DFT, Monte Carlo and molecular dynamics simulations for the prediction of corrosion inhibition efficiency of novel pyrazolylnucleosides on Cu(111) surface in acidic media

Five novel pyrazolylnucleosides have been evaluated theoretically for their corrosion inhibition efficiency on the Cu(111) surface in acidic media. DFT calculations were carried out to exhibit the intrinsic properties such as lowest unoccupied (ELUMO) and highest occupied (EHOMO) molecular orbital energies, as well as energy gap (∆E), chemical hardness (η), chemical softness (σ), electronegativity (χ), electrophilicity (ω) and nucleophilicity (ε). The theoretical FT-IR spectra were recorded to indicate the presence of the specific bonds in the studied molecules. The surface interactions between the inhibitor molecules and the metal surface were investigated using molecular dynamics simulations and Monte Carlo (MC) simulations. As a result, we have found that the inhibitor pyrazolylnucleosides 5a–e have strong interactions with Cu(111) surface, and therefore have excellent predictive inhibition power against copper corrosion.


Results and discussion
DFT results. The synthesis of the novel pyrazolylnucleosides 5a-e used in the present study has been reported earlier by our Groups 17 . The inhibitory efficiency of the pyrazolylnucleosides 5a-e ( Fig. 1) has been studied by finding out the local parameters and quantifying the global parameters such as chemical hardness (η), softness (σ), electronegativity (χ), electrophilicity (ω) and nucleophilicity (ε). The protection abilities of these inhibitors have been evaluated based on the understanding of the distinctive and determining factors involved in their inhibitory capacities. The optimized structures of the pyrazolylnucleosides are presented in Fig. 2. Figure S1 illustrates the labeled model. Using density functional theory (DFT) calculations, these geometric structures were established using the Dmol 3 software (Biovia). Optimization of the structure is a specific preliminary procedure that allows for a complete study of the reactivity of the inhibitors to interpret their effectiveness. In our approach, the optimized structures of the pyrazolylnucleosides 5a-e were achieved by using the double numerical polarization basis set (DND) in combination with the M-11L functions within GGA.
Optimized structures were further subjected to the quantum chemical calculations in order to describe local properties such as the frontier molecular orbital (FMO) density distributions, i.e., the HOMO and the LUMO which, as presented in the discussion to follow, allowed us to determine the global parameters 49 . These studies collectively helped us to obtain insight into the inhibition mechanisms of these pyrazolylnucleosides towards the Cu(111) surface by examining the structure-reactivity correlation 49 . Figures 3 and 4 show, respectively, the density distributions in frontier molecular orbitals, i.e. the HOMO and the LUMO; both HOMOs and LUMOs distributions are marked by inequality in all of the molecules. These results indicate that the pyrazolylnucleoside molecules possess active sites through which they can react with the metallic surface 50 . This finding could be explained by the fact that HOMOs are often associated with the ability to give electrons by inhibitor molecules to a suitable acceptor such as surface atoms to be protected from corrosion 51,52 , this could be explained later by the high values of E HOMO energies which are indicative of the tendency of the molecule to donate an electron. Further, we have noticed that HOMOs and LUMOs distributions of these five pyrazolylnucleosides were concentrated preferentially within the structure around nitrogen (N) atoms and with a similar degree also around the oxygen (O) atoms despite their presence in several sites. This finding indicates that the reactions of these molecules with the surface Cu(111) will presumably take place through the  53,54 . Donor sites, as we reported previously, are the suitable sites for molecules preferentially bonded with positively polarized anodic reaction sites as with copper surface Cu(111) in acid media [55][56][57] , thereby reducing the migration of corrosive species onto the copper surface, which reflects a decreased rate of anodic copper dissolution reaction 58 . LUMO distribution depicts acceptor parts of the molecules 59 ; this could explain the possibility of an interaction (adsorption) of the inhibitor molecules through its acceptor atoms on the metallic surface, often having a positive charge as mentioned previously [55][56][57] .
Electrostatic potential maps (ESP). By convention, the ESP map is related to nucleophilic and electrophilic activity sites in molecules; the red refers to the negative region while the green and blue ones refer to the positive region. As evidenced in Fig. 5, all of the red to yellow regions were distributed in negatively charged groups with heteroatoms, such as O, N atoms and around a few carbon atoms on their side or O-heterocyclic and N-heterocyclic rings 60,61 . The ESP maps reveal the reactive sites of inhibitors; in the case of pyrazolylnucleosides, oxygen and nitrogen atoms are shown to be the main adsorption sites. Therefore, it makes reasonable sense to consider that the pyrazolylnucleosides inhibitors contain several adsorption sites which are distinguished from each other predominantly by the N, O atoms.
Mulliken charges. Table 1 lists the charges of C, Br, N, O, F, Cl atoms of the five studied pyrazolylnucleosides inhibitors. Many studies indicate a correlation between the corrosion inhibition efficiency of an inhibitor and its Mulliken charges 48,60,62-64 . It has been previously shown that atoms bearing most negative charges will share electrons more easily with the unoccupied orbital of the metal surface atoms with which they react 65 .
Besides, such studies have indicated that the reactivity of these atom sites increases as the absolute value of charge density increases [66][67][68] . Consequently, the atoms that carry a pronounced negative charge in the pyrazolylnucleosides 5a-e act probably as the active sites, through which these inhibitors adsorb onto the metallic surface Cu(111), the surface under studies in the present work. Indeed, the obtained results conclusively show that the negative charges concentrated on atoms like O, N, F, Br and Cl are the active sites in the five pyrazolylnucleosides as highlighted in Fig. 5 showing the charge distribution over the entire structures of the inhibitors under study.
Vibrational spectroscopy. Figure 6 shows the vibrational spectra using an FT-IR spectrometer for the compounds 5a-e. As shown in Fig. 6, the appearance of the characteristic bands of the base molecules was observed 69,70 which confirmed their structures.

Monte Carlo simulations.
In the present study, the pyrazolylnucleosides 5a-e are present in the proto-  Fig. 7. Further, in the side view pictures shown in Fig. 8, the pyrazolylnucleosides 5a, 5c and 5e look parallel to the Cu(111) surface and the pyrazolylnucleosides 5b and 5d are seen as quasi-parallel to the metal surface. This may be due to the differences between the sizes and www.nature.com/scientificreports/ the extents of their −I or +I effects of the five substituents (CH 3 , OCH 3 , F, Cl and Br) [71][72][73][74] . These MC simulations, as seen in the later discussion are quite useful in understanding the detailed mechanism of adsorption behavior of these inhibitors on the Cu(111) surface. In order to demonstrate and confirm the equilibration of the systems, the correlation between the stable mean values of temperature and energy fluctuation was studied 43 . Figure 9 shows thermal fluctuations of the pyrazolylnucleosides 5a-e, according to simulation time.

Molecular dynamics (MD) calculations.
To explain the interactions between the studied surface of copper and the active sites of the pyrazolylnucleosides 5a-e, we launched the MD simulations in a system containing 600 water molecules and one molecule of each of the five inhibitors on the Cu(111) surface 43,75 ; the visual simulations showed the corresponding adsorption mechanism of the pyrazolylnucleoside derivatives on the copper surface to gain a deeper understanding of the interaction between each inhibitor and Cu(111) surface. The results presented in Figs. 10 and 11 show, respectively, the top and side views of the realistic simulations 76,77 of the pyrazolylnucleosides 5a-e on the studied copper surface Cu(111) at equilibrium in the aqueous phase. All of the novel five inhibitors 5a-e adsorb tightly onto the copper surface with a parallel orientation, more particularly the inhibitor 5e, which appears close and parallel with the Cu(111) surface. It is entirely consistent with the previous results shown earlier by Monte Carlo simulations. This positioning is facilitated by the formation of bonds between the inhibitor and copper surface, formed through the sharing of p electrons from the active donor sites of the inhibitor pyrazolylnucleosides to the vacant orbitals of the positively charged copper surface 78 . www.nature.com/scientificreports/ The adsorption of the inhibitor by adopting parallel placement of the inhibitor molecule and the Cu(111) surface explains how an inhibitor can minimize the contact area between corrosive elements and surface of Cu(111) in a corrosive environment 79 , in addition to the distinction between studied inhibitors according to the predictive efficacy. The different energies of the studied inhibitor molecules 5a-e and Cu(111) substrate have been calculated and are summarized in the Tables S1, S2, S3, S4 and S5 (supporting informations). We have taken into account other corrosive species such as H 3 O + , Cl − and H 2 O present in the environment in these calculations 80,81 . The output data determined via this simulation method gives the total energy (symbolized as E tot ), which equals the sum of the internal and the adsorption energies of the inhibitor as an adsorbate on the metallic surface 82 . The total energy can be envisaged to correlate the reactivity of the inhibitor and we noticed that the pyrazolylnucleosides 5a-e are quite stable since their energies are small, not exceeding − 7.21 E +03 . The average of all the total energies calculated was found to be − 7.23 E +03 . Adsorption energy (E ads ) is the energy released when an inhibitor molecule (adsorbate) attaches to the metal surface Cu(111) (substrate), and includes the rigid adsorption energy and the deformation energy 83 . The adsorption energy refers to the energy released during the adsorption of the inhibitor on the Cu(111) surface in its stable state (also called the geometric optimization step), and the deformation energy is that released when the adsorbed inhibitor is released from the Cu(111) surface. It can be seen from the   it is not possible to predict the inhibitory power of a molecule accurately from its adsorption energy alone; other elements also contribute in determining the effectiveness of an inhibitor, one of them being the desorption energy (dE ads /dN i ). These results can help in picking efficient inhibitors against corrosion of any metallic surface in a corrosive environment combining the two factors viz. the adsorption energy and the desorption energy. Also, one can predict the inhibitory efficacy of the inhibitors as these studies help in classifying them according to their effectiveness against corrosion of Cu(111) surface; we conclude from these results that the effectiveness of the pyrazolylnucleoside inhibitors under study follows the order: 5e > 5b > 5a > 5c > 5d. www.nature.com/scientificreports/ To further confirm our results, we have performed the energy fluctuation curves as obtained from MD simulations; the equilibration of the system is confirmed by the stable mean values of energy fluctuations, as shown in Fig. 12.
The pair correlation function quantifies how other particles surround the particle of interest (or the targeted atom); based on this, we have used the radial distribution function (RDF) to estimate the length of the bond g(r) [86][87][88] . Knowing that the peak between 1 and 3.5 Å corresponds to chemisorption and that physisorption is  www.nature.com/scientificreports/ associated with peaks greater than 3.5Å24, we have carried out RDF calculations as shown in Fig. 13a,b, respectively, for the RDF O and RDF N. The optimal short distances between the probable active sites of the studied inhibitors 5a-e and the copper(111) surface atoms were: length of the bond of Cu\\O (2.85 to 3.36 Å) and Cu\\N (3.16 to 3.40 Å) which are less than 3.5 Å. The obtained RDF results show that the five pyrazolylnucleoside inhibitors have a great capacity to adsorb on Cu(111) surface, and subsequently protect it from dissolution 89,90 .

Mechanism of adsorption and inhibition.
We have worked out a simple approach to explain the reaction of the inhibitor molecules 5a-e and the surface of copper, which is positively charged; interactions of organic inhibitors with metal surfaces involve donor-acceptor interactions [91][92][93] . Figure 14 illustrates the adsorption mechanism of the organic corrosion inhibitors 5a-e on the copper metal surface in the acidic medium (1 M HCl). The metallic element Cu undergoes rapid oxidation due to the aggressive environment that makes the metal surface positively charged, which in turn favors the fixation of negatively charged counter chloride ions resulting in a negative metallic surface. As shown in Fig. 14, neutral nitrogen atoms of the five-membered pyrazole rings of the inhibitor molecules 5a-e get protonated in the acidic solution according to the following reaction: The protonated inhibitor molecules bind to the negatively charged metal surface through attractive electrostatic forces. In parallel, the lone pair electrons of the -CN moiety, the non-protonated pyrazole ring nitrogen atom and the oxygen atom of the sugar moiety of the inhibitor molecules, as well as the π-electrons of the benzene ring, could supply electrons to the vacant d-orbitals of the Cu atoms which leads to the phenomenon of chemisorption and retro-donation, respectively 94,95 . However, this type of electron transfer causes electrons to accumulate in the d-orbitals of the metal atoms resulting in inter-electron repulsions. In order to avoid this repulsion phenomenon, a reverse transfer of electrons takes place from the d-orbitals of the surface metal atoms to the unoccupied molecular orbitals of the inhibitor molecules (retro-donation), thus reinforcing the adsorption of the inhibitor molecules on the metal surface.
Consequently, it can be expected that the adsorption of different inhibitor molecules on the metal surface of copper in an aggressive acidic solution (1 M HCl) happens by three types of phenomena: physisorption, chemisorption and retro-donation. Furthermore, theoretical studies presented here show a good correlation with electrochemical studies, which show that these inhibitors have high metal corrosion inhibition performance. The presence of electron-donating mesomeric substituents -OCH 3 , Cl, Br and F further enhances the inhibitory efficacy of the pyrazolylnucleosides 5a-e against copper corrosion.

Conclusion
The inhibitory effects of five novel pyrazolylnucleosides have been evaluated theoretically against corrosion of copper surface in an acidic environment. Density functional theory (DFT) calculations were carried out to exhibit their intrinsic properties and reactivities. We used molecular dynamics simulation to describe the different probable interactions such as van der Waals and electrostatic interactions between the inhibitors 5a-e and Cu(111) surface. The following conclusions can be drawn from the results: 1. Molecular dynamic simulations show that the inhibitor pyrazolylnucleosides 5a-e have strong interactions with Cu(111) surface. 2. Molecular quantum chemical calculations showed that the reactive sites in the inhibitors 5a-e are mainly the N-atoms and O-atoms. 3. Based on the analysis of the different outputs, we have suggested a probable reaction mechanism for the binding of the pyrazolylnucleosides 5a-e at the Cu(111) surface. 4. A combination of adsorption energy (E ads ) and the desorption energy (dE ads /dN i ) values helps in determining the effectiveness of the pyrazolylnucleosides 5a-e against corrosion of Cu(111) surface. 5. Molecular dynamic simulations reveal that the effectiveness of these inhibitors follows the order: 5e > 5b > 5a > 5c > 5d. www.nature.com/scientificreports/