Investigation of corrosion inhibition and adsorption properties of quinoxaline derivatives on metal surfaces through DFT and Monte Carlo simulations

4.1 Quantum chemical calculations

Calculations involving quantum chemicals have long been used to investigate reaction processes. They are a very effective tool for researching corrosion inhibition processes (Mamand et al. 2023). Theoretical estimation of corrosion inhibitor performance is gaining popularity, coinciding with advances in computer hardware and the establishment of efficient methods that aided the routine construction of molecular quantum mechanical simulations. All quantum chemical characteristics were derived following geometric optimization when compared to all nuclear coordinates at the DFT level employing the Kohn–Sham technique (Andzelm et al. 1995). A chemical species’ border orbital (highest occupied molecular orbital HOMO and lowest unoccupied molecular orbital LUMO) is crucial in determining its reactivity, which was observed for the first time by Fukui. A strong relationship involving corrosion rates and E_HOMO, which is connected with the molecule’s propensity to donate electrons, has been discovered. Obot and Obi-Egbedi (2010) reported that the inhibitor can bind to the metal surface via donor–acceptor interactions between the π-electrons of the heterocyclic compound and the unoccupied d-orbitals of the metal surface atoms. According to the characterization of the frontier molecular orbital (FMO) hypothesis, the capacity of inhibitor compounds to donate and take electrons, respectively, is frequently connected with the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). E_HOMO is connected to a molecule’s capacity for electron donation. Several investigations have demonstrated that inhibitors with high E_HOMO values are more likely to transfer electrons to a suitable acceptor with a low empty molecular orbital energy. Their E_LUMO value determines molecules’ electron-accepting capacity. A higher E_LUMO value indicates a decreased probability of electrons being received by the molecule. For example, the inhibitor can contribute an electron from the metal’s d orbital to the vacant d orbital on the metal surface. Figure 2A demonstrates that the HOMO position inhibitors are related to the benzene ring, C–H, and LUMO sites in both inhibitors located near the heteroatoms. These represent the inhibitors’ sensitive locations for interaction between metal surfaces and inhibitor molecules. According to the literary works (Shokry 2014), Mulliken population and HOMO population studies can be utilized to determine probable inhibitor adsorption sites Yadav et al. (2016) and ElBelghiti et al. (2016). Several writers agree that the greater the amount and quantity of negatively charged heteroatoms available in an inhibitor molecule, the greater its capacity to be adsorbed on the metal surface through a donor–acceptor type bond. The excellent coordination and chelation properties of (Q4) improved its inhibitory behavior. These corrosion inhibitors reacted significantly with metals (Fe, Al, and Cu) by forming powerful coordination interactions. The formation of coordination bonds involving 8-HQ and metals was predominantly attributed to heteroatoms (N, O, P), aromatic rings, and polar functional groups. These electron-rich places are known as adsorption or coordination bonding locations, and they transfer nonbonding and π-electrons to the outermost metal atom’s vacant d-orbitals to form coordination bonds. This type of charge transfer creates interelectronic repulsion due to the electron concentrations of metals. Consequently, metals are compelled to contribute electron densities to these molecules’ unoccupied orbitals by retro- (back-) donation. Aromatic rings are better for retro-donation since their molecules possess lower LUMO energies. These operations take place on the metal surface at the same time. In coordination bonding, this is known as the synergistic effect. The materials listed in this study with their respective prices are identified in Figure 2A, considering that the values differ by state. In nonprotonated states, Q3 > Q6 > Q5 > Q4 > Q2 > Q1 in gas and aqueous phases. In protonated species, Q3 ≅ Q4 > Q6 > Q5 > Q2 > Q1. As a result, we found that Q3 has the highest value for E_HOMO and Q1 has the lowest value compared to other molecules. The lowest values for E_LUMO obtained and calculated by the Gaussian program are Q1 and Q5, as shown in Figure 2B.

Figure 2:

Quantum chemical calculations in different states gas aqueous phases at protonated and nonprotonated species based on DFT at 6–311 ++ G(d,p) basis set. (A)–(D) represents quantum chemical calculations.

Because a large bandgap requires a significant amount of ionization energy to remove an electron from the final occupied orbital, the inhibitor with the largest bandgap is the least effective corrosion inhibitor in terms of efficiency. Given the impact of both tiny and large bandgaps on the reactivity of compounds, the energy gap is essential in determining the inhibitor material’s sensitivity to adsorption on the metallic surface. Strong chemical activity and poor kinetic stability are connected with the lowest band gap energy, maximum softness, and highest systems. Q6 is the chemical that inhibits bandgap energy, the lowest and softest. The most significant corrosion inhibitors are often chemical molecules, which absorb free electrons from the metal and supply electrons to the vacant orbital of the metal. The order of corrosion inhibition efficiencies is as Q6 > Q2 > Q3 > Q4 > Q5 > Q1. As shown in Figure 2C and Tables 1–6, the resulting bandgap energy calculations show that Q6 has the lowest and Q1 has the highest value in terms of bandgap energy. The dipole moments of protonated and nonprotonated species in the gas and aqueous phases were calculated (Tables 1–6). The dipole moment of the molecules is the most commonly used measure to characterize polarity. A polar covalent bond’s dipole moment is an indication of its polarity. It is the product of atom charge and distance between two bound atoms. The molecular dipole moment of a whole molecule can be described as the vector sum of individual bond dipole moments. Dipole moment (in Debye) is another significant electrical characteristic from the nonuniform distribution of charges on the different atoms in the molecule. The creation of heavily adsorbed layers on the metal surface is caused by the intermolecular interactions becoming stronger and more significant as the dipole moment increases. The total surface coverage of inhibitors on the Fe, Al, and Cu surfaces can be predicted using dipole moments. The strong dipole moment most likely improves adsorption with chemical compounds and metal surfaces. The energy of deformability increases, allowing the molecule to adsorb on the metal surface. The volume of the inhibitors increases and increases the contact area between the molecule and the metal surface, enhancing the inhibitors’ capacity to stop corrosion. The corrosion-inhibiting action of these compounds is increased when compounds having a higher dipole moment, which enhances their corrosion resistance, are adsorbed on a metal surface. Increasing polarization leads the electrons to be more readily moved from a high level to a suitable lower level in an empty orbital due to an increase in the dipole moment’s value. The inhibitor with a high dipole moment has a high softness value, and the large adsorption capacity occurs in areas of high softness, increasing the inhibition corrosion performance, the softness of organic molecules may be influenced by the dipole moment. The order of all inhibitors for corrosion levels is arranged as follows: Q6 > Q2 > Q3 > Q4 > Q5 > Q1, which is precisely the same as the practical outcomes. The ionization potential (I) can be considered as important factor for interpreting the interaction of atoms or molecules. Low values of ionization potential indicate that molecules are inactive, and high values of ionization potential indicate that compounds are highly reactive, potentially playing a significant impact on the activity or inactivity of chemical processes. Tables 1–4 show that the increasing ionizability is rising, which is consistent with an upward trend in E_HOMO. A good corrosion inhibitor is one that has a low electronegativity value. According to the findings in Tables 1–6, the electronegative order follows a pattern of Q4 > Q3 > Q2 > Q6 > Q5 > Q1 rises. The greatest electronegativity is found in molecule Q4, which implies the highest inhibition efficiency, according to Sanderson’s electronegativity matching approach. Q1 is predicted by low electronegativity and a high differential in electronegativity. DFT has effectively estimated electronegativity, one of the crucial chemical parameters for determining inhibition. Because electronegativity is the capacity of a molecule to attract electrons, a molecule with a high electronegativity draws the electron with greater force from the metal surface (Çakir and Emregül 2022). Because of their higher electronegativity than neutral states, protonated Q4 and Q3 inhibitors demonstrated superior inhibitory activity.

Kinetic, internal, and potential energy combine to form a system’s total energy. Hohenberg and Kohn proved that the total energy of a system is a unique effect of charge density (like atomic nuclei), including electron many-body implications (exchange and correlation) and the presence of a static external potential. The smallest value of the total energy functional represents the ground state energy of the system. This minimum is subsequently given by the electronic charge density, which is the actual single particle ground state energy. According to our analysis and ranking of the best inhibition efficiency, Q6 has the highest total energy of all the inhibitors, followed by Q2 > Q3 > Q4 > Q5 > Q1. Pearson and Songstad (1967) classified molecules as well as ions into four groups: hard acids, hard bases, soft acids, and soft bases and demonstrated that species from the same groups like to react with one another (the Hard and Soft Acid/Base (HSAB) Principle). Hard acids like to coordinate with hard bases, whereas soft acids prefer to interact with soft bases. Polarized chemical species are called hard, and unpolarized chemical species are called soft. Hard–hard interactions are mostly ionic, whereas primarily covalent are soft–soft interactions. Electrons are transferred between chemical species during chemical reactions. In comparison to hard molecules, soft molecules are more susceptible to charge transfer. Chemical hardness is directly related to chemical stability because hard compounds are less reactive. It can be observed that the molecular hardness values of chemical species in a reaction give vital hints to the anticipated process and assessment of reaction products. Chemical hardness is a key reactivity attribute of matter, and it is defined as resistance to electron cloud polarization or deformation of chemical species is an estimate of the stabilities and reactivities of molecules. In regard to chemical reactivity, soft molecules are more susceptible to reactivity than hard molecules in unimolecular processes like isomerization and dissociation. A molecule with a high softness value indicates low bandgap energy and increases the ability to donate and accept electrons. Whenever electron transfer occurs, it indicates a good corrosion inhibitor, and increasing hardness leads to decreased corrosion inhibition. As indicated in Tables 1–6, the ranking of the materials specified for corrosion prevention is as follows Q6 > Q2 > Q3 > Q4 > Q5 > Q1. The number of electrons transferred (∆N_max) in a molecule is proportional to its capacity to donate electrons to the metal’s surface. The ∆N_max values for the four compounds investigated vary from 1.538 to 4.790. A larger N value suggests a stronger proclivity to donate electrons to the electron-deficient site and a greater proclivity to interact and adsorb on the metal surface. N grows in the following order for molecules Q3 > Q6 > Q2 > Q4 > Q5 > Q1. The molecule Q3 (4.79) has the highest proportion of electrons transmitted (N), whereas Q1 and Q5 have the lowest proportions, which results in the lowest inhibitory efficiency. An electronic back donation process can occur as a result of the interaction between the inhibiting molecule and the surface of a metal in a basic model of charge transfer for donations and back donation of charges. Tables 1–6 reveal that electronic back-donation charges can occur during the process of interaction between the examined molecules and metal ions since their values are less than zero. When a zero and E_{Back-donation}, the charges transferred to the molecule are energetically favorable, as results of the Q6 and Q3 are more energetically favored than others. The positive number of electrons transported (N) demonstrates that the molecules are electron acceptors, whereas the negative number of electrons transferred (N) demonstrates that the molecules are electron donors. As a result, as these inhibitors’ electron-donating capability to the metal surface increases, so does their inhibition effectiveness. The inhibitory efficiency increased as the metal surface’s electron-donating capacity increased (Lukovits et al. 2001). The quinolines studied in this study exhibit charge transfer characteristics toward mild steel. ∆N_max < 3.6 eV represents a molecule’s inclination to donate electrons to a metal surface. In this study, all electron transfer values for all compounds and in all different states are positive. However, these values have changed. In some states, values are very high, such as nonprotonated Q6 and Q4, which have the highest value. Electrophilicity is a measure of a chemical species’ propensity to take electrons. The molecule with the greatest electrophilicity rating may accept the most electrons. A strong electrophile has a low electrophile and chemical potential, whereas a strong nucleophile has a significant electrophile and chemical potential. Lgaz et al. (2020) reported that a molecule increases its electron acceptance capacity if the electrophilic value is high, but conversely, if the electrophilic value is low, its electron acceptance capacity decreases. Moreover, molecules with a high nucleophile value have a high electron-donating ability. Therefore, it can be indicated which molecule has the highest electron-donating capacity or which molecule has the highest electron-accepting capacity, as shown in Tables 1–6. In general, Q3 and Q6 have the highest values in terms of electrophilicity. It implies that these two molecules have a higher ability to accept electrons than other molecules. Therefore, the best inhibitor against corrosion is a molecule with high electron acceptance.

Electrophilicity and nucleophilicity depend on several essential chemical factors. A molecule’s capacity to behave as an electrophile is determined by its ability to be an electron sink and receive a negative charge. Therefore, the molecule must be electron-deficient to accept the link to an electron source, and a positive molecule is an ideal electrophile. Because of its resonance, a neutral molecule can also be a good electrophile. If a resonance structure is viable, an electron sink at a bond site can certainly accept electrons to form a bond.

Furthermore, removing a good leaving group in a neutral molecule might cause an orbital to empty, resulting in a positive charge. An anion is an electron producer, and it cannot receive more electrons and, hence, cannot be a suitable electrophile. Weak polar or polarizable linkages are common in good electrophiles. It means that electrons might preferentially favor one side of a bond over the others, resulting in dipoles, and on one side of these bonds, there will be a partial positive charge.

4.2 Thermodynamic parameters

As seen in Figure 3, all compounds’ thermodynamic parameters – entropy (S), enthalpy (H), and Gibbs free energy (G) – were determined using DFT with the B3LYP/6–311 ++ G(d,p) basis set in the gas phase between 100 and 1,000 K. Such parameters characterize the progress and direction of a chemical process. Positive enthalpy values indicate an endothermic reaction, making dissolution difficult (Mamand et al. 2023; Rasul et al. 2023). It is known that an increase in temperature results in an increase in entropy, heat capacity, and enthalpy. Furthermore, Gibbs free energy decreases with increasing temperatures. The positive entropy value observed in this study confirms that the corrosion process exhibits a favorable entropic behavior, as shown in Figure 3. The phenomenon of spontaneous adsorption is indicated by the presence of negative values for the Gibbs free energy. From a comprehensive perspective, physisorption phenomena are characterized by Gibbs free energy values that are typically less than approximately (−40 kJ mol⁻¹), and chemisorption is observed when the values are around or more negative than (−40 kJ mol⁻¹). According to the calculations, the Gibbs free energy values for acenaphtho[1,2-b]pyrazine (Q3) and 8-hydroxyquinoline (Q4) are −14.402 kJ mol⁻¹ and −21.362 kJ mol⁻¹, respectively. These numerical values closely approximate the critical thresholds associated with physisorption.

Figure 3:

Thermodynamic parameters for all compounds.

Quinoxalines have been studied as corrosion inhibitors for different metals and alloys. Including a pyrazine ring next to the phenyl ring enhances the coverage of the target metals. Such an achievement by the two nitrogen atoms was adsorbed through sharing their lone pair electrons. 1,3-Bis(quinoline-8-yloxy) propane (Q1) is made composed of a central propane backbone with quinoline-8-yloxy groups connected to it. The presence of quinoline rings in the structure indicates protonation sites. Q1 comprises quinoline rings, which can serve as protonation sites. The nitrogen atoms in the quinoline rings have lone pairs of electrons, allowing them to receive protons in acidic situations. The protonation of Q1 would result in the formation of quinolinium cations, in which the nitrogen atoms carry positive charges. Acenaphtho[1,2-b]quinoxaline (Q2) comprises acenaphthene and quinoxaline rings fused. It lacks easily protonatable functional groups like amino or hydroxyl groups, which may limit its ability to undergo protonation. Although, under highly acidic conditions, protonation of Q2 could occur through an acid-aromatic ring reaction. However, compared to molecules with readily protonatable groups, the protonation of Q2 might be relatively less significant.

Q3, like Q2, is a polycyclic aromatic compound. However, it differs from Q2 because it incorporates a pyrazine ring instead of a quinoxaline ring. Similar to Q2, it also lacks easily protonatable functional groups. As a result, Q3 may exhibit relatively low reactivity toward protonation. 8-Hydroxyquinoline Q4, often known as oxine, is a quinolone hydroxy derivative. Q4 is a well-known chelating ligand commonly employed in qualitatively detecting metallic ions. Q4 will likely experience proton loss, forming Q4 chelate complexes with various metal ions. The coordination and chelation properties of Q4 are well recognized. As a result, Q4 has an extremely high potential for corrosion inhibition. Q4 strongly coordinates with metallic surfaces by using nonbonding electrons of oxygen and nitrogen, resulting in significant corrosion inhibition. When 8-hydroxyquinoline is dissolved in an acidic solution, the acidic nature of the solution provides protons that can interact with the basic nitrogen atom of Q4. The results indicated the formation of a protonated species often referred to as a quinolinium cation, where the nitrogen atom carries a positive charge. The protonation of 8-hydroxyquinoline can significantly affect its reactivity and chemical behavior. 1,4-Dibutyl-6-methyl-1,4-dihydroquinoxaline-2,3-dione Q5 and butyl and methyl substituents affect its protonation reactivity. Protonation is less likely because of the carbonyl groups and the dione functionality. As a result, compared to compounds having functional groups that may protonate more readily, Q5 may have comparatively low protonation reactivity. The electron-rich system of Q5 may interact with the acid under very acidic circumstances, resulting in protonation. However, protonation could be less advantageous due to the dione functionality’s electron-withdrawing properties. Q6 is 3-phenyl-5-quinoxalin-6-yl-4,5-dihydropyrazol-1-yl]butan-1-one that consists of a quinoxaline ring, a pyrazole ring, a phenyl group, and a butanone group. The nitrogen atoms in the quinoxaline and pyrazole rings can potentially undergo protonation. Due to electron-rich aromatic rings and nitrogen atoms with lone pairs of electrons, Q6 can accept protons under suitable conditions, displaying protonation reactivity. In acidic environments, the acid can interact with the lone pairs of electrons on the nitrogen atoms or other suitable sites within Q6. This interaction leads to protonation and the formation of a positively charged species.

4.3 Mulliken charge distribution

Predicting the active sites of inhibitor compounds is essential for studies on corrosion inhibition processes as shown in Figure 4. FMOs, Mulliken charge distribution, molecular electrostatic potential (MEP), and Fukui functions are frequently used to determine charge density distribution and possible binding sites. The FMOs are made up of HOMO and LUMO, and it is often believed that their energies are related to their ability to give and receive electrons. See Supplementary Material, it is feasible to distinguish between an inhibitor molecule’s active site – which is under attack from electrophile metal cations – and its site – which is prepared to take electrons (LUMO). The Mulliken charge distribution is used to identify the locations of an inhibitor molecule interacting with a metal surface. The HOMO energy density allocation is frequently used in conjunction with the Mulliken charge distribution to forecast the active site of the inhibitor molecule. A computer method called MEP indicates a molecule’s chemical reactivity. It explains how the electrical potential generated by the nuclei and electrons encircling molecules is distributed spatially. The electrostatic potential at each position r in the vicinity of a molecule is represented by Equation (7).

where (ZA) is the charge of the nucleus A at position R→A, and ρ(r→) is the molecular electron density function. The sign of V(r→), it depends on whether the electron or nucleus impact is noticeable at a particular place. Three-dimensional diagrams called MEP maps display the distribution of charges within molecules. Charges are related to their qualities. Color-graded mapping of the contours of the total electron density can be used to determine the active sites of nucleophiles and electrophiles in a molecular system. Different surface electrostatic potentials are indicated and depicted by the different colorings. The blue executive summary on most MEP maps shows the largest positive site. The red outline typically represents the largest negative site, which is easy to contribute electrons to. These are the preferred targets for nucleophilic and electrophilic attacks (Sanz et al. 1988). MEP maps to determine which regions of all inhibitors were the most active Sanz and others. The oxygen and nitrogen atoms in the ring are redder than those in other areas, based on color correction and the surrounding environment. Hence, the oxygen and nitrogen atoms in the rings are more active compared to other atoms. The change in a molecule’s electron density at a given position as the number of electrons changes is represented by the Fukui function, which is defined as the first derivative of the electron density (r) concerning the number of electrons N at a constant external potential v(r), as shown in Equation (8). The Fukui indices (fk+, fk−, and fk0) may be calculated to evaluate the local reactivity of a molecule. Koumya et al. (Boussalah et al. 2012; Roy et al. 1999) reported that greater f_(r) correlates to a more reactive active center of a molecule.

where the corresponding electrical densities of site k for cationic, anionic, and neutral species are ρ_k(N), ρk(N+1), and ρk(N−1). The highest values of fk+ and fk−, respectively, indicate the locations most likely to experience nucleophilic and electrophilic attacks. The condensed Fukui functions can be used to investigate an inhibitor’s active site. Active sites in molecules with the most condensed Fukui functions encourage greater reactivity. These functions indicate which atoms in a molecule are more likely to give or take an electron or pair of electrons. The active site for nucleophilic assaults is the atom in the molecule with the greatest value of fk+. Meanwhile, the active site for electrophilic attacks is the atom in the molecule with the highest value of f_k. In this study, we obtained active sites on heteroatoms Supplementary Material. In heteroatoms, electronic charges, Fukui functions, and proton affinities (PA) are critical in determining active sites on inhibitor compounds. Molecular electrostatic potential (MEP) is a descriptor for defining active areas for electrophilic and nucleophilic assaults that is related to electronic density. MEP of protonated and nonprotonated in the gas and aqueous phase inhibitors. The sections of the MEP of the selected inhibitors in this study are calculated by utilizing the optimized geometry at the 631 ++ G(d,p) to examine reactive sites for electrophilic and nucleophilic assault. The red and yellow colors represent electrophilic reactivity in the negative sections of the MEP, whereas blue colors suggest nucleophilic reactivity in the positive parts. The estimated findings suggest that the negative potential sites are on electronegative atoms (oxygen, nitrogen, and sulfur), while the positive potential sites are around the hydrogen atoms. In this work, the heteroatom plays an important role in determining the active sites.

Figure 4:

Chemical structures of selected inhibitors.

4.4 Molecular dynamic simulation

The adsorption behavior and orientation of corrosion inhibitors on metal–electrolyte interfaces are studied using Monte Carlo simulations (MC) and molecular dynamics (MD) models. The results provide useful guidance. MD simulations are a computer-based modeling technique that may describe a molecule’s development as a trajectory or time function according to classical Newtonian physics principles (Guo et al. 2015). Since MC computations are the first ab initio force field that can efficiently, precisely, and concurrently estimate the condensed-phase characteristics for a wide range of chemical systems and gas-phase features, it is very beneficial to perform a fast simulation. In a specifically created simulation box, the computations model the interaction between the inhibitor and the metal surface when the inhibitor is in direct contact with the surface (Khaled 2009). The adsorption system or simulation results are composed of the optimized inhibitor molecules and the formed layers of iron atoms. The Fe, Cu, and Al (110) surface is widely utilized as the adsorption substrate because of its low surface energy and large coordination number of substrate atoms, resulting in more active interaction sites between the metal and the inhibitor molecules (Mamand and Qadr 2023b).

COMPASS is the first ab initio force field to enable a simultaneous and accurate prediction of condensed-phase and gas-phase features for a broad range of polymers and molecules. The COMPASS force field has been extended to span a more comprehensive range of molecules relevant to researchers researching ionic liquids. This is known as the COMPASSII force field (Sun et al. 2016). Copper and copper alloys are widely used in a wide range of manufacturing processes in the aquatic and nonaqueous. Copper is widely used in the electrotechnical field since it has excellent electrical conductivity.

Moreover, silver has higher electrical conductivity at room temperature than other metals. The significant energy differential allows electrons to flow between the valence and conduction bands. To prevent copper corrosion, several organic compounds are utilized. Adsorption at the metal–solution interface is the first stage in the mechanism of action of organic corrosion inhibitors in acidic environments. The electrical properties of the molecules (adsorbate), the chemical makeup of the solution, the characteristics of the metal’s outer layer, the temperature at which it happens of the reaction occurs, and the electrochemical potential at the metal–solution interface all influence the mechanism of adsorption (Dumont 1991). The attractive forces between the adsorbate and the metal are required for adsorption. Physisorption is the result of electrostatic interactions between the electrically charged surface of the metal and inhibitory organic ions or dipoles (El-Hajjaji et al. 2018).

The substrate–adsorbate configuration parameters consist of the total energy, which is the combined energies of the adsorbate components, rigid adsorption energy, and deformation energy as shown in Table 7–9. Adsorption energy is the energy required to adsorb the relaxed adsorbate component onto the substrate. The adsorption energy is the combined total of the rigidity and deformation energies of the adsorbate component. Rigid adsorption energy quantifies the energy produced or needed to adsorb the unrelaxed adsorbate component onto the substrate without any geometric adjustments. Deformation energy quantifies the energy generated during the relaxation of the adsorbate component on the substrate surface. The term (dE_ad/dNi) represents the energy of substrate–adsorbate combinations when one adsorbate component is eliminated. Monte Carlo simulations were employed to investigate the adsorption characteristics of quinoxaline derivatives (Q1–Q6) on various metal surfaces (Fe(110), Cu(111), and Al(110)) in neutral and their protonated states. The data in Tables 7–9 reveal that the adsorption energies varied significantly across the different inhibitors and metal surfaces. Monte Carlo simulations revealed that specific quinoxaline derivatives displayed remarkably stable low-energy adsorption arrangements on each investigated metal surface (Fe(110), Cu(111), and Al(110)) as shown in Figure 5. Our theoretical calculations identified promising adsorption behavior for quinoxaline derivatives on various metal surfaces. Notably, Q5 emerged as the frontrunner on Fe(110) with an exceptional adsorption energy (−1,277.413 kcal/mol), suggesting its potential as a highly effective iron corrosion inhibitor. Similarly, Q6 exhibited the highest favorable adsorption energies on Cu(111) (−723.728 kcal/mol) and Al(110) (−769.109 kcal/mol), indicating its potential for copper and aluminum applications. Interestingly, despite not having the highest adsorption energy on every surface, Q6 displayed consistently strong adsorption across different metals. This can be attributed to several factors: its larger conjugated electron system leading to enhanced π-backbonding, its smaller substituent allowing for closer interaction with the metal surface compared to Q5, and a potential additional interaction from the nitrogen atom in its pyrazole ring. These findings not only contribute to understanding the structure–property relationship between quinoxaline derivatives and their adsorption behavior but also pave the way for the development of novel and targeted corrosion inhibitors for specific metal compatibility.

Figure 5:

Molecular simulations for the most favorable adsorption modes were obtained for the selected molecules on the Al, Cu, and Fe (110) surface (side view).

The total energy of the substrate–adsorbate configuration is characterized as a combination of the energies of the adsorbate components, deformation energy, and rigid adsorption energy. In this study, we have observed that the highest value of deformation energy can determine the highest corrosion resistance of the material, as shown in Tables 7–9. Adsorption energy is the energy released during the adsorption of the relaxation adsorbate element on the substrate. The rigid adsorption energy and the deformation energy of the adsorbate component add up to the adsorption energy. The energy released (or required) each time the unrelaxed adsorbate component was adsorbed on the substrate before the geometry optimization stage is represented by the rigid adsorption energy (Aquino-Torres et al. 2020). The energy produced when the deposited adsorbate constituent was loosened on the substrate surface is reported as the deformation energy. All adsorption energies shown in Tables 7–9 are negative, implying that adsorption is carried out spontaneously. The inhibitor molecules’ significant adsorption can explain the metal surfaces’ higher negative interaction energy values. Recognizing the adsorption phenomenon is critical in corrosion issues. Theoretical investigations aid in identifying the most stable adsorption sites for a wide range of compounds. The obtained data may be used to learn more about the corrosion system, including the probable location of the attack on a surface, the most enduring location for inhibitor adsorption, and the adsorption energy of the adsorbed layer. In light of these calculations, we can point out that the ranking of these molecules for anticorrosion is according to this ranking Q6 > Q2 > Q3 > Q4 > Q5 > Q1.

4.5 Nonlinear optical properties (NLO)

Nonlinear optical (NLO) materials are important in nonlinear optics, especially for information technology and industrial applications. The first static calculation was done on the optimized molecular geometry using the B3LYP/6–311 ++ G(d,p) computational method. The mean polarizability (|α₀|) and first hyperpolarizability (β₀) can be defined in terms of their x, y, and z components (Al-Shamiri et al. 2022; Evangalin et al. 2018; Villemin et al. 2018).

Large values of the polarizability and hyperpolarizability components in one direction imply significant delocalization of charge in that direction. Table 10 displays the calculated mean polarizability (α₀) and initial hyperpolarizability (β₀) for all compounds. The polarizability (α₀) and first hyperpolarizability (β₀) parameters of the GAUSSIAN 09 output are achieved in atomic units (a.u.), and the computed values have been converted into electrostatic units (e.s.u.) (for α;1 a.u = 0.1482 × 10⁻²⁴ e.s.u., for β;1 a.u = 8.6393 × 10⁻³³ e.s.u.). Urea is used to study molecular NLO properties. Since there were no experimental standards of NLO characteristics of the compounds, it is commonly utilized as a reference point for comparisons (Guerrab et al. 2020). The polarizability of Q4 is found to be the lowest, while Q1 exhibits the highest polarizability among the calculated values. Furthermore, the determination of the molecular hyperpolarizability magnitude (β₀) holds significant importance within a nonlinear optical (NLO) system. Urea’s first hyperpolarizability (β) exceeds that of all other compounds in terms of their first hyperpolarizability. These results indicate that the entirety of the compounds may not possess the potential for nonlinear optical (NLO) applications, as presented in Table 10.

4.6 NBO analysis

NBO analysis describes intramolecular interactions and charge transfer. NBO analysis explains the donor–acceptor behavior of atoms in the molecule. Density Functional Theory (DFT) is used to study electron delocalization and the interactions between occupied and empty orbitals. Furthermore, the degree of stabilization resulting from orbital interaction is directly proportional to the disparity in energy levels between the orbitals involved. Therefore, the interaction that exhibits strong stabilization occurs between efficient donors and efficient acceptors.

Moreover, the E2 value represents the magnitude of the interaction energy between an electron acceptor and electron donors. A higher E2 value indicates a stronger propensity for electron donation from the donor to the acceptor (Evangalin et al. 2018; Kanmazalp 2017; Villemin et al. 2018). The NBO analysis results for the molecule were obtained using the B3LYP/6–311 ++ G(d,p) level of theory, as presented in Supplementary Material.

where q_i is the donor orbital occupancy, ε_j and ε_i are the diagonal elements, and F(i,j) is the off diagonal NBO Fock matrix element (İzzet et al. 2016; Khalid et al. 2020).

In this investigation, several types of electronic transitions were commonly observed: σ → σ*, π → π*, n → σ*, n → π*, and π* → π* as tabulated. In Q4 and Q3, the greatest interaction is between π*(C4–C5) → π*(C1–C6) and π*(C5–C6) → π*(C1–C2) with the stabilization energy of 252.09 kcal/mol and 249.09 kcal/mol, respectively. In Q6 and Q4, the electron donating from LP(2) (O26) and LP(1) (N11) to the antibonding acceptor π*(N18–C22) and π*(C1–C6) with stabilization energy of 26.99, and 34.41 kcal/mol is the most important interactions. Besides, LP(1)O13 to the antibonding acceptor π*(C8–C9) stabilization energy of 22.68 kcal/mol is also a significant interaction in Q5.