Evaluating the anticorrosive properties of Camellia chrysantha flower extract on carbon steel in acidic solutions: A computational approach

2.1.1. Predicting microspecies of the phytochemicals

The determination of the predominant microspecies of the four inhibitors across various pH levels was performed using the MarvinSketch software. The pH range spanned from 0.0 to 14.0. Based on the output from MarvinSketch, it was observed that CTCH, QRCT, and QCTO exhibited 18 distinct forms, while KMFR showed 14 forms. In an experimental setup [16], HCl was chosen as the corrosive medium, with a pH of approximately 0.00. As a result, the dominant form of each inhibitor molecule at pH = 0.00 was identified and has been illustrated in Figure 2. It was found that the predominant microspecies of these inhibitors were largely in their neutral forms, with CTCH displaying 100% neutral species, while the other compounds were around 98%. These forms were subsequently used for theoretical calculations.

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Figure 2.

Optimized geometrical structures of the four investigated phytochemicals. The Deviation from the Plane (SDP) and molecular planarity parameters (MPP) values are superimposed.

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3.1.1. Optimized geometries (planarity, ESPMs, and FMOs distribution)

The Span of Deviation from the Plane (SDP) and Molecular Planarity Parameters (MPP) were calculated using the Multiwfn software [29]. This was performed to determine the degree of planarity of each molecule since this will affect the adsorption mechanism of the phytochemical on the metal surface, especially in the case of parallel orientation. The MPP assesses the overall deviation of the entire structure from the reference plane, whereas the SDP quantifies the deviation of individual structural segments from the same plane [30]. Lower values of MPP indicate greater planarity, while a lower SDP signifies reduced deviation from the fitting plane. The planarity of the four molecules according to MPP and SDP values can be arranged as follows: QRCT = QCTO > KMFR > CTCH. Since QRCT and QCTQ are totally in-plane molecules, see Figure 2.

The planarity of a molecule directly impacts its adsorption behavior by influencing the extent of contact with the metal surface. Molecules with higher planarity, such as QRCT and KMFR, can achieve more effective parallel adsorption on the Fe(110) surface, maximizing the overlap of their π-electrons with the d-orbitals of iron. This increased contact area enhances electronic interactions, leading to stronger adsorption energies. In contrast, less planar molecules, such as CTCH, exhibit reduced overlap and weaker adsorption interactions, as evidenced by their lower adsorption energies.

The interaction between inhibitor molecules and metal surfaces is primarily influenced by molecular orbitals, especially the HOMO and LUMO. This interaction is facilitated through two primary mechanisms: (i) donation of electrons from the inhibitor’s HOMO to the vacant d-orbitals of the metal, and (ii) the reverse process, where electrons are donated back from the filled d-orbitals of the metal to the inhibitor’s LUMO. These complementary electron exchange processes work synergistically to enhance the adsorption strength of the inhibitor on the metal surface.

Figure 3 illustrate the 3d-isosurfaces of HOMOs, LUMOs, electrostatic potential maps (ESPMs), energies of HOMOs and LUMOs, and the energy gaps of the four investigated phytochemicals. Figure 3 indicates that the HOMOs and LUMOs of investigated molecules are distributed over the entire moiety of the investigated phytochemicals, indicating the possibility of using these inhibitors to be adsorbed on the Fe surface. Exception should be noticed here for the HOMO of the CTCH molecule, which is distributed on the pyrocatechol unit of the molecule, reflecting that this part is reasonable for electron’s donation during the adsorption process. These results are also confirmed by plotting the 3D-isosurfaces of the total density at HOMOs and LUMOs surfaces (TD-HOMO and TD-LUMO) as shown in Figure 4. The strong red color on the oxygen atoms and the phenyl groups marks these regions as favourable for electrophilic attacks , while the strong blue color on some C and H atoms reflect the ability of these site to undergo nucleophilic attacks.

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Figure 3.

3D iso-surface representations of (a) frontier molecular orbitals (FMOs), (b) energy gap diagrams (energies are in eV units), and (c) electrostatic potential maps (ESPMs) in aqueous solution. The parameters used for these visualizations include an iso-value of 0.02 au, a density of 0.0004 au, and a Laplacian value of 0.00 au.

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Figure 4.

3D-Iso-surface total densities of HOMO and LUMO (TD-HOMO and TD-LUMO) of the investigated phytochemicals in aqueous solution (Iso-value: 0.02 au; Density: 0.0004 au; Laplacian = 0.00 au).

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In addition, the ESPMs indicate the site of electronic accumulation (red-colored regions, negative potential) and sites of electronic depletion (blue-colored regions, positive potential). From, the heteroatom sites or functional group regions such as O atoms and hydroxyl or ketonic regions are colored red, while C and H atoms are surrounded by blue color, see Figure 3.

The electron-donating capability of an inhibitor is determined by the energy of its HOMO. A higher (less negative) HOMO energy (E_HOMO) indicates a greater ease of electron donation, corresponding to a lower ionization energy (I = -E_HOMO). On the other hand, the inhibitor’s capacity to accept electrons depends on the energy of LUMO. A lower (more negative) LUMO energy (E_LUMO) reflects a higher electron affinity (A = -E_LUMO), facilitating easier electron acceptance. When a molecule displays a favorable alignment between its HOMO and LUMO, it is considered chemically soft. According to hard and soft acids and bases (HSAB) theory, soft materials tend to form more stable interactions with each other, a characteristic that holds particular importance for bulk metals, which are chemically classified as soft. Figure 3 presents the HOMO and LUMO energies, along with the energy gaps, for the studied phytochemicals. Based on the energies of HOMOs, our results in Figure 3 indicate that the order of the inhibition efficiencies of the investigated phytochemicals in their isolated form would be: QRCT > QCTO > CTCH > KMFR. However, from the results of E_LUMO, the trend would follow the order CTCH > QCTO > QRCT > KMFR.

Furthermore, to enhance the reactivity of the inhibitor toward anti-corrosive behavior, minimization ofthe HOMO-LUMO energy gap (ΔE_g= E_LUMO- E_HOMO) is desirable. Figure 3 illustrates the energy gas values and the energy gap diagram of the investigated inhibitors. Our results in Table 1 and Figure 2 indicate that the energy gaps of the investigated inhibitors have the following theoretical trend: CTCH (5.739 eV) > QCTO (4.034 eV) > KMFR (3.993 eV) > QRCT (3.683 eV). These results reflect that QRCT with the lowest ΔE_g value has the lowest energy gap giving it the most powerful anticorrosive effect, while the CTCH molecule with the highest energy gap could have the least chemical reactivity, and hence, could have the least inhibition performance.

As the metal and the inhibitor come close to each other, the electrons start to flow. Therefore, the electron’s flow from phytochemical to Fe or from Fe to phytochemical can be energetically described by estimating the differences between the HOMOs and LUMOs of the Fe and phytochemicals (ΔE₁ and ΔE₂). The following Eq. (2) are employed to calculate each parameter listed in Table 1 based on previous works [31,32]:

Here, the HOMO and LUMO energy levels of iron, denoted as ${\text{E}}_{\text{HOMO}}^{\text{Fe}}$ and ${\text{E}}_{\text{LUMO}}^{\text{Fe}}$ are considered to be -7.902 eV and -0.151 eV, respectively [33]. In this contest, ΔE₁ is the energy required to flow the electron from the HOMO of Fe to the LUMO of the phytochemical. Whereas ΔE₂ denotes the energy required to flow the electrons from the HOMO of the phytochemicals to the metal. The results are graphically shown in Figures 3 and 5.

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Figure 5.

Energy gaps of the Fe-inhibitors of the four investigated phytochemicals (ΔE₁ and ΔE₂).

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Our results show that for the four investigated inhibitors, ΔE₁ is larger than ΔE₂, reflecting that electron transfer from inhibitors to Fe metal is energetically favored than the opposite process. This means that during the adsorption process, the investigated phytochemicals act as Lewis’s base and the Fe metal acts as Lewis acid. Comparison of ΔE₁s of the investigated inhibitors show that the energetic trend of the electron’s flow from the HOMO of the inhibitors to the Fe metal exhibits the following order: KMER (6.247 eV) > QRCT (6.375 eV) > QCTO (6.523 eV) > CTCH (8.190 eV). On the other hand, when the electrons flow from the HOMO of Fe metal to the LUMO of the investigated inhibitors, the required energy follows the order as follows: QRCT (5.058 eV) > QCTO (5.262 eV) > CTCH (5.30 eV) > KMFR (5.498 eV).

3.1.2. Quantum global reactivity parameters

It should be mentioned that the adiabatic ionization potentials (AIP) and adiabatic electron affinities (AEA) were calculated and used to extract the most relevant global chemical reactivity parameters, as indicated in Table 1. The applied equations are indicated in the last row of the table.

Previous studies reported that the inhibitor molecule with a low electronegativity value has a good corrosion inhibition performance [34]. The obtained results indicate that the order of electronegativity follows the trend QRCT (3.167) < QCTO (3.175 eV) < KMER (3.282 eV) < CTCH (3.341). By taking into account the electronegativity of Fe-metal as 7.0 eV, therefore, the difference between the electronegativity of inhibitor and metal exhibits the trend QRCT (3.833 eV) > QCTO (3.825 eV) > KMER (3.718 eV) > CTCH (3.487 eV). According to Sanderson’s electronegativity equalization principle [35], QCTO, with the lowest electronegativity and the highest difference of electronegativity, could have the highest anti-corrosion performance, while CTCH exhibits the least corrosion inhibition efficiency.

Hardness (η) and softness (σ) are key molecular reactivity indicators that provide insights into the stability and chemical behavior of molecules, particularly within the framework of HSAB theory [36]. Lower values of hardness (η) and higher values of softness (σ) correlate with increased chemical reactivity, which enhances the efficiency of corrosion inhibition. The results presented in Table 1 demonstrate a predicted order of corrosion inhibition effectiveness for the studied phytochemicals, following the trend QRCT > QCTO > KMFR > CTCH.

As the electrophilicity increases, the propensity to accept electrons increases, and consequently, the inhibition efficacy increases [37]. From our results of electrophilicity (ω), the anticorrosive performance of the investigated species follows can be arranged as follows: KMFR > QRCT > QCTO > CTCH.

The donor-acceptor capacity of a chemical species can be quantified by calculating the electron-accepting power (denoted as ω^-), electron-donating power (denoted as ω⁺), and net electrophilicity (denoted as Δω^±). According to our results, it is found that ω^- > ω⁺ for all species and KMFR phytochemical with the highest ω⁺, ω^- and Δω^± values is expected to have the highest ability to accept and donate electron during the adsorption process and the general trend exhibits the order as follows: KMFR > QRCT > QCTO > CTCH.

Δψ, calculated as the square of the difference in electronegativity between the inhibitor and the metal divided by the sum of their chemical hardnesses, quantifies the energy stabilization due to charge transfer. Lower Δψ values indicate stronger charge transfer interactions, enhancing adsorption. From Table 1, Δψ follows the order KMFR (0.089 eV) < QCTO (0.164 eV) < QRCT (0.176 eV) < CTCH (0.156 eV), suggesting KMFR exhibits the most favorable charge transfer conditions among the studied phytochemicals.

The negative values ∆E_B-D descriptor indicates that back-donation from molecule to metal is energetically favored. Examination of Table 1 indicates that ∆E_B-D are < 0 for all species, and the following order is expected: QRCT > QCTO > KMFR > CTCH, signifying that the process of electron transfer from the metal to the molecule, followed by electron back-donation, is energetically advantageous. Given that enhanced adsorption of the molecule onto the metal surface is likely to improve anticorrosive efficacy, this performance can be further optimized by increasing the stabilization energy between iron and the inhibitor.

The current study calculated the fraction of electrons transferred, ∆N₁₁₀, and the results are also gathered in Table 1. Investigation of Table 1 indicates that ∆N₁₁₀ values of all species were positive and less than 3.6, indicating that these inhibitors act as electron donors (Lewis’s base) during the adsorption process. Also, the higher the ∆N₁₁₀ value, the higher the anticorrosive performance of the investigated inhibitors, and they can be arranged as follows: QRCT > QCTO > CTCH > KMFR.

These trends in global reactivity parameters align with the structural features of the studied phytochemicals. For instance, QRCT and KMFR, which exhibit higher nucleophilicity and lower hardness, have more electron-rich functional groups (e.g., hydroxyl and carbonyl groups) that facilitate stronger interactions with the metal surface. The higher softness (σ) of these molecules also enhances their adaptability to the electronic environment of the Fe(110) surface, improving their adsorption efficiency. Additionally, the negative back-donation index (∆E_B−D) values confirm that electron transfer from the inhibitors to the iron surface, followed by back-donation, is energetically favorable. These findings align with established principles of soft acids and bases [38], further supporting the strong inhibitory performance of QRCT and KMFR.

3.1.3. Fukui indices

Kenichi Fukui [39,40] introduced the idea of Fukui functions, which have since become crucial descriptors for understanding local reactivity. These functions take into account structural variations in molecules, providing a more detailed assessment of atomic reactivity [41]. They are particularly useful for identifying the regions within a molecule that are more likely to undergo nucleophilic or electrophilic reactions. Additionally, Fukui functions enable the analysis of electron-donating and electron-accepting tendencies within a molecule. To quantify these characteristics, condensed Fukui descriptors for nucleophilic ( ${\text{f}}_{\text{k}}^{+}$ ​) and electrophilic ( ${\text{f}}_{\text{k}}^{-}$ ) regions, as well as a dual descriptor ( ${\text{f}}_{\text{k}}^2$ ​), were calculated and listed in Table 2. This was accomplished through Mulliken charge analysis within the framework of conceptual density functional theory (CDFT), utilizing the Multiwfn software [29]. The following expressions were employed for these calculations by Morell et al. (Eq. 3) [42]:

A high value of the nucleophilic attack descriptor ( ${\text{f}}_{\text{k}}^{+}$ ​) for a given atom k suggests that the atom exhibits strong electrophilic characteristics, whereas a high value of the electrophilic attack descriptor ( ${\text{f}}_{\text{k}}^{-}$ ) indicates nucleophilic tendencies [43]. Morell et al. [42] expanded on this concept by introducing a more refined descriptor known as the dual local Fukui index ( ${\text{f}}_{\text{k}}^2$ ​), which integrates both ${\text{f}}_{\text{k}}^{+}$ and ${\text{f}}_{\text{k}}^{-}$ ​ values. This descriptor is defined by the following equation (Eq. 4):

The purpose of ${\text{f}}_{\text{k}}^2$ is to simultaneously assess the nucleophilic and electrophilic behavior of an atom.

A positive ${\text{f}}_{\text{k}}^2$ ​ value indicates that the atom is more likely to undergo nucleophilic attack, identifying it as a favorable site for electron acceptance. In contrast, a negative ${\text{f}}_{\text{k}}^2$ ​ value suggests the atom is more vulnerable to electrophilic attack, designating it as an ideal center for electron donation [44]. In this study, the most significant results of ${\text{f}}_{\text{A}}^2$ for the phytochemical compounds under investigation are presented graphically in Figure 6.

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Figure 6.

Dual local Fukui indices of the investigated phytochemicals (f_k²). Note: for atomic numbering refer to Figure 2.

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For the CTCH molecule, nucleophilic attack is most likely at C₁₅, C₁₈, and C₁, as indicated by their positive ${\text{f}}_{\text{k}}^2$ ​ values, while electrophilic attack is favored at O₂₀, C₂, C₁₆, and O₁₃ due to their negative ${\text{f}}_{\text{k}}^2$ ​ values. In QRCT, nucleophilic interactions are primarily associated with the C₁₃, C₄, and O₄ centers, whereas electrophilic interactions predominantly occur at O₇, O₂, and O₆ atoms. Similarly, in QCTO, the nucleophilic sites with the highest reactivity are C₁₅, C₁, and C₁₈, while O₂₀, C₂, C₁₆, and O₁₃ exhibit the strongest propensity for electrophilic interactions. For KMFR, nucleophilic attack centers are identified at C₁₃, O₄, and C₁₄, whereas O₇, O₂, and O₆ demonstrate the highest capability for electron donation to the Fe surface, facilitating electrophilic interactions. These differences in reactive sites across the molecules are strongly influenced by their structural features, with hydroxyl and carbonyl groups consistently playing key roles in adsorption interactions.

3.2.1. Geometrical and energetic aspects of adsorption

The SCC-DFTB calculations can provide a deeper understanding of how the investigated phytochemicals interact with the iron surface [10]. In this section, the adsorption behavior of the four investigated phytochemicals on the Fe(110) surface is explored using SCC-DFTB simulations. Figures 7 and 8 present graphical depictions of the adsorption configurations of CTCH, QRCT, KMFR, and QCTO on the Fe(110) surface, optimized using the SCC-DFTB method. The configurations include both parallel and perpendicular orientations relative to the surface.

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Figure 7.

Self-consistent-charge density-functional tight-binding method (SCC-DFTB) optimized parallel adsorption configurations of selected phytochemicals on the Fe(110) surface. (a), (b), (c) and (d) represent CTCH, QRCT, KMFR and QCTO, respectively. The bond distances are measured in angstroms (Å).

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Figure 8.

Optimized perpendicular adsorption configurations of selected phytochemicals on Fe(110) surface by self-consistent-charge density-functional tight-binding method (SCC-DFTB). (a), (b), (c) and (d) represent CTCH, QRCT, KMFR and QCTO, respectively. The bond distances are measured in angstroms (Å).

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Organic inhibitors in acidic media typically mitigate metal corrosion through physicochemical adsorption, beginning with physisorption followed by chemisorption [4]. It is useful to categorize molecule-metal bonds by comparing the sum of the covalent radii of the interacting atoms. Bonds classified as covalent typically fall within this sum, whereas bonds considered physical are characterized by distances exceeding 3 Å [45].

Visual inspection of Figures 7 and 8 shows that CTCH molecules do not bond with iron atoms in their stable parallel and perpendicular adsorption geometries. On the other hand, QRCT establishes connections with iron atoms through multiple carbon and oxygen atoms in both parallel and perpendicular adsorption configurations, Figure 7(b) and 7(c). In the parallel adsorption mode, QRCT forms three bonds with iron atoms: one Fe-C bond (2.301 Å) and two Fe-O bonds (2.022 and 2.029 Å). The perpendicular mode forms one Fe-O bond (1.885 Å) and one Fe-C bond (2.250 Å), indicating QRCT’s high affinity for iron atoms. KMFR exhibits strong bonding with iron atoms in its stable parallel geometry, forming three Fe-C bonds (2.265 to 2.312 Å) and three Fe-O bonds, with distances of 1.992, 2.003, and 1.938 Å. However, KMFR does not bond in its perpendicular geometry, suggesting its stability is higher in the parallel form. QCTO, in its stable parallel mode, forms two Fe-O bonds (2.142 and 2.048 Å) and one Fe-C bond (2.213 Å), while the perpendicular mode forms a single Fe-O bond (1.917 Å). These differences in bonding highlight the varying affinities of the phytochemicals for iron atoms: KMFR shows strong affinity in the parallel mode, while QRCT and QCTO bond in both geometries. CTCH shows no bonding, indicating a weak affinity for the iron surface.

The characteristics of the bonds formed between the adsorbed molecules and the iron surface can be analyzed by comparing the measured bond distances with the combined covalent radii of the interacting atoms. For Fe-C and Fe-O bonds, previous research has determined these sums to be approximately 2.08 Å and 1.98 Å, respectively [46]. In this study, the calculated bond distances fall within these thresholds, suggesting the possibility of chemical interactions.

The nature of these bonds can be determined by comparing the bond lengths to the total covalent radii of the atoms involved [47]. Previous studies indicate that the covalent radii for Fe-C and Fe-O interactions are approximately 2.08 Å and 1.98 Å, respectively [46]. The calculated bond lengths align with these values, indicating that the interactions between the molecules and the iron surface are likely to involve chemical bonding rather than mere physical adsorption.

For further assessment of the molecules’ interactive force, interaction energies were analyzed. Table 3 presents these energies, revealing that KMFR, when adsorbed in a parallel orientation, exhibits the most negative interaction energy (-2.784 eV), indicative of the strongest adsorption among the compounds studied. QRCT follows with an interaction energy of -2.206 eV, and QCTO registers at -1.974 eV. CTCH, however, shows the weakest interaction, with an energy of -0.165 eV. The consistently negative interaction energies across all molecules point to the thermodynamic favorability of their adsorption onto the iron surface, affirming the stability of these interactions [48]. The perpendicular geometries show significantly lower interaction energies, with QRCT displaying the strongest interaction (-1.342 eV), followed by QCTO (-0.345 eV), KMFR (-0.103 eV), and CTCH (-0.132 eV).

These results suggest that the number and nature of functional groups in each phytochemical do not strongly influence adsorption strength. Despite having fewer hydroxy groups than QRCT, KMFR shows a stronger affinity for the iron surface. QCTO, with a methoxy group instead of a hydroxy group as in QRCT, still shows a different adsorption strength. This indicates that the adsorption strength is likely associated with the nature of the bonding, its strength, and structural factors such as steric effects, explaining the observed interaction magnitudes.

3.2.2. PDOS analysis

The PDOS analysis offers valuable insights into the electronic structures corresponding to the optimized adsorption configurations of the phytochemicals on the Fe(110) surface [49]. This method allows for the mapping of electronic states across the s and p orbitals of the phytochemicals and the 3d orbitals of the iron atoms. Figure 9 illustrates the PDOS for the isolated molecules situated at a distance of 7 Å from the iron surface, providing a baseline for comparison. In contrast, Figure 10 displays the PDOS after the molecules have adsorbed onto the iron surface, capturing the changes in electronic interactions due to bonding.

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Figure 9.

PDOSs for the adsorption of selected phytochemicals on the Fe(110) surface. Panels (a)-(d) show the PDOS for molecules located at a distance of 7 Å above the topmost layer of the Fe(110) surface.

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Figure 10.

PDOSs for the adsorption of selected phytochemicals on the Fe(110) surface. (a)-(d) represent the PDOSs of adsorbed molecules on the Fe(110) surface.

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To ensure focus on significant adsorption behavior, only configurations where bonding occured, were considered for the PDOS analysis . Both figures also include the PDOS for the iron’s 3d orbitals, consistent with earlier findings [45], allowing for a clear comparison between the pre-adsorption and post-adsorption electronic states.

As shown in Figure 9, the PDOS patterns for the phytochemicals prior to adsorption display noticeable peaks, several of which lie in the energy range between -5 and 5 eV. This range when compared with that of iron, indicates a possible orbital overlap and hybridization between the s and p orbitals of the molecules and the vacant d-orbitals of the iron atoms. Such an overlap suggests the presence of substantial bonding interactions [50].

After adsorption, as illustrated in Figure 10, the PDOS for the phytochemicals exhibits a noticeable broadening of molecular peaks in comparison to their pre-adsorption state. The reduction in intensity and the vanishing of certain peaks within the energy range of -5 to 5 eV indicate a stronger interaction between the molecules and the iron surface. This broadening could be a result of increased electronic disorder or localized structural changes upon adsorption. Additionally, the PDOS after adsorption shows a shift to lower energy values, indicating that the system has stabilized [45]. It suggests that this energy shift plays a key role in reinforcing the stability of the molecule-surface interactions, leading to a more robust adsorption configuration.

The interaction between the phytochemicals and iron appears to be strongly influenced by orbital hybridization, as evidenced by the notable overlap between the s and p orbitals of the phytochemicals and the 3d orbitals of iron [51]. This hybridization is indicative of the formation of strong covalent bonds between the atoms of phytochemicals and the iron surface. As a consequence, the molecular orbitals of the adsorbed compounds likely fuse with the iron’s d-orbitals, leading to the creation of hybridized orbitals through a charge transfer mechanism. This process results in noticeable shifts and reorganization within the PDOS peaks, highlighting the substantial alterations in the electronic structure induced by the adsorption event.