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Journal of New Technology and Materials
JNTM
Vol. 00, N°00 (0000)00-00
OEB Univ. Publish. Co.

1?formyl?3?phenyl?5?aryl?2?pyrazoline derivatives as corrosion inhibitors of steel in acidic medium: Computational simulations study.

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Abstract
Quantum chemical calculations and Molecular dynamic (MD) simulations were performed on two synthesized pyrazoline derivatives namely: 1?Formyl?3?phenyl?5?(4?methylphenyl)?2?pyrazoline (P1) and 1?Formyl?3?phenyl? 5?(4?chlorophenyl) ?2?pyrazoline (P2) in order to study their reactivity and adsorption behavior towards steel corrosion inhibition. Quantum chemical parameters such as EHOMO, ELUMO, energy gap (?E), fraction of electron transfers (?N) and Fukui index have been studied. Moreover, Molecular dynamics simulation is performed to simulate the best adsorption configuration of the investigated inhibitors on Fe (1 1 0) surface. Quantum chemical calculation results indicate that the active sites of the molecules were mainly located on the pyarazoline ring and on the carbonyl group. The binding strength of the studied inhibitor molecules on Fe surface follows the order P1>P2, which is in good agreement with the results of quantum chemical calculations.
Keywords: Corrosion inhibitors; Molecular dynamics simulation; pyrazoline derivatives.

Introduction
Corrosion of metals is considered as a major problem in many sector of industries, causing a huge damaged of materials and financial pert. To provide confront this problem several methods were employed but amongst which the use of corrosion inhibitor is considered as one of the most practical and effective method for protection of metals 1. In recent years, organic compounds especially N-heterocyclic compounds have been widely used as an effective corrosion inhibitors 2-4. Pyrazoline derivatives are the most important nitrogen containing heterocyclic compounds due to their significant antimicrobial properties 5, antifungal 6, antidepressant 7, and anti? inflammatory 8. Recently, these compounds received more attention in the field of corrosion inhibitor and reported as a good corrosion inhibitor of steel in acidic medium 9-10. Several experimental techniques have been utilized to evaluate the inhibition efficiency of an inhibitor. However, these techniques are expensive and time-consuming; also, it is deficient to explain the inhibition mechanism 11-12. Actually, nowadays, and with the development of computer simulation techniques, the use of quantum chemical methods in corrosion inhibitor studies draws much attention. Density functional theory (DFT) and Molecular dynamics simulation (MD) become fast, inexpensive and effective tools to determine the molecular structure, elucidate the electronic structure and reactivity as well as predict the corrosion inhibition performance of organic compounds 13-15. The aim of this study is a prophecy of the corrosion efficiency and inhibition mechanism of two pyrazoline derivatives synthesized and published in our previous work 16, namely 1?Formyl?3?phenyl ?5? (4?methylphenyl)?2?pyrazoline (P1) and 1?Formyl?3? phenyl?5?(4?chlorophenyl)?2?pyrazoline (P2) (see Fig.1) . Quantum chemical calculation and MD simulation approach have been performed to determine the most theoretically effective corrosion inhibitor among them.
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Fig.1. Chemical structures of studied molecules.

Computational details
Quantum chemical calculation
Full geometry structures optimizations structures and various quantum chemical calculations were performed using DMol3 module uncorrupted in materials studio software 17. Different quantum chemical parameters such as the Highest Occupied Molecular Orbital energy (EHOMO), the Lowest Unoccupied Molecular Orbital energy (ELUMO), energy gap (?E) and Fukui indices analyses were have been accomplished by using double numerical polarization (DNP) basis set in conjunction with generalized gradient approximation (GGA) functional of Becke exchange plus Lee–Yang–Parr correlation (BLYP) 18 . The COSMO model has been included to study the effect of solvent (aqueous solution).
Molecular dynamics (MD) simulation
Molecular dynamics simulation of the two-pyrazoline derivatives were carried out in a simulation box (24.82×24.82×35.63 A°) with periodic boundary conditions using Discover module in Materials studio 7.0 (from Accelrys Inc.). More simulation details on the methodology of molecular dynamics simulations can be found elsewhere 19-21. The simulation was performed at 298 K, NVT ensemble, with time step of 1 fs and simulation time of 50 ps using the COMPASS force field 22. The interaction energy Einteraction between Fe surface and inhibitor molecule and the binding energy was calculated using the following equations 23:
Einteraction=Etotal-Esurface+H2O+Einhibitor (1) Ebinding= – Einteraction (2) Where the Etotal is defined as the total energy of the entire system, Esurface+H2O is defined as the total energy of Fe surface and water molecule and the Einhibitor is the energy of the adsorbed inhibitor molecule on the surface.

Results
Quantum chemical calculation
Equilibrium structure geometry structure
The optimized geometries of molecules P1 and P2 are represented in Fig. 2, and the calculated parameters of the optimized structures of the two-pyrazoline derivatives at the level BLYP of theory in aqueous solution, such as the bond lengths and bond angles are summarized in Table 1. The inspection of Table 1 shows that all the bond lengths and angles in the pyrazoline ring are in the expected range and there is a little difference between their values in the two tested molecules. The C=N and C-N bond lengths values of the pyrazoline ring in all the molecules are found changing within the to range within 1.283-1.285 A° and 1.508-1.514 A° respectively, which are similarly to those found in analogous structures (C=N: 1.291-1.300 A°) and (C-N: 1.482- 1.515 A°) 24,25. Therefore, the N10-N11 bond length value of P1 and P2 is 1.403 and 1.402 A°, respectively, which is near close to the reported literature data (1.373-1.380) 26. The observed difference could be attributed to the effect of the substitution of carbonyl group and phenyl rings on the pyrazoline ring (add a reference). From all the above-mentioned bond lengths of the optimized P1 and P2 molecules, it can be concluded that, there geometry configuration is ideal.( add a reference)
Table 1. Bond length (A°), bond angle (°) for the optimized molecules P1 and P2
Geometry parameters P1 P2
Bond length C7-C8 1.534 1.535
C8-C9 1.504 1.500
C9-N10 1.285 1.283
N10-N11 1.403 1.402
N11-C7 1.514 1.508
N11-C20 1.358 1.360
C20-O21 1.238 1.234
Bond angle C7-C8-C9 103.297 103.637
C8-C9-N10 114.695 114.252
C9-N10-N11 108.431 108.035
N10-N11-C7 112.165 112.047
N11-C7-C8 100.795 100.652
N11-C20-O21 126.010 125.246
Frontier orbital energies
In general, the predicting of the adsorption sites and/or fragments and the molecular reactivity of an inhibitor are related to it is the its frontier molecular orbital (FMOs) involving the highest occupied molecular orbital energy (EHOMO) and the lowest unoccupied molecular energy (ELUMO). The energy of HOMO (EHOMO) is often associated with the electron donating ability of a molecule; therefore, the ELUMO is allied to depends upon the tendency of a molecule to accept electrons. It was generally acknowledged established that the inhibition efficiency increases with the enhancement of EHOMO values. The higher is the value of EHOMO of an inhibitor, the greater is its ability of donating electrons to unoccupied d-orbital of the metal atoms 27. Additionally the energy gap ?E between HOMO and LUMO energy levels of the molecule (?E= EHOMO – ELUMO) is an important index, As since the ?E value decreases when the reactivity of an inhibitor increases, and hence increases there its adsorption ability 28. The spatial distribution of the frontier molecular orbital’s HOMO and LUMO of the studied inhibitors are represented in Fig 2, and there quantum chemical parameters are listed in Table 2.
The analysis of the Fig. 2 shows that the electron density distribution of HOMO and LUMO is the almost similar and strongly spread on the pyrazoline ring, carbonyl group and phenyl ring. This kind of distribution could be attributed to the presence of conjugation effect and high electron density of these segments, which indicate that these segments are responsable reflecting their involvement in the adsorption process on the metal surface. (add a reference).

From Table2, it can be seen that P1 has the a higher EHOMO and a lower ?E value than P2 , which indicates that P1 has more ability to donate the electrons to unoccupied d-orbital of the metal. Whereas, the ELuMO of P2 is lower than P1, which could be attributed to the presence of – Cl group in the phenyl ring. This result is often interpreted by the presence of complex interactions perhaps playing the crucial role in the adsorption process 29.
Table 2. Quantum chemical parameters of the studied compounds
P1 P2
HOMO -5.423 -5.647
LUMO -2.143 -2.363
?E 3.280 3.284
I 5.423 5.647
A 2.143 2.363
? 3.783 4.005
? 1.640 1.642
?N 0.316 0.248
The ionization potential (I) and electron affinity (A) of the inhibitor are related to the EHOMO and ELUMO, respectively, as follows 29:
I= – EHOMO (3)
A= – ELUMO (4)
The absolute electronegativity (? ) and global hardness (? ) can be calculated by using the following equations 30:
?=(I+A)/2 (5) ?=(I-A)/2 (6)
The fraction of electron (?N) transferred is calculated using the following equation 30:
?N=?Fe-?inh2(?Fe+?inh) (7)Where the theoretical values of ?Fe and ?Fe are 7.0 eV and 0 eV, respectively, Recently, it was reported that the value of ?Fe = 7 eV is not acceptable theoretically since electron-electron interactions were not considered, only free electron gas Fermi energy of iron was considered 29. Therefore, the researchers are recently using work function (?) of the metal surface instead of ?Fe, and the equation (7) is rewritten as follow:
?N=?-?inh2(?Fe+?inh) (8)
The obtained DFT derived ? for Fe (110) surface “the higher stabilization energy” is 4.82 eV 31.
I. Lukovit has reported that the inhibition efficiency increased with increasing electron donating ability at the metal surface when the value of ?N;3.6 32. In the present study, we observed (via Table 2) that the calculated values ?N of both P1 and P2 are positive and lower than 3.6, meaning implying the high ability of these molecules to donate electrons to the iron surface.

It can is be concluded from the discussion above that the inhibition efficiency of this inhibitors can be follows the following order: P1;P2.

Local reactivity
The local reactivity of the inhibitors was analyzed by means of Fukui function( fk) which is defined as the first derivative of the electronic density (? (r))with respect to the number of electrons N in a constant external potential vr 33:
fk=?? (r?Nv(r) (9)
The condensed Fukui function can be calculated as follows:
fk+=qkN+1-qkN (10)
fk-=qkN-qkN-1 (11)
Where qkN+1, qkN and qkN-1are the atomic charges of the anionic, neutral and cationic species, respectively.

An analysis of the Fukui indices for nucleophilic and electrophilic sites are represented in Tables 3. The nucleophilic and electrophilic attacks are respectively characterized by fk+ andfk-.
In P1, atoms C9, N11, C12, O21 and in P2, atoms C9, N10, N11, and O21 are the most susceptible sites for nucleophilic attacks. On the other hand, atoms N10, C15, C17, C20 in P1 and atoms C9, N10, C15 in P2 are the most probable centers for electrophilic attacks. Nevertheless, in P1, the atom C9 has the highest value of fk- whereas in P2, the atom O21 has the highest value of fk- .These sites are the most reactive sites for nucleophilic attacks. As for fk?, electrophilic attacks, N10 is has the highest value for both P1 and P2.

Table 3. The calculated Fukui function of the P1 and P2 molecules
P1 P2
Atoms fk-fk+fk-fk+C(1) 0.071 -0.060 0.014 -0.003
C(2) -0.029 0.056 0.006 0.014
C(3) 0.037 -0.027 0.004 0.007
C(4) 0.064 -0.044 0.018 0.000
C(5) -0.022 -0.012 0.003 -0.041
C(6) -0.041 0.068 0.009 0.019
C(7) 0.016 -0.035 -0.034 0.017
C(8) -0.050 -0.004 -0.033 -0.023
C(9) 0.154 0.040 0.098 0.113
N(10) 0.037 0.192 0.081 0.137
N(11) 0.077 -0.013 0.092 -0.029
C(12) 0.082 -0.057 0.016 0.016
C(13) 0.073 0.028 0.046 0.063
C(14) 0.007 0.014 0.015 0.010
C(15) 0.042 0.138 0.083 0.116
C(16) 0.008 -0.005 0.004 -0.002
C(17) -0.039 0.158 0.041 0.087
C(19) 0.004 -0.013 – –
Cl(19) – – 0.024 0.008
C(20) 0.028 0.113 0.030 0.064
O(21) 0.145 0.047 0.122 0.063
Molecular dynamics simulation
Nowadays many researchers in the field of studies dealing with corrosion inhibition studies use the molecular dynamics simulation as an important tool in understanding the interaction between inhibitors and metal surface.

Fig.3 represents the energy and temperature equilibrium curves obtained using MD simulation for both P1 and P2 molecules. As can be seen, from this figure that both energy and temperature reach balance, which indicating that, the whole system have reached equilibrium 34. The equilibrium adsorption configuration of the studied inhibitor on Fe (1 1 0) surface is illustrated in Fig. 4 and the calculated interaction energy and binding energy are listed is Table 4. It could be observed from Fig.4, that the studied inhibitor molecules was are adsorbed close to the Fe surface. The high negative values of the binding energies (via Table 4) indicate that the adsorption of inhibitors on Fe (1 1 0) surface is spontaneous, strong, and stable 28. The binding energies are found to increase in the order P1 ; P2, which showing that P1 will adsorbs more strongly on the iron surface and possesses better inhibition performance than P2. This result is in a good agreement with the quantum chemistry analysis mentioned above.

Table 4. Interaction energies between the inhibitors and Fe (110) surface in aqueous phase (kJ/mol).

System Binding energy Interaction energy
Fe+P1 635.952 -635.952
Fe+P2 618.076 -618.076
Conclusion
Quantum chemical calculations and Molecular dynamics simulation (MD) were employed to predict the inhibition efficiencies of two pyrazoline derivatives as corrosion inhibitors for carbon steel. The following insightful conclusions can be obtained from this the present study:
Inhibition efficiency was enhanced with an increasing in EHOMO. P1 had the highest inhibition efficiency because it had the highest HOMO energy and ?N values, and it was most more likely capable of offering to provide electrons.

The distribution of electronic density and fukui analysis showed that the pyrazoline derivatives compounds had many active electron-donating centers.

MD simulation indicates that all values of binding energy values are negative and following the order: P1;P2, which is in accordance with the result obtained from quantum chemical calculations.

This study has shown that theoretical calculations and MD simulation can be used as reliable approaches to screen organic corrosion inhibitors prior to experimental validation.

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