Phytochemical components of Allium Jesdianum flower as effective corrosion-resistant materials for Fe(1 1 0), Al(1 1 1), and Cu(1 1 1): DFT study

3.1.1 Radial distribution function

It is possible to gain a further understanding of the interactions between phytochemical inhibitor molecules and metal surfaces by analyzing radial distribution functions (RDFs). An important indicator of inhibitor interaction with metal surfaces is the first prominent peak in the RDF curve. Because physical interactions tend to produce peaks of greater than 3.5 Å, whereas peaks between 1.0 Å and 3.5 Å indicate chemisorption (Xie, 2015). MD simulation trajectories were used to determine the total radial distribution function of the three phytochemical inhibitors (Fig. 5).

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Fig. 5

RDFs of investigated phytochemical inhibitors adsorbed on the metal surfaces.

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From Fig. 5, we can see that the first peaks of the three phytochemical inhibitors appear at 2.87 Å, 2.55 Å, and 2.54 Å in Al(1 1 1), Cu(1 1 1), and Fe(1 1 0), regardless of the type of inhibitor molecule. The bond length between the metal surface inhibitor is less than 3.5 Å, indicating a chemosorption interaction. Additionally, the strength of interaction with the three metals increases as follows: Al(1 1 1) < Cu(1 1 1) < Fe(1 1 0). This order of the strength of interaction ( $g(r)$ vs $r$ curve) comes very consistent with the order of increasing the adsorption energies.

3.2.1 Frontier molecular orbitals and energy gaps

Inhibitor molecules are reacted chemically with metal surfaces through the highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbitals. Two processes dominate the interaction between the metal surface and the inhibitor molecule. The two processes are: electrons are donated from the inhibitor molecule to the empty d-orbital of the metal (transition metal), and electrons are given back to the inhibitor molecule from the filled d-orbital. Therefore, the two processes complete each other, and both benefit enhancing the adsorption process. The ability of the inhibitor molecule to donate an electron to the metal surface is measured by the energy of the HOMO orbital ( $E_{\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}}$ ), as the $E_{\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}}$ becomes high (less negative; destabilized) as the donation process becomes more accessible. Accordingly, its ionization energy ( $I=-E_{\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}}$ ) should be small in value. In contrast, inhibitor molecules' ability to accept an electron from the metal surface is measured by the energy of its LUMO orbital ( $E_{\mathrm{L}\mathrm{U}\mathrm{M}\mathrm{O}}$ ), as the $E_{\mathrm{L}\mathrm{U}\mathrm{M}\mathrm{O}}$ becomes low (more negative; stabilized) as the accepting process becomes easier. Accordingly, its electron affinity ( $A=-E_{\mathrm{L}\mathrm{U}\mathrm{M}\mathrm{O}}$ ) should be large in value. A molecule with such HOMO-LUMO alignment is chemically soft. In accordance with the HSAB principle, bulk metals are chemically the softest of all materials, so they interact better with soft materials.

In addition, the HOMO-LUMO energy gap ( $\mathrm{\Delta }{E}_{\mathrm{g}\mathrm{a}\mathrm{p}}=E_{\mathrm{L}\mathrm{U}\mathrm{M}\mathrm{O}}-E_{\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}}$ ) should be as small as possible to indicate a more reactive inhibitor molecule toward the anticorrosive behavior. Table 2 and Fig. 6 show the optimized geometries, energies of HOMOs and LUMOs, gaps, and special distributions in an aqueous medium. Simulation in the aqueous medium is essential as the corrosion of the metals occurs in the hummed environment.

The results from Table 2 and Fig. 6 show that the $E_{\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}}$ values increase (less negative; destabilized) in the following order: GC1 < GC3 < GD2, and thus the ability to donate electrons would be predicted following the same order. While the $E_{\mathrm{L}\mathrm{U}\mathrm{M}\mathrm{O}}$ values decrease (more negative; stabilized) in the following order: GC3 < GC1 < GD2, and thus the ability to accept electrons would be predicted following the same order. In contrast, the $\mathrm{\Delta }{E}_{\mathrm{g}\mathrm{a}\mathrm{p}}$ values of GC1 and GC2 are small equal 3.468 and 5.520 eV, respectively, and thus indicate the ease of polarization of these two investigated phytochemical molecules. $\mathrm{\Delta }{E}_{\mathrm{g}\mathrm{a}\mathrm{p}}$ values decrease in the following order: GC3 > GC1 > GC2, and thus the reactivities of the inhibitor molecules will follow the reverse order. We should mention here that a smaller $\mathrm{\Delta }{E}_{\mathrm{g}\mathrm{a}\mathrm{p}}$ value, however, as Kokalj and coworkers demonstrate, it does not unambiguously indicate a better inhibitor (Kokalj, 2021).

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Fig. 6

Densities of HOMOs and LUMOs, their energies and energy gaps (in eV) in aqueous medium. Note: Isovalue: 0.03 au.

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Inspection of the special distribution of electron density of HOMOs and LUMOs is essential to the qualitative determination of which part/s of the molecule are capable of donating/accepting electrons. The hydrocarbon parts of GC1 and GC3 seem unreactive to donate or accept electrons since any HOMOs and LUMOs do not occupy them. The HOMOs and LUMOs are delocalized mainly on the terminal alcoholic unit in GC3 and the ester unit in GC1. In GC2, part of the hydrocarbon chain can donate electrons since the HOMO orbital is delocalized over it. At the same time, the ester unit can accept electrons since the LUMO orbital is delocalized over this part of the molecule.

3.2.2 Molecular quantum chemical descriptors

Hard and soft acids and bases (HSAB) theories can explain the reactivity of three phytochemical molecules toward metal surface adsorption (Pearson, 1963; Geerlings et al., 2003). According to HSAB principal, several molecular quantum chemical descriptors (MQCDs) such as global hardness ( $h$ ), global softness ( $s$ ), global electronegativity ( $\chi$ ), chemical potential $(\mu$ ), electrophilicity ( $\omega$ ), nucleophilicity $(\epsilon$ ), electron-accepting power $({\omega }^{-})$ , electron-donating power ( ${\omega }^{+}$ ), and net electrophilicity ( ${\mathrm{\Delta }\omega }^{\pm }$ ) can be evaluated. Detailed equation used to evaluate these descriptors can be found next to each descriptor in Table 2.

Global hardness is synonymous with the $\mathrm{\Delta }{E}_{\mathrm{g}\mathrm{a}\mathrm{p}}$ apart from the factor of ½ (Kokalj, 2021). On the other hand, upon contact between inhibitor and metal, there will be a flow of electrons from lower $\chi$ (inhibitor) to higher $\chi$ (metal) until the chemical potentials becomes matched. Sanderson's electronegativity equalization principle says that the inhibitor with a large electronegativity difference will require a longer time to reach equalization. This will lead to a high level of reactivity, which implies a high level of inhibition (Geerlings and De Proft, 2002). Therefore, low global hardness and electronegativity values suggest that phytochemical inhibitors are highly reactive molecules capable of accepting and transferring electrons during the interaction between metals and inhibitors (Dagdag, 2020). Among the three molecules, GC2 is the softest molecule ( $h=$ 2.386 eV), and GC3 has the smallest $\chi$ value (2.222 eV). Electro- and nucleophilicity descriptors indicate the inhibition molecule's ability to accept and donate electrons.

A charge transfer model for donation and back-donation charges make up another essential descriptor, i.e., the total energy change ( ${\mathrm{\Delta }E}_{\mathrm{B}-\mathrm{D}})$ . Based on the value of the molecular hardness, as shown in the following equation, the charge transfer model can be calculated:

Thus, it is suggested that if $h>0$ or ${\mathrm{\Delta }E}_{\mathrm{B}-\mathrm{D}}<0$ , the electron back-donation from the metal surface to the empty orbitals of inhibitor molecules is energetically favorable. ${\mathrm{\Delta }E}_{\mathrm{B}-\mathrm{D}}$ are negative, and the maximum value is −0.936 eV for GC3, indicating the stronger charge back-donation to this inhibitor.

Among the three phytochemical molecules, GC3 has the lowest $\omega$ and the largest $\epsilon$ values, showing that the molecule is more likely than the other two to give electrons to the empty d-orbital of the metal surface. On the other hand, GC1 has the largest $\omega$ and the lowest $\epsilon$ values. The tendency of GC1 to accept electrons from the occupied d-orbital of the metal exceeds that of the other two molecules. We can conclude that the adsorption mechanism involves the transport of electrons from the inhibitor to the metal surface in light of the adsorption behavior of the three molecules on the three metal surfaces.

3.2.3 Local Fukui functions

A local Fukui function in inhibitor molecules could reveal nucleophilic ( $f^{+}$ ) and electrophilic ( $f^{-}$ ) attack sites (Fukui, 1982). Fig. 7 presents the 3D plots of the isosurfaces of the three investigated phytochemical inhibitors with nucleophilic and electrophilic Fukui functions in water. There is no domination of the distribution of electrophilic and nucleophilic Fukui functions on the molecular skeletons of the three investigated inhibitors. For GC1 and GC3, the $f^{+}$ and $f^{-}$ functions are delocalized on the same sections of the molecule, i.e., ester in GC1 and alcoholic unit in GC3. Therefore, these sites are responsible for both electrophilic and nucleophilic attacks. Conversely, the existence of an ester unit in GC2 does not mean that it is the site for both attacks. Since it is where $f^{+}$ function is relocated, and therefore electrophilic attack occurs at this site, electrophilic attack occurs at this site, whereas nucleophilic attack occurs at the branched alkene since it is occupied by $f^{-}$ function.

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Fig. 7

3D plots of isosurface for the electrophilic and nucleophilic Fukui functions in an aqueous solution (Isovalue: 0.03 au).

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3.2.4 Inhibitor-metal interactions descriptors

When assessing the phytochemical inhibitor's interaction with a specific metal, the inhibitor-metal interaction descriptors are necessary, and they are listed in Table 3. Such descriptors included the number of transferred electrons ( $\mathrm{\Delta }N$ ) from the inhibitor to the metallic surface. Based on the obtained values of $\chi$ and $h$ , $\mathrm{\Delta }N$ value can be calculated (Parr and Pearson, 1983):

Electron transfer is driven by electronegativity difference, and resistance is determined by the sum of hardness parameters (Khalil et al., 2016). According to the free electron gas model, the values of electronegativity are related to the Fermi energy of metal in free-electron gases. As a result, electron–electron interactions are ignored. As for the metal surface, the workfunction ( ${\phi }_{\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{a}\mathrm{l}})$ is taken as its electronegativity (Kovačević and Kokalj, 2011). Thus, ${\phi }_{\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{a}\mathrm{l}}$ of the metal has been incorporated, so the electronegativity measurement is at the appropriate level. In contrast, a lack of attention is paid to chemical hardness since bulk metals have relatively low Fermi state levels, and their hardness is determined by the density of those states (Yang and Parr, 1985). Thus $\mathrm{\Delta }N$ value can be expressed as follows:

The experimental values of ${\phi }_{\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{a}\mathrm{l}}$ for bulk metals are: 4.82, 4.24, and 4.98 eV for Fe, Al, and Cu metals, respectively (Michaelson, 1977). If $\mathrm{\Delta }N>0$ , inhibitor molecule is donor and metal is acceptor and if $\mathrm{\Delta }N<0$ , the reverse is true. With greater electron-giving capacity at the metal surface, inhibition efficiency also increased, i.e., $\mathrm{\Delta }N<3.6$ , according to Lukovits. The computed electronegativities of the three phytochemical inhibitors are 3.413 eV (GC1), 3.054 eV (GC2), and 2.222 eV (GC3). All are smaller than the workfunctions of metals, so $\mathrm{\Delta }N$ is positive. The inhibitor molecule will flow electrons to the metal more readily than the metal will flow electrons to the inhibitor molecule (Kokalj, 2010). The most electrons were transferred for all metals by GC3, then GC2, and then GC1, according to the order of adsorption strength on metal surfaces. On the other hand, inhibitors and metal types also affect the number of electrons transferred.

Another essential descriptor is the initial molecule–metal interaction energy $(\mathrm{\Delta }\psi$ ). $\mathrm{\Delta }\psi$ is an estimate of the initial molecule–metal interaction energy, which is given by the following equation:

The conclusion for $\mathrm{\Delta }\psi$ values is in the same vein as the one derived for $\mathrm{\Delta }N$ values. Calculating the adsorption free energy ( ${\mathrm{\Delta }G}_{\mathrm{a}\mathrm{d}\mathrm{s}}$ ) is a way to understand the adsorption mechanism (chemisorption or physisorption). If the metal Fe/Al/Cu would act as an anode, the inhibitor would serve as a cathode. The value of ${\mathrm{\Delta }G}_{\mathrm{a}\mathrm{d}\mathrm{s}}$ can be determined according to the following equations:

Similarly to what was perfumed earlier, their workfunctions will replace the electronegativities of metals. The values of ${\mathrm{\Delta }G}_{\mathrm{a}\mathrm{d}\mathrm{s}}$ of the three investigated phytochemical inhibitors are listed in Table 3. Values of ${\mathrm{\Delta }G}_{\mathrm{a}\mathrm{d}\mathrm{s}}\gg$ $\pm 40$ kJ/mol, clearly indicating chemosorption as the adsorption mechanism. As for the three metals, ${\mathrm{\Delta }G}_{\mathrm{a}\mathrm{d}\mathrm{s}}$ values of GC3 are much greater than those of GC1 and GC2, followed by GC2 and then GC1, this result is very consistent with MC simulations of their adsorption trend.