English

• 1. INTRODUCTION

  Hydrochloric acid solution is one of the most widely used agents for industrial acid cleaning, oil well acidizing, acid descaling and so on. The metal dissolution in the corrosive media leads to economic loss, decreasing the lifetime of equipment and wasting resources. Nowadays, organic inhibitors containing hetero-atoms, unsaturated bonds, or plane conjugated system are widely used as corrosion inhibitors by forming a protective film on metal surface^[1-4]. Even so, the stability of the inhibitor filmformed over the metal surfacedepends on many factors such as the functional groups, aromaticity, possible steric effects, electronic density of donors andnature of interaction between the p-orbital of inhibitors with the d-orbital of iron^[5-8]. Thus, discov ering a suitable corrosion inhibitor that exhibits a greater inhibition effect remains a challenging objective in the field of corrosion chemistry.

  With the development of modern computer technology, theoretical methods are used in the field of corrosion to explain the inhibition mechanism, including quantitatively characterizing the electronic structures of organic inhibitors from the molecular and electronic levels, establishing the relationship between the corrosion inhibition efficiencies and the molecular reactivity as well as a rigorous modeling of the interaction between metal surface and inhibitors^[9-13]. All these kinds of researches require the understanding of electronic properties of inhibitors and the clarification of interaction between inhibitor molecules and the metal surface. So far, DFTcalculations and molecular dynamics (MD) simulations which can provide insights into the design of inhibitor systems with superior properties and elucidate the adsorption process at molecular level^[18] are the effective tools for the study.

  Benzimidazole and its derivatives play a vital role in biological fields such as antimicrobial^[19], antitumor^[20], antidiabetic^[21] and antispasmodic^[23]. A perusal of literature^{[1, 22]} revealed that many benzimidazole derivatives also perform different inhibitive propertieswith the differences in substituent positions on the imidazole rings and different substituent groups. Of all the benzimidazole derivatives, 2-substituted benzimidazole derivatives have been found to be biologically most potent as well as to be effective inhibitors for mild steel in acidic media. Though the use of benzimidazole and its derivatives as corrosion inhibitors for mild steel in acidic media have been reported^[24], the use of DTF studies and MD method in probing the mechanismof inhibition action is scanty.

  In the present work, four newly synthesized benzimidazole derivatives: 1-butyl-2-(4-methylphenyl) benzimidazole (a), 1-butyl-2-(4-bromolphenyl) benzimidazole (b), 1-ethyl-2-{(4-(9H-carbazole-9-yl) phenyl}benzimidazole (c) and 4-(1-ethyl-¹H-benzimidazol-2-yl)-N, N-diaphenylbenzenamine (d) were synthesized (reported in a recent experimental study^[25]). The substituent R1 was selected as methyl (-CH₃), Br, carbazolyl or N, N-diphenylamino groups, and the C, Br, N atoms in the substituents are marked as C (16), Br (16) and N (16), respectively (Scheme 1). Potentiodynamic polarization measurementwas used to study the inhibition performance of the four benzimidazole compounds in 1.0 M HCl. And then, DFT calculation and MD methodswere used to explain the inhibition mechanism as well as to reveal the relationship between the molecular structures and inhibition performance.

  Figure Scheme 1

  

  Figure Scheme 1.  Skelton structure of the studied benzimidazoles

  DownLoad: Full-Size Img PowerPoint

  2. EXPERIMENTAL

  2.1. Electrochemical studies of the corrosion inhibition

  Electrochemical experiments were carried out using a ZAHNER IM6ex electrochemical workstation, which was controlled by ZAHNWR THALES software. A classical three-electrode cell, which contained 100 mL of electrolyte solution, was used with a platinum counter electrode and a saturated calomel reference electrode (SCE). The working electrode (WE), which was a flat carbonsteel specimen with an exposed area of 0.5 cm 2, was mechanically polished using different grades of emery paper (120 ～ 1200) for the study, as the specimen must be degreased with acetoneand washed with distilled water to avoid carbon pollution. An aggressiveHCl solution (1.0 M) was used asa corrosive medium. In order to apply the electrochemical Table 1 extrapolation, a polarization study was carried out in the corrosion potential range from-300 up to 300 mV. The scan rate was 1.0 mV/s as thisvalue allowed the quasi-stationary state measurements.

  2.2. Quantum chemical calculations

  Theoretical calculations were carried out using density functional theory (DFT/B3LYP) at the 6-31+G^* basis set for all atoms with Gaussian 03W program^[26]. Since the phenomenon of electrochemical corrosion appears in acidic solution, it is necessary to consider the effect of a solvent in the theoretical calculations. Thus, the IEFPCM model was used to perform calculations in solution. By using the theoretical calculation, the following quantum chemical indices were determined: such as energy of the highest occupied molecular orbital (E_HOMO), energy of the lowest unoccupied molecular orbital (E_LUMO), energy gap (ΔE) between LUMO and HOMO, dipole moment (μ) and Mulliken charges. The optimized molecular structures and HOMO, LUMO surfaces were visualized using Gauss View.

  2.3. Molecular dynamics simulations

  In order to reveal the most suitable adsorption modes and elucidate the adsorption process at the molecular level,the molecular dynamics simulation studies were performed to discover the interaction between the benzimidazole compound molecules and iron surface using the software of Materials Studio 4.3^[26]. Fe(001) surface was chosen using the sketching in Materials Visualizer. The MD simulations were performed in a three-dimensional simulation box (27.30Å × 27.30Å × 28.08Å) with periodic boundary conditions to model a representative part of the interface devoid of any arbitrary boundary effects. The box contains a Fe and a H₂O slabs including the studied inhibitor molecules. The COMPASS (condensed-phase optimized molecular potentials for atomistic simulation studies) force field was used to optimize the structures of components of the system (Fe + H₂O + inhibitors). During simulations,all the bulk atoms in the Fe(001) plane were kept “frozen”,and both the inhibitor and H₂O molecules were allowed to contact the metal surface freely. The MD simulations were carried out at 298 K,NVT ensemble,with a time step of 12 fs and the simulation time of 1000 ps. The interaction energy (E_interaction) between the iron surface and the inhibitor molecules was calculated according to the following equation:

  1 ${{E}_{\text{interaction}}}={{E}_{\text{total}}}-\left( {{E}_{\text{surface+}{{\text{H}}_{2}}\text{O}}}+{{E}_{\text{nhibitor}}} \right)$ $

  where E_total is the total energy of the simulation system, and E_{surface + H2O} and E_inhibitor are the total energies of the system containing the iron surface together with H₂O molecules and the energy of free inhibitor molecules, respectively.

  3. RESULTS AND DISCUSSION

  3.1. Potentiodynamic polarization experiments

  The kinetics of the cathodic and anodic reactions occurring onWE at 30 oC in 1.0 M HCl in the absence and presence with several concentrations of the four benzimidazolecompounds were studied through the potentiodynamic polarization measurem ents and the polarization curves are shown in Fig. 1. The values of related electrochemical parameters, i.e., corrosion potential ( E_corr ), corrosion current density ( i_corr ), the anodic Table 1 slope ( b_a ) and the cathodic Table 1 slope ( b_c ), obtained by extrapolating the anodic and cathodic Table 1 curves are listed in Table 1. The corrosion inhibition efficiency (E), calculated by Eq. (2), is also listed in Table 1.

  2 $E = \frac{{i_{{\rm{corr}}}.0 - {i_{{\rm{corr}}}}}}{{{i_{{\rm{corr}}}}}} \times 100\% $ $

  Table 1

  

  Table 1.  Electrochemical Parameters for Carbon Steel in 1 M HCl Containing Various Concentrations of a, b, c, d at 30 oC

  DownLoad: CSV

  C_inh(mg·L^-1)E_corr(mV vs. SCE)i_corr(μA cm^-2)b_c(mV dec^-1)b_aE(%)(mV dec^-1)E (%)Blank–459.91.52413480.9–25–467.30.77613185.949.125–461.90.82412473.245.925–473.70.59412867.66125–479.60.49412498.467.6150–503.90.17913513088.3

  a	50	–476.9	0.352	122	81.2	76.9
  	100	–489.5	0.22	119	95.3	85.6
  	150	–493.9	0.164	119	110	89.2
  b	50	–485.1	0.388	128	77.2	74.5
  	100	–497.3	0.246	123	87.7	83.9
  	150	–506.7	0.153	118	89.4	90
  c	50	–478.8	0.47	114	79.5	69.2
  	100	–492.9	0.364	123	91.9	76.1
  	150	–493.4	0.284	126	83.5	81.4
  d	50	–484.5	0.366	122	95.4	76
  	100	–486.7	0.25	122	111	83.6

  Figure 1

  

  Figure 1.  Potentiodynamic polarization curves for carbon steel in 1 mol·L^-1 HCl containing inhibitors a, b, c and d

  DownLoad: Full-Size Img PowerPoint

  where i_corr⁰ and i_corr are the corrosion current density values without and with inhibitor, respectively. It can be seen from Fig. 1 that the addition of the four benzimidazole compounds all causes a remarkable shift in both anodic and cathodic Table 1 curvesto lower the current densities. This phenolmenon indicates that both anodic metal dissolution and cathodic hydrogen evolution reactions are drastically inhibited. The cathodic Table 1 curves give riseto almost parallel lines, meaning the hydrogen evolution is activation-controlled and the reduction of H⁺ on the WE surface occurs mainly through a charge transfer mechanism. For the anodic part of the Table 1 curves, it is apparent that the anodic reaction is evidentlyinhibited in the presence of inhibitors. The higher concentration of inhibitors provides better inhibition efficiency. The effect was maximal for the concentration of 150 mg L^-1, which is the optimum concentration of inhibitor required to achieve the efficiency (E = 90%).

  With the inspection of Table 1, no obvious shift wasfound in the corrosion potential in response to the addition of different benzimidazole compound concentrations. This can be interpreted that all these compounds act as the mixed type inhibitors. After adding inhibitors to the blank solution, the values of corrosion current density decrease, and the inhibition efficiencies increase sharply. Furthermore, the cathodic Table 1 slope remains almost constant and the anodic Table 1 slope changes in the presence of these benzimidazole compounds. It can be inferredthat the four inhibitors can affect the kinetics of the anodic process. The order of inhibition efficiencies obtained from potentiodynamic polarization meas urements for the concentration 20 mg L^-1 is d > c > a > b.

  3.2. Quantum chemical calculations

  The optimized molecular structuresof the studied molecules using hybrid DFT functional (B3LYP/631+G^*) are shown in Fig. 2, and their HOMO and LUMO orbitals are also depicted in Fig. 2. The effectiveness of an inhibitor can be related with its electronic and spatial molecular structures. Also, there are quantum-chemical parameters that can be related to the interaction metal-inhibitors, which are HOMOthat is often associated with the capacity of a molecule to donate e lectrons (E_HOMO), the gap energy (ΔE), and the dipole moment (μ). By using the DFT calculations (both in gas phase and solvent, ε= 78.39), all these indices were predicted. Their values are presented in Table 2. The calculation parameters in gas phase as well as in the presenceof acidic solution do not exhibit important difference. However, the dipole moment values in aqueous are muchhigher than in gas phase due to the polarity of the solvent that increases the polarity of the chemical bonds of the inhibitor molecules.

  Figure 2

  

  Figure 2.  Optimized molecular structures, HOMO and LUMO forthe inhibitors using DFT/B3LYP/6-31+G^*

  DownLoad: Full-Size Img PowerPoint

  The global molecular reactivity can be studied according to the frontier molecular orbital theory: the formation of a transition state is due to an interaction between the frontier orbitals (HOMO and LUMO) of reacting species^[27]. Thus,the HOMO energy can indicate the disposition of the molecule to donate electrons to an appropriated acceptor with empty molecular orbitals,and also an increase in the values of E_HOMO can facilitate the adsorption,and then the inhibition efficiency will increase. E_LUMO indicates the ability of the molecules to accept electrons. The lower values of E_LUMO,the more probable it is that the molecule would accept electrons^[28]. The obtained values of E_LUMO corresponding to each organic inhibitor have a small difference between them,which indicates a very similar capacity for charge donation to the metallic surface. The corrosion efficiency must decrease with the increase in HOMO energy (less negative). As seen from Table 2,the trend of E_HOMO is d > c > a > b,which agrees very well with the experimental results (Table 1). These results can be interpreted in terms of the increasing number of centers of adsorption on the inhibitor molecules,which will be confirmed in the later Fukui indices discussion. Thus,it can conclude that E_HOMO is a good quantity to correlate with experimental inhibition efficiencies of the inhibitors under investigation.

  Table 2

  

  Table 2.  Total Energy, HOMO and LUMO Energies, HOMO-LUMO Gap (ΔE) and DipoleMoment for a, b, c and d, Obtained with DFT/B3LYP/6-31+G^* in the Gas Phase and in the Presence of Acidic Solution

  DownLoad: CSV

  Molecule gas/solventTotal energy(Ha)E_HOMO(eV)E_LUMO(eV)ΔE(eV)μ(Debye)a-807.52/-807.53-5.94/-6.22-1.16/-1.284.78/4.943.53/5.40d-1207.04/-1207.06-5.31/-5.40-1.28/-1.384.03/4.023.91/5.95

  b	-3260.71/-3260.72	-6.15/-6.31	-1.50/-1.50	4.65/4.81	3.63/5.42
  c	-1205.86/-1205.88	-5.67/-5.79	-1.51/-1.50	4.16/4.29	4.11/5.99

  The gap energy between the frontier orbitals ΔE (ΔE = E_HOMO E_LUMO) is usually of great vital importance in describing the static molecularreactivity. Indeed, the large values of ΔE imply high electronic stability and then low reactivity, when low values imply high reactivity^[30]. In our case, compound d has the smallest ΔE that implied the highest reactivity and the best corrosion inhibition efficiency, which is also a good quantity to correlate with the experimental investigation.

  The dipole moment μprovides information on the polarity of the whole molecule. High dipole moment is reflected in important molecular polarity which probably gives rise to high chemical reactivity^[30]. The values of the dipole moment displayed in Table 2 showed that compounds c and d have relatively higher dipole moment values,which will increase their molecular reactivity,thus leading to stronger adsorption onto the mild steel surface. This study is also in nearly good agreement with the experimental corrosion inhibition efficiencies.

  It can be concluded from the results of most global descriptors in gas and aqueous phases that compound d is the best inhibitor among the four studied molecules.

  3 ${f_k} = {\left( {\frac{{\partial \rho \overrightarrow {\left( r \right)} }}{{\partial N}}} \right)_{v\overrightarrow {\left( r \right)} }}$ $

  The condensed Fukui functions can be calculated as:

  $\begin{array}{l} f_k. + = {q_k}\left( {N + 1} \right) - {q_k}\left( N \right)\\ f_k. - = {q_k}\left( N \right) - {q_k}\left( {N - 1} \right) \end{array}$ $

  where q_k(N),q_k(N+1) and q_k(N-1) are the electronic densities of neutral,anionic and cationic species,respectively; f_k⁺ and f_k^- are for electrophilic and nucleophilic attack,respectively. Generally,the preferred site for nucleophilic attack is the region with high values of f_k ⁺ ,while the region with high value of f_k^- is the preferred site for electrophilic attack^[32].

  The local molecular reactivity of the studied inhibitors is investigated using the condensed Fukui functions. In case of an electron-transfer controlled reaction,these descriptors inform about the sites in a molecule on which nucleophilic,electrophilic or radical attacks are most likely possible. Table 3 displays the most relevant values of the natural population ( q_k(N) ,q_k(N+1) and q_k(N-1) ) with the corresponding values of the Fukui functions ( f_k⁺ and f_k^- ) of the studied inhibitors.

  Table 3

  

  Table 3.  Mulliken Atomic Charges and Fukui Indicesfor Compounds a, b, c and d

  DownLoad: CSV

  MoleculeAtomq_k(N+1)q_k(N)q_k(N-1)f_k⁺f_k^-aC(2)–0.401–0.300–0.1960.1010.104bC(2)–0.385–0.324–0.2370.0610.087cC(2)–0.549–0.490–0.4830.0590.007dC(2)–0.521–0.454–0.4440.0670.01N(16)0.1460.1770.2780.0310.101

  C(5)	–0.810	–0.700	–0.634	0.11	0.066
  N(7)	–0.082	–0.058	–0.005	0.024	0.053
  N(8)	–0.466	–0.347	–0.192	0.119	0.155
  C(9)	0.512	0.451	0.345	–0.061	–0.106
  C(10)	0.075	0.232	0.262	0.157	0.03
  C(11)	–0.259	–0.163	–0.089	0.096	0.074
  C(16)	–0.787	–0.754	–0.733	0.033	0.021
  C(5)	–0.705	–0.630	–0.568	0.075	0.062
  N(7)	–0.162	–0.137	–0.084	0.025	0.053
  N(8)	–0.457	–0.346	–0.191	0.111	0.155
  C(9)	0.487	0.442	0.379	–0.045	–0.063
  C(10)	–0.335	–0.280	–0.198	0.055	0.082
  C(11)	0.037	0.094	0.094	0.057	0
  Br(16)	–0.069	0.013	0.068	0.082	0.055
  C(5)	–0.691	–0.612	–0.605	0.079	0.007
  N(7)	–0.121	–0.094	–0.086	0.027	0.008
  N(8)	–0.436	–0.323	–0.298	0.112	0.025
  C(9)	0.424	0.344	0.304	–0.080	–0.040
  C(10)	–0.314	–0.206	–0.205	0.108	0
  C(11)	–0.193	–0.133	–0.114	0.06	0.019
  N(16)	0.313	0.37	0.525	0.057	0.155
  C(5)	–0.755	–0.669	–0.656	0.087	0.013
  N(7)	–0.161	–0.134	–0.121	0.027	0.013
  N(8)	–0.455	–0.349	–0.306	0.106	0.044
  C(9)	0.408	0.353	0.301	–0.055	–0.052
  C(10)	–0.463	–0.384	–0.403	0.079	–0.019
  C(11)	0.032	0.082	0.138	0.05	0.056

  The calculated Fukui functions are in good agreement with the results of HOMO electron densities (see Fig. 2),given that the N(16) atom in compounds c and d have the highest value of f_k^- ,which means that it would probably be the favorite site for nucleophilic attacks. Moreover,the results show that the C(2),C(5),C(10) and C(11) atoms can also be suitable sites to undergo both nucleophlic and electrophlic attacks,indicating all four inhibitors have several adsorption active-centers. And we can predict that these four molecules adsorb parallelly on the surface of the iron metal.

  3.3. Molecular dynamics simulations

  In order to investigate the most suitable adsorption modes for the inhibitor molecules, molecule dynamics tools were used to investigate the four inhibitors on the Fe (001) plane, respectively. Admittedly, the simulations in the vacuum slab can not reflect the real adsorption condition. Hence, the MD simulations in aqueous solution were carried out, as shown in Fig. 3. The system reaches equilibrium only if both of the energy and temperature reach balance^{[33, 34]}. It could be noticed from Fig. 3 that all the inhibitors adsorbed nearly parallelly to the iron surface where a chemical bond could occur through donating π electrons of the benzimidazole rings as well as the benzene rings and the lone pair electrons of the nitro atoms to the metal. Table 4 lists the values of interaction and binding energies (E_binding = -E_interaction)^[35]. All values of adsorption E are negative, which means that the adsorption could occur spontaneously. The high values of adsorption E (absolute value) for compounds c and d reflect higher stability of the formed complex and accordingly increase their inhibition efficiencies, which agrees well with the experimental results. The higher the value of binding energy, the easier the inhibitor adsorbs on the metal surface, and the higher the inhibition efficiency shows.

  Figure 3

  

  Figure 3.  Adsorption configurations of the four inhibitor molecules on the steel surface

  DownLoad: Full-Size Img PowerPoint

  Table 4

  

  Table 4.  Adsorption and Binding Energieson the Iron (001) Surface for theFour Inhibitors

  DownLoad: CSV

  InhibitorE_ads.(kcal/mol)E_bind(kcal/mol)a–128.77128.77d–165.23165.23

  b	–109.94	109.94
  c	–175.00	175

  4. CONCLUSION

  The inhibition efficiency of four 1-alkyl-2-substituted benzimidazole compounds (a, b, c and d) has been studied as inhibitors for the corrosion of carbon steel in 1.0 M HCl using potentiodynamic pola- rization and the correlation between the quantum chemical parameters and inhibition efficiency of these compounds was investigated using DFT/B3LYP calculations as well as molecular dynamics. The following conclusions were drawn from this study:

  (1) The four benzimidazole inhibitors act as mixed-type inhibitors and the inhibition efficiency increases when the concentration of inhibitor increases.

  (2) The EHOMO and the gap energy between the frontier orbitals (ΔE) and the dipole moment μ are in good agreement with the experimental observations.

  (3) The local molecular reactivity indicates that all the four inhibitors have several adsorption activecenters. As for compounds c and d, their N (16) atoms are the main adsorption active-centers.

  (4) Molecular dynamics results show that these four molecules adsorb nearly parallelly on the surface of iron metal, and it was observed that the adsorption occurs mostly through benzene ring and the lone pair electrons of nitro atoms

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  Scheme 1  Skelton structure of the studied benzimidazoles

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  Figure 1  Potentiodynamic polarization curves for carbon steel in 1 mol·L^-1 HCl containing inhibitors a, b, c and d

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  Figure 2  Optimized molecular structures, HOMO and LUMO forthe inhibitors using DFT/B3LYP/6-31+G^*

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  Figure 3  Adsorption configurations of the four inhibitor molecules on the steel surface

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  Table 1.  Electrochemical Parameters for Carbon Steel in 1 M HCl Containing Various Concentrations of a, b, c, d at 30 oC

  C_inh(mg·L^-1)E_corr(mV vs. SCE)i_corr(μA cm^-2)b_c(mV dec^-1)b_aE(%)(mV dec^-1)E (%)Blank–459.91.52413480.9–25–467.30.77613185.949.125–461.90.82412473.245.925–473.70.59412867.66125–479.60.49412498.467.6150–503.90.17913513088.3

  a	50	–476.9	0.352	122	81.2	76.9
  	100	–489.5	0.22	119	95.3	85.6
  	150	–493.9	0.164	119	110	89.2
  b	50	–485.1	0.388	128	77.2	74.5
  	100	–497.3	0.246	123	87.7	83.9
  	150	–506.7	0.153	118	89.4	90
  c	50	–478.8	0.47	114	79.5	69.2
  	100	–492.9	0.364	123	91.9	76.1
  	150	–493.4	0.284	126	83.5	81.4
  d	50	–484.5	0.366	122	95.4	76
  	100	–486.7	0.25	122	111	83.6

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  Table 2.  Total Energy, HOMO and LUMO Energies, HOMO-LUMO Gap (ΔE) and DipoleMoment for a, b, c and d, Obtained with DFT/B3LYP/6-31+G^* in the Gas Phase and in the Presence of Acidic Solution

  Molecule gas/solventTotal energy(Ha)E_HOMO(eV)E_LUMO(eV)ΔE(eV)μ(Debye)a-807.52/-807.53-5.94/-6.22-1.16/-1.284.78/4.943.53/5.40d-1207.04/-1207.06-5.31/-5.40-1.28/-1.384.03/4.023.91/5.95

  b	-3260.71/-3260.72	-6.15/-6.31	-1.50/-1.50	4.65/4.81	3.63/5.42
  c	-1205.86/-1205.88	-5.67/-5.79	-1.51/-1.50	4.16/4.29	4.11/5.99

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  Table 3.  Mulliken Atomic Charges and Fukui Indicesfor Compounds a, b, c and d

  MoleculeAtomq_k(N+1)q_k(N)q_k(N-1)f_k⁺f_k^-aC(2)–0.401–0.300–0.1960.1010.104bC(2)–0.385–0.324–0.2370.0610.087cC(2)–0.549–0.490–0.4830.0590.007dC(2)–0.521–0.454–0.4440.0670.01N(16)0.1460.1770.2780.0310.101

  C(5)	–0.810	–0.700	–0.634	0.11	0.066
  N(7)	–0.082	–0.058	–0.005	0.024	0.053
  N(8)	–0.466	–0.347	–0.192	0.119	0.155
  C(9)	0.512	0.451	0.345	–0.061	–0.106
  C(10)	0.075	0.232	0.262	0.157	0.03
  C(11)	–0.259	–0.163	–0.089	0.096	0.074
  C(16)	–0.787	–0.754	–0.733	0.033	0.021
  C(5)	–0.705	–0.630	–0.568	0.075	0.062
  N(7)	–0.162	–0.137	–0.084	0.025	0.053
  N(8)	–0.457	–0.346	–0.191	0.111	0.155
  C(9)	0.487	0.442	0.379	–0.045	–0.063
  C(10)	–0.335	–0.280	–0.198	0.055	0.082
  C(11)	0.037	0.094	0.094	0.057	0
  Br(16)	–0.069	0.013	0.068	0.082	0.055
  C(5)	–0.691	–0.612	–0.605	0.079	0.007
  N(7)	–0.121	–0.094	–0.086	0.027	0.008
  N(8)	–0.436	–0.323	–0.298	0.112	0.025
  C(9)	0.424	0.344	0.304	–0.080	–0.040
  C(10)	–0.314	–0.206	–0.205	0.108	0
  C(11)	–0.193	–0.133	–0.114	0.06	0.019
  N(16)	0.313	0.37	0.525	0.057	0.155
  C(5)	–0.755	–0.669	–0.656	0.087	0.013
  N(7)	–0.161	–0.134	–0.121	0.027	0.013
  N(8)	–0.455	–0.349	–0.306	0.106	0.044
  C(9)	0.408	0.353	0.301	–0.055	–0.052
  C(10)	–0.463	–0.384	–0.403	0.079	–0.019
  C(11)	0.032	0.082	0.138	0.05	0.056

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  Table 4.  Adsorption and Binding Energieson the Iron (001) Surface for theFour Inhibitors

  InhibitorE_ads.(kcal/mol)E_bind(kcal/mol)a–128.77128.77d–165.23165.23

  b	–109.94	109.94
  c	–175.00	175

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