Monte Carlo and DFT calculations on the corrosion inhibition efficiency of some benzimide molecules

Calculations using density functional theory (DFT) and Monte Carlo methods were 9 performed on 2-methylbenzimidazole, 2-mercaptobenzimidazole, 2-aminobenzimidazole, benzotriazole, and benzimidazole to determine their corrosion inhibition efficiency. The molecular structure was optimized geometrically using DFT calculations at the B3LYP/6– 12 311 G++(d,p) and b2plypd3/aug-cc-pvdz basis set level in protonated and non-protonated species in gas and water. In this study, HOMO, LUMO, bandgap, ionization energy, electronegativity, hardness, softness, electrophilicity and nucleophilicity, electron transfer, 15 back donation energy and condensed Fukui indices are used to assess a molecule's local reactivity. Theoretical investigations can precisely establish the geometrical dimensions of a molecule and correctly explain the quantum properties of inhibitors. The mechanism of 18 interaction between inhibitors and metal surfaces in a specified molecule is studied using molecular dynamics. The benzimidazole functional groups absorbed energy linearly on metal surfaces, with quantum characteristics determined using density functional theory and 21 an ab initio technique. Importantly, the findings of this conceptual model are consistent with the corrosion inhibition efficiency of earlier experimental investigations.


INTRODUCTION
The oxide layer in metals causes structural deterioration. Corrosion conditions, such as hydrochloric acid and nitric acid, typically activate this reaction [1,2]. Corrosion is a complex process to overcome, and if left uncontrolled, it can cause high economic losses. As a result, 30 considerable research is already being conducted to identify corrosion inhibitors that are ecologically benign, inexpensive, and efficient [3,4]. Natural organic molecules have a strong potential for development as corrosion inhibitors. This molecule was chosen as a 33 corrosion inhibitor because it fits the requirements of high efficiency, low cost, environmental friendliness, non-toxicity, and no hazardous pollutants. Several experimental studies on the corrosion inhibition efficacy of organic product molecules have been conducted. Alkaloids 36 derived from natural products, for instance, have great potential as corrosion inhibitors. The main mechanisms that limit corrosion are related to electron acceptors, electrostatic interactions, electron donors, and heteroatom groups on inhibitor molecules. In the alkaloid 39 structure, heterocyclic benzene and heteroatom groups such as Nitrogen, Sulphur, Oxygen and heteroatoms perform roles as electron donors, electrostatic interactions, and the metal surface interactions with electron donor acceptors. The inhibitor will use these 42 characteristics to get securely adhered to the metal surface and build a thin coating that will prevent the pace of corrosion.
2-Methylbenzimidazole is a significant pharmacophore that is frequently utilized in 45 biomedical sciences to synthesize a variety of antibacterial and antifungal drugs. It can serve as a crucial precursor in the synthesis of substituted benzimidazole [5,6]. 2mercaptobenzimidazole is frequently utilized as a rubber accelerator and as an antioxidant 48 for rubber and plastics. 2-Mercaptobenzimidazole and its products are insecticides, and it is also a prominent analytical reagent for mercury, had been used to determine Cd(II), Cu (II) and Fe(II) metal ions in industrial wastewater samples and sewage water [7][8][9]. As 51 antibiofilm agents, 2-aminobenzimidazole and its derivatives have been produced. Several studies have shown that 2-aminobenzimidazole may selectively suppress and disperse Gram-positive and Gram-negative bacterial biofilms without affecting free germ cell growth. 54 A no microbicidal chemical that affects biofilm formation may be used as an additional ingredient in an antibiofilm approach. Because even if a chemical efficiently suppresses biofilm formation without killing the microbial cells, planktonic cells can attach to other sites 57 and form a biofilm. As a result, 2-aminobenzimidazole derivatives and antibiotics are effective against bacterial biofilms [10]. Benzimidazole and its derivatives are recognized as a major heterocyclic motif with several pharmacological uses, especially anti-diabetics, anti- cancer, anti-convulsant, antivirals, antifungals, anti-hypertensives and anti-HIVs [11].

Quantum chemical parameters:
Quantum chemical calculations have long been used to 111 study reaction processes. They have very effective tools for studying metal corrosion inhibition [21,22]. The electrostatics and spatial molecules of a corrosion inhibition efficiency are directly related to its performance, the relationships between quantum chemical 114 properties and inhibitory effect studied in this work. The calculation of quantum chemical parameters in corrosion inhibition investigations includes two basic characteristics: first, identifying the correlation between inhibitor molecular structure and inhibitory behavior; and 117 second, developing a hypothesized inhibition mechanism in terms of chemical reactivity of compounds [23]. In addition, quantum chemical descriptor variables were related to experimental values to explore inhibitor molecular reactivity. The frontier molecular orbitals capacity to receive electrons is indicated by a lower value of ELUMO, which will also improve 129 the adsorption of the inhibitor on the metal surface and therefore improve inhibition effectiveness [24]. As can be seen in Tables 1 and 3, the greatest value of EHUMO and the lowest value of ELUMO for the caffeine compound compared to other findings in gas phase 132 and solvent phase (water) show that 2-methylbenzimidazol has a higher inhibitory efficiency, which is consistent with the experimental result. 135 A c c e p t e d m a n u s c r i p t Gas phase Aqueous phase

Fig. 2. Bandgap and harness of selected inhibitors in gas and aqueous phase
The ionization energy of an element is the ability of materials to participate in chemical 138 processes that require ion creation or electron donation. It is also often connected to the type of chemical bonding in the elements' complexes [25]. The ionization potential of an inhibitor can be used to determine its reactivity. As displayed in Tables 1-4, a high ionization 141 potential value implies that the compound is very reactive, whereas a low ionization potential value suggests that the molecule is inactive. 2-amino benzimidazole has the highest corrosion inhibition efficiency.

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The frontier energy gap between EHOMO and ELUMO is an essential characteristic for inhibitor molecule adsorption on metallic surfaces. Lower energy differences improve inhibition efficiency and reactivity, because it takes less energy to remove an electron from the last  Nucleophilicity and electrophilicity are plausible quantum chemical variables for predicting molecule chemical behavior. These values can be used to evaluate inhibitor performance 168 [27]. It should be mentioned that a compound with a high electrophilicity value is useless for corrosion inhibition. In contrast, 2-mercaptobenzimidazol, which has a high nucleophilicity value, is an excellent corrosion inhibitor [28]. metallic bulk IP =EA [29]. When ΔN is less than 3.6, the capacity of the compounds (inhibitors) to donate electrons to the metal surface increases the inhibition efficiency. In our investigation, inhibition efficiency also increased as ΔN values increased [30]. Therefore,  A c c e p t e d m a n u s c r i p t   m a n u s c r i p t  processes [17,33]. The thermodynamic parameters are illustrated in Fig. 4. It was observed that entropy, heat capacity, and enthalpy increase as temperature rises. Whereas, free energy decreases with increasing temperatures. is the most reactive site for electrophilic attack for 2-mercaptobenzimidazole. A c c e p t e d m a n u s c r i p t    for all identified molecules. It is assumed that the more negative the atomic charges of the adsorbed center, the more readily the atom gives its electrons to the metal/metal oxide's empty orbital. interaction between a molecule inhibitor and a metal surface [37]. This method can illustrate one of the most important aspects of the corrosion problem: the adsorption phenomena.
The most stable adsorption sites are found on low-energy metal surfaces. In molecular 276 dynamics simulations done with the adsorption locator and the Forcite code, to determine a feasible position for the interaction between the inhibitor and the Fe surface provided in Material Studio 7.0 software [38].

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Using a Monte Carlo simulation, Fig. 6 depicts the most stable low-energy energy adsorption arrangement of inhibitors in the Fe (110) system of a typical energy (total energy, average total energy, van der Waals energy, electrostatic energy, and intermolecular energy. These 282 properties, which include structural, conformational, vibration and state equations, cohesive energy, and interaction energy for a wide range of organic metal molecules, metal oxides, and metal halides, make use of a variety of solid properties such as cell unit structure, lattice 285 energy, and even polymers [6]. The initial phase in this computer analysis is to optimize the shape of the inhibitor molecule, which will adsorb next on the iron surface with the least A c c e p t e d m a n u s c r i p t amount of energy [39]. The Forcite computation was completed with excellent estimation 288 accuracy utilizing the COMPASS forcefield for this reason [40]. As a result of using the Monte Carlo method, several properties were obtained such as total adsorption e, solid adsorption and deformation energies as shown in Table 17. The adsorption energy is the energy released during the adsorption process. The adsorption 294 energy, is ascribed to the energy produced by the flexible adsorption compounds placed on the substrate. The adsorption energies of the inhibitors are estimated by summing energy of solid adsorption and adsorbent structural deformation, as shown in Table 17. Higher

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A c c e p t e d m a n u s c r i p t negative adsorption energy values, as displayed in Fig. 7, indicate that the association between a metal and inhibitor molecules is more stable and stronger.  A c c e p t e d m a n u s c r i p t 2-methylbenzimidazol was the most efficient inhibitor for iron metal in gas and solvent 309 medium.
Our calculations using Fukui function predicted the nucleophilic and electrophilic attacking sites of the inhibitors. The results of quantum chemical computations and experimental 315 investigations were in a good agreement. m a n u s c r i p t m a n u s c r i p t