Electrochemical and Quantum Chemical Studies on Corrosion Inhibition Performance of 2,2’-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] on Mild Steel Corrosion in 1M HCl Solution

The inhibitory effect of Oxethazaine drug, 2,2’-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] on corrosion of mild steel in 1M HCl solution was studied by weight loss measurements, electrochemical impedance spectroscopy and potentiodynamic polarization methods. The results of gravimetric and electrochemical methods demonstrated that the inhibition efficiency increased with an increase in inhibitor concentration in 1M HCl solution. The results from electrochemical impedance spectroscopy proved that the inhibition action of this drug was due to adsorption on the metal surface. Potentiodynamic polarization studies revealed that the molecule was a mixed type inhibitor. The adsorption of the molecule on the metal surface was found to obey Langmuir Adsorption isotherm. Potential of zero charge at the metal-solution interface was measured to provide the inhibition mechanism. The temperature dependence of the corrosion rate was also studied in the temperature range from 30 to 50 °C. Quantum chemical calculations were applied to correlate electronic structure parameters of the drug with its inhibition performance. The obtained theoretical results have been adapted with the experimental experimental results and theoretical structural parameters of inhibitor molecule. The present with the corrosion inhibition nature of Oxethazaine drug, 2,2’-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] in the acid medium utilizing; weight loss measurements, the polarization method and electrochemical impedance spectroscopy (EIS). to Quantum calculations the


Introduction
The surface of iron and steel, existing in many forms ranging from exposed metal to oxidized to different degrees, finds many industrial applications [1][2][3] . Recent investigations have emphasized the importance for the protection of the metal surfaces in various applications. The spontaneous destruction of metals, starting from their surfaces, due to the corrosive attack of environment brings the undesirable changes at the surfaces and reduces their lifetime, strength and changes the desirable properties of surfaces. In some cases the corrosion products formed are toxic. An accurate description of surface not only helps to identify the prevailing form of corrosion but also the prescription of appropriate anti-corrosion measures. Acid solutions, in general HCl solutions are widely used in industries for many purposes, such as acid pickling, industrial acid cleaning, acid descaling and oil well acidizing [4][5][6][7] . Due to the general aggressive nature of acid solutions, the corrosive attack will be severe 4 and bring undesirable changes at the surface of metals. Chemical inhibitors are often used to control the corrosive attack and acid consumptions of environment 8,9 . Most of the well-known acid corrosion inhibitors are the organic compound containing N,S,O and P atoms 10,11 . These organic compounds reduce the metal dissolution by the absorption on the metal surfaces 12 . The adsorption and inhibition efficiency of these compounds greatly depend on the electron density around the hetero atoms, the number of adsorption active centers in the molecule and their surface charge density, molecular size, mode of adsorption and formation of metallic complexes [10][11][12][13][14][15][16][17][18][19][20][21] . However, the choice of inhibitors are based on the two considerations, first economic consideration and second the presence of the electronegative atoms such as N,O in the relatively long compounds. Thermodynamic model is an important tool used for analyzing the corrosion inhibition mechanism of inhibitors and their adsorption on the metal surface 14,15 . Using the type of adsorption isotherm that the molecule follows for the adsorption on mild steel surface, the values of thermodynamic parameters such as adsorption equilibrium constant (K ads ) and free energy change of adsorption(ΔG ads ) can be calculated and used for predicting the adsorption and inhibition mechanism.
Many authors generally agree that drugs are the good corrosion inhibitors that can complete favorably with green corrosion inhibitor. Moreover, most drugs can be synthesized from natural products. The reasons for using drugs as corrosion inhibitors are ;(1) drug molecule contains oxygen, nitrogen and sulphur as active centers, (2) drugs are reported environmentally friendly and important in biological reactions 22,23 . In modern scenario, development of novel biodegradable and less toxic corrosion inhibitors is gaining importance. Biologically active molecules like sulfadimidine, sulfamethoxazole, cefatrexyl, *e-mail: danaee@put.ac.ir apart from other antibacterial and antifungal drugs have been reported as good corrosion inhibitors [24][25][26] . The use of drugs as corrosion inhibitors for metals in different aggressive environments is widely reported. These include the use of sulpha drugs 27,28 , antimalerial drugs 29 and analgesic drugs 30 as efficient corrosion inhibitors for metals in various media. Moreover, many expired drugs have been reported to be very effective corrosion inhibitors for the protection of mild steel in acidic media [31][32][33][34][35][36] . This area of research is much important because in addition to being environmentally friendly and ecologically acceptable, expired pharmaceutical drugs are inexpensive, readily available and prevent pollution. On the other hand, deactivation of this expired drug is generally carried out with the risk of air pollution with toxic compounds containing N, S, P or halogen atoms. The expiry date is merely an assurance from the manufacturer that the drug is expected to retain at least 90% of its original efficacy up to that time and its active substance degrades only negligibly. This type of research can solve two major environmental and economical problems: limitation of environmental pollution with pharmaceutically compounds and reduction of the disposal costs of expired drugs. Thus, this area would give effective nonhazardous alternatives to toxic corrosion inhibitors.
Recently, the research activities are centered on the development of cheaper and greener corrosion inhibitors. In this context, the application of expired drugs as corrosion inhibitors can satisfy both environmental and economic provisos of green chemistry. Dohare et al. on 2017 have used expired Tramadol drug as inhibitor for mild steel corrosion in hydrochloric acid 35 . They employed DFT and experimental studies on the inhibition potentials of expired drug and the inhibition efficiency about 96% was achieved. Anaee et al. on 2019 studied expired Etoricoxib as a corrosion inhibitor for steel in acidic solution 36 . Expired Etoricoxib indicated high inhibition efficiency in different temperatures.
Density functional theory (DFT) has become a useful theoretical method to interpret the experimental results, enabling one to obtain various structural parameters, even the inhibitor is a larger complex molecule, i.e. DFT links some traditional empirical concepts with quantum mechanical results 37,38 . Therefore, DFT is a connecting bridge between the experimental results and theoretical structural parameters of inhibitor molecule.
The present work deals with the corrosion inhibition nature of Oxethazaine drug, 2,2'-(2-Hydroxyethylimino)bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] in the acid medium utilizing; weight loss measurements, the polarization method and electrochemical impedance spectroscopy (EIS). Potential of charge (PZC) was also determined to establish the inhibition mechanism. Quantum chemical calculations have been performed, and several quantum chemical indices are calculated and correlated with the corrosion inhibition nature of the inhibitor in 1 M HCl medium.

Materials
Mild steel specimens of dimensions 2.5 cm×1.0 cm ×0.1cm with a composition 0.087% C,0.039%mn, 0.03%P,0.02%S and rest iron were used for weight loss studies. The specimens were mechanically polished using emery sheets of grade 1/0, 2/0, 3/0, 4/0, and 5/0 and thoroughly washed with double distilled water. Finally the specimens were degreased with acetone and dried. A Teflon coated cylindrical mild steel rod, having an exposed area of 0.02826 cm 2 , with previously mentioned composition was used for electrochemical studies. Solutions of 1 M HCl with and without inhibitor were prepared from A.R. grade reagents using double distilled water. 3% ethanol by volume was added for solubility reasons. The inhibitor purchased from Guide Chem (Analytical Grade), was used as received without further purification. The structure of the inhibitor molecule is shown in Figure 1.

Weight loss measurements
Weight loss measurements were carried out according to the American Society for testing and Materials (ASTM) standard procedure G 31-72. The mild steel specimens in triplicate were immersed for the period of 2 hours in 100 mL of corrosive media with and without the inhibitor at room temperature (300±1 K). The average weight loss of these specimens was used to calculate the inhibition efficiency employing the formula: where W and W´ represent the weight losses in the uninhibited and inhibited solutions respectively. The relative difference between the replica experiments was found to be less than 3% at room temperature, which shows a good reproducibility.

Electrochemical measurements
The impedance measurements were performed using a computer-controlled potentiostat (model Solartron ECI-1286) and the data were analyzed using frequency response analyzer (Solartron FRA-1286). A three electrode set up was used for the electrochemical impedance measurements with a Pt counter electrode and a saturated calomel electrode (SCE) as the reference electrode. A Teflon coated mild steel cylinder, with surface prepared as described in the weight loss experimental method, served as the working electrode. The measurements were carried out in the frequency range 100 kHz to 0.01 Hz at the open circuit potential by super imposing a sinusoidal AC signal of small amplitude (10 mV). The time interval of 25-30 minutes was given for steady state attainment of open circuit potential. The electrochemical impedance parameters such as double layer capacitance (C dl ) and polarization resistance (R p ) were obtained from the Nyquist plots as described elsewhere. The potentiodynamic polarization curves were recorded after carrying out the electrochemical impedance measurements, using the same cell setup employed in the impedance measurement, at the potential sweep rate 1.67 mV s -1 from -700 mV to -200 mV vs. SCE. The inhibition efficiencies were calculated using the relationship. % corr corr Where I corr and I´c orr are the corrosion current densities in the absence and presence of the inhibitor in 1 M HCl solutions, respectively. The electrochemical impedance spectra were recorded at the 200 Hz applied single AC frequency at different applied DC potentials and the double layer capacitance values obtained were plotted against the applied DC potentials to determine PZC. All the measurements were taken at room temperature (27±1ºC).

Scanning electron microscopy
The surface morphology of mild steel specimen was analyzed after immersing in the blank and inhibited HCl solution by Scanning Electron Microscopy (Model-JEOL-JSM-6390). The surface morphological characterization was carried out at the magnification 2.0 KX operated at an accelerating voltage 15 kV.

Quantum chemical calculations
All quantum chemical calculations were performed with complete geometry optimization using the Gaussian 98 code. The molecular sketches of the inhibitor are drawn using GaussView 3.0. Geometry optimizations were accomplished by two different methods; ab initio methods at the Hartree-Fock (HF) level with the 3-21G and 6-31G(d,p) basis sets and at the density functional theory (DFT) level with the non-local hybrid density functional B3LYP, combining Becke's three-parameter hybrid exchange functional with the correlation functional of Lee et al.at the basis sets 3-21G and 6-31G(d,p) 39 . After the geometry optimization, vibrational analysis was performed and the resulting geometry was checked with respect to true minima on the potential energy surface, as shown by the absence of imaginary frequencies 40 .
The quantum chemical investigations were used to explain the results obtained in gravimetric and electrochemical studies on the corrosion inhibition property of 2,2'-(2-Hydroxyethylimino) bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide], looking for good theoretical parameters to characterize its inhibition performance. Statistical analyses were performed using SPSS program version 15.0 for windows. Non-linear regression analyses were performed by unconstrained sum of squared residuals for loss function and the estimation methods of Levenberg-Marquardt using SPSS program version 15.0 for windows.

Weight loss measurements
Weight loss measurements provide the most reliable results concerning the inhibition efficiency of the compounds 41 . The variation of weight loss of mild steel specimens in 1 M HCl solutions in the absence and presence of the inhibitor is shown in Table 1. It is apparent that the inhibition efficiency increases with an increase in inhibitor concentration in 1M HCl solutions. The decrease in corrosion rate in the presence of inhibitor is due to the strong interaction of the inhibitor molecules with the metal surface which lead to forming protective film by the adsorbed inhibitor on the metal surface, separating it from corrosion medium 42,43 . The extent of adsorption increases with an increase in the inhibitor concentration and the maximum adsorption was found at 200 ppm. The corrosion suppression ability of the inhibitor might be originated from its tendency to form either strong or weak chemical bonds, with Fe atoms on the metal surface, using the lone pair of electrons present on the O and N atoms and the π electrons in the benzene ring.

Electrochemical impedance spectroscopy
The impedance spectra obtained for the dissolution of mild steel in 1M HCl solutions in the absence and presence of inhibitor at various concentrations are shown in Figure 2. The Nyquist plots obtained are semicircles. The simple -R(CR)-model describes best the situation at the metal solution interface. However, the complex plane plots obtained are depressed semicircles, indicating non-ideal capacitive behavior of metal-solution interface. This capacitance dispersion at the solid surfaces can be attributed to the surface roughness, the degree of polycrystallinity, the chemical inhomogeneities and anion adsorption. A precise modeling for the experimental results was obtained by replacing a capacitor by a constant phase element (CPE) in the equivalent (Figure 3), whose impedance function is given as 19 :  ( ) where Y 0 represents the admittance of the corrosive system at 1rad s -1 and n, a constant (-1≤ n ≤1). When n = 0, CPE represents a pure resistor, if n = +1 the CPE represents a pure capacitor and an inductor if n = -1.
The electrochemical impedance parameters obtained by fitting the experimental curves into an equivalent circuit shown in Figure 3, are given in Table 2. In this equivalent circuit, polarization resistance R p indicates the contributions of charge transfer resistance, film resistance, accumulation resistance and double layer resistance. The results demonstrate that the polarization resistance values increase and the double layer capacitance (C dl ) values decrease with an increase in inhibitor concentration. The increase in the R p values with inhibitor concentration indicates an increase in the surface coverage by the inhibitor molecules, resulting in an increase in inhibitor efficiency 44,45 . The decrease in C dl values is caused by decreasing in the surface area of the metal, which is in contact with corroding medium. The adsorption of inhibitor molecules on the metal surface takes place by replacing water molecules at the metal-solution interface that lead to decreasing in local dielectric constant and/or an increase in the electrical double layer. Hence, the change in C dl values cause by the gradual displacement of water molecules by the adsorption of the inhibitor molecules at the metal-solution interface decreases the extent of metal corrosion 46 . From Table 2, it can be seen that the value of the constant 'n' , which is a measure of the surface heterogeneity, increases with the inhibitor concentration towards unity, indicating that the mild steel surface becomes more and more homogeneous as the concentration of the inhibitor increases due to its uniform surface coverage at higher concentration.

Potentiodynamic polarization studies
The potentiodynamic polarization curves recorded for the corrosion of mild steel in 1M HCl solutions in the presence and absence of inhibitor at various concentrations are shown in Figure 4. From this figure it is clear that the addition of inhibitor to the corrosive medium shows a reduction of both anodic and cathodic currents. This indicates that the inhibitor is of mixed type. Moreover, the cathodic branches in the presence of inhibitor give rise to almost parallel lines, indicating that the increase in inhibitor concentration doesn't modify the hydrogen evolution mechanism and the reduction of H + ions at the mild steel surface is charge transfer controlled 47,48 . The corresponding electrochemical parameters obtained from polarization studies (Tafel plots) are shown in Table 3. As it is apparent from Table 3, the corrosion current density values decrease with an increase in inhibitor concentration. The values of Tafel constants (β c and β a ) also change with inhibitor concentration indicating that the addition of inhibitor affects both cathodic and anodic reactions. However, a higher β c value than β a in the presence of inhibitor indicates that the cathodic reaction is retarded to a higher extent than anodic reaction. This behavior can be also seen from the Tafel plots, where the cathodic curves are shifted toward lower current densities to a higher extent than the anodic curves with an increase in inhibitor concentration. The E corr values are also shifted to more negative side with an increase in inhibitor concentration. All these could be attributed to the decrease in the rate of hydrogen evolution reaction caused by the adsorption of inhibitor molecules on the mild steel surface 49 .
According to Tables 1 and 3, the variation of calculated corrosion rates with respect to inhibitor concentrations from weight loss and Tafel polarization have the same manner but with almost different values. This is due to high applied cathodic and anodic overpotentials in the Tafel diagrams. More accurate data can be obtained by weight loss method. Moreover, weight loss is according to standard for corrosion rate calculation but needs long time. For weight loss method, test condition is more similar to natural situation and therefore more precision data can be calculated. The predominance

Adsorption isotherm
Adsorption isotherm provides information about the nature of interaction between inhibitor molecules and metal surface 50 . As mentioned earlier, the adsorption process can be considered as the replacement of water molecules at the corroding surface by inhibitor molecules 51 . Various adsorption isotherms were tested for the data obtained in weight loss measurements (also impedance and Tafel) and the data fit well with the Langmuir Adsorption isotherm, given by the expression; inh inh ads Where C inh is concentration of the inhibitor, θ is fraction of total surface covered by inhibitor molecules and K ads is adsorption equilibrium constant. The plot is linear with a correlation coefficients higher than 0.99. The value of K ads , determined from the plot of C inh /θ vs. C inh at constant temperature is used to calculate the value of standard free energy of adsorption (ΔG ads ) using the expression 52 : The calculated value of ΔG ads for adsorption of inhibitor molecules on the mild steel surface in 1 M HCl solution is -32 kJ mol -1 . The negative value of ΔG ads shows that the interaction between the inhibitor molecule and metal surface is strong and the adsorption of the inhibitor molecules on to the mild steel surface takes place spontaneously 53,54 . In general, the values of -ΔG ads less than 20 kJ mol -1 imply the columbic electrostatic interaction between the charged molecules and the metal surface 55,56 and greater than 40 kJ mol -1 imply the formation of chemical bond between the inhibitor molecules and the atoms on the metal surface through charge sharing or charge transfer 57 . Any value in between these two values corresponds to adsorption of inhibitor molecules on the metal surface by both physisorption and chemisorption. In the present study the calculated -ΔG ads value is close to 40 kJ mol -1 and far from 20 kJ mol -1 , indicating that the adsorption of inhibitor molecules on the metal surface involves both physisorption and chemisorption.

Effect of temperature
The change of corrosion rate with the temperature was studied in M HCl solutions with and without inhibitor by weight loss measurements at the temperatures 30, 40 and 50 ˚C by weight loss measurements. The variation of corrosion rate with temperature is shown in Figure 5 The calculated values of activation energy from the slopes of Arrhenius type plots are 72.34 kJ mol -1 and 64.23 kJ mol -1 for the uninhibited and inhibited (200 ppm) solutions respectively. The lower activation energy in the presence of inhibitor suggests that the inhibitor molecules are adsorbed on the metal surface by chemisorptions 59 .

Potential of zero charge (PZC) and inhibition mechanism
The adsorption of inhibitor molecules on the metal surface generally depends on the surface charge of the metal, the charge on the inhibitor molecule or the dipole moment of the inhibitor molecule and the other ions that are specifically adsorbed on the metal surface 53 . The surface charge on the metal surface in the corroding medium is determined from the position of open circuit potential with respect to PZC 54 . At the open circuit potential the surface charge on the mild steel surface is given by the expression: where E r is Antropov's "rational" corrosion potential 60 .
The values of E OCP and E r determined from Figure 6 for mild steel in 1M HCl solutions in the presence and absence of inhibitor are given in Table 4. As it is clear from this table that the surface charge on the mild steel surface in

Molecular orbital theoretical studies
Some of the molecular properties, describing the global reactivity such as; the total energy (E T ), the energy of the Highest Occupied Molecular Orbital (E HOMO ), the energy of the Lowest Unoccupied Molecular Orbital (E LUMO ), the dipole moment, the Ionization Potential (I), the Electron Affinity (A), the electronegativity (χ), the global hardness (η), the global softness (S), the fraction of electron transferred (ΔN) and electrophilicity index (ω) are calculated using quantum chemical calculations. Other parameters describing According to Pearson, operational and approximate definitions of the electronic chemical potential (μ) and the absolute hardness (η) of a chemical system are given by the following equations: While the global softness, which is the inverse of the global hardness, is given as: Recent progress in computational methods has provided a very useful tool for understanding the properties and for describing the behavior of atoms in molecules. Recently, computational methods have become very popular due to their accuracy and less computational burden. The mechanism of the inhibition action can be elucidated with the help of quantum chemical calculation, which is widely reported in the literature [70][71][72] . In this study, quantum chemical calculations are carried out at two different methods; ab initio methods at the Hartree-Fock (HF) level and the density functional theory (DFT) level with the 3-21G and 6-31G(d,p) basis sets by geometry optimization of the studied molecule to establish the relationship between the molecular structure of 2,2'-(2-Hydroxyethylimino) bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] and its inhibition effects. It is obvious that the inhibition performance of an inhibitor on a metal surface is determined by the interplay of both spatial molecular and electronic parameters 71 . Figure 8 represents the optimized structure of 2,2'-(2-Hydroxyethylimino)bis[N-(alphaalphadimethylphenethyl)-N-methylacetamide]. The selected bond lengths and bond angles for 2,2'-(2-Hydroxyethylimino) bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] are tabulated in Table 5. It can be seen that, the studied molecule is not completely planar, which may result in relatively weak interaction between molecule and metal surface. However, elucidation of orientation of organic molecules on the electrode surface needs to consider different factors. The interaction between atoms and groups of the inhibitor molecules and the electrode surface depend on the geometry of the inhibitor as well as the nature of their frontier molecular orbitals.
The HOMO and LUMO populations of the studied molecule are shown in Figure 9. It can be seen in Figure 9 that, the frontier molecular orbital distribution obtained from four different calculation methods have given very close results. The compound investigated in the present study contains of two symmetrical parts consisting of two benzene rings and two imide groups. The LUMO location of inhibitor is relatively distributed over the benzene ring and a small part of the carbon chain that occur one side of the molecule whereas the HOMO is entirely localized on the heteroatoms. According to HOMO distribution, it can be said that 2,2'-(2-Hydroxyethylimino) bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] molecule carries its rich negative center in a small region. The molecules are oriented toward to cathodic sites of the steel surface through the parts of the molecules with low HOMO density and afterwards adsorption occurs by sharing of electrons. In addition, the inhibitor molecule can accept electrons from a Fe atom with its antibonding orbitals to form back-donating. These donation and back-donation processes strengthen the adsorption of inhibitor onto the mild steel surface 73 .
It is important to consider the situation corresponding to a molecule that is going to receive a certain amount of charge at some center and is going to back-donate a certain amount of charge through the same center or another 74 . To describe the energy change associated with these two processes, the second order simple charge transfer formula is regarded as a two-parameter expression, in which the donation and back-donation processes are differentiated through the use of the values of the chemical potential for each case, while the hardness is fixed to the value of The most favorable situation corresponds to the case when the total energy change becomes a minimum with respect to ΔN + , which implies that The calculations from Table 6 indicate that η > 0 and ΔE T < 0 in all used computational methods. This result implies that the charge transfer to inhibitor molecule followed by back-donation from the molecule is energetically favorable. Similar observation has been reported 76 . However, it is important to note that ΔE T values obtained don't predict that a back-donation process is going to occur; it only establishes that if both processes occur (charge transfer to the molecule and back-donation from the molecule), the energy change is directly proportional to the hardness of the molecule.
The binding ability of the inhibitor to the metal surface increases with increasing HOMO and decreasing LUMO energy values. Thus, the lower the value of E LUMO , the most probable it is that the molecule would accept electrons. Moreover, the gap between the HOMO and LUMO energy levels (ΔE) of the molecule is an important parameter that determines the reactivity of the inhibitor molecule toward the adsorption on the metallic surface. In addition to ΔE parameter, for effective overlapping, the energy difference between the orbitals generally must be low, and the overall energy difference between the orbitals (HOMO and HOMO-1) is 1.02 eV for the studied compound, indicating their participation in the metal-ligand interaction. In addition, the energy difference between the HOMO-2 and HOMO-1 is very low confirming the involvement of HOMO-1 and HOMO-2 in the ligand-metal interaction (as shown in Figure 10) and also, suggesting that the parameters of orbitals such as HOMO, HOMO-1 and HOMO-2 are important for chemical reactivity over metal surface 77-79 .  The fraction of electrons transferred from inhibitor to the iron molecule by different computational methods, is calculated and listed in Table 6. According to other reports 80,81 , the values of ΔN show inhibition effect resulted from electrons donation.
Agreeing with Lukovits's study 81 if ΔN < 3.6, the inhibition efficiency increases with increasing electron-donating ability at the metal surface. Thus, in the present study, inhibitor molecule is donor of electrons and the mild steel surface is the acceptor of electrons. The electrophilicity index, ω, which measures the electrophilic power of a molecule, is calculated for this molecule. The positive value of ω suggests the high capacity of the molecule to accept electrons 82 . This process increases the adsorption capacity of 2,2'-(2-Hydroxyethylimino) bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] on the steel surface. In a corroding system, it is important to note that the inhibitor acts as a Lewis base while the metal acts as a Lewis acid.
The Fukui functions indicate the regions on the inhibitor molecule on which nucleophilic and electrophilic reactions are likely to occur. The Fukui function is defined as 83 : where ν(r) is the external potential, ρ(r) is total charge density, and N is the total number of electrons. Due to discontinuity in the ρ(r) versus N curve, we can define three different types of Fukui function, viz (for nucleophilic attack) (20) [ ] [ ] The preferred site for nucleophilic attack is the atom in the molecule where the value of f + is the highest while the preferred site for electrophilic attack is the atom in the molecule where fhas the highest value. However, the average of both measures reactivity towards a radical. The calculated values of the Fukui functions for the non-hydrogen atoms are reported in Table 7. In addition to oxygen atoms, the value of f + is highest on C4, C7, C23 and C26 atoms in 2,2'-(2-Hydroxyethylimino)bis[N-(alphaalphadimethylphenethyl)-N-methylacetamide] indicating that these atoms are likely to be the preferred sites for nucleophilic attack. These results agree with the analysis of the electron density of this molecule in the case of N+1 electron system which indicated that each C and O atoms is able to stabilize additional electrons (top panel of Figure 11). The value of f is highest on the same atoms approximately, in addition to N1 and N2 atoms. From bottom panel of Figure 11, it can be seen that these sites are the regions where electron removal destabilizes the molecule the least. The observed similarity in the sites for electrophilic and nucleophilic attacks suggests similarity in mechanism of inhibition.
The local reactivity of molecules is often analyzed in terms of the local softness index s, which is defined as the product of the Fukui function and the global softness, S. It is expressed using the equations 84 : Also, the relative nucleophilicity (s + /s -) and relative electrophilicity (s -/s + ) are the indices that are also related to the local softness and can be applied for the prediction of the sites for nucleophilic and electrophilic attacks. It is observed that both the approaches and the local softness values give results similar to those obtained from the Fukui function calculations. Figure 12 (top panel) shows the Mulliken atomic charges calculated for inhibitor compound. It has been reported that the more negative the atomic charges of the adsorbed center, the more easily the atom donates its electron to the unoccupied orbital of the metal 85 . It is clear from Figure 12, that the oxygen and nitrogen atoms as well as some carbon atoms carry negative charge centers which could offer electrons to the mild steel surface to form a coordinate bond. The direction of the dipole can be understood by considering the electrostatic potential (middle and bottom panels of Figure 12), which discerns electron density rich regions centered on the mentioned atoms, indicating the preferred zone for nucleophilic attack.

Quantitative structure activity relationship (QSAR).
An attempt has been made to correlate the results obtained from quantum chemical studies and the observed inhibition efficiencies of the inhibitor. The approach in which several where IE Theor is the inhibition efficiency, A and B are the regression coefficients determined by regression analysis, x i is a characteristic quantum index for the inhibitor molecule (i), and C i denotes the concentration of the inhibitor. Such linear Table 7. The Mulliken population analysis of the condensed Fukui functions and local softness parameters on the selected atoms of oxetacaine.

Selected atoms
Mullikene charge From the results obtained, it can be seen that there is a good and acceptable coefficient correlation (R 2 =0.8491) between the experimental and calculated/estimated inhibition efficiencies of the stud1ied inhibitor using the B3LYP/6-31G(d,p) method as shown in Figure 13A (other computational methods show the same results). Figure 13B shows a plot of the theoretical and experimental inhibition efficiencies versus the concentrations of the studied inhibitor, which confirms the accuracy of the obtained results from Figure 13A. It is also important to mention that it is difficult to predict the corrosion inhibition ability of a compound through an inclusive approach or to find some universal type of correlations. Other than a number of excluded parameters such as, effect of solvent molecules, surface nature, adsorption sites of the metal atoms or oxides sites or vacancies, competitive adsorption with other chemical species in the fluid phase and solubility should also be taken into consideration. Thus, the electron rich heteroatoms such as O and N can be protonated and this form could be in equilibrium with the molecular(unprotonated) form. The positively charged protonated form of 2,2'-(2-Hydroxyethylimino) bis[N-(alphaalpha-dimethylphenethyl)-N-methylacetamide] can get adsorbed on to the metal surface by physisorption. approach is not found to be satisfactory for correlating the present results. Consequently, the nonlinear model (NLM) proposed by Lukovits et al. 81 and also used by Khaled 88 for

Conclusion
The adsorption and the inhibition effect of 2,2'-(2-Hydroxyethylimino)bis[N-(alphaalphadimethylphenethyl)-N-methylacetamide] on the corrosion behavior of mild steel in the 1 M HCl was studied by using weight loss and electrochemical methods and the experimentally observed inhibition efficiency was explained theoretically using quantum chemical calculations. The following points emphasized the conclusion of the present work:  an excellent inhibition effect on corrosion of mild steel in 1M HCl solution, which was concentration and temperature dependent. 2. The inhibition performance can be attributed to the adsorption of this molecule on mild steel surface to form a protective film. 3. The inhibition behavior obtained from electrochemical studies showed the same trend as noticed in the weight loss studies. The inhibition efficiency increased with the increase in inhibitor concentration. The adsorption mechanism involved both physisorption and chemisorption. 4. The potentiodynamic polarization curves indicated that the inhibitor act as a mixed type of inhibitor with properties more cathodic in nature. 5. The adsorption of inhibitor on the metal surface followed Langmuir adsorption isotherm and the ΔG ads value calculated from adsorption studies had negative sign, indicating that the adsorption is spontaneous. 6. Determination of PZC indicated the formation of chloride bridge between protonated form of inhibitor molecules and metal surface. 7. Different computational methods were correlated to the inhibitive effect of 2,2'-  bis[N-(alphaalpha-dimethylphenethyl)-Nmethylacetamide] . 8. The Fukui function results indicated that the preferred sites for both nucleophilic and electrophilic attack were nitrogen, oxygen, and some carbon atoms.
The results also show that electronic factors, such as electron density, often have a greater influence in determining a good corrosion inhibitor than geometric factors of cases where more of the inhibitor is in contact with the metal surface. Therefore, even if a molecule has less planar geometry, it manages to have most of its electron donor centers in contact with the metal surface, it would have greater inhibition efficiency than a molecule that is planar but has less electron density. 9. The quantitative structure activity relationship (QSAR) approach has provided a good indication that an optimum of some quantum chemical parameters is required for good correlation with experimentally determined inhibition efficiency of the inhibitor.