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1?formyl?3?phenyl?5?aryl?2?pyrazoline derivatives as corrosion inhibitors of steel in acidic medium: Computational simulations study. 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. 1. Introduction 1 Corrosion of metals is considered as a major problem in many sector of industries, causing a huge damaged of materials 2 and financial pert. To provide confront this problem several methods were employed but amongst which the use of 3 corrosion inhibitor is considered as one of the most practical and effective method for protection of metals 1. In recent 4 years, organic compounds especially N-heterocyclic compounds have been widely used as an effective corrosion inhibitors 5 2-4. Pyrazoline derivatives are the most important nitrogen containing heterocyclic compounds due to their significant 6 antimicrobial properties 5, antifungal 6, antidepressant 7, and anti? inflammatory 8. Recently, these compounds 7 received more attention in the field of corrosion inhibitor and reported as a good corrosion inhibitor of steel in acidic 8 medium 9-10. Several experimental techniques have been utilized to evaluate the inhibition efficiency of an inhibitor. 9 However, these techniques are expensive and time-consuming; also, it is deficient to explain the inhibition mechanism 11-10 12. Actually, nowadays, and with the development of computer simulation techniques, the use of quantum chemical 11 methods in corrosion inhibitor studies draws much attention. Density functional theory (DFT) and Molecular dynamics 12 simulation (MD) become fast, inexpensive and effective tools to determine the molecular structure, elucidate the electronic 13 structure and reactivity as well as predict the corrosion inhibition performance of organic compounds 13-15. The aim of 14 this study is a prophecy of the corrosion efficiency and inhibition mechanism of two pyrazoline derivatives synthesized and 15 published in our previous work 16, namely 1?Formyl?3?phenyl ?5? (4?methylphenyl)?2?pyrazoline (P1) and 1?Formyl?3? 16 phenyl?5?(4?chlorophenyl)?2?pyrazoline (P2) (see Fig.1) . Quantum chemical calculation and MD simulation approach have 17 been performed to determine the most theoretically effective corrosion inhibitor among them. 18 19 20 21 22 23 24 25 Fig.1. Chemical structures of studied molecules. 26 2. Computational details 27 2.1. Quantum chemical calculation 28 Full geometry structures optimizations structures and various quantum chemical calculations were performed using 29 DMol3 module uncorrupted in materials studio software 17. Different quantum chemical parameters such as the Highest 30 Journal of New Technology and Materials JNTM Vol. 00, N°00 (0000)00-00 OEB Univ. Publish. Co.

2 Occupied Molecular Orbital energy (EHOMO), the Lowest Unoccupied Molecular Orbital energy (ELUMO), energy gap (?E) and 31 Fukui indices analyses were have been accomplished by using double numerical polarization (DNP) basis set in conjunction 32 with generalized gradient approximation (GGA) functional of Becke exchange plus Lee–Yang–Parr correlation (BLYP) 18 33 . The COSMO model has been included to study the effect of solvent (aqueous solution). 34 35 2.2. Molecular dynamics (MD) simulation 36 Molecular dynamics simulation of the two-pyrazoline derivatives were carried out in a simulation box 37 (24.82×24.82×35.63 A°) with periodic boundary conditions using Discover module in Materials studio 7.0 (from Accelrys 38 Inc.). More simulation details on the methodology of molecular dynamics simulations can be found elsewhere 19-21. The 39 simulation was performed at 298 K, NVT ensemble, with time step of 1 fs and simulation time of 50 ps using the 40 COMPASS force field 22. The interaction energy Einteraction between Fe surface and inhibitor molecule and the binding 41 energy was calculated using the following equations 23: 42 =?+ (1) = ? (2) Where the is defined as the total energy of the entire system, is defined as the total energy of Fe 43 surface and water molecule and the is the energy of the adsorbed inhibitor molecule on the surface. 44 45 3. Results 46 3.1. Quantum chemical calculation 47 3.1.1. Equilibrium structure geometry structure 48 The optimized geometries of molecules P1 and P2 are represented in Fig. 2, and the calculated parameters of the 49 optimized structures of the two-pyrazoline derivatives at the level BLYP of theory in aqueous solution, such as the bond 50 lengths and bond angles are summarized in Table 1. The inspection of Table 1 shows that all the bond lengths and angles in 51 the pyrazoline ring are in the expected range and there is a little difference between their values in the two tested molecules. 52 The C=N and C-N bond lengths values of the pyrazoline ring in all the molecules are found changing within the to range 53 within 1.283-1.285 A° and 1.508-1.514 A° respectively, which are similarly to those found in analogous structures (C=N: 54 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 55 1.402 A°, respectively, which is near close to the reported literature data (1.373-1.380) 26. The observed difference could 56 be attributed to the effect of the substitution of carbonyl group and phenyl rings on the pyrazoline ring (add a reference). 57 From all the above-mentioned bond lengths of the optimized P1 and P2 molecules, it can be concluded that, there 58 geometry configuration is ideal.( add a reference) 59 60 Table 1. Bond length (A°), bond angle (°) for the optimized molecules P1 and P2 61 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

3 3.1.2. Frontier orbital energies 62 In general, the predicting of the adsorption sites and/or fragments and the molecular reactivity of an inhibitor are related 63 to it is the its frontier molecular orbital (FMOs) involving the highest occupied molecular orbital energy (EHOMO) and the 64 lowest unoccupied molecular energy (ELUMO). The energy of HOMO (EHOMO) is often associated with the electron donating 65 ability of a molecule; therefore, the ELUMO is allied to depends upon the tendency of a molecule to accept electrons. It was 66 generally acknowledged established that the inhibition efficiency increases with the enhancement of EHOMO values. The higher 67 is the value of EHOMO of an inhibitor, the greater is its ability of donating electrons to unoccupied d-orbital of the metal atoms 68 27. Additionally the energy gap ?E between HOMO and LUMO energy levels of the molecule (?E= EHOMO – ELUMO) is an 69 important index, As since the ?E value decreases when the reactivity of an inhibitor increases, and hence increases there its 70 adsorption ability 28. The spatial distribution of the frontier molecular orbital’s HOMO and LUMO of the studied 71 inhibitors are represented in Fig 2, and there quantum chemical parameters are listed in Table 2. 72 The analysis of the Fig. 2 shows that the electron density distribution of HOMO and LUMO is the almost similar and 73 strongly spread on the pyrazoline ring, carbonyl group and phenyl ring. This kind of distribution could be attributed to the 74 presence of conjugation effect and high electron density of these segments, which indicate that these segments are 75 responsable reflecting their involvement in the adsorption process on the metal surface. (add a reference). 76 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 77 more ability to donate the electrons to unoccupied d-orbital of the metal. Whereas, the ELuMO of P2 is lower than P1, which 78 could be attributed to the presence of – Cl group in the phenyl ring. This result is often interpreted by the presence of 79 complex interactions perhaps playing the crucial role in the adsorption process 29. 80 81 Table 2. Quantum chemical parameters of the studied compounds 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 The ionization potential (I) and electron affinity (A) of the inhibitor are related to the EHOMO and ELUMO, respectively, as 98 follows 29: 99 I= ? EHOMO (3) 100 A= ? ELUMO (4) 101 The absolute electronegativity (? ) and global hardness (? ) can be calculated by using the following equations 30: 102 ?=(+)/2 (5) ?=(?)/2 (6) 103 The fraction of electron (?N) transferred is calculated using the following equation 30: 104 ?=???2(?+?) (7) 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

4 Where the theoretical values of and are 7.0 eV and 0 eV, respectively, Recently, it was reported that the value of 105 ?Fe = 7 eV is not acceptable theoretically since electron-electron interactions were not considered, only free electron gas 106 Fermi energy of iron was considered 29. Therefore, the researchers are recently using work function (?) of the metal 107 surface instead of ?Fe, and the equation (7) is rewritten as follow: 108 ? N =???inh2(?Fe+?inh) (8) 109 The obtained DFT derived ? for Fe (110) surface “the higher stabilization energy” is 4.82 eV 31. 110 I. Lukovit has reported that the inhibition efficiency increased with increasing electron donating ability at the metal 111 surface when the value of ?NP2. 116 3.1.3. Local reactivity 117 The local reactivity of the inhibitors was analyzed by means of Fukui function( fk) which is defined as the first derivative 118 of the electronic density ( (?))with respect to the number of electrons N in a constant external potential v(?) 33: 119 = (?()? (9) 120 The condensed Fukui function can be calculated as follows: 121 =(+1)?() (10) 122 =()?(?1) (11) 123 Where (+1),() and (?1)are the atomic charges of the anionic, neutral and cationic species, 124 respectively. 125 An analysis of the Fukui indices for nucleophilic and electrophilic sites are represented in Tables 3. The nucleophilic 126 and electrophilic attacks are respectively characterized by and. 127 In P1, atoms C9, N11, C12, O21 and in P2, atoms C9, N10, N11, and O21 are the most susceptible sites for 128 nucleophilic attacks. On the other hand, atoms N10, C15, C17, C20 in P1 and atoms C9, N10, C15 in P2 are the most 129 probable centers for electrophilic attacks. Nevertheless, in P1, the atom C9 has the highest value of whereas in P2, the 130 atom O21 has the highest value of .These sites are the most reactive sites for nucleophilic attacks. As for ?, 131 electrophilic attacks, N10 is has the highest value for both P1 and P2. 132 133 134 Table 3. The calculated Fukui function of the P1 and P2 molecules P1 P2 Atoms C(1) 0.071 -0.060 0.014 -0.003 C(2) -0.029 0.056 0.006 0.014

5 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 3.2. 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 4. 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:

6 ? 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.