Understanding the interaction properties of an eco-friendly corrosion inhibitor on Zn (1 1 0) surface: Comprehensive DFT-based MD simulation

Regarding the deleterious effects of corrosion for a wide range of metals and alloys, many different techniques have been developed to protect the metals against corrosion. Utilizing organic inhibitors, especially those that contain heteroatoms and multiple bonds has been found an effective approach. In this research, the adsorption of a novel green inhibitor, Laurhydrazide N′-propan-3-one (LHP), on the Zn (110) surface was investigated using dispersion corrected DFT calculations. Interaction energy and electronic structures were calculated for different orientations of the inhibitor toward the Zn surface. The validity of calculated interaction energy has been veried by the MP2 level of theory. The AIM theory analysis revealed that LHP bound strongly to the Zn surface through its O active site and also its orientation affects greatly the interaction energy. Furthermore, diffusion of LHP through its O atoms active sites was observed with the state-of-the-art DFT-MD simulation during the simulation procedure that agrees well with the experiments for similar molecules adsorbed on the metal surfaces. The presented ndings afford a vital insight into the interactive nature of adsorbed inhibitors on metallic surfaces and will help to develop advanced functional materials in coating technologies.


Introduction
In general, the rst technical innovation and utilization of metallic zinc date back to the mid-13 th century.
Despite the fact that zinc has reasonable resistance against corrosion, distinct aggressive media such as aqueous/acidic (pH‹6)/alkaline (pH›12.5) solutions, atmospheric ambient and the circumstances implemented to accelerate the experiments, for instance, cyclic and spray tests, can create detrimental corrosion effects on the surface of zinc [22][23][24][25][26][27][28]. One of the well-established approaches for the protection of diverse metals against devastating corrosions is using chemical interaction inhibitors [29][30][31][32][33]. According to the literature, organic inhibitors, particularly those contain heteroatoms, namely, P, S, O, and N, and also multiple bonds, for example, C=C, N=N, C=O, C≡N, etc., are able to diminish the probability of corrosion and also protect the metal surface effectively [34][35][36][37]. The distinguished performance of this class of organic inhibitors could be ascribed to the adsorption of monomers on the surface of metals via aromatic rings, multiple bonds, and electron donor heteroatoms [38][39][40]. It is worth to point that the simultaneous presence of -bonding and heteroatoms within inhibitor structure can improve the protection ability of applied inhibitor through strong chemical or physical adsorption and forming a mono-/multilayer protective lm on the metal surface [41][42][43]. A great deal of investigations has been allocated to the corrosion inhibition behavior of amino acids for different metals and alloys [44][45][46][47][48]. Amino acids are a group of fundamental biomolecules that play a key role in building blocks of elemental substances including medicine and nutrition [49][50][51][52]. The primary structure of amino acids is mainly constructed from carboxyl (-COOH) and amino (-NH 2 ) groups [53,54]. Amino acids are also known as inexpensive, ecoenvironmentally friendly, simply producible corrosion inhibitor [55][56][57]. Badawy et al. studied about corrosion inhibition behavior of various amino acids to protect the surface of Cu-Ni alloys in neutral chloride media [58]. For this purpose, they utilized electrochemical technics and they found out that amongst several considered amino acids, cysteine exhibited the greatest inhibition e ciency. Ashassi-Sorkhabi and coworkers by taking advantage of potentiodynamic polarization assessed the inhibitory effects of three different amino acids for steel corrosion in acidic solutions [59]. They realized that the compounds can act as e cient inhibitors. Kaya  method [60]. The obtained results were compared to experimental counterparts and it was revealed that there is a favorable correlation between them. In the present research, the formation of a protective molecular layer of Laurhydrazide N′-propan-3-one (LHP) as a diamino acid on Zn (110) is comprehensively studied. The brilliant protective behavior of this environmental-friendly inhibitor has been already con rmed by a group of researchers using various experimental techniques [61]. Herein, for the rst time, the interactive nature and adsorption mechanism of the formed protective LHP layer on the surface of Zn (110) will be studied. For this aim, Density Functional Theory (DFT) was executed to conduct a precise investigation of the electronic and structural features of interacting molecular systems. Moreover, DFT-based molecular dynamic (MD) simulation was employed to model realistic molecular systems at ambient conditions. Our obtained results illuminate that LHP adsorbed strongly on the Zn surface and different orientations of LHP toward the Zn surface can greatly in uence the formation of a protective layer on the surface. Meanwhile, DFT-MD simulation showed that LHP diffused on the Zn surface at environmental conditions.

Computational Procedures
In order to scrutinize the possible formation of the protective layer and adsorption con gurations of LHP on the surface of Zn, ab initio DFT approach was carried out with SIESTA (Spanish Initiative for Electronic Simulations with Thousands of Atoms) simulation computer program [62,63]. All computational procedures with the SIESTA code were executed in a platform of generalized gradient approximation (GGA) considering Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional (GGA-PBE) [64] and Troullier-Martins pseudopotential for the description of exchange-correlation potential [65][66][67]. The SIESTA code is able to make intelligible the atomic cores of valence electrons by using localized numerical basis sets, periodic boundary conditions (PBCs), and norm-conserving nonlocal pseudopotentials. Furthermore, the Norm-conserving pseudopotentials were all meticulously assembled to de ne the interaction of valance electrons containing atomic cores [68,69]. In addition, for the valance wave function and also double-ζ basis sets, the localized atomic orbitals were implemented and cutoff energy of 200 Ry was considered for the studied systems.
Moreover, DFT-MD simulation was carried out too by utilizing SIESTA code and employing the dynamics approximation of Born-Oppenheimer to simulate the molecular systems. The interaction amongst ions and electrons was explained through the GGA-PBE model of the theory. In order to solve Newton's equations of motion, the Verlet algorithm was utilized. The NVT ensemble was ful lled by considering a Nosé-Hoover thermostat to retain the temperature at 300 K.
Furthermore, rst-principle computations were carried out by resorting to the DFT approach utilizing OpenMX code which stands for Open Source Package for Material eXplore. The OpenMX code is mainly founded on the norm-conserving pseudopotentials and linear combination of pseudo-atomic orbital (LCPAO) basis function through the local density approximation (LDA) [70]. Further, the pseudo-atomic orbitals were used as a basis set. The electron cores were explained by Kleinman-Bylander Pseudopotentials, norm-conserving Morrison, and also the GGA considering the PBE functional was implemented for correlation and exchange terms [67,71]. In order to evaluate the charge density in real space, the cutoff in kinetic energy was regulated 200 Ry for the grid integration. In furtherance of structural relaxation, till the net forces reach to 1 × 10 − 4 a.u, the rational function (RF) approach of quasinewton was performed. In this investigation, a supercell consisted of 110 zinc atoms is considered, and a periodic boundary condition (PBC) was enforced. The interaction energies (E int ) of the adsorbate, namely, LHP and Zn sheet as the substrate were measured via the following equation: In this equation, E (complex) , E (ads) and E (sub) represent the total energies of the studied complexes, adsorbates, and substrates, respectively. Moreover, the impact of the Basis Set Superposition Error (BSSE) in the calculation of the interaction energy was taken into account through the counterpoise correction (CP) approach [73] (δ BSSE term).
In all calculations, with both SIESTA and OpenMX codes, the long-range dispersion correction for nonbonding vdW interactions was considered investigated by the DFT-D2 method proposed by Grimme [72].
Moreover, the accuracy of the results achieved through the performed DFT-PBE method was evaluated by the second-order Møller-Plesset perturbation (MP2) level of theory. For this purpose, the triple-ζ valence plus polarization basis set without considering f orbitals (def2-TZVP(-f)) for light atoms described by Ahlrichs was enforced for geometrical optimization [74]. Besides, the theoretical model of def2-TZVP was used for electronic structures and total energy. Since transition metal exists in our fundamental structure, effective core potential (ECP) for Zn atoms was used [75,76]. The method of nucleus effective charge was applied for Zn atoms, too.
We also employed the theory of atoms in molecules (AIM) method to explore the interactive nature of interacting systems. Further details and discussions about the AIM theory can be found in the research literature [77][78][79]. To this object, the ORCA software was utilized to realize the wave-function engaged in the bonding survey at the DFT level of theory. Furthermore, the calculation of topological parameters and local features analysis of interacting molecules was performed by Multiwfn visualizer software [80].

Results And Discussions
In the rst step, all considered structures including the Zinc-based substrate which is supposed to be coated with the selected inhibitor, namely LHP, were meticulously optimized using DFT-D calculations. A supercell of 26.23 Å × 10.50 Å sheet containing two-atom-thickness and 110 Zn atoms were considered. The optimized structures indicated that in the Zn sheet the bonding distance between two vicinal Zn atoms is about 2.627 Å and the bond angle between two adjacent bonds was around 60° (See Fig. 1a). Besides, the difference between the two considered parallel layers of the Zn sheet was about 3.013 Å, as depicted in the gure (side-view). In the case of the optimized structure of LHP, the bonding distances and dihedral torsion between O-C-N-H were determined and presented in Fig. 1b. Our structural geometries data with DFT-D/PBE method for both considered systems has a desirable agreement with published reports [81][82][83][84].

Adsorption of LHP on Zn (110) surface
In order to investigate the adsorption behavior of LHP inhibitor on the Zn surface, two main con gurations were considered. Regarding the various active sites of our selected inhibitor and metal surface, in the rst con guration, LHP was located through one of its O atoms and the backbone of the inhibitor was perpendicular to the surface of the Zn sheet. In this con guration, the O atom either can be located above a single Zn atom (top-site) or above three Zn atoms (hollow-site). For the second con guration, the inhibitor was positioned so that both O atoms were approached to the Zn atoms and its backbone was paralleled to the surface. Three modeled orientations are shown in Fig. 1c-e.
Following the full structural relaxation of the whole system, the most stable complex was ascertained by calculating the interaction energies with the BSSE correction for all considered con gurations. The obtained data revealed that when LHP is parallel to the surface of the Zn sheet, the interaction energy is − 2.322 eV, while for other con gurations, namely, LHP is perpendicular to the Zn surface the interaction energy is about − 1.144 eV (Table 1). Therefore, the parallel orientation of LHP to the Zn surface results in better protection of the surface owing to the better coverage through strong adsorption between O and Zn atoms accompanied by the attraction of -CH 2 groups over the Zn atoms. In the rst con guration (perpendicular top-site), it was found that only a single O atom tends to interact with the Zn atom. The equilibrium distance of the O atom with the Zn atom is about 2.16 Å and the equilibrium distance of H atoms with the surface is about 2.39 Å. The relaxed structure of this con guration is depicted in Fig. 2a.
Moreover, for this con guration, the bonding distance of Zn-Zn was about 2.695 Å. In the case of the second con guration (parallel), the equilibrium distance of O and H atoms with Zn atom after relaxation were about 2.341 and 2.526 Å, respectively (Fig. 2b). The bonding distance of Zn-Zn near the O atom was 2.786 Å. Meanwhile, the calculated Zn…O distances was found to be almost larger than the sum of the covalent radii of O and Zn atoms (about 1.88 Å) and also seems to be rather larger than the reported covalent bond lengths for Zn-O (~ 1.9 Å) reported in the literature [85][86][87][88]. Accordingly, this bond is not likely to be typical of a net covalent bond and needs further clari cation by specialized analysis. The charge transfer analysis was performed through the Mulliken method and the attained data are presented in Table 1. It was found that when LHP is located in parallel to the Zn surface, a notable amount of electron (about 0.282 e) was transferred from LHP to the Zn surface. For the perpendicular orientation of LHP on the surface, the amount of 0.253 e was transferred. The aforementioned amount of interaction energy, bonding distance, and electron transfer between the substrate and LHP, all declare the chemisorption nature of interaction [89][90][91][92][93][94].
To further elucidate the interactive nature of adsorbed inhibitor the long-range dispersion forces that play a signi cant role in the stability of such molecular systems [67,68] was investigated. The exact description of non-local dispersion forces has been discerned as a major challenge for molecular systems due to the required great degree of electron correlations to be accounted for. Thanks to unparalleled endeavors by Grimme, it is a reasonable route to supplement empirical corrections to the energy of Kohn-Sham and take account of the dispersion forces for quantum mechanics methods. Our obtained PBE-D results indicate that adsorbed LHP molecule on the Zn surface for energetically con guration experience dispersion forces of − 31.935 eV. However, these forces for perpendicular orientation were estimated to be − 30.661 eV as the consequence of the characteristic differences amongst the con guration of adsorbed molecules. From the obtained values for dispersion interactions, it was found that these forces play a signi cant role in LHP adsorption onto the Zn surface. In other words, it is obvious that dispersion forces make a strong impact on the adsorption and stability of such inhibitors on the metal surface.
We next evaluate the validity of the employed DFT-D2/PBE method in explaining the interaction of LHP with the surface of Zn through benchmark calculation using the second-order Møller-Plesset perturbation (MP2) level of theory. In this regard, a cluster of Zn atoms consisted of seven Zn atoms was considered (Fig. 2c) and the corresponding interaction energy of the LHP-Zn system was calculated. First, we have performed full structural relaxation of the modeled cluster system and then the interaction energy was calculated with the BSSE correction through both above-mentioned methods. It was found the E int about − 0.453 eV according to the data attained via DFT-D2/PBE method whilst the interaction energy through the MP2 method was calculated about − 0.317 eV. We found that the MP2 outcome con rms the PBE counterpart and both interaction energies for this con guration were in suitable agreement.

Interactive nature of LHP/Zn system
It was found from interaction energies with DFT-D calculations that the interactive nature of LHP with Zn surface is strong and estimated to be typical for the chemisorption. However, the type of interactions should be further evaluated to precisely clarify the interaction properties of the system under investigation. To this aim, the total electron density plots of the LHP-Zn system (cluster model) were calculated within the MP2 method and demonstrated in Fig. 2d. It can be observed from the obtained maps that there is a small charge accumulation in the interacting area between O and Zn atoms. This small electron density in the LHP-Zn interface can be attributed to a minor covalent bonding between adsorbed molecules on the surface which needs to be evaluated by further analysis such as the AIM theory scheme.
We next give deeper insight into the interactive nature of involved bonds in the complex through the AIM analysis ful lled by the DFT method for the cluster system. The electronic charge density (ρ(r)) as well as Laplacian (∇ 2 ρ(r)) and energy densities H(r) were calculated and reported in Table 2. Also, the bond critical points (BCPs) for the relaxed structure of the LHP-Zn cluster system were estimated and represented in Fig. 2e. For comparison, the BCPs have been estimated for Zn-Zn bond, and the data are listed in the table. As it was found, similar trends were observed for ∇ 2 ρ and H(r) values that demonstrate the same type of bonding between Zn…Zn atoms in the metal system (highly polar/partly covalent). Furthermore, the proportion of G(r)/V(r) that categorized in three levels (0.1-0.5: covalent bond, 0.5-1: polar covalent bond and > 1: electrostatic bond) reveals that both Zn…O and Zn…Zn bonds are classi ed as a polar covalent bond with G(r)/V(r) ratio between 0.5-1 (0.727 and 0.924, respectively). For validation and comparison, the related value of BCPs for a C − C bond in LHP was measured, and the achieved outcomes showed negative values for ∇ 2 ρ and H(r), as listed in Table 2. These parameters indicate that exists a covalent bond between carbon atoms in LHP [95]. From the value estimated for G(r)/V(r), 0.229, one can also predict a covalent bond between the neighbor nuclei.  In continue, DFT-MD simulation was implemented to simulate a realistic system comprised of Zn (110) and LHP inhibitor at environmental conditions. For this objective, the most stable con guration with a stronger interaction energy of the LHP-Zn system (parallel orientation) was considered. Through plotting the total energy of the whole system vs. simulation time step the stability of LHP-Zn was assessed (See Fig. 3a). This plot exhibited that at the initial steps of MD simulation a noticeable decrease in uctuation occurs at constant values about − 193945.77 eV from 200 fs which exhibits steady stability of the systems after this duration of the simulation. Regarding the outcomes of the DFT-MD simulation, the uctuation of temperature related to the system occurred at about 300 K. This temperature explains the equilibrium circumstance within simulation time steps (Fig. 3b).
The achieved data indicated that LHP moved toward the Zn surface about 1.58 Å during the simulation procedure (the initial distance between the Zn surface and LHP molecule was considered about 5.0 Å), as depicted in Fig. 3c. The observed movement could be further explained through the plots of the distance of Zn…O against the time steps of the simulation. It was found that when LHP has approached in parallel to the Zn atoms, in the rst steps of the simulation, the initial distance of Zn number 88 (Zn:88) with O atom number 145 (O:145) was about 5 Å (See Fig. 3d). After 250 fs, this distance notably decreased and reached about 2.2 Å.
It was also found that adsorbed LHP diffused on the Zn surface during the simulation time procedure as demonstrated in Fig. 3e. After LHP adsorption on the Zn surface, an increase in distance of Zn…O was observed and in 500 fs, the distance was about 4.1 Å. However, after 500 fs the distance of Zn:88 decreased to about 2 Å, it had an almost stable nuance until 3000 fs and the average distance of Zn:88 with O atom was about 2.5 Å. At about 3000 fs an incredible increase occurred and the distance of Zn…O acceded about 3 Å. From the range of 3500-4000 fs, the distance was increased and at about 4000 fs, the O:145 atom shifted toward the vicinal Zn:96 (see Fig. 3f). The initial distance of the Zn:96 and O:145 atoms was about 6 Å. After 500 fs the distance decreased to 3.8 Å. From the range of 500 fs to 1500 fs, the distance increased, and at the time step of 1500-4500 fs, the Zn…O distance faced a gradual decline.
The nal distance of Zn and O atoms was found about 2.8 Å. The schematic structure of Zn atoms in the exposure of O atoms of LHP is shown in Fig. 3d. A similar trend for Zn:97 and O:139 was surveyed.
According to the results of the DFT-MD simulation, when LHP has approached the surface of the Zn sheet the initial distance of Zn and O was about 4.8 Å (Fig. 3g). This distance experienced a remarkable decrease and reached about 2 Å at 480 fs. After a slight increase from 500-1000 fs, the distance increased, and it was almost stable until 2800 fs. However, it had a sudden decrease in 2000 fs. From the range of 2700-4100 fs the distance of Zn…O gradually decreased and reached to 4 Å. After that, the O atom shifted toward Zn:112 (Fig. 3h). The initial distance of Zn and O was 6.3 Å. Except for two important increases at 1500 and 2500 fs, the whole trend of this plot was declining. The nal distance of Zn and O was about 2.8 Å.
It should be mentioned that the diffusion of adsorbed molecules on the various metallic surfaces has been observed and reported in detail in the literature [96][97][98][99][100]. For examples, diffusion of large molecules such as acetylene on Pd [96] and Cu [97] surfaces, PVBA on Pd [98], and also aromatic compounds decacyclene (DC) and hexatert-butyl decacyclene (HtBDC) on Cu [99], azobenzene on Cu [100] surface investigated with obtaining sequences of time-resolved STM.
Furthermore, in Fig. 3k, the plot for the angle between C-C-C (C:135, C:138, and C:142) vs. time step can be seen. According to this plot, it was apperceived that when LHP was located in parallel to Zn atoms, the initial C-C-C angle was 120°. After 350 fs the angle decreased to 150° and then, it immediately increased to 130°. From the range of 500-1000 fs, a decrease occurred and at 1000 fs the angle of C-C-C was about 110°. The same increasing and decreasing trend were repeated until 3000 fs and after this time steps, the trend was completely decreasing. At about 4200 fs the angle of C-C-C bonding reached 110°. As a consequence, LHP could be adsorbed strongly on the Zn surface through its O active site as well as -CH groups, though it was diffused on the surface.

Conclusion
This research was earmarked to the investigation of the behavior of Laurhydrazide N′-propan-3-one (LHP) as an e cient organic inhibitor on Zn (110) sheet by using DFT-MD simulation. In the rst step, all considered structures, namely, two parallel layers of Zn sheet and LHP were optimized by the framework of the DFT-D2 method. Two distinct con gurations were assigned to assess the interaction of LHP with a metallic substrate. In the rst con guration, a molecule of LHP perpendicularly approached the Zn sheet through its O atom as an active site. In this con guration, the O atom was able to be located either on one single Zn atom (top site) or among four Zn atoms (hollow site). In the second con guration, the LHP molecule was approached in parallel toward the Zn sheet. Interaction energy for both con gurations was calculated and it was revealed that when LHP has approached in parallel, creates a more stable con guration with an interaction energy of about − 2.322 eV compared to the rst con guration with an energy of about − 1.144 eV. The parallel orientation of LHP toward the Zn sheet was predicted to cover and consequently protect the surface e ciently. In continue, a realistic system comprised of Zn(110) and the most stable con guration of LHP was simulated using the state-of-the-art DFT-MD method. It was shown that as a result of approaching the LHP, an obvious uctuation on total energy and bonding distance of Zn…O was observed during simulation time steps. Further, it was deduced that uctuation in energy could result in the diffusion of LHP on the surface. In a way that after about 4500 fs of simulation duration, one O atom shifted from a close neighbor Zn atom to a further Zn atom. The same trend was also observed for the second O atom and adjacent Zn atoms during the simulation time. In the last part, the calculated adsorption for the most stable con guration was validated by the MP2 level of theory. Our DFT-MD simulation ndings meet the goal of the punishment to develop new materials and devices applicable to future coating and corrosion technologies. At the molecular scale, the edge of knowledge between chemistry and physics presented here, provide deep insight into the recent challenges about the interactive nature of inhibitor compounds adsorbed on the metallic surface.