bonds were recorded for all the molecules. The best binding affinity was recorded for b as -5.50 kcal/mol. The H-bonds with Gln161, Lys321, Gln369, and Leu398 of the target molecules could be effective in this recorded binding affinity as well as pi- and alkylic-interactions with Arg160 and Val399. The binding affinity of MG (-5.16 kcal/mol) is also remarkable. This molecule has H-bonds with Asp157, Arg160, Lys321, Lys362, Gln369, Ser397 and Leu398 of tyrosine kinase. Accordingly, binding affinity orders of the compounds have been determined as DOG (-4,02) < HPG (-4.35) < GA (-4.377) < HG (-4.41) < PG (-4.55) < OG (-4.73) < DG (-4.78) < EG (-4.82) < PNG (-4.83) < MG (-5.16) < BG (-5.50). All molecules' interactions and residues are represented in Fig. 7, Table 5, and Figures S1-S10.

Table 5 Binding analysis of the molecules against Tyrosine Kinase, Heme Oxygenase and Serum Albumin (green: H-bonds; blue: van der Waals interactions; red: alkylic interaction, purple: pi-interactions).

Comp.	Bind. Aff.*	Amino Acids Residue
Tyrosine Kinase
BG	-5.50	Gln161, Lys321, Gln369, Leu398, Val399, Arg160, Asp157, Ala164, Asp320, Lys362..
DG	-4.78	Gln161, Lys321, Gln369, Leu398, Val399, Arg160, Phe150, Ile153, Asp157, Ala164,...
DOG	-4.02	Lys321, Gln369, Leu398, Val399, Arg160, Asp157, Gln161, Ala164, Ser248, Asp320,.
EG	-4.82	Arg160, Lys321, Lys362, Gln369, Ser397, Leu398, Val399, Gln161, Asp320, Asp365,.
HG	-4.41	Asp157, Lys321, Gln369, Ser397, Val399, Arg160, Gln161, Leu163, Ala164, Pro165,..
HPG	-4.35	Gln161, Lys321, Lys362, Gln369, Leu398, Val399, Arg160, Ala164, Cys245, Asn167,.
MG	-5.16	Asp157, Arg160, Lys321, Lys362, Gln369, Ser397, Leu398, Val399, Gln161, Asp365,.
OG	-4.73	Arg160, Lys321, Lys362, Gln369, Ser397, Leu398, Val399, Asp157, Gln161, Ser248,..
PG	-4.83	Asp157, Arg160, Gln161, Ser397, Leu398, Val399, Ala164, Asp320, Lys321, Lys362,.
PNG	-4.55	Arg160, Lys321, Gln369, Leu398, Val399, Ala164, Cys24, Gln161, Asn167, Met246,..
GA	-4.37	Asp157, Lys321, Lys362, Gln369, Ser397, Leu398, Val399, Gln161, Asp320, Asp365,.
Heme Oxygenase
BG	-5.80	Tyr123, Val124, His15, Leu127, Phe195, Arg8, Thr11, Gly128, Ser131, Arg171
DG	-4.29	Tyr123, Ser131, Arg8, Leu127, Thr11, Ser12, His15, Val124, Gly128, Lys167, Arg171.
DOG	-4.50	Tyr123, Val124, Phe195, His15, Ala18, Phe44, Arg125, Leu127, Gly128, Asp129,…..
EG	-6.03	His15, Glu19, Arg125, Ala18, Ile24, Phe27, His40, Phe44, Phe195, Phe202
HG	-4.22	Ser131, Arg8, Thr11, Ser12, His15, Tyr123, Val124, Leu127, Gly128, Gly132, Phe195
HPG	-4.81	Glu19, Val124, Arg125, Phe195, Ala18, His40, Phe44, Phe202, His15, Ile24, Phe27,..
MG	-5.74	Glu19, Arg125, Ala18, Ile24, His15, Phe27, His40, Phe44, Leu136, Phe195, Phe202
OG	-4.55	Glu19, Asp129, Arg125, Leu136, His15, Ala18, Ile24, His40, Phe44, Tyr48, Gly128,..
PG	-6.38	Tyr123, Val124, Ser131, His15, Leu127, Arg8, Arg125, Gly128, Phe195
PNG	-4.69	His15, Glu19, Val124, Arg125, Ala18, Phe195, Phe202, Ile24, Gly128, Asn198
GA	-4.80	Arg8, Tyr123, Val124, Gly128, Leu127, His15, Arg171, Phe195
Human Serum Albumin
BG	-4.91	Asp451, Ser454, Lys195, Lys199, Leu203, Phe211, Leu198, Ser202, Phe206, Trp214,..
DG	-5.49	Ser202, Ala210, Phe211, Trp214, Leu453, Leu198, Lys199, Val344, Glu450, Ser454,..
DOG	-5.44	Asp451, Ser454, Lys195, Leu198, Lys199, Leu219, Leu238, Ser202, Phe211, Ala215,..
EG	-4.99	Gly207, Ala210, Lys199, Cys200, Ser202, Leu203, Phe206, Phe211, Trp214, His242,..
HG	-5.67	Asp451, Ser454, Lys199, Phe206, Ala210, Lys195, Leu198, Ser202, Leu203, Gly207,..
HPG	-5.48	Gly207, Trp214, Leu203, Ala210, Leu198, Lys199, Ser202, Phe206, Glu208, Phe211,..
MG	-4.75	Leu203, Gly207, Ala210, Lys199, Ser202, Phe206, Glu208, Phe211, Trp214, Leu481
OG	-6.02	Ser202, Leu481, Arg484, Leu457, Leu198, Phe206, Trp214, Val344, Glu450, Leu453,..
PG	-4.65	Lys199, Leu203, Gly207, Leu198, Ala210, Ser202, Phe206, Glu208, Phe211, Leu481
PNG	-4.84	Lys199, Ser202, Glu450, Asp451, Ser454, Trp214, Leu481, Lys195, Leu198, Ala210,..
GA	-5.43	Ser202, Lys205, Phe206, Leu198, Leu481, Trp214, Ser454, Asn458, Arg484
* Binding Affinity in kcal/mol.

Heme oxygenase (HO) is an enzyme crucial for heme-containing proteins in various biological processes, including oxygen transport, electron transfer, and catalysis [117]. Heme oxygenase has two main isoforms, Heme Oxygenase-1 (HO-1) and Heme Oxygenase-2 (HO-2). HO, especially HO-1, is important for antioxidant mechanisms through its role in heme catabolism. Biliverdin, Bilirubin, and Carbon Monoxide are the products of heme catabolism, which can scavenge free radicals and protect cells against oxidative stress [118, 119]. Sathe et al. analyzed a set of new benzamide derivative molecules that are structurally like paracetamol for their antioxidant activity, also studied the interactions of the molecules against heme oxygenase by molecular docking techniques and recorded the interactions with Gly139, Asp140, and Arg136 [120]. El-Wahab et al. evaluated the antioxidant activity of two polypropylene-type molecules and represented the interaction with Glu66, Lys69, Pro10, and Lys204 of the heme oxygenase-1 [121]. In this study, all the molecules interacted with the same residue of the target molecule with different orientations. H-bonds were recorded for all the molecules. The best binding affinity was recorded for P as -6.38 kcal/mol. The H-bonds with Tyr123, Val124, and Ser131 of the target molecules could be effective in this recorded binding affinity and alkylic interactions with His15 and Leu127. The binding affinity of EG (-6.03 kcal/mol) is also remarkable. This molecule has H-bonds with His15, Glu19, Arg125 of heme oxygenase. Accordingly, binding affinity orders of the compounds have been determined as HG (-4,22) < DG (-4.29) < DOG (-4.50) < OG (-4.55) < PNG (-4.69) < GA (-4.80) < HPG (-4.81) < MG (-5.74) < BG (-5.80) < EG (-6.03) < PG (-6.80). The interactions and the residues of all molecules are represented in Fig. 8, Table 5, and Figures S11-S20

Serum albumin, one of the most important blood proteins, transports various substances such as hormones, fatty acids, bilirubin, and some drugs through the blood in the body [122, 123]. Additionally, albumin is vital in removing toxins and heavy metals from the body. This protein also protects the body against infections and diseases by affecting the activity of immune cells and cytokines. Additionally, serum albumin is an antioxidant molecule with heparin-like activity. It is possible to review many articles in which the antioxidant activity of serum albumin is evaluated with in vitro and silico methods such as molecular docking [124, 125]. Singh et displayed the results between nocodazole, a benzimidazole derivative molecule, and human serum albumin and recorded the interactions with Tyr148, Lys195, Lys199, Cys200, His 242, Cys245 and Cys253 [126]. Abdullah et al researched the binding site of tizaparin against HSA to get insight into the details of fluorescence experiments by molecular docking methods and they found that Glu153, Ser192, Arg222, Arg257 have the key role in the interactions [127]. Liao et al. explored the interactions of two sulfonamides, sulfametoxydiazine and sulfamonomethoxine, with human serum albumin, and the antibiotics were located in the residues including Ala291, Leu238, Phe211, Arg222, His242, Lys199 [128].

In this study, all the molecules interacted with the same residue of the target molecule with different orientations. H-bonds were recorded for all the molecules. The best binding affinity was recorded for OG as -6.02 kcal/mol. The H-bonds with Ser202 and Leu481 of the target molecules could be effective in this recorded binding affinity and alkylic- and π-interactions with Arg484 and Leu457. The binding affinity of HG (-5.67 kcal/mol) is also remarkable. This molecule has H-bonds with Asp451 and Ser454 of serum albumin. Accordingly, binding affinity orders of the compounds have been determined as PG (-4,65) < M (-4.75) < PNG (-4.84) < BG (-4.91) < EG (-4.99)< (-5.43) < DOG (-5.44) < HPG (-5.48) < DG (-5.49) < EG (-5.67) < OG (-6.02). All molecules' interactions and residues are represented in Fig. 9, Table 5, and Figures S21-S30.

Tyrosine Kinase Hck, Heme Oxygenase, and Human Serum Albumin were used to get insight into the molecules' interactions by molecular docking methods. All the molecules interacted with the identical residues of the target molecules with different orientations. Many H-bonds were recorded for all the molecules against all target molecules. The best binding affinity was recorded for BG as -5.50 kcal/mol against Tyrosine Kinase Hck, while PG has − 6.38 kcal/mol against Heme Oxygenase. Additionally, -6.02 kcal/mol binding affinity was recorded for OG against Human Serum Albumin.

This investigation demonstrates that the antioxidant efficacy of alkyl gallates is intricately dependent on their molecular structure and the solvent used. Key insights include the significant role of alkyl chain length and solvent polarity in modulating antioxidant properties, with shorter chains in polar environments exhibiting optimal activity. Moreover, the study elucidates the cut-off effect, highlighting the non-linear relationship between chain length and antioxidant potential. These findings advance our understanding of the molecular dynamics of alkyl gallates and guide the development of more effective antioxidants, emphasizing the need for tailored molecular designs to harness their full potential in various applications.

Funding Declaration:

This research was conducted without specific financial support from public, commercial, or not-for-profit funding agencies. No dedicated grants or financial resources were allocated to this study from external sources. The work presented here was solely supported by the researchers' institutional resources and personal dedication, without reliance on external funding.

Author Contribution

Nihat KarakuşPerformed computations, wrote and edited the manuscript, and managed the submission process. Additionally, he contributed to the analysis and interpretation of computational results, and ensured the overall coherence of the manuscript.

Acknowledgement

I am grateful to TUBITAK ULAKBIM, High Performance and Grid Computing Center (TR-Grid e-Infrastructure), for providing the computational resources necessary for my calculations. Their support has been invaluable to the success of my work.

Data availability:

The supplementary information files include all relevant data supporting this study's findings. No additional datasets were generated or analyzed during the current study.

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Revealing the Antioxidant Properties of Alkyl Gallates: A Novel Approach through Quantum Chemical Calculations and Molecular Docking

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Abstract

Figures

1. Introduction

2. Computational methods

3. Results and discussion

3.1. Frontier molecular orbitals (FMOs) analysis.

3.2. Molecular electrostatic potential (MEP) analysis.

3.3. Global Reactivity Descriptors (GRDs).

3.4. Analysis of spin density distribution.

3.5. Evaluation of Thermochemical Parameters and Antioxidant Mechanisms

3.5.1.Hydrogen Atom Transfer Mechanism (HAT)

3.5.2. Single Electron Transfer Followed by Proton Transfer Mechanism (SET-PT)

3.5.3. Sequential Proton Loss Electron Transfer Mechanism (SPLET)

3.6. Molecular Docking Analysis

4. Conclusion

Declarations

Funding Declaration:

Author Contribution

Acknowledgement

Data availability:

References

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