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Quantum chemical study of some cyclic nitrogen compounds as corrosion inhibitors of steel in NaCl media
Corrosion Science 51 (2009) 1876–1878
Contents lists available at ScienceDirect
Corrosion Science journal homepage: www.elsevier.com/locate/corsci
Short Communication
Quantum chemical study of some cyclic nitrogen compounds as corrosion inhibitors of steel in NaCl media Gökhan Gece *, Semra Bilgiç Department of Physical Chemistry, Faculty of Science, Ankara University, 06100 Besßevler, Ankara, Turkey
a r t i c l e
i n f o
Article history: Received 16 February 2009 Accepted 7 April 2009 Available online 17 April 2009 Keywords: A. Steel B. Modelling studies C. Acid corrosion
a b s t r a c t Corrosion inhibition efficiencies of 3-amino-1,2,4-triazole (3-ATA), 2-amino-1,3,4-thiadiazole (2-ATDA), 5-(p-tolyl)-1,3,4-triazole (TTA), 3-amino-5-methylmercapto-1,2,4-triazole (3-AMTA) and 2-aminobenzimidazole (2-ABA) as corrosion inhibitors on steel in sodium chloride media were investigated by using semiempirical PM3 and density functional theory (DFT) methods. Quantum chemical parameters such as highest occupied molecular orbital energy (EHOMO), lowest unoccupied molecular orbital energy (ELUMO), energy gap (DE) and dipole moment (l) have been calculated for these compounds by using semiempirical PM3 and 6-31G(d), 6-311G(d,p) DFT methods. It was found that theoretical data support the experimental results. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Corrosion control can be achieved by many methods, being corrosion inhibitors one of the most effective alternatives for the protection of metallic surfaces against corrosion. A perusal of the literature on corrosion inhibitors reveals that most organic inhibitors employed as corrosion inhibitors contain nitrogen, oxygen, sulphur and/or aromatic ring in their molecular structure [1–4]. Between the organic compounds of interest, triazoles have been studied extensively because of their corrosion inhibition properties [5–10]. The corrosion inhibition efficiency of various organic compounds on the corrosion of steel in NaCl medium has been investigated experimentally by several researchers [11–15]. Experimental means are useful in explaining the inhibition mechanism but they are often expensive and time-consuming. Advances in computer hardware and software and in theoretical chemistry have brought high-performance computing and graphic tools within the reach of many academic and industrial laboratories. Recently, more corrosion publications contain substantial quantum chemical calculations [16]. Such calculations are usually used to explore the relationship between the inhibitor molecular properties and their corrosion inhibition efficiencies. However, far too little attention has been paid to the quantum chemical studies of triazole derivatives in NaCl media [17–20]. The inhibitive properties of five different organic compounds, namely 3-amino-1,2,4-triazole (3-ATA), 2-amino-1,3,4-thiadiazole (2-ATDA), 5-(p-tolyl)-1,3,4-triazole (TTA), 3-amino-5-methylmercapto-1,2,4-triazole (3-AMTA) and 2-aminobenzimidazole (2-
* Corresponding author. Tel.: +90 312 2126720; fax: +90 312 2232395. E-mail address: [email protected] (G. Gece). 0010-938X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.corsci.2009.04.003
ABA) have been reported in a previous experimental study [15]. The aim of this paper is to extend these investigations in order to discuss the relationship between quantum chemical calculations and experimental inhibition efficiencies of the inhibitors by determining the quantum chemical parameters such as the energies of highest occupied molecular orbital (EHOMO) and the lowest unoccupied molecular orbital (ELUMO), the energy difference (DE) between EHOMO and ELUMO and dipole moment (l). 2. Calculation method In order to find optimized conformations of the compounds studied and to speed up the calculations, the molecular structures were optimized initially with PM3 [21] semiempirical calculation. The convergence was set to 0.001 kcal mol 1. The structures obtained from PM3 calculation were fully re-optimized by using DFT (density functional theory) methods to estimate the quantum chemical parameters. Calculations at the DFT level were performed using two basis sets, 6-31G(d) and 6-311G(d,p) with Becke-3-Lee– Yang–Parr (B3LYP) functional [22,23]. In all cases, total structure optimization together with the vibrational analysis of the optimized structures were carried out by means of the HyperChem software [24] in order to determine whether they correspond to a maximum or a minimum in the potential energy curve. 3. Results and discussion The chemical structures of the compounds studied are given in Fig. 1. The optimized molecular structures of the studied molecules using hybrid DFT functional (B3LYP/6-31G*) are shown in Fig. 2 and the calculated quantum chemical indices EHOMO, ELUMO, DE and dipole moment (l) are given in Table 1.
1877
G. Gece, S. Bilgiç / Corrosion Science 51 (2009) 1876–1878
H N
H
N 3-Amino-1,3,4-triazole
N H
N
N 2-Amino-1,3,4-thiadiazole
3-ATA
N
H
H N H
H S
2-ATDA
NH 2 N 3-Amino-5-methylmercapto-1,2,4-triazole
H3C S
N
3-AMTA
N N H
N CH3
5-(p-Tolyl)-1,3,4-triazole
TTA
N H
N 2-Aminobenzimidazole
NH2
2-ABA
N H Fig. 1. Abbreviations and molecular structures of the studied compounds.
According to the frontier molecular orbital theory, the formation of a transition state is due to an interaction between frontier orbitals (HOMO and LUMO) of reacting species [25]. Thus, the treatment of the frontier molecular orbitals separately from the other orbitals is based on the general principles governing the nature of chemical reactions. HOMO is often associated with the electron donating ability of a molecule. High EHOMO values indicate that the molecule has a tendency to donate electrons to appropriate acceptor molecules with low energy empty molecular orbital. Increasing values of the EHOMO facilitate adsorption (and therefore inhibition) by influencing the transport process through the adsorbed layer [16]. ELUMO indicates the ability of the molecules to accept electrons. The lower values of ELUMO, the more probable it is that the molecule would accept electrons [16]. Low absolute values of the energy band gap (DE) gives good inhibition efficiencies, because the energy to remove an electron from the last occupied orbital will be low [16]. The results obtained by 6-311G(d,p)/B3LYP/6-311G(d,p) method (Table 1) show that 2-ABA has the highest HOMO energy (EHOMO) and the lowest LUMO energy (ELUMO) among these organic heterocyclic compounds. Another point to be considered is the HOMO–LUMO gap (DE), i.e., the difference between the HOMO and LUMO energies for the compounds. 2-ABA has the smaller energy gap as compared to other molecules. According to these theoretical results and the experimentally found inhibition efficiencies, it can be said that 2-ABA has more inclination to get adsorbed on the metal surface than TTA. The binding capability of a molecule with metal depends also on the electronic charge on the chelating atom. Thus, the atomic charge values were obtained by the Mulliken population analysis [26]. Table 2 presents Mulliken charges of the selected atoms of the compounds
studied. From the atomic charge values listed, 10N atom of 2-ABA has excess electron density ( 0.42) which increases the p-electron density in the aromatic ring. However, 6N ( 0.09) and 7N ( 0.04) atoms in the triazole ring of TTA would contribute less to the p-system when compared to 2-ABA. It is well known that the chelating or binding capability of a molecule with a metal depended on the electronic charge on the chelating or active atoms, i.e. the more negative the charge, the stronger of the binding capability. Therefore, 2-ABA is easier to bond with metal than TTA. Since 3-ATA, 3-AMTA and 2-ATDA molecules do not have an aromatic ring, they can be judged considering their electron-donating groups. 6S (0.44) atom in the thiadiazole ring of 2-ATDA makes the molecule less polar than the triazole ring in 3-ATA and 3-AMTA due to the scarcity of electron density. Thus, 3-ATA and 3-AMTA have been presumed to be more effective inhibitors than 2-ATDA. 10S ( 0.34) atom of 3-AMTA breaks the planarity of the molecule and imparts a nonpolar character. This accounts for the higher inhibition efficiency of 3-ATA, compared to 3-AMTA. The dipole moment (l) is another indicator of the electronic distribution in a molecule and is one of the properties used to discuss and to rationalize the structure [27]. No significant relationship has been found between the dipole moment values and inhibition efficiencies. Besides, there is a lack of agreement in the literature on the correlation between the dipole moment and inhibition efficiency [28–31].
4. Conclusions Through PM3 semiempirical and DFT quantum chemical calculations a correlation between parameters related to the electronic
1878
G. Gece, S. Bilgiç / Corrosion Science 51 (2009) 1876–1878
Table 1 Calculated quantum chemical parameters of the studied compounds. Molecule
PM3 EHOMO
2-ATDA 3-AMTA 3-ATA TTA 2-ABA a
9.473 8.748 8.927 9.195 8.747
6-31G(d) ELUMO 0.935 0.467 0.222 2.357 0.135
DE
l
8.538 8.281 9.149 6.838 8.612
3.39 1.67 2.41 5.69 2.79
EHOMO 6.366 5.898 5.755 6.842 5.791
g (%)a
6-311G(d,p) ELUMO 2.294 0.427 1.368 4.168 3.510
DE
l
4.072 5.471 4.387 2.674 2.281
3.99 1.66 1.92 5.82 3.84
EHOMO
ELUMO
6.742 5.936 5.911 5.894 5.838
0.342 0.407 0.162 0.247 0.526
DE
l
6.400 5.529 5.749 5.647 5.312
4.01 1.68 2.12 5.84 3.86
74 77 82 86 94
Values from Ref. [15].
Table 2 Mulliken charge data of the compounds. 3N 2-ATDA 3-AMTA 3-ATA TTA 2-ABA
0.11 0.17 0.21 0.20 –
4N
5N
–
0.13 0.21
– – –
– – – –
6N – 0.17 0.19 0.09 –
7N 0.64 0.38 0.26 0.04 0.21
8N
10N
6S
10S
– –
– – – –
0.44 – – – –
–
0.39 – 0.28
0.42
0.34 – – –
References
Fig. 2. Optimized structures of the compounds.
structure of some cyclic nitrogen compounds and their ability to inhibit the corrosion process could be established. The highest occupied molecular orbital energy levels and energy gaps calculated by 6-311G(d,p) DFT study show reasonably good correlation as compared to other calculated data. Comparison of theoretical and experimental data exhibit good correlation confirming the reliability of the method employed here.
[1] R. Hasanov, M. Sadıkog˘lu, S. Bilgiç, Appl. Surf. Sci. 253 (2007) 3913. [2] M. Özcan, R. Solmaz, G. Kardasß, I. Dehri, Coll. Surf. A: Physicochem. Eng. Aspects 325 (2008) 57. [3] K. Bhrara, H. Kim, G. Singh, Corros. Sci. 50 (2008) 2747. [4] M. Behpour, S.M. Ghoreishi, N. Soltani, M. Salavati-Niasari, M. Hamadanian, A. Gandomi, Corros. Sci. 50 (2008) 2172. [5] S. Ramesh, S. Rajeswari, Electrochim. Acta 49 (2004) 811. [6] L.G. Qiu, A.J. Xie, Y.H. Shen, Mater. Chem. Phys. 91 (2005) 269. [7] E.H. El Ashry, A. El Nemr, S.A. Esawy, S. Ragab, Electrochim. Acta 51 (2006) 3957. [8] H.H. Hassan, E. Abdelghani, M.A. Amin, Electrochim. Acta 52 (2007) 6359. [9] F. Xu, J. Duan, S. Zhang, B. Hou, Mater. Lett. 62 (2008) 4072. [10] M. Lebrini, M. Traisnel, M. Lagrenée, B. Mernari, F. Bentiss, Corros. Sci. 50 (2008) 473. [11] F. Blekkenhorst, G.M. Ferrari, G.J. van der Wekken, F.B. Ijsseling, Brit. Corros. J. 21 (1988) 165. [12] F.B. Ijsseling, Brit. Corros. J. 24 (1989) 55. [13] Y.C. Lin, S.L. Chang, S.L. Lee, J. Appl. Electrochem. 29 (1999) 911. [14] G. Yang, L. Ying, L. Haichao, Corros. Sci. 43 (2001) 397. [15] M. S ß ahin, S. Bilgiç, H. Yılmaz, Appl. Surf. Sci. 195 (2002) 1. [16] G. Gece, Corros. Sci. 50 (2008) 2981. [17] O. Blajiev, A. Hubin, Electrochim. Acta 49 (2004) 2761. [18] N.K. Allam, Appl. Surf. Sci. 253 (2007) 4570. [19] M. S ß ahin, G. Gece, F. Karcı, S. Bilgiç, J. Appl. Electrochem. 38 (2008) 809. [20] M. Finšgar, A. Lesar, A. Kokalj, I. Milošev, Electrochim. Acta 53 (2008) 8287. [21] J.J.P. Stewart, J. Comput. Chem. 10 (1989) 209. [22] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [23] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1998) 85. [24] HyperChem (TM) Professional 7.5 (evaluation version), Hypercube Inc., Gainesville, FL, USA. [25] K. Fukui, Theory of Orientation and Stereoselection, Springer-Verlag, New York, 1975. [26] J.N. Murrell, S.F. Kettle, J.M. Tedder, The Chemical Bond, John Wiley & Sons, Chichester, 1985. [27] O. Kikuchi, Quant. Struct.-Act. Relat. 6 (1987) 179. [28] G. Gao, C. Liang, Electrochim. Acta 52 (2007) 4554. [29] N. Khalil, Electrochim. Acta 48 (2003) 2635. [30] L.M. Rodrigez-Valdez, A. Martinez-Villafane, D. Glossman-Mitnik, J. Mol. Struct. (THEOCHEM) 713 (2005) 65. [31] A. Stoyanova, G. Petkova, S.D. Peyerimhoff, Chem. Phys. 279 (2002) 1.
Contents lists available at ScienceDirect
Corrosion Science journal homepage: www.elsevier.com/locate/corsci
Short Communication
Quantum chemical study of some cyclic nitrogen compounds as corrosion inhibitors of steel in NaCl media Gökhan Gece *, Semra Bilgiç Department of Physical Chemistry, Faculty of Science, Ankara University, 06100 Besßevler, Ankara, Turkey
a r t i c l e
i n f o
Article history: Received 16 February 2009 Accepted 7 April 2009 Available online 17 April 2009 Keywords: A. Steel B. Modelling studies C. Acid corrosion
a b s t r a c t Corrosion inhibition efficiencies of 3-amino-1,2,4-triazole (3-ATA), 2-amino-1,3,4-thiadiazole (2-ATDA), 5-(p-tolyl)-1,3,4-triazole (TTA), 3-amino-5-methylmercapto-1,2,4-triazole (3-AMTA) and 2-aminobenzimidazole (2-ABA) as corrosion inhibitors on steel in sodium chloride media were investigated by using semiempirical PM3 and density functional theory (DFT) methods. Quantum chemical parameters such as highest occupied molecular orbital energy (EHOMO), lowest unoccupied molecular orbital energy (ELUMO), energy gap (DE) and dipole moment (l) have been calculated for these compounds by using semiempirical PM3 and 6-31G(d), 6-311G(d,p) DFT methods. It was found that theoretical data support the experimental results. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Corrosion control can be achieved by many methods, being corrosion inhibitors one of the most effective alternatives for the protection of metallic surfaces against corrosion. A perusal of the literature on corrosion inhibitors reveals that most organic inhibitors employed as corrosion inhibitors contain nitrogen, oxygen, sulphur and/or aromatic ring in their molecular structure [1–4]. Between the organic compounds of interest, triazoles have been studied extensively because of their corrosion inhibition properties [5–10]. The corrosion inhibition efficiency of various organic compounds on the corrosion of steel in NaCl medium has been investigated experimentally by several researchers [11–15]. Experimental means are useful in explaining the inhibition mechanism but they are often expensive and time-consuming. Advances in computer hardware and software and in theoretical chemistry have brought high-performance computing and graphic tools within the reach of many academic and industrial laboratories. Recently, more corrosion publications contain substantial quantum chemical calculations [16]. Such calculations are usually used to explore the relationship between the inhibitor molecular properties and their corrosion inhibition efficiencies. However, far too little attention has been paid to the quantum chemical studies of triazole derivatives in NaCl media [17–20]. The inhibitive properties of five different organic compounds, namely 3-amino-1,2,4-triazole (3-ATA), 2-amino-1,3,4-thiadiazole (2-ATDA), 5-(p-tolyl)-1,3,4-triazole (TTA), 3-amino-5-methylmercapto-1,2,4-triazole (3-AMTA) and 2-aminobenzimidazole (2-
* Corresponding author. Tel.: +90 312 2126720; fax: +90 312 2232395. E-mail address: [email protected] (G. Gece). 0010-938X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.corsci.2009.04.003
ABA) have been reported in a previous experimental study [15]. The aim of this paper is to extend these investigations in order to discuss the relationship between quantum chemical calculations and experimental inhibition efficiencies of the inhibitors by determining the quantum chemical parameters such as the energies of highest occupied molecular orbital (EHOMO) and the lowest unoccupied molecular orbital (ELUMO), the energy difference (DE) between EHOMO and ELUMO and dipole moment (l). 2. Calculation method In order to find optimized conformations of the compounds studied and to speed up the calculations, the molecular structures were optimized initially with PM3 [21] semiempirical calculation. The convergence was set to 0.001 kcal mol 1. The structures obtained from PM3 calculation were fully re-optimized by using DFT (density functional theory) methods to estimate the quantum chemical parameters. Calculations at the DFT level were performed using two basis sets, 6-31G(d) and 6-311G(d,p) with Becke-3-Lee– Yang–Parr (B3LYP) functional [22,23]. In all cases, total structure optimization together with the vibrational analysis of the optimized structures were carried out by means of the HyperChem software [24] in order to determine whether they correspond to a maximum or a minimum in the potential energy curve. 3. Results and discussion The chemical structures of the compounds studied are given in Fig. 1. The optimized molecular structures of the studied molecules using hybrid DFT functional (B3LYP/6-31G*) are shown in Fig. 2 and the calculated quantum chemical indices EHOMO, ELUMO, DE and dipole moment (l) are given in Table 1.
1877
G. Gece, S. Bilgiç / Corrosion Science 51 (2009) 1876–1878
H N
H
N 3-Amino-1,3,4-triazole
N H
N
N 2-Amino-1,3,4-thiadiazole
3-ATA
N
H
H N H
H S
2-ATDA
NH 2 N 3-Amino-5-methylmercapto-1,2,4-triazole
H3C S
N
3-AMTA
N N H
N CH3
5-(p-Tolyl)-1,3,4-triazole
TTA
N H
N 2-Aminobenzimidazole
NH2
2-ABA
N H Fig. 1. Abbreviations and molecular structures of the studied compounds.
According to the frontier molecular orbital theory, the formation of a transition state is due to an interaction between frontier orbitals (HOMO and LUMO) of reacting species [25]. Thus, the treatment of the frontier molecular orbitals separately from the other orbitals is based on the general principles governing the nature of chemical reactions. HOMO is often associated with the electron donating ability of a molecule. High EHOMO values indicate that the molecule has a tendency to donate electrons to appropriate acceptor molecules with low energy empty molecular orbital. Increasing values of the EHOMO facilitate adsorption (and therefore inhibition) by influencing the transport process through the adsorbed layer [16]. ELUMO indicates the ability of the molecules to accept electrons. The lower values of ELUMO, the more probable it is that the molecule would accept electrons [16]. Low absolute values of the energy band gap (DE) gives good inhibition efficiencies, because the energy to remove an electron from the last occupied orbital will be low [16]. The results obtained by 6-311G(d,p)/B3LYP/6-311G(d,p) method (Table 1) show that 2-ABA has the highest HOMO energy (EHOMO) and the lowest LUMO energy (ELUMO) among these organic heterocyclic compounds. Another point to be considered is the HOMO–LUMO gap (DE), i.e., the difference between the HOMO and LUMO energies for the compounds. 2-ABA has the smaller energy gap as compared to other molecules. According to these theoretical results and the experimentally found inhibition efficiencies, it can be said that 2-ABA has more inclination to get adsorbed on the metal surface than TTA. The binding capability of a molecule with metal depends also on the electronic charge on the chelating atom. Thus, the atomic charge values were obtained by the Mulliken population analysis [26]. Table 2 presents Mulliken charges of the selected atoms of the compounds
studied. From the atomic charge values listed, 10N atom of 2-ABA has excess electron density ( 0.42) which increases the p-electron density in the aromatic ring. However, 6N ( 0.09) and 7N ( 0.04) atoms in the triazole ring of TTA would contribute less to the p-system when compared to 2-ABA. It is well known that the chelating or binding capability of a molecule with a metal depended on the electronic charge on the chelating or active atoms, i.e. the more negative the charge, the stronger of the binding capability. Therefore, 2-ABA is easier to bond with metal than TTA. Since 3-ATA, 3-AMTA and 2-ATDA molecules do not have an aromatic ring, they can be judged considering their electron-donating groups. 6S (0.44) atom in the thiadiazole ring of 2-ATDA makes the molecule less polar than the triazole ring in 3-ATA and 3-AMTA due to the scarcity of electron density. Thus, 3-ATA and 3-AMTA have been presumed to be more effective inhibitors than 2-ATDA. 10S ( 0.34) atom of 3-AMTA breaks the planarity of the molecule and imparts a nonpolar character. This accounts for the higher inhibition efficiency of 3-ATA, compared to 3-AMTA. The dipole moment (l) is another indicator of the electronic distribution in a molecule and is one of the properties used to discuss and to rationalize the structure [27]. No significant relationship has been found between the dipole moment values and inhibition efficiencies. Besides, there is a lack of agreement in the literature on the correlation between the dipole moment and inhibition efficiency [28–31].
4. Conclusions Through PM3 semiempirical and DFT quantum chemical calculations a correlation between parameters related to the electronic
1878
G. Gece, S. Bilgiç / Corrosion Science 51 (2009) 1876–1878
Table 1 Calculated quantum chemical parameters of the studied compounds. Molecule
PM3 EHOMO
2-ATDA 3-AMTA 3-ATA TTA 2-ABA a
9.473 8.748 8.927 9.195 8.747
6-31G(d) ELUMO 0.935 0.467 0.222 2.357 0.135
DE
l
8.538 8.281 9.149 6.838 8.612
3.39 1.67 2.41 5.69 2.79
EHOMO 6.366 5.898 5.755 6.842 5.791
g (%)a
6-311G(d,p) ELUMO 2.294 0.427 1.368 4.168 3.510
DE
l
4.072 5.471 4.387 2.674 2.281
3.99 1.66 1.92 5.82 3.84
EHOMO
ELUMO
6.742 5.936 5.911 5.894 5.838
0.342 0.407 0.162 0.247 0.526
DE
l
6.400 5.529 5.749 5.647 5.312
4.01 1.68 2.12 5.84 3.86
74 77 82 86 94
Values from Ref. [15].
Table 2 Mulliken charge data of the compounds. 3N 2-ATDA 3-AMTA 3-ATA TTA 2-ABA
0.11 0.17 0.21 0.20 –
4N
5N
–
0.13 0.21
– – –
– – – –
6N – 0.17 0.19 0.09 –
7N 0.64 0.38 0.26 0.04 0.21
8N
10N
6S
10S
– –
– – – –
0.44 – – – –
–
0.39 – 0.28
0.42
0.34 – – –
References
Fig. 2. Optimized structures of the compounds.
structure of some cyclic nitrogen compounds and their ability to inhibit the corrosion process could be established. The highest occupied molecular orbital energy levels and energy gaps calculated by 6-311G(d,p) DFT study show reasonably good correlation as compared to other calculated data. Comparison of theoretical and experimental data exhibit good correlation confirming the reliability of the method employed here.
[1] R. Hasanov, M. Sadıkog˘lu, S. Bilgiç, Appl. Surf. Sci. 253 (2007) 3913. [2] M. Özcan, R. Solmaz, G. Kardasß, I. Dehri, Coll. Surf. A: Physicochem. Eng. Aspects 325 (2008) 57. [3] K. Bhrara, H. Kim, G. Singh, Corros. Sci. 50 (2008) 2747. [4] M. Behpour, S.M. Ghoreishi, N. Soltani, M. Salavati-Niasari, M. Hamadanian, A. Gandomi, Corros. Sci. 50 (2008) 2172. [5] S. Ramesh, S. Rajeswari, Electrochim. Acta 49 (2004) 811. [6] L.G. Qiu, A.J. Xie, Y.H. Shen, Mater. Chem. Phys. 91 (2005) 269. [7] E.H. El Ashry, A. El Nemr, S.A. Esawy, S. Ragab, Electrochim. Acta 51 (2006) 3957. [8] H.H. Hassan, E. Abdelghani, M.A. Amin, Electrochim. Acta 52 (2007) 6359. [9] F. Xu, J. Duan, S. Zhang, B. Hou, Mater. Lett. 62 (2008) 4072. [10] M. Lebrini, M. Traisnel, M. Lagrenée, B. Mernari, F. Bentiss, Corros. Sci. 50 (2008) 473. [11] F. Blekkenhorst, G.M. Ferrari, G.J. van der Wekken, F.B. Ijsseling, Brit. Corros. J. 21 (1988) 165. [12] F.B. Ijsseling, Brit. Corros. J. 24 (1989) 55. [13] Y.C. Lin, S.L. Chang, S.L. Lee, J. Appl. Electrochem. 29 (1999) 911. [14] G. Yang, L. Ying, L. Haichao, Corros. Sci. 43 (2001) 397. [15] M. S ß ahin, S. Bilgiç, H. Yılmaz, Appl. Surf. Sci. 195 (2002) 1. [16] G. Gece, Corros. Sci. 50 (2008) 2981. [17] O. Blajiev, A. Hubin, Electrochim. Acta 49 (2004) 2761. [18] N.K. Allam, Appl. Surf. Sci. 253 (2007) 4570. [19] M. S ß ahin, G. Gece, F. Karcı, S. Bilgiç, J. Appl. Electrochem. 38 (2008) 809. [20] M. Finšgar, A. Lesar, A. Kokalj, I. Milošev, Electrochim. Acta 53 (2008) 8287. [21] J.J.P. Stewart, J. Comput. Chem. 10 (1989) 209. [22] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [23] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1998) 85. [24] HyperChem (TM) Professional 7.5 (evaluation version), Hypercube Inc., Gainesville, FL, USA. [25] K. Fukui, Theory of Orientation and Stereoselection, Springer-Verlag, New York, 1975. [26] J.N. Murrell, S.F. Kettle, J.M. Tedder, The Chemical Bond, John Wiley & Sons, Chichester, 1985. [27] O. Kikuchi, Quant. Struct.-Act. Relat. 6 (1987) 179. [28] G. Gao, C. Liang, Electrochim. Acta 52 (2007) 4554. [29] N. Khalil, Electrochim. Acta 48 (2003) 2635. [30] L.M. Rodrigez-Valdez, A. Martinez-Villafane, D. Glossman-Mitnik, J. Mol. Struct. (THEOCHEM) 713 (2005) 65. [31] A. Stoyanova, G. Petkova, S.D. Peyerimhoff, Chem. Phys. 279 (2002) 1.