Quantum chemical studies on corrosion inhibition of some lactones on mild steel in acid media

Corrosion Science 51 (2009) 1428–1435

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Quantum chemical studies on corrosion inhibition of some lactones on mild steel in acid media E. Jamalizadeh a, S.M.A. Hosseini a,*, A.H. Jafari b a b

Department of Chemistry, Faculty of Science, Shahid Bahonar University of Kerman, 22 Bahman, Kerman 76175, Iran Materials Science and Engineering Department, Shahid Bahonar University of Kerman, Kerman 76188, Iran

a r t i c l e

i n f o

Article history: Received 17 January 2009 Accepted 21 March 2009 Available online 31 March 2009 Keywords: A. Mild steel A. Acid solutions B. Modelling studies C. Acid inhibition

a b s t r a c t Study of the efficacy of some lactones to counter iron corrosion in 1 M hydrochloric acid using ab initio quantum chemical deductions and its comparison with the available experimental data forms a part of this research. It is believed that the inhibition efficiency has lucid correlation with the charge of oxygen atoms of inhibitor molecules. Furthermore, thermo-chemical calculations for oxepan-2-one (L3) on iron cluster result in adsorption energies close to experimental values. However, the interaction energies of L3 and iron cluster with the natural bond orbital are also reported. Furthermore, interaction energy of hydrogen ion and inhibitor with iron surface is investigated. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction Organic substances have been used extensively as corrosion inhibitors during the last four decades [1], which some of them adsorbed on the metallic surfaces, slow down the cathodic reaction as well as the anodic process of dissolution of the metal [2]. Recently, Tebbji and co-workers [3] experimentally found that lactones i.e., dihydrofuran-2(3H)-one (L1), tetrahydro-2H-pyran-2-one (L2) and oxepan-2-one (L3) show inhibitive properties for mild steel in 1 M HCl solutions. Their results indicate that these lactones act as cathodic type inhibitors and addition of them hindered the acid attack on the mild steel electrode. During the development of novel and more efficient organic corrosion inhibitors, several quantum chemical studies have been performed in order to relate the inhibition efficiency to the molecular properties of different types of compounds [1,2,4,5]. The efficiency of an inhibitor does not only depend on its structure, but also on the characteristics of the environment in which it acts, the nature of the metal and other experimental conditions [1]. The quantum chemical calculations of the systems consisting of the corrosion inhibitor and the metal atoms (Fe, Al, Cu, Cr) were reported [6–13]. The role of surface defects in particular corners were investigated for aluminium and copper clusters [12,13]. This research find apparent correlation between parameters resulted by quantum chemical calculations related to the structure of lactones and their ability to inhibit the corrosion process. Furthermore, since investigation of interaction * Corresponding author. Tel./fax: +98 341 3222033. E-mail addresses: [email protected], [email protected] (S.M.A. Hosseini). 0010-938X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.corsci.2009.03.029

of inhibitor and metal surface is need for the study of inhibition mechanism, we calculate adsorption energy of L3 on a single iron atom which is 26 kJ/mol. The calculated adsorption energy is typical of physisorption process and generally shows good agreement with the experimental data [3]. For having a model closer to the reality, theoretical findings on a single iron atom simulating a surface site are further expanded to 16 member matrixes (Fe16). The obtained results are in agreement with the issues of a single iron atom. In addition, according to the NBO results the number of Fe atoms in selected cluster is enough because no charge transfers shown from inhibitor to the far iron atoms in Fe16. Since lactone molecules act as cathodic type inhibitors, it seems that the observed corrosion inhibition by them is the results of a different inhibition mechanism, which are possibly associated with properties of the mild steel surface. With this in mind this study is focused mainly in the role of Hydrogen ion and inhibitor adsorption on iron atoms representing defect free surface and Fe3C surface in mild steel structure as responsible for the inhibition mechanisms. The Fe3C is a former part of the original steel in the non-oxidised state that accumulates on the surface as corrosion of the iron proceeds, hence calculations are expanded on (0 1 0), (0 0 1), and (1 0 0) Fe3C surfaces. The corrosion rate initially decreases with time and finally increases, an effect attributed to the Fe3C, which is suggested to increase the cathodic reaction [14]. Hydrogen evolution is a common cathodic reaction in acid media. The hydrogen ions must be first adsorbed or attached to the surface before the reaction can proceed [15]. The studies have been extended to investigate the adsorption energies of hydrogen ion on Fe surface in the presence and absence of inhibitor molecule.

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Nomenclature A AB B BD BSSE C Cald. CR d DFT E EXP F^ fCP Fe Fe3C H H2 HF IE% kJ L1 L2 L3 LP mol O17 O18 PCM

molecule A dimmer molecule B 2-center bond basis set extension effect carbon atom calculated 1-center Core pair oxygen–iron distance density functional theory energy experimental Fock operator (full) function counterpoise-corrected energy iron atom cementite hydrogen ion hydrogen molecule Hartree–Fock inhibition efficiencies kilo Joule dihydrofuran-2(3H)-one tetrahydro-2H-pyran-2-one oxepan-2-one 1-center valence lone pair mole ðC—ðC@OÞ—OÞ ðC—ðC@OÞ—OÞ polarized continuum model

2. Computational details 2.1. Method of calculation According to the cluster model, the interaction of the corrosion inhibitor molecule with the metal surface is considered locally, thus, the quantum chemical analysis could be restricted to the calculation of interaction energies between the molecule and metallic atoms upon which direct adsorption is taking place [9]. However, transition metals being electron-rich, bring about one limitation to their quantum chemical calculations, at ab initio level, computations are huge and thus very time-consuming. Furthermore, they encounter some convergence problems. Among quantum chemical methods, the DFT has some merit [16,17] since its calculation time is roughly the same as a Hartree–Fock procedure which includes the relativistic effect as an electron correlation term. Recently, a hybrid version of DFT and Hartree–Fock (HF) methods, i.e., B3LYP, has been introduced [18] which incorporates a Becke’s 3parameter functional (B3) as well as a mixture of HF with DFT exchange terms associated with the gradient-corrected correlation functional of Lee et al. Although the three semi-empirical parameters are arrange primarily to reproduce thermo-chemistry of small organic molecules, it has been shown to perform exceptionally well on transition metal systems as well, with much less convergence problems than commonly found with pure DFT method. The geometry of inhibitor molecules and inhibitor/iron (single iron atom) system were optimize via the B3LYP/6-31++(d,P) method. The calculation of the interaction energies between theses molecules and surface sites which were based on the clusters Fe16 and Fe3C were obtained via the LANL2DZ basis set. This basis set use effective core potential (ECP) of Hey and Wadt [19] for core electrons, which have less effect on chemical bond formation. By use

q R2 RY DG DH

e l w °C

electron charge best adjusted linear regression coefficient center Rydberg change in Gibbs free energy change in enthalpy diagonal NBO matrix element dipole momentum wave function Celsius degree

Superscripts 1,2,3,. . . atom’s number in L3Fe cluster * antibond 0 equal basis set a a basis set b b basis set a[b a and b basis sets Subscripts 16(9:4:3) planer cluster having 16 atom in three layer A geometry of molecule A AB geometry of dimmer acc acceptor ads adsorption B geometry of molecule B don donor H highest occupied molecular orbital L lowest unoccupied molecular orbital rel relaxation

of these basis sets, computational time and convergence difficulties were considerably reduced. All calculations were performed with the aid of Gaussian 03 computer codes [20], working on 2.3 GHz dual processors. 2.2. Cluster model The structure of cluster with 16 atoms is Fe16(9:4:3) representing defect free iron surface which is built with nine iron atoms in one, four iron atoms in the second and three iron atoms in the third layer (Fig. 1). The distance of the closest adjacent atoms is 2.8664 Å and the two planes are separated by 1.4332 Å [21]. Since, the Fe3C is a former part of the original steel in the nonoxidised state that accumulates on the surface as corrosion of the iron proceeds, calculations are further expanded on (0 1 0), (0 0 1), and (1 0 0) Fe3C surfaces. Its complicated structure consists of four formula units per orthorhombic unit cell, and has the space group Pnma (No. 62) [22,23], Fig. 2 and Table 1. The unit cell contains eight iron atoms in ‘‘general” positions (8Feg), four

Fig. 1. The studied iron cluster Fe16(9:4:3).

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Fig. 2. Top and front views of Fe3C(0 1 0) (a); Fe3C(0 0 1) (b); and Fe3C(1 0 0) (c) in a bulk unit cell.

Table 1 The cementite primitive unit cell structure in lattice coordinates. Atom

Basis vectors (a0x, b0y, c0z)

C Fes Feg

ðþx1 ; þ 14 ; þz1 Þ; ðx1 ; þ 34 ; z1 Þ; ð12  x1 ; þ 34 ; 12 þ z1 Þ; ð12 þ x1 ; þ 14 ; 12  z1 Þ ðþx2 ; þ 14 ; þz2 Þ; ðx2 ; þ 34 ; z2 Þ; ð12  x2 ; þ 34 ; 12 þ z2 Þ; ð12 þ x2 ; þ 14 ; 12  z2 Þ ðþx3 ; þy3 ; þz3 Þ; ðx3 ; y3 ; z3 Þ; ð12 þ x3 ; 12  y3 ; 12  z3 Þ; ð12  x3 ; 12 þ y3 ; 12 þ z3 Þ; ðx3 ;

1 2

þ y3 ; z3 Þ; ðþx3 ;

1 2

 y3 ; þz3 Þ; ð12  x3 ; y3 ;

1 2

þ z3 Þ; ð12 þ x3 ; þy3 ;

1 2

 z3 Þ

The unit cell is scaled by the lattice constants (a0; b0; c0). The listed basis vectors determine the lattice positions of each of the four C atoms, four Fes atoms, and eight Feg atoms, as they depend on the parameters xi, yi, and zi, numbers on [0, 1].

iron atoms in ‘‘special” positions (4Fes), and four carbon atoms in the large interstices (4 C), Fig. 2(a). The Feg are 14-coordinate, with 11Fe–Fe bonds and 3Fe–C bonds. The Fes are also 14-coordinate, but with 12Fe–Fe bonds and 2Fe–C bonds. The C is eightcoordinate and encased within six Fe atoms in a triangular prism structure, with two other Fe atoms slightly further out. Fes has a 0.05 Å greater mean radius than Feg, resulting in interatomic Fe– Fe distances d(Fes–Fes) > d(Fes–Feg) > d(Feg–Feg). However, the Fe– C interatomic distances are greater for Feg than Fes: d(Feg– C) > d(Fes–C) [22]. The bulk material is metallic and ferromagnetic. Although the structure is difficult to visualize, one may roughly consider the structure to be a series of zigzag folded hexagonal close-packed (hcp) basal planes of Fe, with C occupying the interstitial regions at the fold vertices. It has been shown that the Fe3C (1 0 0) and Fe3C (0 0 1) surfaces contain surface carbon atoms, while the Fe3C (0 1 0) surface is metallic and does not have surface carbon atoms [24,25]. 2.3. Natural bond orbital (NBO) analysis In order to derive the direction and magnitude of charge-transfer (CT) interactions the case of the L3–Fe16(9:4:3) cluster was considered and an NBO (Natural Bond Orbital) analysis for the minima found on the studied standard surfaces energy potentials was performed [26] along with a Second-Order Perturbation Theory (SOPT) analysis of the KS (Kohn–Sham) analogous to the Fock matrix within the NBO analysis.

2.4. Solvent effect It is expected that the inhibitor molecules in solution behave differently from that in vacuum. The solvent effect on molecular structure of solute can be studied by a model which is known as polarized continuum model (PCM) [27]. In this model, solvent is treated as an expanse of dielectric media and the solute as a trapped molecule in a cavity surrounded by the solvent. The obtained energies of inhibitor/Fe cluster are done in water solvent and IEFPCM is used for this purpose. 3. Results and discussion The calculated quantum chemical parameters for geometrical optimization of L1, L2, and L3 inhibitor molecules (Fig. 3) are represented in Table 2 together with the best adjusted linear regression coefficient (R2) for inhibition efficiency (IE) versus their calculated quantum chemical parameters. Highest occupied molecular orbital energy levels (HOMO), as a measure of electron donating ability of a molecule with a de-localized pair of p electrons could enable it to get adsorbed on metallic surfaces. A high EH value expresses intrinsic electron donating tendency to an appropriate acceptor i.e., any molecule with lower HOMO energy and empty molecular orbital. On the other hand, EL, the energy of the lowest unoccupied molecular orbital denotes the electron receiving tendency of a molecule. Consequently, the difference between LOMO and HOMO energy levels (EL  EH) demonstrates

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Fig. 3. Optimised geometry of investigated inhibitor molecules.

Table 2 Quantum chemical calculated parameters and experimental data for substituted lactones in gaseous phase. Inhibitor designation

EH (au)

EL (au)

EL–EH (au)

l (D)

qO17 (eV)

qO18 (eV)

IE% (Exp.) [3]

IE% (Cald.)

L1 L2 L3 R2

0.281 0.274 0.272 0.924

0.019 0.021 0.021 0.777

0.262 0.253 0.251 0.900

4.912 5.108 5.194 0.964

0.089 0.096 0.113 0.931

0.307 0.291 0.274 0.998

61 71 80

61 70 80

inherent electron donating ability and projects the interaction of the inhibitor molecule with the metal surface, the dipole momentum (l) and the charge of oxygen atoms ðqO1 & qO18 Þ, Fig. 4. As results show the differences of inhibition efficiencies between inhibiting molecules can be explained best in terms of the charge of oxygen atoms ðqO17 & qO18 Þ of inhibitor molecules specially ðqO18 Þ with correlation coefficients above 0.99. Table 2, data reveal the lower negative value of ðqO18 Þ for L3 amongst experimentally evaluated compounds. Thus, L3 is expected to give enhanced protection against corrosion in contrast to L1 with more negative (qO18 Þ value conveying a lower protecting capability. Assessing (IE) impact by regression analyses of IE% versus (qO18 Þ plots are represented in Table 2. Comparison between

these findings and reported experimental results satisfactorily correlate which in turn, validates the method employed here. 3.1. Interaction energy The standard [28] and the counterpoise-corrected [29] surface potential energy of L3–Fe cluster were explored at B3LYP/631G++(d,P) level. Employing the notation of Xantheas [30], not accounting for the basis set extension effects, i.e., basis set superimposition error – BSSE, the interaction energy of a dimmer AB is given by: a[b DE ¼ EAB ðABÞ  EaA ðAÞ  EbB ðBÞ;

ð1Þ

where the superscripts denote the basis set and the subscripts refer to the geometry used for energy calculation. However, DE is usually calculated in the following manner: a[b DE0 ¼ EAB ðABÞ  EaAB ðAÞ  EbAB ðBÞ;

ð2Þ

that is, in the sense of ‘‘vertical” interaction energy. The full function counterpoise-corrected energy through Boys–Bernardi [31] method for the BSSE is given as: a[b a[b a[b DEðfCPÞ ¼ EAB ðABÞ  EAB ðAÞ  EAB ðBÞ;

ð3Þ

and BSSE is, thus, often calculated by:

BSSE ¼ DEðfCPÞ  DE0 :

ð4Þ

Due to the fact that the reference energies of monomeric units are calculated for different geometries, upon approaching the complete basis set limit, the Eqs. (1) and (3) do not converge to the same result. Therefore, it is proper to include the relaxation energy due to deformation in the following manner:

DEðBSSEÞ ¼ DEðfCPÞ þ Earel ðAÞ þ Ebrel ðBÞ;

ð5Þ

where relaxation energies are given by:

Fig. 4. The L3 molecule in interaction with iron cluster: L3Fe16(9:4:3).

Earel ðAÞ ¼ EaAB ðAÞ  EaA ðAÞ;

ð6Þ

Earel ðBÞ ¼ EaAB ðBÞ  EaB ðBÞ:

ð7Þ

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Table 3 Interaction and dissociation energies for L3Fe1 clusters calculated by DFT methods in solvent water (all values in kJ/mol). Energy

Standard PES

Counterpoise corrected PES

DE DE0 DEðfCPÞ DEðBSSEÞ Erel(L3) Erel(Fe) Erel BSSE

164.60 164.60 59.66 164.60 224.26 0.00 224.26 224.26

170.49 170.49 53.89 170.49 224.36 0.00 224.36 224.36

As shown in Table 3 the gaseous phase standard and counterpoise-corrected DE(fCP) interaction energies for L3–Fe cluster were calculated as (60 kJ/mol) and (54 kJ/mol), respectively, which the gaseous phase standard and counterpoise-corrected DE(fCP) interaction energy is closer to the experimental value of heat of adsorption (65 kJ/mol), which is used for the subsequent adsorption energy calculations. But the gaseous phase standard and counterpoise-corrected DE and DE0 interaction energies for L3–Fe cluster are quite difference to the experimental value. The superimposition error DE(BSSE) calculated at employed theoretical level for the standard and counterpoise-corrected surface potential energy of L3–Fe1 cluster indicates this difference, Thus it is necessary use of DE(fCP) for calculation of interaction energy. Furthermore, the issue of standard DE(fCP) interaction energy is closer to the experimental value of adsorption energy, thus this calculation is used for all the subsequent adsorption energy calculations. 3.2. Adsorption energies Computations considered one iron atom as the surface and the optimized L3–Fe1 system adsorption energy and (O–Fe) distance for the corresponding cluster by B3LYP/6-31++(d,p) level of theory were calculated to be 1.83 A° in gaseous phase. The results of system optimization for inhibitor/iron show the most stable state via the lone pair electron of the O18 atom ðC—ðC@OÞ—OÞ as depicted in Fig. 4. Thermo-chemically calculated values obtained from frequency calculation by DFT study in 25 °C, show adsorption enthalpy energy for L3–Fe cluster in gaseous phase to be (60 kJ/mol) and the adsorption free energy as (26 kJ/mol). Both quantities are in good agreement with experimental data (DHexp = 65 kJ/mol, and DGexp = 29 kJ/mol) [32] and confirming the physical adsorption of the L3 on the metal surface. The negative value of DGads means that the adsorption of lactones on iron surface is a spontaneous but rather weak interaction of the inhibitor molecule onto the iron surface process. It is accepted that, DGads values around (20 kJ/mol) are consistent with the electrostatic or physical interaction between the molecules and the charged metal while those more negative than (40 kJ/mol) entail charge sharing or transfer from the inhibitor molecules to the metal surface to form a coordinate type of bond (chemisorption) [32,33]. For investigated lactone inhibitors, one can see that the calculated DGads value, the adsorption mechanism of the lactones on 1 M HCl solution was typical of physisorption. For more actual iron surface modeling theoretical findings on a single iron atom simulating a surface site are further expanded 16 member matrixes for L3 inhibitor, while iron atoms were considered separately and optimized geometries established to evolve the L3/Fe cluster systems and the total interaction energy of the inhibitor molecule-cluster model were calculated as a function of inhibitor distance from the iron surface by B3LYP/LANL2DZ level in water solvent. From the obtained data, the L3-cluster distance

(O–Fe) is 1.75 Å and the adsorption energy for the L3 with the cluster Fe16(9:4:3) is being nearly experimental adsorption energy of L3 on mild steel, with value of 56 kJ/mol. The results from NBO analysis (at B3LYP/LANL2DZ level of theory) in water solvent are summarized in Table 4. Obviously, the most significant CT occurs for O18 atom’s lone electron pair to the s and d antibond lone pair of the closest iron atom (Fe19) to the O18 of inhibitor molecule (Fig. 4). While the possibility of charge transfer from L3 to the other iron atoms of Fe16(9:4:3) cluster is slight, the most significant back-donation from Fe to L3 occurs for the s and d antibond lone pair of Fe19 to the s and p antibond extra-valence-shell of O18 as well as the d lone pair of Fe19 to the p antibond lone pair of C2 and the possibility of charge transfer from other iron atoms of Fe16(9:4:3) cluster to the L3 is slight. According to applied method in previous work [12] the number of Fe atoms in selected cluster is enough, since according to the NBO results interactions between L3 and far iron atoms of cluster is slight. The estimated energetic effects due to these interactions are calculated by the second-order perturbation theoretical expressions of the form [26]:

DEð2Þ wdonor!wacceptor  2:

^ w i2 hwdon jFj acc ; eacc  edon

ð8Þ

where ei is a diagonal NBO matrix element of the Fock operator F^ or, ^ KS . in the case of the DFT mode, the KS one-electron equivalent h Hydrogen ion adsorption is one stage of cathodic reaction which is investigated on mild steel surface in recent work. In like manner, the adsorption energy for the H ion and H2 molecule with the cluster Fe16(9:4:3) is calculated as a function of inhibitor distance from the iron surface by B3LYP/LANL2DZ level. From the results, the H-cluster and H2-cluster distance is 1.6 and 3.5 Å, respectively. The adsorption energies for H-cluster and H2-cluster with the Fe16(9:4:3) cluster are 3572 and +101 kJ/mol, respectively. As shown H ion is inclined adsorb by Fe cluster, while H2 molecule prefer to separate from iron surface. These results certify hydrogen cathodic reaction mechanism. The total adsorption energy of the hydrogen ion and inhibitor molecule-cluster model were calculated as a function of inhibitor distance from the Fe3C surface by B3LYP/LANL2DZ level in water solvent. Table 5 represent the highest interaction energy calculated on different iron and carbon atoms on three Fe3C surfaces. The results of system optimization for both inhibitor/iron and inhibitor/ carbon show the most stable state via the lone pair electron of the O18 atom ðC—ðC@OÞ—OÞ. From the obtained data, in L3–Fe3C system (O–Fe) and (O–C) distances are 1.85 and 1.90 Å, respectively. The H–Fe3C clusters distance (O–Fe) and (O–C) is 1.50 and 1.20 Å. The results show interaction energy of L3–(0 0 1)Fe3C is strong and L3 is adsorb on both iron and carbon atoms. Meanwhile, L3 is not adsorb on (1 0 0)Fe3C surface and it is only adsorbed on iron atom of (0 1 0)Fe3C surface. But hydrogen adsorption on Fe16 and all the surfaces of Fe3C is strong. Thus, as hydrogen ions cover the surface of iron and carbon atoms of mild steel, L3 is also adsorb on both cathodic and anodic sites. In addition, since the experimental results proves that lactones act as cathodic inhibitors [3], therefore the studies have been extended to investigate the adsorption energies of hydrogen ion on the Fe surface in presence and absence of inhibitor molecule by B3LYP/LANL2DZ level. For this purpose: The first calculation is carried out by placing nine hydrogen ions on Fe16(9:4:3) surface (H9– Fe16) in the absence of inhibitor molecule, Fig. 5(a). For the second calculation eight hydrogen ions and one L3 inhibitor molecule are placed together on Fe16 (L3H8–Fe16), Fig. 5(b). The L3-cluster distance (O–Fe) and H-cluster distance are 1.75 and 1.6 Å, respectively. As shown in Table 6 the process of adsorption of the L3 molecule in presence of H ions (L3H8-cluster) is spontaneous

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Table 4 Results from the second-order perturbation theory analysis of the KS analogous of the Fock matrix within the NBO basis for L3 complexes with Fe16(9:4:3) cluster representing the Fe surface at B3LYP/LANL2DZ level of theory in water solvent.

DEð2Þ /kJ mol1

ðeacc  edon Þ/a.u.

^ hwdon jFjw acc i/a.u.

From L3 molecule to the iron cluster atoms From L3 to the Fe19 (closest iron atom to the L3 molecule, see Fig. 3) LP Fe19 (s,d) LP O18(s,p) LP Fe19 (s,d) CR O18(s) LP Fe19 (s,d) BD C2–O18(s,p) RY Fe19(s,p,d) BD C2–O18(s,p) RY Fe19(s,p,d) BD C2–O18(s,p) BD C2–O18(s,p) RY Fe19(s,p,d) RY Fe19(s,p,d) BD C2–O18(s,p) RY Fe19(s,p,d) LP O18(s,p) LP Fe19(s,d) LP O18(p) RY Fe19(s,p,d) BD C2–O18(s,p) RY Fe19(s,p,d) LP O18(s,p) BD Fe19-Fe33(s,d) LP O18(p)

84.66 7.37 4.83 2.99 2.63 1.95 1.73 1.46 1.24 1.07 1.05 1.01

0.77 19.00 1.15 14.58 6.90 2.39 3.83 14.20 0.37 3.04 6.52 0.29

0.244 0.378 0.075 0.187 0.121 0.061 0.073 0.135 0.021 0.051 0.078 0.017

From L3 to the other iron atoms in first layer BD C2–18(s,p) RY Fe20(s,p,d) RY Fe21(s,p,d) BD C2–O18(s,p) RY Fe23(s,p,d) BD C2–O18(s,p) RY Fe22(s,p,d) BD C2–O18(s,p)

0.61 0.54 0.54 0.54

2.03 2.86 2.58 1.43

0.032 0.035 0.034 0.025

From L3 to the iron atoms in second layer LP O18(s,p) RY Fe31(s,p,d) RY Fe33(s,p,d) LP O18(s,p) RY Fe34(s,p,d) LP O18(s,p) RY Fe32(s,p,d) LP O18(s,p)

0.73 0.64 0.60 0.58

3.93 3.78 3.69 3.61

0.050 0.046 0.044 0.043

From L3 to the iron atoms in third layer LP O18(s,p) LP O18(s,p)

RY Fe29(s,p,d) RY Fe30(s,p,d)

0.66 0.63

1.70 1.65

0.031 0.030

From iron cluster to the L3 molecule From Fe19 to the L3 LP Fe19(s,d) LP Fe19(d) CR Fe19(s) LP Fe19(s,d) LP Fe19(d) LP Fe19(d) LP Fe19(s,d) LP Fe19(s,d) CR Fe19(p) LP Fe19(s,d) LP* Fe19(s,d) LP Fe19(d) LP Fe19(d) LP Fe19(s,d)

RY O18(s,p) LP C2(p) BD C2–O18(s,p) BD C2-O18(s,p) RY O18(p) RY O18(p) RY O18(p) RY O18(s,p) BD C2-O18(s,p) RY O18(s,p) RY O18(s,p) RY O18(p) LP C2(p) RY O18(s,p)

17.01 10.14 6.29 5.07 3.49 2.72 3.11 1.85 1.82 1.46 1.31 1.23 1.04 1.01

2.59 0.02 3.86 0.48 1.22 1.12 0.57 0.76 2.70 0.51 0.51 1.20 0.03 1.91

0.398 0.014 0.140 0.091 0.060 0.052 0.079 0.071 0.063 0.051 0.049 0.036 0.006 0.083

From the other iron atoms of first layer to the L3 BD Fe25–Fe31(s,p,d) RY O18(s,p) RY C2(s,p) Lp Fe22(s,d) RY O18(s,p) BD Fe26–Fe33(s,p,d) RY C2(s,p) Lp Fe23(s,d) BD Fe24–Fe32(s,p,d) RY O18(s,p) RY O18(s,p) BD Fe27–Fe34(s,p,d)

1.52 0.93 0.81 0.78 0.68 0.67

2.83 0.75 2.79 0.76 2.82 2.82

0.067 0.034 0.049 0.032 0.044 0.044

From iron atoms of second layer to the L3 RY Fe33(s,p) RY O17(s,p) RY O18(s,p) RY Fe33(s,p) RY O18(s,p) LP Fe34(s,p,d)

1.09 1.04 0.60

0.32 1.42 2.74

0.045 0.092 0.053

From iron atoms of third layer to the L3 LP Fe28(s,p,d) LP Fe28(s,p,d)

0.90 0.86

2.67 0.70

0.066 0.033

Donor orbital

Acceptor orbital

RY O18(s,p) RY C2(s,p)

Table 5 The calculated adsorption energies for hydrogen and L3 adsorbed on carbon and iron atoms of Fe3C surfaces (all values in kJ/mol). Fe3C surfaces On On On On On On

iron atom of Fe3C(0 1 0) carbon atom of of Fe3C(0 1 0) iron atom of Fe3C(0 0 1) carbon atom of of Fe3C(0 0 1) iron atom of Fe3C(1 0 0) carbon atom of of Fe3C(1 0 0)

Adsorption energy of H

Adsorption energy of L3

1640 1621 1394 1735 1206 1363

47 129 167 60 74 189

(28 kJ/mol). Furthermore, the adsorption energy of H ion in the absence of L3 molecule (H9-cluster) is negative (2172 kJ/mol) indicating strong adsorption. Where as the adsorption energy of H ion in the presence of adsorbed L3 molecule (L3H8-cluster) is positive, showing the H ion is not adsorb on Fe surface, i.e., retarding the cathodic process. 4. Conclusions A correlation between parameters related to the electronic structure of lactones and their ability to inhibit the corrosion pro-

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Fig. 5. The adsorption of H ion in the absence of L3 molecule, H9–Fe16 (a) and in the presence of adsorbed L3 molecule, L3H8–Fe16 (b).

Table 6 The calculated adsorption energies for hydrogen and L3 adsorbed together on Fe16(9:4:3) cluster. System

Adsorption energy (kJ/mol)

H–H8Fe16 H–L3H7Fe16 L3–H8Fe16

2172 +24 28

cesses was established using DFT study method. It is believed that the inhibition efficiency has lucid correlation with the charge of oxygen atoms of inhibitor molecules. It is observed that the results of standard DE(fCP) interaction energy is closer to the experimental findings. Thermo-chemistry results based on frequency calculation by DFT method in 25 °C, gives adsorption enthalpy and adsorption free energy for L3–Fe cluster which is in good agreement with experimental data. The results are indicative of a physisorption interaction. The theoretical findings of expanded 16 member matrixes iron atom are supporting results of a single iron atom for L3 inhibitor. The interaction energies of L3 on Fe16 cluster with the natural bond orbital indicate the most significant charge transfer occurs for O18 atom to the closest iron atom of the O18 and also interactions between L3 and far iron atoms of cluster is slight, therefore the number of Fe atoms in selected cluster is enough. Furthermore, the role of hydrogen ion and inhibitor adsorption on Fe16 and Fe3C surface proves that hydrogen ions cover the surface of iron and carbon atoms of mild steel and L3 is also adsorb on both cathodic and anodic sites. In addition, the adsorption energy of H ion in the presence of adsorbed L3 molecule is positive, indicating the H ion is not adsorb on Fe surface, i.e., retarding the cathodic process which is in good agreement with experimental results. Acknowledgment The authors wish to pay tribute to the memory of the Late Professor M. Karaminezhaad for his support in initializing this project. References [1] E.S.H.E. Ashry, A.E. Nemr, S.A. Esawy, S. Ragab, Corrosion inhibitors Part II: quantum chemical studies on the corrosion inhibitions of steel in acidic medium by some triazole, oxadiazole and thiadiazole derivaties, Electrochim. Acta 51 (2006) 3957–3968.

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