Corrosion inhibition performance of organic compounds and theoretical calculations based on density functional theory (DFT)

1 Introduction

As corrosion inhibitors reduce the corrosive ratio in acidic and basic solutions, they prevent corrosion on metal surfaces. Descaling, cleaning, pickling, and acidizing oil wells are all businesses that use hydrochloric acid (Al-Amiery et al. 2013; Al-Baghdadi et al. 2021; Qadr 2020). In acidic solutions, the corrosion inhibitors used are mostly heterocyclic molecules such as sulfur, phosphorous, oxygen, nitrogen, and aromatic or aliphatic organic chemicals, which are adsorbed on the surfaces of metals (Habeeb et al. 2018). Due to the vacant d-orbital of iron atoms, the creation of a metal cation among inhibitor molecules as electron donors and metal surface atoms as electron acceptors have been hypothesized in corrosion research. Organic molecules containing nitrogen, sulfur, and oxygen atoms make up the majority of well-known acid inhibitors (Erdoğan et al. 2017). Several studies have looked at the effects of nitrogen-containing organic chemicals such as heterocyclic compounds and amines on steel corrosion in acidic conditions (Keri and Patil 2014; Wang et al. 2015). Several organic inhibitors work via adsorption on the metal surface. An important aspect of compounds to be effective inhibitors is their ability to form a chemisorbed barrier film on metal surfaces. They also have high adsorption energy on the surface of the metal. Thus, the barrier layer established increases the inner layer’s surface area (Bentiss et al. 2000; Finšgar and Jackson 2014; Qadr 2021; Zaferani et al. 2013). Oxadiazoles have a strong attraction to metal surfaces where they displace water molecules (Ali et al. 2003). Furthermore, oxadiazoles have unshaped electron pairs and a lot of electrons on the oxygen and nitrogen atoms, which can react with iron’s d-orbitals to form a protective coating (Salman et al. 2019). Many N-heterocyclic compounds have been employed to prevent iron or steel from corroding in acidic conditions including pyridazines triazole (Ansari et al. 2014; Tourabi et al. 2013), purines (Palomar-Pardavé et al. 2012), thiadiazole (Gutiérrez et al. 2016), benzimidazoles (Elayyachy et al. 2005), and pyrazoles (Bentiss et al. 2006). A review of the literature suggests that the use of oxadiazole derivatives in the prevention of steel corrosion has received little attention. Thiosemicarbazide is utilized as a corrosion inhibitor because it possesses three chelating sites—two nitrogen atoms, thione and imine groups with unshared electron pairs—that are appropriate for interacting with the iron atoms of mild steel surfaces. Thiophenes regulate or obstruct corrosion by adhering to the surface of mild steel (Zhang et al. 2009). Associated with molecules B and C as shown in Figure 1, the metal is protected from the corrosion media by the adsorption inhibitor. It has been shown that the presence of electrons and heteroatoms favors the increased adsorption of inhibitor molecules on the surface of mild steel, which are the main determinants of adsorption. Because they often provide superior inhibition compared to molecules that simply have nitrogen or sulfur, molecules that combine both nitrogen and sulfur are particularly important (Quraishi et al. 1996). The D inhibitor has several unique characteristics. First off, it can be manufactured quickly and cheaply from basic ingredients. The aromatic rings are believed to promote greater molecule adsorption on the steel surface, resulting in a more effective inhibition. DAPO utilizes five distinct atoms (four nitrogen atoms and one oxygen atom) (Bouanis et al. 2016). This paper reviews the comparison of corrosion rate and performance to empirical research on the corrosion inhibitory efficiency of oxadiazole. A quantum computational analysis was performed to investigate the electronic structure of selected molecules and the reason for corrosion inhibition.

Figure 1:

Chemical structure of inhibitors.

2 Calculation method

Experimentation is important in elucidating the inhibition process, but it is typically costly and time-consuming. In recent years, advances in computer hardware, software, and theoretical chemistry have contributed to excellent visual and computing tools that can be utilized by universities and industries alike. Recently, more corrosion articles have included considerable quantum chemical computations (Mamand et al. 2022; Qadr and Mamand 2021). These computations are typically used to investigate the link between electronic structure (or inhibitor molecular characteristics in gas and solutions) and corrosion inhibition efficiency. However, a small focus has been placed on quantum chemical investigations on oxadiazole and 2-acetyl thiophene thiosemicarbazone (2-AT) in gas and aqueous phases. The molecular structures were originally optimized by Gaussian09 software to determine several parameters of the investigated molecules (Mamand 2020; Mamand and Qadr 2022, 2023). DFT calculations were carried out using 6–311++G(d, p) basis set and Becke-3-Lee–Yang–Parr (B3LYP).

3 Quantum computational analysis

To explain and characterize the experimental data based on the electronic and structural features of these inhibitory compounds, theoretical elements of the inhibitor molecules’ effectiveness have been explored. A set of thermodynamic parameters derived from DFT, namely chemical potential (μ), hardness (η), and Fukui function (f(r)), are used to predict the active surface area, as well as the inhibitory properties of the various corrosion inhibitors as shown in Figure 1. Electronic density (ρ(r)) is a DFT-related variable, which is divided by the β and α spin contributions (Galvan et al. 1988; Parr et al. 1999). The variables associated to DFT are the electronic density divided in spin contributions β and α, the electron number (N), and system energy (E|ρ^α(r),ρ^β(r)|), the multiplicity, the magnetic field, the external potential (V(r)) associated to the media (B(r)), and dependent on Bohr’s magneton μ_°, which can be used to specify spin conditions. These quantities can be found the energy (ε_i(r)) of molecular orbitals (∅_i(r)) (Ayers and Levy 2000). Various functional equations have been used to calculate the energy of the system.

where E_xc is the exchange and correlation contribution and J is the coulombic energy functional that allows measurement of the electron interaction in the system when three or more bodies are interacted (Galvan et al. 1988).

When energy is differentiated with a set of system parameters, distinct thermodynamic responsiveness coefficients are produced that may be used to predict the development of a chemical reaction. The response coefficients acquired after the initial separation, which are connected with the spin potential μ_s and the chemical potential μ_N (Galvan and Vargas 1992):

The electronegativity of the molecule is represented by χ, and the chemical potential of the boundary orbital energies can be calculated as follows.

The response coefficients related with hardness may be obtained from of the second differentiation:

Furthermore, a molecule (M) receiving charge has the following directional components:

Similarly, the electrophilicity index (W) can be calculated using the chemical potential and global hardness definitions, as follows:

Additionally, the following derivation technique helps to obtain another important thermodynamic response coefficient, the Fukui function (Ayers and Levy 2000; Parr et al. 1999):

Equations (8) and (9) can be used for the generalized Fukui functions:

The analysis of the Fukui functions related to a molecule is useful to obtain a term related to the ability of a system to modify its charge and/or multiplicity. These phenomena can be described by Fukui functions of the form:

Because changes in the electrical potential at the electrodes’ surface can reflect charge changes related to the generation of cationic or anionic species, using the following approximations, both spin and charge changes were considered in this study. This can also be approximated using the following expressions:

Quantum chemical parameters such as softness, hardness, electronegativity, and local description of a molecule such as Fukui function were used to investigate the electron transfer processes to evaluate the sites for charge donation (f⁻(r)) when entangled by an electrophilic component and the favored sites for charge receiving f⁺(r)) when entangled by a nucleophilic component (Abreu-Quijano et al. 2011; Wang et al. 2007). More comprehensive research can be utilized to evaluate the influence of a certain functional group in a compound or to make a most specific atomic analysis. From these investigations, the condensed Fukui’s functions (also Known Fukui’s indexes) were derived. To calculate such parameters, it is important to use a strategy for dividing the electronic density between all the atoms of the molecule. In this case, the electron density (ρ) surrounding an atom is related to its net charge. When the electron density around the nuclear charge of the ith atom is ρNi(r) and the nuclear charge of the ith atom is Z_i, then the net charge can be expressed of the ith atom of the molecule (M) as qNi=Zi−∫dr ρNi(r), finally the following equation indicated the Fukui indexes (Bentiss et al. 2004; Şahin et al. 2008):

It was important to consider that the simulation process used to calculate the electron density must adequately describe the system in order to estimate the hardness, Fukui function, and Fukui’s indexes. As a result, a Hartree–Fock-type density is significant, but it also contains a correlation type density (Özcan and Dehri 2004).

4 Theoretical calculation

Figure 1 shows the outcomes of the geometry’s optimization of the chosen compounds. All of the inhibitors have planar structures in the frameworks of these geometries. Tables 1–4 summarize the several quantum-chemical indices such as E_HOMO, E_LUMO, ΔE = E_HOMO − E_LUMO, chemical potential, electrophilicity, softness, electronegativity, hardness, and dipole moments. To interpret the theoretical data obtained that the experimental inhibitor’s efficiency tendency is D > C > B > A. It is well known that E_HOMO is frequently correlated with the electron donation capacity of inhibitor compounds toward metallic surfactant molecules, and a higher E_HOMO value is likely to favor a higher charge transfer (Obot et al. 2016).

According to our results, the values of E_HOMO in gas phase was C > D > B > A, but the values of E_HOMO in aqueous phase was D > C > B > A. In this situation, the highest E_HOMO corresponds to molecule C (see Table 3) and the lowest E_HOMO belongs to molecule A, which is the worst inhibitor in terms of activity. Some researchers found that a lower hardness value was associated with better stability of the surface inhibitor complex (Udhayakala et al. 2012). Furthermore, lower E_LUMO values indicate that the inhibitor has a greater ability to receive electrons. As shown in Tables 1–4, the trend achieved for E_LUMO value was A > C > D > B and for hardness was A > B > C > D. The higher the hardness value it appears, the greater the inhibitor efficiency, which is consistent with experimental results (Popova et al. 2003). While publications indicated that the E_LUMO value was greater than the Fermi level, the computational results for the recently investigated molecules show that the E_LUMO value is negative, indicating the ability to take electrons (Rodríguez-Valdez et al. 2005). Electrochemical corrosion occurs in aqueous phase, but theoretical parameters are determined in a vacuum. As a result, the Polarizable Continuum Method (PCM) was used in the computations to account for the solvent effect (water). The findings in Table 2 are also illustrated when water is included. The study found that the higher the total stabilization energy, the greater the rise in dipole moment achieved. The solvent action stabilizes the molecules, as shown by ΔE_solvent in Tables 1–4. Also, the HOMO energies values with solvent effect are higher than in vacuum states for all the inhibitors in protonated states and opposite with nonprotonated states. Looking at the solvent, the value of E_LUMO in the case of molecule A jumped from −2.009 to −2.01 eV. The E_LUMO value of inhibitor B decreased from −2.19 to −2.015 eV. The values of E_LUMO for the molecules C and D increased in both phases.

The bandgap energy (E_g) and adsorption have a strong relationship, in which E_g is a crucial characteristic of the inhibitor molecule’s responsiveness to adsorption on the metallic surface. The reactivity of the molecule increases as the E_g decreases. The reason why ionization is necessary to remove an electron from the final occupied molecular orbital for minimal reasons. Bereket et al. (Bereket et al. 2002) made an important discovery and showed that the best corrosion inhibitors are generally organic compounds that not only give electrons to the metal’s empty orbital but also take free electrons from the metals. Furthermore, a more polarizable molecule represents the lower bandgap energy and is continually associated with lowered kinetic stability, increased chemical activity and is called a soft molecule (Ebenso et al. 2010a). Tables 1–4 show that molecule D has the lowest E_g in all circumstances, suggesting it may be more effective as a corrosion inhibitor. In this study, the predicted order for fluctuations in inhibition efficiency of the investigated selected inhibitors is as follows: D > C > B > A.

A polar covalent bond’s dipole moment is a measure of its polarity. The dipole moment (in Debye) is another significant electronic characteristic of molecules A, B, C, and D, resulting from their nonuniform distribution of charges. The computation of the total energy (T.E) gives good information, the higher T.E is −1315.853 Hartree, which confirms the higher stability of inhibitor molecule D. Figure 2 shows LUMOs and HOMOs of selected molecules at 6–311++G(d, p) basis set for nonprotonated species in gas and aqueous phases.

Figure 2:

LUMOs and HOMOs of selected molecules.

5 Chemical potential and electronegativity

A low electronegativity value is characteristic of an excellent corrosion inhibitor. Tables 1–4 show the distribution of electronegativity which was C < B < D < A in gas phase protonated, and also C > A > B > D in aqueous phase protonated. Moreover, the trend obtained for the electronegativity values was D > A > B > C in gas phase nonprotonated. It is predicted that inhibitor C would have a low electronegativity and a high differential in electronegativity resulting in good inhibition efficiency based on Sanderson’s electronegativity equalization concept. A similar discussion may be used on the chemical potential, the chemical potential in gas and aqueous phases protonated, inhibitor D has the highest value. On the other hand, inhibitor C has the highest value in the nonprotonated, which indicates good corrosion inhibition efficiency.

6 Hardness and softness

Absolute softness and hardness are well-known parameters, which used to assess molecule reactivity and stability. The chemical hardness under minor chemical reactions denotes the resistance of molecules or atoms to deformation or polarization of the electron cloud. A small and lower bandgap energy E_g demonstrates a soft molecule, while a wide and large E_g indicates a hard molecule (Obot and Obi-Egbedi 2010). As a result, for bulk metals in acidic conditions, molecules with the lowest global hardness values are projected to be excellent corrosion inhibitors. Inhibitor adsorption should be considered and occurs on a metal surface in the softest and smallest hard part of the molecules (Ebenso et al. 2010b; Mamand et al. 2022; Obi-Egbedi et al. 2011). Tables 1–4 can be shown that inhibitor D was a softer molecule than A, B, and C. The best inhibition efficiency was DAPO, and the worst inhibition efficiency was 2-AT. The results from calculations of hardness in both phases are summarized in Tables 1–4, which reveal that the inhibitor A exhibits the largest overall hardness values in both phases, with protonated and nonprotonated, which is about 2.7 eV. The adsorption might occur at the soft portion of the molecule, a local parameter has the maximum value for the shortest transfer of an electron. Our results have been shown that inhibitor D with the highest softness value of 6.1 eV in aqueous phase at protonated species has the best inhibition efficiency. The lowest inhibition efficiency is inhibitor A with the lowest softness value of 0.42 eV in gas phase protonated.

7 Electrophilicity and nucleophilicity

Electrophilicity (w) is one of the quantum chemical parameters that indicates tendency of the inhibitor molecule to accept and donate an electron, which is used for measuring a chemical species’ tendency to receive electrons (Kaya et al. 2016). The highest value of w indicates the better molecule’s ability to accept electrons. As an outcome, a good nucleophile has low CP and w. Based on the quantum chemical parameter, the appropriate electrophoresis increased the values μ and w. The electrophilicity and nucleophilicity calculations in this study are shown in Tables 1–4. The corrosion inhibition effectiveness ranking of oxadiazoles and 2-AT is in good agreement with the experimental results: D > C > B > A. Figure 3 shows a comparison between theoretical and experimental results for inhibition efficiencies of inhibitors A, B, C, and D (Figure 4).

Figure 3:

Comparison between theoretical and experimental results for inhibition efficiencies of inhibitors A, B, C, and D.

Figure 4:

Variation of quantum chemical parameters in protonated and nonprotonated species in gas and aqueous phases with the nature of the inhibitors A, B, C, and D.

8 Electron transfer electron back-donation

When two systems are with different electronegativities such as iron and inhibitor, the electron will be transferred from low electronegativity toward higher electronegativity until the chemical potentials or electronegativities are the same (Mamand et al. 2022). Pearson (Parr and Pearson 1983) proved that the electronegativity contrast between two molecules enhances electron transfer, and the sum of the global hardness factors acts as resistance. As a result, the value of a global hardness η_Fe is 0, and electronegativity of iron metal χ_Fe was used 7 eV (Pearson 1988, 1989) for computation of electron transferred, by assuming that for a metallic bulk, ionization energy I is equal to electron affinity A. The number of electrons transported (ΔN_max) of the oxadiazoles and 2-AT molecules under investigation estimated in this study as shown in Tables 1–4. The positive value of (ΔN_max) shows the molecules operate as electron acceptors, whereas the negative value of (ΔN_max) implies the oxadiazoles dramatization as electron donors. As a result, the inhibition efficiency improves as the electron-donating capability of these inhibitors to the metal surface increases. The value of N_max < 3.6 eV reflects a molecule’s proclivity to donate electrons to the metal surface. If N_max > 3.6 eV, the inhibitory efficiency grew as the metal surface’s electron-donating capacity rose. The oxadiazole and 2-AT molecules investigated in this theoretical study have charge transfer properties toward mild steel. The value of N_max > 3.6 eV reflects a molecule’s proclivity to best inhibition efficiency and donate electrons to the metal surface. Tables 1–4 show that the compounds under investigation behave as electron donors (Lukovits et al. 2001). The results can be shown that the best inhibitor D is related to the highest proportion of electrons transported. Whereas the lowest fraction binds to 2-AT with the lowest inhibition efficiency (inhibitor A). The electron-donating capability of the inhibitor molecules continues the trend: D > C > A > B in all circumstances. These results are consistent with those of experimental research. When a molecule is protonated to become its conjugate acid, it loses one negatively charged unit and, therefore, becomes more electron-poor. When a molecule is protonated to become the base of its conjugate, it acquires a negative charge and, therefore, becomes more electron-rich. Electrons are the “currency” of chemistry. So, acid–base reactions by increasing or decreasing electron density have a drastic effect on the reactivity of a molecule. In chemical reactions, electron-rich regions are likely to be the source of electrons in chemical reactions and electron-poor regions are likely to be the final electron destinations (Shabaan et al. 2012).

9 Back-donation of charges

The chemical interaction between the metal surface and the inhibitor molecules controlled by a mechanism is called back donation. This process is based on a charge transfer model for donation and back-donation process. According to this approach, if both back-donation from the molecule, atoms, and electron transfer process to the molecule occurs at the same time, the energy change is precisely proportional to the molecule’s hardness (Gómez et al. 2006).

Back-donation from the molecule to metal is energetically preferred when η > 0 or ΔE_b−d < 0. Tables 1–4 show ΔE_b−d < 0, implying that charge transfer to a molecule obeyed by ΔE_b−d from the molecule is actively beneficial. It is assumed that the inhibition efficiency of molecules grows when the molecule is sufficiently adsorbing on the metal surface. The inhibition efficiency of the molecules related to the charge transfer. The best inhibition efficiency rises with the increase of the stabilization energy that appears from the exchange between the inhibitor and the metal surface. The estimated ΔE_b−d values show the following propensity, which is consistent with the experimental results: D > C > B > A.

10 The initial molecule–metal interaction energy

The initial molecule–metal interaction energy ΔΨ is another parameter to evaluate the inhibition efficiency of the molecule, which has been calculated by Sastri and Perumareddi using equation (13) (Sastri and Perumareddi 1997).

Tables 1 –4 can be shown that molecule–metal interaction energy |ΔΨ| has the highest value at protonated and nonprotonated species in gas and aqueous phases. Furthermore, C has the highest |ΔΨ|, followed by D and B, while A has the lowest value.

11 Solvent effect

Any theoretical physical or chemical properties evaluated in this study in a single solvent may differ from those determined in other phases or solutions and vacuum (Cances et al. 1997). More specifically, it is widely known that the electrochemical corrosion process of inhibitors occurs in the liquid phase, and the inhibition efficiency of molecules in the solvent function is expected mainly from that of the vacuum phase. As a result, for better realism and a clearer picture of the manners of the investigated selected inhibitors, the solvent impact was taken into account in the estimations by computing the several quantum chemical characteristics in the existence of water solvent. Furthermore, it is critical to consider the consequences that may manifest themselves in both geometric and electrical qualities. A model identified as the polarized continuum model (PCM) might be utilized to examine the solvent influence on the chemical structure of a solute (Lukovits et al. 2001). The solvent is modeled as a continuous dielectric medium in this model, while the solution is modeled as a stranded molecule in a cavity enclosed by solvent. The Gaussian09 software employed IEFPCM (an integral equation based PCM) in conjunction with DFT/6–311++G(d, p) to investigate the solvent effect. The computed different quantum chemical behaviors in the absence of a water solvent and in gas phase do not differ significantly (see Tables 1–4).

It was concluded from the outcomes of different electrochemical and weight loss measurements that selected compounds to inhibit corrosion. Metal corrosion is inhibited in acidic media via their adsorption at the metal/solution interaction. The selected compounds can be easily protonated because the molecules of the selected compounds (compound A) are formed of thiosemicarbazone and the thiophene ring, and the compounds B, C, and D are made of planar aromatic rings of benzene and diazole and also include S and N atoms and electrons. In general, metallic corrosion is inhibited in acid solutions. The electrostatic interaction of protonated molecules with chloride ions as well as the interaction between the unoccupied d-orbitals of iron atoms and the p electrons of aromatic rings act as donors and acceptors, as well as the interaction between the unoccupied d-orbitals of iron atoms and the unshared electron pairs of heteroatoms. In addition, the protonation increases the protected metal’s ability to accept electrons from the conduction band. Their electron cloud is deformed during the protonation reaction, which enhances their ability to inhibit corrosion.

12 Mulliken charge distribution

Charge transfer between reactant portions of molecules is common in chemical processes. As a result, local features are important in a reactivity-oriented description of molecular systems. Then, one of the fundamental challenges of chemical reactivity is determining the most advantageous location to remove or add one electron to a molecule. The distribution of electrons is fundamental to understanding chemical reactivity; nucleophilic and electrophilic assaults may be explained by electrostatic interactions. Furthermore, the charge in electron density under the impact of an approaching reagent is quite important. Initially, Fukui realizes the significance of the border orbital as a key component influencing the ease of chemical reactions and the stereoselective route. In a landmark study, Yang and Par showed that DFT could rationalize most Frontier theories (Parr et al. 1999). They established the Fukui function for a molecule, which reflects a site’s reactivity, as:

The difference in electron density is caused by variations in the number of electrons which is equal to the functional derivation of the chemical potential caused by a change in the external potential due to the Maxwell equation (Obi-Egbedi et al. 2011). As a result, it quantifies the susceptibility of a system’s chemical potential to external disturbances at a certain moment. Fukui functions are normalized, as shown by the integration of the preceding equation (Obi-Egbedi et al. 2011). Because the Fukui functions are local, they reflect the features of the many places inside the molecule. The derivation of the following equation for a molecular or atomic system is discontinuous and difficult to assess. As a result, Yang and Par presented three numerical definitions of Fukui functions.

Fukui functions are calculated by using the finite difference approximation, as follows:

where q_N−1, q_N, and q_N+1 denote the Hirshfeld and Mulliken charge of the atom with N + 1, N, and N − 1 electrons, respectively. The concentrated Fukui functions of atom x in a molecule with N electrons are determined by using the finite-difference assumption.

The maximum of the electrophilic Fukui functions f⁻ represents the preferred locations for electrophilic agent adsorption, like the metal surface. The f⁻ maxima for DAPO occurs around site oxygen atom 3O and 33N in gas phase of 1,3,4 oxadiazole ring. But in aqueous phase, the maximum f⁻ in the 1,3,4 oxadiazole ring increased for the same atoms at 0.59 and 0.218. The maxima for CMO are delocalized near 1,3,4 oxadiazole ring moiety and the cinnamyl in gas phase group for 13C and 4C equal to 0.42 and 36, respectively. The f⁻ in cinnamyl group increased in aqueous phase, especially at 12C and 4C. For PMO, the f⁻ maxima exhibit the greatest degree of delocalization, which is associated with low inhibitory efficacy at 5S and 11N in mercaptan and 1,3,4 oxadiazole ring in gas phase. But in aqueous phase, the phenyl group has the highest f⁻, and the electrophilicity has a highest value relative to the gas phase in all cases as shown in Tables 5–8. 16S and 14N have the highest f⁻ in the 2-ADT molecule, which are located at the mercaptan group.

27C, 28C, and 3O atoms have the highest nucleophilic Fukui functions f⁺of DAPO and have the best inhibition efficiency in this study in gas and aqueous phases of the 1,3,4 oxadiazole ring. 16S and 15C of CMO inhibitor in gas phase and 22N in aqueous phase have the highest f ⁺ at mercaptan and 1,3,4 oxadiazole group. The best nucleophilic site of PMO inhibitor observed at 5S in gas phase and 3C in aqueous phase, which is equal to 0.112 and 1.63. Associate with the worst inhibition efficiency, the highest nucleophilic site obtained at 16S, 15N, and 13O in gas and aqueous phases.

As the DAPO molecule contains N, S, and benzene ring heteroatoms, it may transfer its electrons to the vacant d-orbital to form a strong metal protective coating through coordinate bonding. One of the most powerful, economical, and practical corrosion inhibitors are the use of organic molecules including heteroatoms of nitrogen (N), oxygen (O), sulfur (S), and phosphorus (P) in their molecular structures (Verma et al. 2018).

On the electron density surfaces, we demonstrate the electrostatic potentials (ESP) and Fukui functions of DAPO (D), HMO (C), CMO (B), and 2-AT (A). The minimum and maximum are displayed in blue and red on these maps, respectively. On the ESP maps, negatively charged blue spots are near heteroatoms. Adsorption to metal surfaces would be ideal in these electron-rich regions. The maximum of the nucleophilic Fukui functions f ⁺ indicates the preferred locations for adsorption of nucleophilic agents. Figure 5 shows electrostatic potential map of selected molecules at 6–311++G(d, p) basis set for nonprotonated species in gas and aqueous phases.

Figure 5:

Electrostatic potential map of selected molecules.

13 Experimental review

Table 5 shows the corrosion rate (CR) and inhibition efficiency value, which have been received at various quantities from the weight loss technique of experimental work associated with 2,5-bis(4-dimethylaminophenyl)-1,3,4-oxadiazole (DAPO) after 6 h of immersion in 1 M HCl at 30 °C (Bouanis et al. 2016). According to the experimental results, when the concentration of DAPO increases, the values of CR was steadily drop, indicating that DAPO increased the corrosion inhibition efficiency, η_WL(%). Definitely, DAPO concentration increased protection inhibition efficacy with a maximum η_WL(%) of 91.2 % was achieved after 6 h in 1 M HCl at 1 mM. With increasing inhibitor concentration, inhibitors A, B, and C showed an optimum inhibition effectiveness at 500 ppm oxadiazoles (Al-Baghdadi et al. 2021; Bouanis et al. 2016; Quraishi and Sardar 2003).

Experimental calculations about surface coverage θ for different inhibitor concentrations in 1 M HCl solution were performed to identify an acceptable adsorption isotherm. Figure 6 shows the lines fit to C_inh/θ versus C_inh results at various temperatures with such a correlation coefficient (r²) of 0.998 acetylthiophene thiosemicarbazone for mild steel in HCl (Al-Baghdadi et al. 2021). The adsorption of the 2-AT compound examined follows Langmuir adsorption isotherm, as (Chang et al. 2020):

where K_ads is the equilibrium constant and C_inh is the concentration of the tested inhibitor. Temperature rises add to a rise in the number of active corrosion centers on the metal surface and intensify the evolution of corrosion processes. Hence, it is vital to safeguard metal goods, apparatus, and structures that operate at high temperatures.

Figure 6:

Corrosion inhibition efficiency and temperature relationship of selected compounds (Al-Baghdadi et al. 2021; Bouanis et al. 2016; Quraishi and Sardar 2003).

14 Conclusions

In order to identify the causes of its apparent success, the research critically evaluates the often-used technique in corrosion inhibition investigations using quantum chemical calculations that depends on the connection between molecule electronic structure characteristics and inhibition. It is demonstrated that the experimental measurements trend of corrosion inhibition performance for acidic medium (DAPO, 2-AT, HMO, and CMO) cannot be purely analyzed in terms of the molecular electronic properties alone. For this reason, the molecular electrical structure of three corrosion inhibitors for copper (DAPO, 2-AT, HMO, and CMO) were evaluated. Theoretically, the best parameter is the band gap energy, because it is related to most other parameters. One of the most effective inhibitors is DAPO because it has the lowest band gap energy, the highest softness value, and the highest polarization. 2-AT inhibitor is the worst efficacy of the two inhibitors compared to other inhibitors. Quantum chemical computations were performed on the nonprotonated and protonated versions of the specified compounds in gas and aqueous phases. Based on the findings of this investigation, the following conclusions can be drawn:

1. According to theoretical results derived from DFT, compounds studied have corrosion inhibition efficiency ranks of D > C > B > A.

2. The compounds studied in this study will be useful in preventing the corrosion of iron metal.

3. The experimental results for corrosion inhibition efficiency between DAPO (D) and CMO (C) inhibitors are very close, and the theoretical study is in good agreement with the results of the experiment.

Consequently, it is determined that a valuable technique is the investigation of the molecule’s electronic characteristics alone, such as on the basis of the HSAB concept. This underlines the significance of accurate modeling of interactions between corrosion system components in investigations using quantum chemical computations.