A theoretical approach to understand the inhibition mechanism of steel corrosion with two aminobenzonitrile inhibitors

Abstract

In this work, the adsorption behavior and corresponding inhibition mechanism of two aminobenzonitrile derivatives, e.g., 2-aminobenzonitrile (2-AB) and 3-aminobenzonitrile (3-AB), in aqueous acidic medium on steel surfaces have been investigated using quantum chemical calculations and molecular dynamics (MD) simulations. Quantum chemical parameters such as E_HOMO, E_LUMO, energy gaps (ΔE), the dipole moment (μ), the global hardness (η), the softness (S), and the fraction of electron transfer from the inhibitor molecule to the metallic surface (ΔN) have been calculated and well discussed. Fukui indices analysis was performed to get local reactive sites of the studied inhibitor molecules. Furthermore, molecular dynamics simulations were applied to search for the most favorable adsorption configuration of the inhibitor over an iron (1 1 0) surface.

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1. Introduction

Nowadays, the prevention of metallic corrosion is an important issue considering the enormous role of metals and their alloys in several industrial applications. Iron and its alloys play crucial roles in almost all mechanical industries.^1–3 In several industrial processes, the use of an acid solution is very common in numerous techniques such as acid cleaning, acid pickling and acid descaling.^4,5 These acid solutions create serious metallic corrosion on the metallic surfaces. Due to this adverse impact on metallic bodies, nowadays, almost all the industries are suffering from a huge amount of economic loss. Therefore, prevention of corrosion is an urgently needed thing and our prima facie interest is to avoid this kind of solution state metallic corrosion. Among the numerous corrosion inhibition techniques, the use of inhibitors is a widely accepted technique due to its low cost, high efficiency and facile feasibility.^6,7 In general, organic compounds having heteroatoms with lone pairs of electrons (N, O, S and P), aromatic rings, π conjugated systems, and conjugated aliphatic bonds are considered to be effective corrosion inhibitors.^8–10 Such organic inhibitors adhere on the metallic surface via a physical adsorption (electrostatic interactions) or chemical adsorption (coordination bonds) route and thereby can prevent metallic corrosion. In physical adsorption, the inhibitor molecules are adsorbed on the metallic surface via electrostatic interactions between the charged inhibitor molecules and the charged metallic surfaces.^11,12 In chemical adsorption, the inhibitor molecules donate their electrons to the vacant d-orbitals of metals for the sake of forming coordinate bonds and have the ability to accept electrons from the metallic surface by using their antibonding orbitals to form a π-backbond.¹³ These two adsorption processes produce a uniform film on the metallic surface, which in turn protect the metallic surface from aggressive acid attacks. However, the in detail description of this surface phenomenon and the factors determining the strength of the interactions is yet to be explored. In this present investigation we have tried to explain how this process occurs and the contributing factors for controlling the adsorption process.

Traditionally, the performance of the inhibitive action is found out from weight loss measurements and using potentiodynamic polarization and electrochemical impedance spectroscopy. However, these experimental methodologies are costly, time consuming and sometimes unable to explore the inhibition mechanisms.^14,15 With the improvement of sophisticated software and hardware related to computational supportive systems, computer-aided simulation has been explored as an easy and powerful tool for investigating a complex system in a corrosion process and may successfully predict the relative inhibition efficiency well in advance. In this case, proper theoretical modelling and the corresponding quantum chemical calculations are very efficient for exploring the relationship between the molecular properties of the inhibitors and their corrosion inhibition efficiencies.^16–20 The corrosion inhibition capability of the molecules can be determined from the frontier molecular orbital energies, energy gap, dipole moment, global hardness, softness, fraction of electron transfer from the inhibitor molecules to the metallic surface, etc. In our previous work, we have successfully investigated the correlation between the quantum chemical calculations and experimentally obtained corrosion inhibition effectiveness of pyrazine derivatives,²¹ mercapto-quinoline derivatives²² and Schiff base²³ molecules. However, Kokalj et al. recently proposed that a quantum chemical approach alone is not sufficient to envisage the inhibition efficiency trend of the inhibitor molecules.^24,25 In many cases, the results obtained from DFT cannot be correlated well with the obtained experimental findings.^26,27 In these circumstances, a precise modelling of the experiment should be emphasized to correlate the theoretical results with the experimental inhibition effectiveness. In practice, modelling of an experiment can only provide the actual interfacial interactions between the concerned metallic surface and the inhibitor molecules. As a result, molecular dynamics (MD) simulations have recently emerged as a modern tool to reasonably predict the actual interfacial configuration and adsorption energies of the surface-adsorbed inhibitor molecules. To date only a few certain groups are working towards getting the interaction and binding energies of surface-adsorbed inhibitor molecules. Obot et al. have recently employed an MD simulation to study the adsorption behaviour of pyrazine derivatives on a steel surface.²⁸ Xia et al. explored the correlation between the structural conformation of imidazoline derivatives and their corresponding inhibition efficiencies by employing MD.²⁹

In this present investigation, we have successfully studied both the quantum chemical calculations and MD simulations to explore the correlation between the theoretical results and previously obtained experimental findings. The aim of this present work is to find an alternative approach to predict which molecules will behave as good corrosion inhibitors and which will not. This is obviously of certain importance with respect to the economic point of view. In view of the above, in our present work, quantum chemical calculations and MD simulations have been carried out on some recently studied inhibitor molecules, namely, 2-aminobenzonitrile and 3-aminobenzonitrile, over a steel surface in acidic media.³⁰ The results obtained from these theoretical studies are in good accordance with the results obtained from the experiments.

2. Computational details

2.1. Quantum chemical calculations

Density functional theory (DFT) is a worldwide accepted ab initio approach for modelling the ground state properties of molecules of interest. In the last few decades, DFT has become popular due to its accuracy in carrying out theoretical calculations in less time with a much smaller amount of investment. In this present work, quantum chemical calculations were carried out using an ORCA program, module version 2.7.0, which is an open source code developed by Prof. Dr Frank Neese (Director, MPI für Chemische Energiekonversion, Mülheim, Germany).³¹ Geometry optimizations of the presently studied inhibitor molecules were performed using the hybrid B3LYP functional.^32–37 The all-electron Gaussian basis sets were developed by the Ahlrichs group.³⁸ In this study, triple-ζ quality basis sets, TZV(P), along with one set of polarization functions on the N-heteroatom were used.³⁹ For carbon and hydrogen-like atoms, relatively smaller polarized split-valence SV(P) basis sets were used which are of double-ζ quality in the valence region and had a polarizing set of d-functions on the non-hydrogen atoms. Self-consistent field (SCF) calculations were converged [with 10⁻⁷ Eh: density change, 10⁻⁸ Eh: energy, and 10⁻⁷: maximum element of the DIIS (Direct Inversion in the Iterative Subspace or Direct Inversion of the Iterative Subspace) error vector]. As electrochemical corrosion always happens in the aqueous phase it is necessary to consider the effect of the solvent in all of the DFT calculations. Therefore, in the present study, the effect of the solvent is included for the sake of accuracy. Here, a COSMO model was applied in order to incorporate the effect of the solvent (water) in these calculations. This method was used for the modelling of water as a continuum of the uniform dielectric constant (ε) and the solute was placed as a uniform series of interlocking atomic spheres.

The local reactivity of the molecule has been analyzed by evaluating Fukui indices (FI). The FI calculations are performed using a Dmol³ module, Material studio™ version 6.1 by Accelrys Inc., San Diego, CA.⁴⁰ All the calculations were accomplished using the double numerical polarization (DNP) basis set (including d- as well as p-orbital polarization functionals) along with a generalized gradient approximation and the BLYP exchange–correlation functionals.^41,42 Detailed information of local reactivity has been obtained using condensed Fukui functions.⁴³ Herein, the Fukui function (f_k) can be expressed as the first derivative of the electronic density with respect to the number of electrons (N) in a constant external potential.⁴⁴

For an electron transfer reaction, Fukui functions enlighten the sites in a molecule where a nucleophilic, an electrophilic or a radical attack are mostly possible. The Fukui functions were calculated by taking the finite difference approximations as:⁴⁵

f_k⁺ = q_k(N + 1) − q_k(N) (for a nucleophilic attack) (2)

f_k⁻ = q_k(N) − q_k(N − 1) (for an electrophilic attack) (3)

where q_k is the gross charge of the k atom, i.e., the electronic density at a particular point (r) in space around the concerned molecule. The q_k(N + 1), q_k(N) and q_k(N − 1) are defined as the charge of the anionic, neutral and cationic species, respectively. Hirshfeld population analysis (HPA) was used for the presentation of the Fukui functions.⁴⁶

2.2. Molecular dynamics simulations

The adsorption process of the aminobenzonitrile compounds on the iron surface was investigated using MD simulations using Material Studio™ software 6.1 (from Accelrys Inc.).⁴⁰ In this present investigation, we have chosen an Fe (1 1 0) surface for the simulations. In the simulation process, the interaction between the studied molecules and the iron surface were carried out in a simulation box (39.47 × 39.47 × 77.23 Å) with periodic boundary conditions in order to avoid any arbitrary boundary effects. Here, we used ten layers of iron atoms as it provided sufficient depth to overcome the issue related to the cutoff radius in this case. In this investigation, the simulation box was created by three layers. The first layer contains an Fe slab, the second layer is the solution slab which contains H₂O, H₃O⁺, and Cl⁻ molecules as well as molecular ions and the remaining part of the box is the vacuum layer. After construction of the simulation box, molecular dynamics simulations were carried out using a COMPASS (Condensed phase Optimized Molecular Potentials for Atomistic Simulation Studies) force field. COMPASS is a highly accepted and authentic ab initio force field that enables the accurate prediction of nature for many chemical entities. In general, the parameterization procedure can be divided into two phases: (i) the ab initio parameterization, and (ii) the empirical optimization.⁴⁷ The MD simulations were performed both at 298.0 K and 328.0 K using a canonical ensemble (NVT) with a time step of 1.0 fs and a simulation time of 500 ps.

The interaction energy (E_interaction) and binding energy (E_binding) of the inhibitor molecule on the Fe (1 1 0) surface were obtained using eqn (4) and (5):⁴⁰

E_interaction = E_total − (E_{surface+H2O+H3O⁺+Cl⁻} + E_inhibitor) (4)

where E_total is the total energy of the simulation system, E_{surface+H2O+H3O⁺+Cl⁻} is the energy of the iron surface together with H₂O molecules and H₃O⁺ and Cl⁻ ions, and E_inhibitor is the energy of the free inhibitor molecule.

The binding energy of the inhibitor molecule is the negative value of the interaction energy as follows:²³

E_binding = −E_interaction (5)

3. Results and discussion

3.1. Comparative experimental studies between two studied inhibitors

G. Sığırcık et al. have recently investigated corrosion inhibition effectiveness of aminobenzonitrile compounds (Fig. 1) on a steel surface in 0.5 M HCl solution via a complete wet chemical experiment.³⁰ The obtained experimental results reflected that these two inhibitors are remarkably good corrosion inhibitors in a 0.5 M HCl medium. The order of inhibition efficiency obtained from potentiodynamic polarization as well as electrochemical impedance spectroscopy measurements follows the order: 3-AB > 2-AB. In the quest of finding out the probable reason for the relative inhibition order of these two inhibitors, it was found that the authors only point out that the steric effect between the two adjacent groups (–NH₂ and –C≡N) plays the crucial role. The authors have stated that the steric effect in 2-AB is comparatively higher than that of 3-AB. For this reason, 3-AB adsorbs in a better way compared to 2-AB and a higher inhibition efficiency is obtained.

Fig. 1 The chemical structure of the studied corrosion inhibitors: (a) 2-aminobenzonitrile (2-AB) and (b) 3-aminobenzonitrile (3-AB).

These authors felt that the explanation was not sufficient to explain this relative order of inhibition efficiency. To get a complete picture of the inhibition mechanism of the two aminobenzonitrile compounds as well as an explanation of this inhibition efficiency trend, quantum chemical calculations and MD simulations are carried out in this present investigation. In addition, correlations among the observed molecular parameters and the experimentally obtained inhibition efficiency outcomes have also been investigated.

3.2. Quantum chemical calculations of the neutral forms of the inhibitor molecules

3.2.1. Equilibrium geometry structures. The optimized geometric configurations of the molecules (2-AB and 3-AB) are shown in Fig. 2 and their bond angles and bond lengths are presented in Table 1. It can be seen from Table 1 that all C–C bond lengths of the benzene ring lie in the range of 1.388–1.427 Å. Thus, the C–C bond lengths in the benzene ring are longer than the general C=C double bonds and shorter than the C–C single bonds.⁴⁸ The tendency of the intermediate bond lengths obviously indicates the presence of conjugation in the benzene ring.

Fig. 2 The optimized geometry: HOMO and LUMO orbitals of 2-AB and 3-AB at the B3LYP/SV(P), SV/J level of the basis set for neutral species in the aqueous phase.

Table 1 Bond lengths (Å) and bond angles (°) of the optimized neutral forms of the inhibitor molecules

Geometry parameters	2-AB	3-AB
Bond length
C1–C2	1.4279	1.4054
C2–C3	1.4144	1.4085
C3–C4	1.3882	1.3985
C4–C5	1.4088	1.3946
C5–C6	1.3890	1.4161
Bond angle
C1–C2–C3	120.67	121.48
C2–C3–C4	120.69	118.07
C3–C4–C5	118.89	121.19
C4–C5–C6	121.34	121.00
C5–C6–C1	121.00	118.16

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From Table 1, it can be seen that the bond angles of the benzene rings in 2-AB and 3-AB molecules lie in the range of 118° to 121.5° which means that the atoms in 2-AB and 3-AB molecules are all sp² hybridized. Therefore, from the bond length and bond angle values it can be concluded that both of the optimized structures of the inhibitor molecules possessed ideal geometric configuration.

3.2.2. Frontier orbital energies. The highest occupied molecular orbital (E_HOMO) and the lowest unoccupied molecular orbital (E_LUMO) are very useful to elucidate the chemical reactivity of a molecule. According to the frontier molecular orbital theory of chemical reactivity, the transition of electrons is mainly related to the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of the reacting species.⁴⁹ The HOMO is associated with the electron donation capability of the molecule. The higher the E_HOMO value, the stronger the electron donating capability of the inhibitor will be and therefore the better the observed inhibition efficiency will be.⁵⁰ The LUMO implies the capability of the molecules to accept electrons from the metallic surface. The lower the value of E_LUMO, the more it will be prone towards accepting electrons.⁵¹ From Table 2 it can be seen that the E_HOMO value increased in the order of 2-AB < 3-AB, which means that the ability to donate an electron from the inhibitor molecule to the metallic surface obeys the order of 3-AB > 2-AB. The calculated E_LUMO value exemplifies that the electron acceptance capability decreased in the order of 3-AB > 2-AB. Hence, the orders (E_HOMO and E_LUMO) correlate strongly with the experimental inhibition efficiencies.

Table 2 Calculated quantum chemical parameters of the studied inhibitors in neutral forms

Inhibitors	EHOMO (eV)	ELUMO (eV)	ΔE (eV)	μ (Debye)	I = −EHOMO	A = −ELUMO	χ (eV)	η (eV)	σ (eV^−1)	ΔN100	ΔN110	ΔN111	Inhibition efficiency^a
a Values obtained from ref. 30.
2-AB	−5.9038	−1.3145	4.5893	6.0119	5.9038	1.3145	3.6091	2.2946	0.4358	0.0655	0.2638	0.0590	89.4 (5 mM)
													93.1 (10 mM)
3-AB	−5.7919	−1.4035	4.3884	8.0848	5.7919	1.4035	3.5977	2.1942	0.4557	0.0712	0.2785	0.0643	93.0 (5 mM)
													94.5 (10 mM)

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Apart from the E_HOMO and E_LUMO, the energy gap (ΔE) is also an important parameter in determining the adsorption of an organic molecule on the metallic surface. As ΔE decreases, the reactivity of the molecule will definitely increase, which in turn leads to an increase in adsorption onto a metallic surface.⁵² In general, a molecule with a comparatively lower energy gap is better polarizable and in turn associated with higher chemical reactivity and lower kinetic stability. As a result, ΔE has been used to elucidate the binding ability of the inhibitor molecule on the metallic surface. It can be seen (vide Table 2) that the ΔE values follow the trend 2-AB > 3-AB, which is again also well in accordance with the results obtained from the experiments. The dipole moment (μ) of a molecule is also an important parameter to elucidate the chemical reactivity of a molecule. A literature survey reveals that the adsorption process is further facilitated with increasing values of dipole moment as the latter influences the transport process through the adsorbed layer.^53,54 In this work it can be observed from Table 2 that the dipole moment values increase in the order of 2-AB < 3-AB, which further strengthens the experimental results.

According to the Koopmans’ theorem, the E_HOMO and E_LUMO of the inhibitor molecule are related to the ionization potential (I) and electron affinity (A) by the following equations:⁵⁵

I = −E_HOMO (6)

A = −E_LUMO (7)

The electronegativity (χ) and global hardness (η) of the concerned inhibitor molecules are obtained from the ionization potential and electron affinity values. These parameters are related to the ionization potential and electron affinity by the following formula:

The global hardness, η, is defined as:

The softness (σ) of the inhibitor molecule is simply the reverse of the global hardness: σ = 1/η. When the inhibitor molecule and the metallic iron surface are brought together, electron flow will occur from the inhibitor molecule to the iron atoms until the chemical potentials become equal. It can be presumed that the fraction of electron transfer from the inhibitor to the metal surface is calculated using the following equation:⁵⁶

From the literature, it can be seen that the fraction of electrons transferred is calculated by taking the theoretical value for the absolute electronegativity of iron as χ_Fe = 7 eV (ref. 56–58) and the global hardness as η_Fe = 0, since I = A for metallic bulk atoms.⁵⁹ Actually, the usage of the χ_Fe value of 7 eV is not conceptually correct as it is only associated with the free electron gas Fermi energy of iron where electron–electron interactions are not taken into consideration.^41,60–62 For this reason, nowadays, researchers use the work function (ϕ) of a metal surface, which is a more appropriate measure of its electronegativity.^41,61,62 Therefore, the ΔN value calculation is more appropriate through the usage of the work function (ϕ). For this reason, to measure the ΔN value more specifically, χ_Fe is replaced by ϕ in eqn (10). Thus, eqn (10) is written as follows:

From DFT calculations, the obtained ϕ values are 3.91 eV, 4.82 eV and 3.88 eV for Fe (100), (110) and (111) surfaces, respectively.^41,61 Electron transfer will happen from the molecule to the metal surface if ΔN > 0 and vice versa if ΔN < 0.⁶⁰ According to Elnga et al., the electron-donating ability of a molecule increases if ΔN < 3.6.⁵² From Table 2 it is seen that the ΔN values are positive and less than 3.6 for the interaction between the inhibitor molecules and the three Fe planes. It is also observed for ΔN within the limit of 3.6 that the increase is in the following order: 2-AB < 3-AB. This result indicates that the 3-AB molecule donates its electron in a higher fraction than 2-AB and this outcome correlates strongly with the experimentally obtained inhibition efficiency.

Adsorption of the inhibitor molecule on the metallic surface also allied with the softness (σ) of the inhibitor molecule. In this donor–acceptor chemistry, the metals are considered as soft acids and the inhibitors as soft bases.²⁸ Thus, soft–soft interactions are the controlling factors for the adsorption of inhibitor molecules. It can be seen from Table 2, that the calculated values of softness follow the trend: 3-AB > 2-AB, which further supports the better adsorption proficiency of 3-AB on the metal surface.

3.3. Active sites

Inhibitor molecules are in general adsorbed on the metallic surface via the donor–acceptor (D–A) type interactions between the inhibitor molecules and the concerned metallic surface. Therefore, it is essential to examine which corresponding active sites are responsible for this. Generally, the more negatively charged a heteroatom is, the more it can participate in D–A type interactions.⁶³ But it is also important to consider the situation where the inhibitor molecules receive a certain amount of charge at some centres and revert back to donate a considerable amount of charge through consecutive centres.⁵⁹ This can be easily achieved by the evaluation of Fukui indices for each individual atom. It provides local reactivity as well as the nucleophilic and electrophilic nature of the molecule.⁶⁴ Nucleophilic and electrophilic attacks are mainly controlled by the maximum threshold values of f_k⁺ and f_k⁻. f_k⁺ measures the changes in electron density when a molecule accepts extra electrons, whereas f_k⁻ measures the electron density changes when a molecule loses electrons.

The calculated Fukui indices of the two studied inhibitor molecules are tabulated in Table 3. It can be seen from Table 3 that in the 2-AB molecule, the C(1), C(2), C(3), C(5), C(6), C(7) and N(9) atoms are the more susceptible sites for a nucleophilic attack (electron acceptance) as those atoms possess higher charge densities. On the other hand, the C(1), C(2), C(3), C(4), C(6), N(8) and N(9) atoms mainly participate in the electrophilic attack (the donation of electrons). Therefore, it can be concluded from these results that all the individual atoms will participate in the D–A type interactions on the iron surface. However, in 3-AB, after the shifting of the –NH₂ group from the ortho position to the meta position, the distribution of active sites and their values are nearly similar. Here, the C(1), C(2), C(3), C(4), C(5), C(7) and N(9) atoms are the favorable sites for electron acceptance while the C(1), C(3), C(5), C(6) and N(8) atoms will be responsible for electron donation.

Table 3 Calculated Fukui functions for the two inhibitor molecules

Atoms	2-AB		3-AB
	fk^+	fk^−	fk^+	fk^−
C(1)	0.057	0.065	0.097	0.088
C(2)	0.073	0.073	0.086	0.047
C(3)	0.098	0.061	0.072	0.111
C(4)	0.056	0.117	0.067	0.055
C(5)	0.119	0.053	0.108	0.083
C(6)	0.079	0.087	0.047	0.069
C(7)	0.100	0.034	0.114	0.023
N(8)	0.046	0.168	0.035	0.190
N(9)	0.159	0.086	0.174	0.056

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In view of the above discussion, it can be concluded that both molecules have a number of active centres for their D–A type interactions with the concerned iron surfaces. It can also be seen that the distribution of electron density in the HOMO and LUMO orbitals of the two inhibitor molecules are in good agreement with the calculated Fukui indices. Thus, the outcomes support the same reactive zones for the nucleophilic and electrophilic attack on the iron surface.

3.4. Molecular structure consideration

According to wet chemical experimentation (potentiodynamic polarization, EIS), the corrosion inhibition efficiencies with varying concentrations followed the order 3-AB > 2-AB. The Fukui indices analysis suggests that both molecules have almost the same active sites for their D–A type interactions on the iron surface. Then the obvious question concerns how 3-AB shows a higher inhibition efficiency in comparison to 2-AB. This question can be successfully explained by their molecular configuration. From the geometry optimized structure of 2-AB it can be seen that the distance between the N atom in the –C≡N group and the H atom in the amine (–NH₂) group is 2.960 Å. Therefore, intramolecular H-bonding between these two atoms can easily occur. However, in 3-AB, the intermolecular hydrogen bonding between the molecules will occur (Fig. 3) as the –NH₂ group is situated in the meta position with respect to the –C≡N group. Possibly these two different types of H-bonding create major differences in their inhibition efficiencies.

Fig. 3 Two different types of hydrogen bonding: (a) intramolecular hydrogen bonding (2-AB); (b) intermolecular hydrogen bonding (3-AB).

Intramolecular hydrogen bonding in 2-AB prevents chain propagation between the molecules and thereby the molecules behave as a single unit, whereas in 3-AB the chain propagation will easily occur through the intermolecular hydrogen bonding. It is well known that higher surface coverage by the inhibitor molecule leads to a higher inhibition efficiency. Therefore, due to the intermolecular H-bonding, 3-AB definitely provides a larger blocking area on the steel surface and prevents a possible acid attack on it. Thus, a higher inhibition efficiency is expected for the 3-AB molecule and it is also observed accordingly in the wet chemical experiments.

The above-mentioned explanation is true in the case of chemisorption. It is well known that molecules adsorb onto a metallic surface via chemisorption and physisorption. Thus, the obvious question concerns how molecules behave in physisorption. This can be explained in terms of Mulliken atomic charges of the neutral forms of the inhibitor molecules. It is found from the Mulliken atomic charges (vide Table 4) that the N atoms in the aminobenzonitrile ring have the highest negative charges among the other atoms, hence, the highest probability of the lowest energy upon their protonation. After the protonation in acidic solution, both molecules behave as a single unit because there is no way to form intramolecular or intermolecular hydrogen bonds. Thus in the protonated form, both molecules adsorb on the iron surface as a single unit. As a result, the differences in the inhibition efficiency between these two molecules come from the chemisorption process. It is already stated that intermolecular hydrogen bonding favours higher surface coverage on the iron surface during the adsorption process, hence, a higher inhibition efficiency is expected and it is observed accordingly in the wet chemical analysis. Therefore, it can be concluded from this explanation that the intermolecular hydrogen bonding in 3-AB plays a significant role for its higher inhibition efficiency.

Table 4 DFT (ORCA) derived Mulliken atomic charges of the two studied inhibitor molecules in their neutral forms

Atoms	2-AB	3-AB
C(1)	0.178722	−0.183255
C(2)	−0.016208	0.008558
C(3)	0.087793	−0.096872
C(4)	−0.090777	−0.063501
C(5)	−0.040834	−0.144072
C(6)	−0.177634	0.221722
C(7)	0.201914	0.268564
N(8)	−0.385521	−0.429527
N(9)	−0.456172	−0.443178

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3.5. Quantum chemical calculations of the protonated forms of the inhibitor molecules

The presence of heteroatoms in aminobenzonitrile molecules suggests their high tendency towards protonation in an acidic medium. Therefore, it is obvious to investigate the protonated forms of the inhibitor molecules. It is apparent from Fig. 1 that in the aminobenzonitrile ring more than one N atom is present. Thus, we have to decide which atom possesses the lowest energy upon their protonation. In order to find this out, the geometry optimization of two possible structures was carried out and it can be observed that the most favourable one with the lowest energy upon their protonation is the N atom which carries the highest negative charge on it.^65,66 From Table 4 it is seen that the N9 atom in both of the inhibitors possesses the highest negative charge. Thus, in this present investigation, the N9 atom is protonated. The optimized geometric configurations and the HOMO and LUMO orbitals of the molecules (2-AB and 3-AB) are shown in Fig. 4 and their bond angles, bond lengths and Mulliken atomic charges are presented in Tables 5 and 6. From Tables 5 and 6 it can be seen that after protonation there is a significant difference in their bond lengths, bond angles and Mulliken atomic charges. Thus, the reactivity of the inhibitor molecules in their protonated forms should be considered. From Table 7 it can be seen that the E_HOMO values for both of the inhibitors are shifted towards the more negative value in comparison to the E_HOMO values of the neutral forms. It signifies that in the protonated forms, the electron donation capability of the inhibitor molecules is decreased and it is also expected as after protonation the inhibitor molecules are not capable of donating their electrons to the metallic surfaces. This fact is further confirmed by the fraction of electrons transferred from the inhibitors to the metallic surface (ΔN). Inspection of Table 7 shows that all the values of ΔN for the Fe (1 0 0) and Fe (1 1 1) surfaces are negative, whereas for the Fe (1 1 0) plane the values are positive but relatively very small. On the other hand, if we look at the E_LUMO values it can be seen that the E_LUMO values are also shifted towards the more negative values compared to the neutral forms, pointing out that the electron acceptance capability in the protonated forms is increased and it can also be seen that the electron acceptance capability of a 3-AB molecule is higher than that of a 2-AB molecule. It is further counter supported by the electronegativity values of the two inhibitors. The comparison of the electronegativity values of the two forms of the inhibitor molecules reflects that the electronegativity values in the protonated forms of the inhibitor molecules are much higher than those of the neutral forms. It reflects that the electron attraction capability of the metal surface is increased by the protonated forms of the inhibitor molecules. Therefore, after a complete analysis of both forms of the inhibitor molecules it can be concluded that the neutral forms of the inhibitor molecules have a higher tendency to donate their electrons and the protonated forms of the inhibitor molecules have a superior tendency to accept electrons. Now it is clear from the above-mentioned discussion that a more complete analysis of reactivity is obtained from both forms of inhibitor molecules.

Fig. 4 The optimized geometry: HOMO and LUMO orbitals of 2-AB and 3-AB at the B3LYP/SV(P), SV/J level of basis set for the protonated species in the aqueous phase.

Table 5 Bond lengths (Å) and bond angles (°) of the optimized protonated forms of the inhibitor molecules

Geometry parameters	2-AB	3-AB
Bond length
C1–C2	1.4372	1.4108
C2–C3	1.4294	1.4121
C3–C4	1.3769	1.3951
C4–C5	1.4176	1.3955
C5–C6	1.3827	1.4166
Bond angle
C1–C2–C3	121.42	122.67
C2–C3–C4	119.90	117.28
C3–C4–C5	119.10	120.99
C4–C5–C6	121.94	121.75
C5–C6–C1	121.04	118.11

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Table 6 DFT (ORCA) derived Mulliken atomic charges of the two studied inhibitor molecules in their protonated forms

Atoms	2-AB	3-AB
C(1)	0.197506	−0.128874
C(2)	−0.070681	−0.048813
C(3)	−0.046695	−0.051847
C(4)	−0.078492	−0.056618
C(5)	−0.019974	−0.098080
C(6)	−0.157599	0.164597
C(7)	0.676637	0.745164
N(8)	−0.336000	−0.390005
N(9)	−0.381233	−0.338468

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Table 7 Calculated quantum chemical parameters of the studied inhibitors in their protonated forms

Inhibitors	EHOMO (eV)	ELUMO (eV)	ΔE (eV)	μ (Debye)	I = −EHOMO	A = −ELUMO	χ (eV)	η (eV)	σ (eV^−1)	ΔN100	ΔN110	ΔN111	Inhibition efficiency^a
a Values obtained from ref. 30.
2-AB	−6.4759	−2.4088	4.0671	7.3572	6.4759	2.4088	4.4423	2.0335	0.4917	−0.1309	0.0928	−0.1382	89.4 (5 mM)
													93.1 (10 mM)
3-AB	−6.3772	−2.6499	3.7273	7.2501	6.3772	2.6499	4.5135	1.8636	0.5365	−0.1619	0.0822	−0.1699	93.0 (5 mM)
													94.5 (10 mM)

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3.6. Molecular dynamics simulation

Molecular dynamics (MD) simulations have been recently considered as a modern tool to study the adsorption behavior of inhibitor molecules on the concerned metallic surfaces. Recently Obot et al., Xia et al., Tang et al., Musa et al. and many other scientists have been working on this to understand the adsorption process of corrosion inhibitors.^28,29,41,57 Thus, in order to get more suitable and favorable adsorption configurations of the studied inhibitor molecules, MD simulations are carried out in this present investigation.

The first step of this investigation is the geometry optimization of the studied inhibitors, solvent molecules (H₂O) and corrosive hydronium ions (H₃O⁺). The geometry optimization was carried out by employing a ‘smart’ algorithm, starting with the steepest descent path followed by the conjugate gradient path and finally ending with the Newton’s method.⁴⁰ During the course of the geometry optimization process, the atomic coordinates were adjusted based on a COMPASS forcefield⁴⁷ until the total energy of the individual structure reached the minimum energy and afterwards a simulation box was created with all the concerned species. In this context, the simulation will be completed when the temperature and energy of the system reach equilibrium. It can be seen from Fig. 5 and 6 that in the middle of the simulation process the system tends towards equilibrium. After the system reaches equilibrium, the E_interaction and E_binding energies of the surface adsorbed inhibitor molecules are calculated according to eqn (4) and (5), respectively. The obtained E_interaction and E_binding values are tabulated in Table 8. The most favorable adsorption configurations of the inhibitor molecules over the Fe (1 1 0) surface are depicted in Fig. 7. It can be seen from this figure that the inhibitor molecules adsorb in an almost flat orientation with respect to the iron surface. This flat orientation can be explained in terms of the chemical bond formation between the inhibitors and the iron surface.

Fig. 5 The temperature equilibrium curve obtained from MD simulations for (a) 2-AB and (b) 3-AB at 298 K.

Fig. 6 Energy fluctuation curves obtained from MD simulations for (a) 2-AB and (b) 3-AB at 298 K.

Table 8 The output obtained from MD simulations for the adsorption of the inhibitors on the Fe (1 1 0) surface

Systems	Einteraction (kJ mol^−1)		Ebinding (kJ mol^−1)
	298 K	328 K	298 K	328 K
Fe + 2-AB	−347.30	−301.27	347.30	301.27
Fe + 3-AB	−361.88	−333.75	361.88	333.75

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Fig. 7 Equilibrium adsorption configurations of the inhibitors 2-AB (a and b) and 3-AB (c and d) on the Fe (1 1 0) surface at 298 K obtained from MD simulations. Top: top view, bottom: side view.

Generally, a bond distance within 3.5 Å indicates the formation of strong chemical bonds between the atoms and a bond distance above 3.5 Å signifies that the interactions between the atoms are of van der Waals type.^67,68 Fig. 7a and c show the shortest bond distances between the heteroatoms of the inhibitors and the Fe atoms. The measured shortest bond distances for the two inhibitors are as follows: 2-AB–Fe interaction: (Fe–N8 = 3.072 Å, Fe–N9 = 3.064 Å) and 3-AB–Fe interaction: (Fe–N8 = 3.331 Å, Fe–N9 = 3.262 Å). From the above-mentioned values it is seen that all the shortest bond distances are within the range of 3.5 Å, indicating that a chemical bond is formed between the inhibitor molecule and the Fe surface atom. Hence, chemical adsorption will occur on the Fe surfaces. Thus, it is further confirmed from MD simulations that the adsorption of the inhibitor molecules on the metallic surfaces mainly occurred via the chemical adsorption phenomenon.

Additionally, it can be seen (vide Table 8) that the calculated interaction energy values of the adsorption systems at 298 K are −347.30 and −361.88 kJ mol⁻¹, respectively. These larger negative values of the interaction energies can be ascribed to the strong interactions between the studied inhibitor molecules and the iron surfaces. Thus, the calculated interaction energy values reveal that 3-AB molecules adsorb on the iron surface more spontaneously than 2-AB molecules. Moreover, the adsorption ability of the molecule on the iron surface can also be measured from the binding energy values. The higher the binding energy, the more adsorption will occur. Thus, it can be seen from the interaction energy and binding energy values that the adsorption ability of the inhibitor molecules on the iron surface at 298 K follows the order: 3-AB > 2-AB. These outcomes are in good agreement with the results obtained from wet chemical experimentation.

In order to investigate the effect of temperature on the corrosion inhibition efficiencies of the inhibitor molecules, in this present investigation MD simulations were also carried out at 328 K. Here, we have increased the simulation temperature from 298 K to 328 K. The obtained temperature equilibrium curves, energy fluctuation curves and most favorable adsorption configurations of the inhibitors over an Fe (1 1 0) surface are depicted in Fig. S1–S3† respectively. The results reflect that (vide Table 8) with increasing temperature the adsorption energy and binding energy values of the inhibitor molecules on the Fe (1 1 0) surface decrease and we know that if the interaction energy and binding energy decrease, a lower inhibition efficiency is expected. From wet chemical analysis it is seen that when the temperature increases from 298 K to 328 K, the inhibition efficiency of the inhibitor molecules decreases. Therefore, the MD simulation results corroborated the experimental findings. As a result, MD simulations can also be used to predict the molecular behavior of the inhibitor molecules at a higher temperature range. Thus, it can be said in conclusion that these results are in good agreement with the results obtained from wet chemical experimentation as well as from quantum chemical calculations.

4. Conclusion

A combined theoretical analysis (classical and quantum chemical approaches) was performed to study the corrosion inhibition performance of two aminobenzonitrile compounds on a steel surface. It is evident from this investigation that purely theoretical studies can provide complete insight into the chemical reactivity of the studied inhibitor molecules. It also offers an atomic level investigation of the experimental findings. The following outcomes can be concluded from this study:

(i) Quantum chemical calculations reveal that the electron donation and electron acceptance capabilities of the studied inhibitors follow the order 3-AB > 2-AB, which is in good accordance with the results obtained from previously performed experiments.

(ii) The active sites of the studied inhibitor molecules are also thoroughly investigated using Fukui indices. Fukui indices describe in detail which particular atoms mainly participate for the electron donation and acceptance processes between the inhibitors and the Fe surface.

(iii) The molecular structure consideration has suggested that two different kinds of hydrogen bonding are formed for the studied inhibitor molecules. In 2-AB, intramolecular hydrogen bonding occurs, whereas intermolecular hydrogen bonding is present in 3-AB. These two different types of hydrogen bonding are responsible for the different inhibition efficiencies of the inibitors.

(iv) MD simulations reveal that all the shortest bond distances between the heteroatoms of the inhibitors and the Fe atoms lie within a range of 3.5 Å. It suggests that a chemical bond is formed between the inhibitors and the Fe atoms. Owing to chemical adsorption, the aminobenzonitrile inhibitors adsorb on the steel surfaces in a parallel orientation. The interaction energy and binding energy values of the two studied inhibitors also obey the order of 3-AB > 2-AB. These outcomes are in good accordance with the experimental findings.

In conclusion, the above-mentioned results obtained from two different domains starting from density functional theory (based on quantum chemistry) to MD simulations (based on classical physics) are in good agreement with the previously obtained experimental results. It can be concluded that DFT along with MD simulations may be a very powerful tool for the rational design of several promising corrosion inhibitors and for the prediction of their inhibition efficiencies well in advance.

Acknowledgements

Department of Science and Technology (DST), Govt of India sponsored Fast Track Project (vide ref. no. SB/FT/CS-003/2012 and project no. GAP-183112) is gratefully acknowledged for getting the computational infrastructure facility for carrying out the DFT and MD calculations. SKS would like to acknowledge the Department of Science and Technology (DST), New Delhi, India for his DST Inspire Fellowship.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available: Temperature equilibrium curves, energy fluctuation curves and equilibrium adsorption configurations of the studied inhibitors (at 328 K). See DOI: 10.1039/c5ra15173b

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