Calculated quantum chemical parameters for non-protonated molecules in gas phase (eV).
Many experts working in the field of corrosion work in laboratories experimentally with long-term procedures and high costs by making changes in the structures of new corrosion inhibitors or existing inhibitors. Advances in computational chemistry and computer software in recent years combine corrosion prevention studies with theoretical chemistry, enabling fast, cheap and highly accurate research. Researchers working in this field can now predict the electronic, molecular and adsorption properties of anti-corrosion molecules at the molecular level with density functional theory (DFT) and Molecular Dynamics Simulation. This section includes: introduction, corrosion mechanisms, introduction to corrosion inhibitors, density functional theory (DFT) and corrosion applications, Molecular Dynamics Simulation, DFT and Molecular Dynamics Simulation applications of the effectiveness of the selected corrosion inhibitor and results. The theoretical data obtained by both the DFT approach and the molecular dynamics simulation approach showed that the corrosion inhibition efficiency order against iron corrosion for the studied Schiff bases and derivatives can be presented as: DBAMTT> SAMTT> AMTT. HOMO energy value of DBAMTT has −8,18144, HOMO energy value of SAMTT has −8,09001, and AMTT has −8,01518 in HF/6–31++G** basis set.
- Molecular Dynamics Simulation
- Corrosion inhibitor
Corrosion prevention studies have been intensified in recent years by the use of many organic compound classes as corrosion inhibitors for metals in acidic environments [1, 2, 3]. Both experimental and theoretical studies are carried out on this subject, but due to the fact that experimental studies are expensive and time-consuming, emphasis is placed on theoretical chemistry with software systems that have developed considerably in recent years [4, 5]. Some quantum chemical methods and molecular modeling techniques are carried out to characterize the molecular structure of the inhibitors by determining the effectiveness of corrosion inhibitors and to suggest the mechanisms of their interaction with surfaces [6, 7, 8].
Corrosion inhibitors, which are one of the easiest methods of protecting metals against corrosion, are gaining importance day by day [9, 10, 11]. The adsorption of these molecules depends on many physicochemical properties of the molecules [12, 13, 14]. There are many physicochemical properties for the studied molecules to be good inhibitors, such as aromaticity, steric factors, electron density etc. [15, 16, 17].
It has been stated in many studies that organic inhibitors contain heteroatoms such as nitrogen, sulfur or oxygen and that congenital double bonded heterocyclic aromatic ring systems are quite good inhibitors for mild steel [18, 19]. Schiff bases are also a very good inhibitor because they have these properties, and many experimental studies are carried out on Schiff bases. In this study, salicylideneamino-3-methyl-1,2,4-triazole-5-thi one26 (SAMTT) and 4- (2,4-dihydroxybenzylideneamino) -3-methyl-1,2,4-triazole-5-thione (DBAMTT) and methyl-1,2,4-triazole-5-thion27 (AMTT) compounds are theoretically studied .
The use of Conceptual density functional theory (DFT) to describe the structure and effectiveness of inhibitors in corrosion processes is becoming a well-known use. With this theory, using the energy of the highest filled molecular orbitals (EHOMO) and the lowest empty molecular orbitals (ELUMO), global chemical descriptors such as hardness , electronegativity , softness , electrophilicity  and chemical potential are calculated for corrosion. It provides information about the effectiveness of inhibitors. In this section, determination of the corrosion inhibition efficiency and best inhibitor of the molecules in Figure 1 on iron corrosion is explained using quantum chemical calculations and molecular dynamics simulations approach.
2. Theory and computational details
Density Functional Theory (DFT), the most common method used to determine the chemical reactivity of molecules, aggregates, and solids, seems to be getting more popular day by day . DFT calculations in this study were made with Gaussian View 5.0.8 program  for the preparation of Gaussian 09  input files. The structures of the compounds in the study are calculated with functional B3LYP [28, 29] based on density functional theory (DFT). High-level 6–311 ++ G (d, p) foundation sets were used in the calculations. This basic sebum is one of the most accurate basic sets. Calculations in both gas and aqueous phases were also made using SDD, 6–31 ++ G (d, p) and 6-31G base sets, as well as HF and DFT/B3LYP methods, using other levels of theory. One of the reasons to investigate the liquid phase in the study is that the corrosion is higher than the liquid phase. For the liquid phase calculations in the study, Tomasi’s polarized continuity model (PCM) and self-consistent reaction area (SCRF) theory were used. These methods model the solvent as a uniform dielectric constant (DC = 78.5) continuity and define the cavity in which the solute is placed as a uniform series of interlocking atomic spheres.
In recent years, DFT methods have been found to be successful in providing insight into chemical reactivity indices such as chemical hardness (η), energy gap (ΔEgap = HOMO–LUMO), electronegativity (χ), chemical potential (μ). Fukui functions
Reactivity indices such as electronegativity (χ), chemical hardness (η), and chemical potential (μ) are defined as derivatives of electronic energy (E) with respect to the number of electrons (N) at external potential,
Pearson and Parr were presented the operational and approximate definitions depending on electron affinity (A) and ionization energy (I) of any chemical species (atom, ion or molecule) for chemical hardness, which measures of the resistance of a chemical species to charge transfer, softness (σ) electronegativity and chemical potential in the light of finite differences method .
Molecular Orbital Theory and Conceptual Density Functional Theory gained a new dimension with the Koopmans theorem  presented in the 1930s, and to predict the ionization energy and electron affinities of chemical species, the ionization energy and electron affinity of a molecule approximate the negative values of the orbital energies of HOMO and LUMO, respectively. He predicted that it was equal. Equations (6) and (7) were obtained using Eqs. (3) and (4) to calculate hardness, electronegativity, and chemical potential with the Koopmans theorem.
The concept of electrophilicity (ω) as a global reactivity index similar to the chemical hardness and chemical potential has been introduced by Parr et al. . This new reactivity descriptor measures the stabilization in energy when the system acquires an additional electronic charge ΔN from the environment. The electrophilicity is defined as in Eq. (8).
The global electrophilicity index (ω) is a descriptor of reactivity that allows a quantitative classification of the global electrophilic nature of a molecule within a relative scale. From the light of this index, electrophilic power of a chemical compounds is associated with its electronegativity and chemical hardness. Nucleophilicity (ε) is physically the inverse of the electrophilicity as is given in the equation below (Eq. (9)).
The solvent effect in the study was examined using the polarized continuity model (PCM) model .
3. Results and discussion
The experimental values of the Schiff bases in the study, 4-Amino-3-methyl-1,2,4-triazole-5-thione (AMTT) and its Derivatives (SAMTT and DBAMTT) were obtained by the study . Experimentally, the inhibition activity of these bases was determined as follows:
Quantum chemical descriptors such as EHOMO, ELUMO, Energy gap (ΔE = ELUMO - EHOMO), chemical hardness, softness, electronegativity, chemical potential, proton affinity, electrophilicity and nucleophilicity were calculated and corrosion inhibition was discussed through these parameters. Numerical values of all calculated parameters of Schiff bases and derivatives and their protonated states are given in Tables 1–4 in gas and water solution.
We will discuss all the parameters in detail below.
3.1 Non-protonated inhibitors
According to the boundary molecular orbit theory FMO, a function of the interaction between HOMO and LUMO levels of the reacting species is defined as chemical reactivity . The molecule’s ability to donate electrons to a suitable acceptor with empty molecular orbitals is called EHOMO, and its ability to accept electrons is called ELUMO. The higher the value of the inhibitor’s EHOMO, the greater the inhibition efficiency and its presenting electrons to the empty d-orbit of the metal surface. The larger the molecule’s ability to accept electrons depends on the lower the value of ELUMO . As a result of the calculations, among the molecules investigated, the lowest energy EHOMO, AMTT had the lowest and DBAMTT the highest corrosion inhibition (Table 2). This situation is compatible with causal results. This means that the molecule that tends to adsorb the most on the metal surface is DBAMTT. SAMTT, on the other hand, has a lower number of OH groups than DBAMTT, so its corrosion inhibition efficiency is less than DBAMTT. Figure 2 shows the areas where the activities of molecules are high. It is seen that these areas are the regions where nitrogen is present.
The ΔE approach, defined as the HOMO - LUMO energy deficit, is a very important stability index and provides the necessary theoretical models to make explanations about the structure and conformation in molecular systems. In order to have a high inhibition efficiency, the ΔE value should be low [47, 48, 49]. When the investigated molecules were compared, it was seen that there was a DBAMTT molecule in the smallest HOMO-LUMO gap (8,68921 eV obtained by HF method) as seen in Table 2. This means that the DBAMTT molecule has a tendency to adsorb more on the metal surface than other molecules and can be expected to be a very good corrosion inhibitor.
Electronegative indicates the strength of atoms in a molecule to attract bonding electrons . The higher the electronegativity value of the molecule, the more the atoms in the molecule will attract the bond electrons. This will cause the inhibitor activity of the molecule to decrease .
The reason for not making a detailed analysis on the dipole moment μ, it should be stated first that there is no consensus on the relationship between dipole moment and inhibition efficiency in literature [7, 11, 38, 39, 40, 41]. The results obtained in the study also show that there is no significant result between μ and inhibition efficiency and that it confirms the previous studies.
One of the ways to measure molecular stability and reactivity is Absolute hardness, η, and softness σ, where a hard molecule has a fairly large energy gap and a soft molecule has a small energy gap. Soft molecules are more reactive than hard molecules because they easily donate electrons to the receiver. While performing a simple electron transfer from the adsorption molecule, the transfer takes place from the part where the σ value of the molecule is highest . In corrosion systems, the metal behaves like a lewis acid and while it is soft acid, the inhibitor acts as a lewis base and the more soft base inhibitors are, the more these metals have an effect on acidic corrosion. In this case, when Table 2 dec-I data were examined, it was seen that the DBAMTT inhibitor had the highest σ value and this was an expected result when compared with the experimental results.
When iron and inhibitor approach each other, electrons flow from low χ (inhibitor) to high χ (iron) until their chemical potential or electronegativity is equal. As a first approximation, the fraction of electrons transferred, N, is given by Eq. (10).
In the Hard Soft Acid Base (HSAB) theory , it was determined that iron behaves like lewis acid, so the difference in electronegativity drives the electron transfer and the sum of the hardness parameters acts as a resistance. This is calculated using the fraction of transferred electrons assuming I = A for a metallic mass, using a theoretical value χ Fe = 7 eV  for cast iron’s electronegativity and a global hardness Fe = 0.  In this study, the number of electrons transferred (ΔNmax) of the compounds under the probe is calculated and the results are shown in Tables 5 and 6. According to Lukovits et al. , if ΔN <3.6, inhibition efficiency increased with increasing ability to donate electrons at the metal surface. A value of ΔNmax <3.6 eV indicates the tendency of a molecule to donate electrons to the metal surface. The results in Tables 5 and 6 revealed that the molecules under the probe act as electron donors outside the protonated AMTT, SAMTT, and DBAMTT species in the gas phase and at the B3LYP/6–31 ++ G (d, p) theory level. Acting as an electron acceptor. The results show that the highest fraction of transferred electrons, ΔNmax, is associated with the best inhibitor (DBAMTT), while the least fraction is associated with the inhibitor with the least inhibitory activity (AMTT). In any case, the ability of inhibitor molecules to donate electrons follows the order DBAMTT> SAMTT> AMTT. These results are in good agreement with experimental studies.
|Gas phase (non-protonated)||Aqueous (non-protonated)|
|Gas phase (protonated)||Aqueous (protonated)|
Recently, according to the theory presented by Gomez et al. , provided that both electron transfer to the molecule and recycling from the molecule are simultaneously, the energy change and the hardness of the molecule change in direct proportion (Eq. (11)).
Eq. (11) implies that when>0 or ΔEb-d < 0, back-donation from molecule to metal is energetically preferred. The results reported in Table 5 show that ΔEb-d < 0, therefore charge transfer to a molecule followed by re-release from the molecule is energetically favorable. Assuming that the inhibition efficiency should increase when the molecule has better adsorption on the metal surface, the inhibition efficiency should increase when the stabilization energy resulting from the interaction between the metal surface and the inhibitor increases. As expected and in line with the experimental results , the calculated values of ΔEb-d tend to: DBAMTT> SAMTT> AMTT.
In the theoretical studies, the ESP calculations of the molecules show the regions where the electron density is high in the molecule . For this reason, molecules interact chemically by donating electrons on atoms with higher electron density. It is seen that the electron density of the sulfur atom is higher than the other atoms in the calculated molecules. For this reason, they try to be good inhibitors by interacting chemically over the molecular sulfur atom .
Apart from these, another important property, Sastri and Perumareddi  discovered by using the following equation molecule-metal interaction energy (Δψ) can be calculated (14).
When the results are examined, molecule-metal interaction Δψ|, is respectively as DBAMTT> SAMTT> AMTT (Tables 5 and 6). In addition, the initial molecule-metal interaction energy (Δψ) order is again DBAMTT> SAMTT> AMTT.
3.2 Protonated inhibitors
The enthalpy of the reaction of a chemical species in the gas phase with the H + ion is defined as the affinity of protons (PA) [50, 52]. PA gives information about the ability of chemical compounds to donate or accept electrons and the degree of alkalinity. Compounds containing hetoroatoms such as oxygen and nitrogen tend to protonate very well in acidic environments and aqueous solutions. Tables 7 and 8 shows the PA values of the compounds in this study with different calculation methods in gas and aqueous solution. When PA values and excision activities were compared, it was determined that the efficiency ranking was DBAMTT> SAMTT> AMTT and was consistent with the experimental result.
|MP2/3 − 21G*||HF/6–31++G**||HF/6–311++G**||DFT/6–31++G**||DFT/6–311++G**|
The following equation is used to calculate the PA values of Schiff bases compounds.
In the above equation, Enon-pro and Epro are energies of non-protonated and protonated inhibitors, respectively. EH + is the energy of the H + ion and is calculated in the figure below.
In the high calculation methods selected in the study, the protonated inhibitors have lower EHOMO values compared to their non-protonated states, and the order is respectively DBAMTT, SAMTT, AMTT, and these results given in Table 3 are consistent with the experimental inhibition efficiency.
Agreement of EHOMO values with experimental data ELUMO and T.E. and there is a correlation between these parameters and the inhibition efficiency. When the ∆E values were examined, it was seen that the lowest value belonged to DBAMTT and it was determined that it was the most intrusive (9,8405 eV).
In addition, when Tables 2 and 3 are examined, it is seen that protonated compounds have higher μ than non-protonated compounds. Similarly, this verification was made for chemical hardness. The results show that the calculations show that non-protonated inhibitors have a more positive ∆N value than the protonated inhibitor. The DBAMTT molecule, on the other hand, has the highest ∆N value in each round, confirming that it has the same highest inhibitory properties as experimental data.
3.3 Solvent effect
The greater occurrence of the corrosion phenomenon in the solvent phase indicates that the solvent phase in the process may be important. Inhibitors may show different properties in a vacuum or in another solvent [1, 27, 50, 51]. In the study, the solvent effect on the molecular structure of the solute was calculated by the polarized continuity model (PCM) model . In the PCM model, the solvent is treated as a continuous dielectric medium, and the solute is considered a molecule trapped in a cavity surrounded by the solvent. In the Gaussian 09 program, CPCM, a special version of PCM based on integral equation formalism, was used together with HF/6–31 ++ G (d, p) to examine the solver effect.). When the results are examined, a small increase is shown for the values of EHOMO, ELUMO, ∆E, T.E., Pi, MV, i and g, while a rather small decrease is shown for values of v and ∆N. For the molecular in this study, it was determined that the quantum chemical parameters calculated in the presence of a solvent (water) and in the gas phase did not differ significantly (Table 5).
3.4 Molecular dynamic simulations
Monte Carlo simulations can be used to predict interactions between inhibitor molecules and metal surface. In the study, the most stable low energy adsorption configurations of AMTT, SAMTT, DBAMTT on the Fe (110) surface were induced by Monte Carlo simulation and the configurations are shown in Figure 3. Outputs and descriptors, including total adsorption, solid adsorption and deformation energies are given in Table 9. Adsorption energy is attributed to the energy released during relaxed adsorbate components adsorbed on the substrate. Adsorption energy is the addition of solid adsorption and deformation energies of the adsorbate component. Higher values of negative adsorption energy indicate the presence of a more stable and stronger interaction between a metal and an inhibitor molecule. Monte Carlo simulation and DFT calculation results showed us once again that the corrosion inhibition efficiency was in the form of DBAMTT, SAMTT and AMTT, respectively, and it was seen to confirm the experimental results .
|Inhibitor||Total energy||Adsorption energy||Rigid adsorption energy||Deformation energy||d|
DBAMTT, SAMTT, and AMTT molecules used in this theoretical study were synthesized by M. Saravana Kumar et al. In order to predict the corrosion inhibition activities of Schiff bases and derivatives against the corrosion of iron metal, density functional theory with different basic sets and molecular dynamics simulation approach were used in Hartree Fock (HF), B3LYP. Quantum chemical calculations of the non-protonated and protonated structures of the molecules examined in this study were made in both gas phase and aqueous solution. At the end of the study, the following results are given in summary.
The studied Schiff bases and derivatives are thought to be very important in preventing the corrosion of iron metal.
The theoretical data obtained by both the DFT approach and the molecular dynamics simulation approach showed that the corrosion inhibition efficiency order against iron corrosion for the studied Schiff bases and derivatives can be presented as: DBAMTT> SAMTT> AMTT.
According to the binding energies presented in Table 8, it was determined that among the molecules examined, DBAMTT was the most effective inhibitor of iron corrosion and the calculated binding energies were similar to the experimental data.
Results and interpretations resulting from the study can give an idea for new corrosion inhibitor studies in the following processes and help in the selection of corrosion inhibitors.
This research was made possible by TUBITAK ULAKBIM, High Performance and Grid Computing Center (TR-Grid e-Infrastructure).
Şaban Erdoğan performed the calculations. Şaban Erdoğan and Burak Tüzün discussed and analyzed the results. All authors equally contributed to preparation of the manuscript. All the authors have read and approved the final manuscript.
This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.
Compliance with ethical standards
Conflict of interest the authors declare that they have no conflict of interest.
Avaibility of data and materials
The datasets generated during the current study are available from the corresponding author on reasonable request.