Volume 22 Preprint 8


The inhibition performance of thiadiazole derivatives on the steel corrosion: DFT and QSAR assessment

Aezeden Mohamed, Ahmad I. Alrawashdeh and John Pumwa

Keywords: corrosion inhibition; density functional theory (DFT); thiadiazole; Fukui indices; QSAR

Abstract:
The performance of five thiadiazole derivatives as steel-corrosion inhibitors in acidic media was investigated using density functional theory. The correlation of inhibition efficiencies of the studied inhibitors with their molecular properties is determined through the calculation of quantum chemical parameters and Fukui functions. Two quantitative structure and activity relationship (QSAR) models are obtained to theoretically predict the efficiencies of the thiadiazole inhibitors in their neutral and protonated species. Our results reveal strong correlations between the performance of the studied inhibitors and most of their calculated quantum parameters. Moreover, the predicted inhibition efficiencies are well compatible with the respective experimental results.

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ISSN 1466-8858 Volume 22, Preprint 8 first submitted 26 February 2019 The inhibition performance of thiadiazole derivatives on the steel corrosion: DFT and QSAR assessment Aezeden Mohameda,d, Ahmad I. Alrawashdehb,c*, and John Pumwad a c Faculty of Engineering and Applied Sciences; bDepartment of Physics and Physical Oceanography, Department of Chemistry, Memorial University of Newfoundland, St. John’s, NL, Canada A1B 3X7 d Department of Mechanical Engineering, PNG University of Technology, Lae, MP 411, Papua New Guinea E-mail: ahmd.raw@mun.ca Abstract The performance of five thiadiazole derivatives as steel-corrosion inhibitors in acidic media was investigated using density functional theory. The correlation of inhibition efficiencies of the studied inhibitors with their molecular properties is determined through the calculation of quantum chemical parameters and Fukui functions. Two quantitative structure and activity relationship (QSAR) models are obtained to theoretically predict the efficiencies of the thiadiazole inhibitors in their neutral and protonated species. Our results reveal strong correlations between the performance of the studied inhibitors and most of their calculated quantum parameters. Moreover, the predicted inhibition efficiencies are well compatible with the respective experimental results. Keywords: corrosion inhibition; density functional theory (DFT); thiadiazole; Fukui indices; QSAR 1. Introduction The corrosion of common metals has been a serious problem since their earliest use and concern about this problem has been dramatically increasing in recent years [1]. In particular, the corrosion of iron and mild steel has attracted significant research interest in both academia and industry [1-4]. With several methods available, corrosion inhibition can provide a simple, costly-effective, and practical technique to prevent the metal’s corrosion especially in acidic and highly corrosive media [5]. Many kind of inhibitors are widely employed in industrial applications for preventing the metal’s dissolution due to corrosion [6]. A number of heterocyclic organic molecules were found as effective inhibitors against the corrosion of mild steels in acidic environments [7-10]. Organic inhibitors containing one or more electron-rich atoms (i.e., O, N, S, or P), unsaturated, or π-conjugated bonds can effectively interact with atoms of the metal or be adsorbed on its surface [2]. The existence of electron1 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work. ISSN 1466-8858 Volume 22, Preprint 8 first submitted 26 February 2019 rich atoms in an inhibitor and its geometry are of great importance in determining its inhibitory properties [2,5]. Organic inhibitors minimize the corrosion process by adsorbing (chemically or physically) on the surfaces of metals providing barriers which protect metals from further corrosion [11]. With the aid of advances in computer science, several computational approaches have been used by researchers for conducting successful studies in the area of metallic corrosion inhibition [12–20]. It is well established that quantum chemical methods provide useful means for the determination of electronic structures, geometries, reactivities, and many other properties of chemical and biological molecules [12]. Quantum methods may provide evaluations and predictions for inhibition efficiencies faster and may cost less than the experimentally traditional methods [16,20]. Density functional theory (DFT) which incorporates some electron correlations is a successful and computationally inexpensive method for the calculation of molecular properties [21]. In DFT calculations, the reactivities, shapes, binding properties, and inhibition efficiencies of organic inhibitors are evaluated and determined using several factors and parameters such as: frontier molecular orbital energies (EHOMO and ELUMO) and their energies gap (∆EHL), electronegativity (χ), dipole moment (µ), ionization potential (I), electron affinity (A), softness (σ), hardness (η), and the fraction of electrons transferred (∆N) [14,19,21]. In this contribution, we employed DFT with the aim of providing theoretical insights and correlating the inhibition efficiencies of five thiadiazole inhibitors to their molecular properties. Our intention is to connect the electronic structure properties of the thiadiazole inhibitors, determined computationally using DFT, with the experimental outcomes. We also aim to provide a quantitative relationship that can be used to predict the inhibition efficiencies of the studied molecules from some of their quantum chemical parameters. We believe that this study can be useful in choosing an appropriate corrosion inhibitor before beginning expensive experimental work. 2. Computational Method We have used the Gaussian 09 program to execute all the quantum chemical computations in this work [22]. For all the calculations and geometry optimizations, we employed the B3LYP [23,24] density functional method with the 6-31++G(df,p) basis set. The effect of solvent (water) on the structures and energetics of each studied inhibitor has been investigated using the polarizable continuum model (PCM) [25]. Full geometry optimization for all studied inhibitors were performed using the B3LYP/631++G(df,p) level in PCM. 2 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work. ISSN 1466-8858 Volume 22, Preprint 8 first submitted 26 February 2019 In this study, we investigate the adsorption behaviour of inhibitors on metallic surfaces and their corrosion inhibition efficiencies using the frontier molecular orbital (FMO) theory [26]. In the FMO theory, the most important molecular orbitals (MOs) that play major roles in the chemical reactivity of molecules are the highest occupied and the lowest unoccupied MOs (HOMO and LUMO). The HOMO (donor) has the ability to donate electrons and this ability increases as its energy (EHOMO) increases. Contrarily, the LUMO (acceptor) has the ability to receive electrons and this ability decreases as its energy (ELUMO) increases. The gap (∆𝐸𝐸𝐻𝐻𝐻𝐻 = 𝐸𝐸𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 − 𝐸𝐸𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 ) between HOMO and LUMO energies is another important parameter that can be used to determine the inhibition efficiencies of organic molecules. The low ∆𝐸𝐸𝐻𝐻𝐻𝐻 value implies a high efficiency of an inhibitor for preventing the metal’s corrosion. In addition to 𝐸𝐸𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 , 𝐸𝐸𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 , and ∆𝐸𝐸𝐻𝐻𝐻𝐻 , we have also calculated other electronic parameters to investigate the inhibition efficiencies of the thiadiazole inhibitors. The ionization potential (I) and the electron affinity (A) are related to the 𝐸𝐸𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 and 𝐸𝐸𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 by the following relations: 𝐼𝐼 = −𝐸𝐸𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 (1) 𝐴𝐴 = −𝐸𝐸𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 (2) 𝜂𝜂 = (𝐼𝐼 − 𝐴𝐴)/2 (3) The absolute hardness (𝜂𝜂) and electronegativity (𝜒𝜒) of the inhibitors are calculated from 𝐼𝐼 and 𝐴𝐴 values as follows: 𝜒𝜒 = (𝐼𝐼 + 𝐴𝐴)/2 (4) 𝜎𝜎 = 1/𝜂𝜂 (5) The softness (𝜎𝜎) can be defined as the reciprocal of 𝜂𝜂. The fraction of electrons (ΔN) transferred between the frontier orbitals of the inhibitor and iron atoms is calculated as: 𝛥𝛥𝛥𝛥 = 𝜒𝜒𝐹𝐹𝐹𝐹 − 𝜒𝜒𝑖𝑖𝑖𝑖ℎ �2(𝜂𝜂 + 𝜂𝜂 ) 𝐹𝐹𝐹𝐹 𝑖𝑖𝑖𝑖ℎ (6) here 𝜒𝜒𝐹𝐹𝐹𝐹 and 𝜒𝜒𝑖𝑖𝑖𝑖ℎ are the electronegativities of the iron atoms and the inhibitor, respectively, and 𝜂𝜂𝐹𝐹𝐹𝐹 and 𝜂𝜂𝑖𝑖𝑖𝑖ℎ are the hardness of the iron atoms and the inhibitor, respectively. We have used values of 𝜒𝜒𝐹𝐹𝐹𝐹 = 7.0 eV and 𝜂𝜂𝐹𝐹𝐹𝐹 = 0 eV for Fe. The polarity of each studied inhibitor molecule is determined from the dipole moment (𝜇𝜇). We have calculated Fukui functions (𝑓𝑓𝑘𝑘+ 𝑎𝑎𝑛𝑛𝑑𝑑 𝑓𝑓𝑘𝑘− ) using Hirshfeld population analysis. The Fukui functions in the finite difference approximation are defined as follows, 3 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work. ISSN 1466-8858 Volume 22, Preprint 8 𝑓𝑓𝑘𝑘+ = 𝑞𝑞𝑘𝑘 (𝑁𝑁 + 1) − 𝑞𝑞𝑘𝑘 (𝑁𝑁) first submitted 26 February 2019 (for nucleophilic attack) 𝑓𝑓𝑘𝑘− = 𝑞𝑞𝑘𝑘 (𝑁𝑁) − 𝑞𝑞𝑘𝑘 (𝑁𝑁 − 1) (for electrophilic attack) (7) (8) where 𝑁𝑁 is the total number of electrons in the inhibitor molecule; and 𝑞𝑞𝑘𝑘 (𝑁𝑁), 𝑞𝑞𝑘𝑘 (𝑁𝑁 + 1), and 𝑞𝑞𝑘𝑘 (𝑁𝑁 − 1) are the gross charge of the 𝑘𝑘 𝑡𝑡ℎ atom in the neutral molecule, anion, and cation respectively. 3. Results and Discussion Five thiadiazole derivatives were investigated in this work: 2-Amino-1,3,4-thiadiazole (ATD), 5-amino 1,3,4-thiadiazole-2-thiol (ATDT), 2-Amino-5-tert-butyl-1,3,4-thiadiazole (ABTD), 2-amino-5-phenyl1,3,4-thiadiazole (APTD), and 2,5-bis(4-dimethylaminophenyl)-1,3,4-thiadiazole (DAPTD). The chemical structures and optimized geometries of these inhibitors are depicted in Fig. 1. Inhibitor Chemical Structure S Optimized Structure NH2 ATD N N HS ATDT S NH2 N N S NH2 ABTD N N S APTD NH2 N N DAPTD N N S N N Fig. 1. Chemical structures and optimized geometries of the inhibitors investigated in this work. 4 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work. ISSN 1466-8858 Volume 22, Preprint 8 first submitted 26 February 2019 The geometries of all inhibitor’s molecules are fully optimized at the B3LYP/6-31++G(df,p) level with PCM in the aqueous medium. These molecules were investigated experimentally as steel’s corrosion inhibitors in 1 M HCl by Fouad et al., Tang et al., and Bentiss et al. [7-9]. Their inhibition efficiencies were reported as 78.1, 85.5, 83.1, 88.6, and 98.1% for ATD, ATDT, ABTD, APTD, and DAPTD, respectively. 3.1. Protonated forms As mentioned above, the investigated inhibitors were experimentally studied using 1M HCl, therefore, it is essential to consider their protonated forms as they can exist in both neutral and protonated species in the acidic medium. As shown in Fig. 1, each inhibitor molecule contains four or five heteroatoms in which the possible protonation could occur. To determine the most probable site for the protonation, we have calculated the proton affinity, basicity, and total energy for each possible protonation and the results are listed in Table 1. Table 1: Proton affinities (PA) and basicities of investigated inhibitors (in kJ mol-1) at 298.15 K and total energies (in hartree) for their possible protonated forms obtained using the B3LYP/6-31++G(df,p) level with PCM in aqueous phase. The labelling of atoms is shown in Fig. 2. Inhibitor ATD ATDT ABTD APTD DAPTD H+ Site N3 N4 N6 S1 N3 N4 N7 S1 S6 N3 N4 N10 S1 N3 N4 N12 S1 N3 N21 S1 PA 1124 1112 1043 910 1120 1108 1043 971 964 1139 1124 1055 995 1403 1115 1046 958 1139 1116 944 Basicity 1093 1082 1012 880 1092 1082 1017 952 938 1099 1091 1018 975 1370 1079 1011 923 1100 1078 910 Total Energy -640.909715 -640.904596 -640.879988 -640.823073 -1039.097659 -1039.092977 -1039.069777 -1039.037067 -1039.035141 -798.190723 -798.186284 -798.160057 -798.133312 -872.091978 -871.986658 -871.961768 -871.921035 -1315.672420 -1315.665983 -1315.594820 5 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work. ISSN 1466-8858 Volume 22, Preprint 8 first submitted 26 February 2019 Proton affinity and basicity are calculated (in kJ mol-1) at 298.15 K as the negative of enthalpy and Gibbs energy, respectively for each possible protonated reaction. It can be clearly seen from Table 1 that the nitrogen atom (N3) in each inhibitor is the most favourable protonated site. Chemical and optimized structures (at the B3LYP/6-31++G(df,p) level with PCM in the aqueous medium) of the protonated inhibitors are presented in Fig. 2. Inhibitor Chemical Structure S Optimized Structure NH2 + ATDH N N H HS S NH2 + ATDTH N N H S NH2 + ABTDH N N H S NH2 + APTDH N N H N DAPTDH+ N S N N H Fig. 2. Chemical structures and optimized geometries of the protonated inhibitors investigated in this work 3.2. Frontier molecular orbitals The FMO theory, as previously mentioned, relates the chemical reactivities of interacting species to their HOMOs and LUMOs [20,26]. Accordingly, the interactions between the steel surface and inhibitors can be explored via the donation of electrons from HOMOs of inhibitors to d-orbitals of steel atoms, and also via the receiving of electrons from d-orbitals of steel atoms by LUMOs of inhibitors. 6 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work. ISSN 1466-8858 Volume 22, Preprint 8 first submitted 26 February 2019 Figs. 3 and 4 depict the electron density distributions for the HOMOs and LUMOs of neutral and protonated species of the studied inhibitors, respectively. As shown in these figures, electron densities of the HOMO and LUMO of each inhibitor in both neutral and protonated forms are distributed throughout the entire molecule. Such distribution could be linked to the electronic properties and the electron densities of π-conjugated bonds in the inhibitor’s molecules. This distribution may suggest parallel orientations of the inhibitors on the steel’s surface leading to strong adsorption of the inhibitors on the steel’s surface. Inhibitor HOMO LUMO ATD ATDT ABTD APTD DAPTD Fig. 3. Frontier molecular orbitals (HOMOs and LUMOs) of the investigated inhibitors obtained using the B3LYP/6-31++G(df,p) level with PCM in aqueous phase. The energies of HOMOs and LUMOs (𝐸𝐸𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 and 𝐸𝐸𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 ) and their gap ∆𝐸𝐸𝐻𝐻𝐻𝐻 are common quantum chemical parameters to study the reactivities and efficiencies of inhibitors. Values of 𝐸𝐸𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 can be used to measure the tendency of inhibitors to donate electrons to atoms of the metal. High values of 7 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work. ISSN 1466-8858 Volume 22, Preprint 8 first submitted 26 February 2019 𝐸𝐸𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 (less negative 𝐸𝐸𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 ) are affiliated with the high electron’s donation ability of inhibitors and with high inhibition efficiencies [1]. On the other hand, 𝐸𝐸𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 measures the ability of inhibitors to accept electrons from metal atoms. Low values of 𝐸𝐸𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 refer to the high ability of inhibitors to accept electrons and therefore high inhibition efficiencies. The energy gap ∆𝐸𝐸𝐻𝐻𝐻𝐻 is also an important electronic parameter that measures the reactivity of an inhibitor towards absorption on the metal surface. Inhibitor HOMO LUMO ATDH+ ATDTH+ ABTDH+ APTDH+ DAPTDH+ Fig. 4. Frontier molecular orbitals (HOMOs and LUMOs) of the investigated protonated inhibitors obtained using the B3LYP/6-31++G(df,p) level with PCM in aqueous phase. Small ∆𝐸𝐸𝐻𝐻𝐻𝐻 values indicate high inhibition efficiencies since electrons can transfer easily both ways; from the inhibitor atoms to metal atoms and vice versa [16]. The computed quantum chemical parameters of the investigated inhibitors (neutral and protonated) obtained using the B3LYP/631++G(df,p) level with PCM in the aqueous phase are listed in Table 2. According to the experimental inhibition efficiencies, the order of our studied inhibitors is ATD < ABTD < ATDT < APTD < DAPTD [6-8]. As shown in Table 2, the order of the values of EHOMO for the neutral species of studied inhibitors 8 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work. ISSN 1466-8858 Volume 22, Preprint 8 first submitted 26 February 2019 is ATD < ABTD < ATDT < APTD < DAPTD. This order agrees well with the experimental inhibition efficiencies as small values of EHOMO correspond with low abilities for donating electrons and hence low inhibition efficiency and vice versa. For the protonated species, the order is ATDH+ < ABTDH+ < ATDTH+ < APTDH+ < DAPTDH+ which is also in good correlation with experimental inhibition efficiencies. Table 2: Quantum chemical parameters of the investigated neutral and protonated inhibitors obtained using the B3LYP/6-31++G(df,p) level with PCM in aqueous phase.* Inhibitor EHOMO ELUMO ∆EHL I Neutral species ATD -6.569 -0.890 5.679 6.569 ATDT -6.222 -1.006 5.216 6.222 ABTD -6.531 -0.780 5.751 6.531 APTD -6.167 -1.735 4.432 6.167 DAPTD -5.203 -1.834 3.368 5.203 Protonated species ATDH+ -8.065 -1.943 6.122 8.065 ATDTH+ -7.378 -1.935 5.443 7.378 + ABTDH -7.879 -1.783 6.095 7.879 APTDH+ -7.069 -2.783 4.287 7.069 + DAPTDH -5.643 -2.715 2.928 5.643 *Units are in eV (except, ∆N in e and μ in Debye). A η σ χ ∆N μ 0.890 1.006 0.780 1.735 1.834 2.840 2.608 2.876 2.216 1.684 0.352 0.383 0.348 0.451 0.594 3.729 3.614 3.655 3.951 3.518 0.576 0.649 0.582 0.688 1.034 5.832 7.081 5.072 5.304 5.975 1.943 1.935 1.783 2.783 2.715 3.061 2.722 3.048 2.143 1.464 0.327 0.367 0.328 0.467 0.683 5.004 4.656 4.831 4.926 4.179 0.326 0.431 0.356 0.484 0.963 4.807 8.468 9.525 11.099 5.793 As can be seen in Table 2, the ELUMO values for the neutral inhibitors follow the order: DAPTD < APTD < ATDT < ATD < ABTD whereas for the protonated inhibitors they are in the following order: APTDH+ < DAPTDH+ < ATDH+ < ATDTH+ < ABTDH+. The ability of the neutral and protonated species to accept electrons and also their inhibition efficiencies are inversely proportional with ELUMO values. Thus, the results of neutral (with the exception of ATD value) agree well with experimentally determined inhibition efficiencies whereas the results of protonated species do not agree with the experimental results. In the case of energy gap (∆𝐸𝐸𝐻𝐻𝐻𝐻 ) values, both neutral and protonated inhibitor results agree well with the experimental inhibition efficiencies, i.e., DAPTD(H+) > APTD(H+) > ATDT(H+) > ABTD(H+) > ATD(H+). 3.3. Ionization energy and electron affinity As shown in Eqs. 1 and 2, the ionization potential (I) is defined as the negative of EHOMO while the electron affinity (A) is defined as the negative of ELUMO. From I and A values, one can predict the tendency of an inhibitor molecule to donate and accept electrons. Lower values of ionization potential 9 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work. ISSN 1466-8858 Volume 22, Preprint 8 first submitted 26 February 2019 imply greater abilities of the inhibitor molecules towards the donation of electrons to the steel’s surface and thus good inhibition efficiency. On the other hand, higher values of electron affinity are associated with greater abilities of inhibitor molecules towards the acceptance of electrons from the steel’s atoms and render good inhibition efficiency [15]. The calculated I and A values for neutral and protonated inhibitors are given in Table 2. The ionization potential results obtained from our theoretical calculations for both neutral and protonated species follow the order: DAPTD(H+) < APTD(H+) < ATDT(H+) < ABTD(H+) < ATD(H+). This order agrees well with the experimental inhibition efficiencies. Similar to the ELUMO results, the values of electron affinity for the neutral inhibitors are of the order: ABTD < ATD < ATDT < APTD < DAPTD and for the protonated inhibitors they are of the order: ABTDH+ < ATDTH+ < ATDH+ < DAPTDH+ < APTDH+. The order of the neutral species (except ATD) agrees well with the experimentally determined inhibition efficiencies while the order of the protonated species does not agree with experimental efficiencies. 3.4. Hardness and softness According to Eq. (4), the hardness of a molecule strongly depends on its HOMO and LUMO energies 1 and it equals a half of their gap (2 𝛥𝛥𝛥𝛥𝐻𝐻𝐻𝐻 ). Thus, the values of the hardness of molecules can be used to measure their stability. The higher the value of an inhibitor’s hardness, the more stable the inhibitor is, and the lower inhibition property it has [4]. Our computed hardness results are presented in Table 2. The trend of hardness results is the same as the results of ΔEHL discussed earlier. Softness is defined as the inverse of hardness and can be used to measure the polarizability of molecules. In contrast to a hard molecule, a soft molecule can easily be polarized and donated electrons to other acceptor molecules. An inhibitor that has a high softness value also has a high inhibition efficiency [14]. In Table 2, we also list our calculated softness values. As can be seen from this table, both neutral and protonated inhibitors follow the following order according to their softness values: DAPTD(H+) > APTD(H+) > ATDT(H+) > ABTD(H+) > ATD(H+) which is in excellent agreement with the experimental inhibition efficiencies. 3.5. Electronegativity and Number of electrons transferred Electronegativity is a useful quantum chemical parameter in the prediction of the ability of a chemical species to attract electrons from other species. Electronegativities (χ) for the studied neutral and protonated inhibitors have been calculated and listed in Table 2. According to Sanderson’s principle of 10 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work. ISSN 1466-8858 Volume 22, Preprint 8 first submitted 26 February 2019 electronegativity equalization; electrons continue transferring between two molecules until their electronegativities reach an equilibrium [14]. The number of electrons transferred (∆N) from inhibitor molecules to steel’s atoms measures the ability of the inhibitor molecules to donate electrons. The high ability of an inhibitor to donate electrons to the steel’s atoms is associated with a high inhibition efficiency. In order to describe the inhibitors ability to donate electrons, the values of ∆N for the studied neutral and protonated inhibitors have been calculated and tabulated in Table 2. According to our theoretical ∆N results shown in this table, the inhibitors obey the following order: DAPTD(H+) > APTD(H+) > ATDT(H+) > ABTD(H+) > ATD(H+). This finding is completely compatible with the experimentally obtained inhibition efficiencies mentioned previously. 3.6. Dipole moment The dipole moment (µ) is a common quantum chemical parameter widely used in corrosion inhibition studies. High values of dipole moment imply strong electrostatic interactions between steel’s atoms and inhibitor molecules and hence strong adsorption of the inhibitor molecules on the steel’s surface. The deformation energy and the volume of the inhibitor molecules increase when dipole moment increases, allowing the inhibitor molecules to be easily absorbed on the steel’s surface [3]. Our calculated dipole moment values as shown in Table 2 have the orders of ATDT > DAPTD > APTD > ATD > ABTD and APTDH+ > ABTDH+ > ATDTH+ > DAPTDH+ > ATDH+ for neutral and protonated inhibitors, respectively. This results are found to be inconsistent with the experimental inhibition efficiencies. 3.7. Local reactivity The inhibitor-metal interactions can be described by the transfer of electrons (donation and acceptance) between inhibitor molecules and the steel’s surface. To understand the inhibitor-metal interactions, it is significant to address the reactive sites of these interactions. We examine the active sites (local reactivities) of the studied inhibitors by means of condensed Fukui functions (𝑓𝑓𝑘𝑘+ ) and (𝑓𝑓𝑘𝑘− ) using Hirshfeld population analysis as given in Eqs. 7 and 8. The 𝑓𝑓𝑘𝑘+ and 𝑓𝑓𝑘𝑘− correspond with nucleophilic and electrophilic attacks respectively. The nucleophilic attack is preferred at the site that has a maximum value of 𝑓𝑓𝑘𝑘+ whereas the electrophilic attack is preferred at the site that has a maximum value of 𝑓𝑓𝑘𝑘− [3,21]. The largest condensed Fukui functions (𝑓𝑓𝑘𝑘+ and 𝑓𝑓𝑘𝑘− ) for three atoms of each studied inhibitor are given in Tables 3 and 4 for neutral and protonated species, respectively. For completeness, Fukui 11 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work. ISSN 1466-8858 Volume 22, Preprint 8 first submitted 26 February 2019 functions (𝑓𝑓𝑘𝑘+ and 𝑓𝑓𝑘𝑘− ) for all atoms of the investigated inhibitors are given in Tables S1-S5 in the Supporting Information. − Table 3: Largest condensed Fukui functions (𝒇𝒇+ 𝒌𝒌 and 𝒇𝒇𝒌𝒌 ) for three atoms of each investigated inhibitors obtained using the B3LYP/6-31++G(df,p) level with PCM in aqueous phase. The labelling of atoms is shown in Figs. 1 and 2. Inhibitor ATD ATDT ABTD APTD DAPTD Atom S1 C5 N4 S1 S6 N4 S1 N10 C2 S1 C2 N3 S1 C2 C5 𝒇𝒇+ 𝒌𝒌 0.2616 0.1886 0.1599 0.2431 0.1590 0.1405 0.2406 0.0941 0.0654 0.1159 0.1129 0.1036 0.1491 0.0746 0.0746 Atom N6 S1 N3 S6 N3 N7 N10 N3 S1 S1 C2 N3 N21 N12 N3 𝒇𝒇− 𝒌𝒌 0.1952 0.1664 0.1616 0.2421 0.1357 0.1328 0.1813 0.1590 0.1337 0.1131 0.1000 0.0919 0.0565 0.0565 0.0435 − Table 4: Largest condensed Fukui functions (𝒇𝒇+ 𝒌𝒌 and 𝒇𝒇𝒌𝒌 ) for three atoms of each investigated protonated inhibitors obtained using the B3LYP/6-31++G(df,p) level with PCM in aqueous phase. The labelling of atoms is shown in Figs. 1 and 2. Inhibitor + ATDH ATDTH+ ABTDH+ APTDH+ DAPTDH+ Atom S1 C5 C2 S1 S6 C2 S1 C2 N10 S1 N4 C5 S1 C2 N3 𝒇𝒇+ 𝒌𝒌 0.2703 0.1448 0.1343 0.2459 0.1331 0.1306 0.2401 0.1477 0.0967 0.1447 0.1168 0.0992 0.1506 0.1008 0.0556 Atom S1 N6 N4 S6 N4 S1 N10 S1 N4 C9 N4 C6 N12 C6 C8 𝒇𝒇− 𝒌𝒌 0.2251 0.1881 0.1311 0.3720 0.1257 0.0985 0.1686 0.1676 0.1251 0.1064 0.1049 0.0825 0.1034 0.0696 0.0626 12 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work. ISSN 1466-8858 Volume 22, Preprint 8 first submitted 26 February 2019 As can be seen from Tables 3 and 4, the sulphur (S1) atom, in all our investigated neutral and protonated inhibitors, is the most appropriate atom for the nucleophilic attack as it possesses the largest value of 𝑓𝑓𝑘𝑘+ . In contrast to the favourable site for the nucleophilic attack, the neutral inhibitors as shown in Table 3 give different favourable sites for the electrophilic attack as follows: ATD (N6), ATDT (S6), ABTD (N10), APTD (S1), and DAPTD (N12, N21) whereas the protonated inhibitors as shown in Table 4 give the following favourable sites: ATDH+ (S6), ATDTH+ (S6), ABTDH+ (N10), APTDH+ (C9), DAPTDH+ (N12). Based on this findings, it can be concluded that the sites responsible for the nucleophilic attack are located in the thiadiazole ring, whereas the sites responsible for the electrophilic attack are most likely to be located outside the thiadiazole ring. 3.8. QSAR Study We used QSAR to further investigate the correlation of the inhibition efficiencies for the investigated (neutral and protonated) inhibitors with some of their computed electronic parameters. Multiple linear regression (MLR) analysis as implemented in the statistical package for social sciences (SPSS) is employed to search for optimal QSAR models for both neutral and protonated species. The following QSAR models in the form of linear equations were obtained for neutral (Eq. 9) and protonated (Eq. 10) species, %𝐸𝐸𝐸𝐸𝑝𝑝𝑝𝑝𝑝𝑝 = 61.766𝐸𝐸𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 − 20.256𝐸𝐸𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 − 342.287𝜎𝜎 − 4.621𝜇𝜇 + 613.247 %𝐸𝐸𝐸𝐸𝑝𝑝𝑝𝑝𝑝𝑝 = 5.450𝐸𝐸𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 + 3.476𝐸𝐸𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 + 24.642𝜎𝜎 + 0.722𝜇𝜇 + 117.276 (9) (10) where, %𝐸𝐸𝐸𝐸𝑝𝑝𝑝𝑝𝑝𝑝 is the predicted inhibition efficiency, and 𝐸𝐸𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 , 𝐸𝐸𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 , 𝜎𝜎, and 𝜇𝜇 are the calculated HOMO energy, LUMO energy, softness, and dipole moment for the studied inhibitors, respectively. The predicted inhibition efficiencies obtained from Eqs. 9 and 10 along with their respective experimental values for both neutral and protonated inhibitors are given in Table 5. As shown in this table, our both QSAR models produce very close %𝐸𝐸𝐸𝐸 values to the corresponding experimental values with a small (insignificant) deviation range from 0.000 to 0.148. The relationship between experimental and predicted %𝐸𝐸𝐸𝐸 values for neutral and protonated inhibitors is depicted graphically in Fig. 5. Once again the graphs in Fig. 5 clearly show a compatible fit between the experimental and predicted %𝐸𝐸𝐸𝐸. Moreover, the coefficients of determination (R2) of both graphs (0.9998 and 1.000) indicate strong correlations between calculated and experimental %EI results. 13 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work. ISSN 1466-8858 Volume 22, Preprint 8 first submitted 26 February 2019 Table 5: Experimental (Exp) and predicted (Pred) inhibition efficiencies of the investigated inhibitors obtained using the B3LYP/6-31++G(df,p) level with PCM in aqueous phase. Inhibitor Neutral species ATD ATDT ABTD APTD DAPTD Protonated species ATDH+ ATDTH+ ABTDH+ APTDH+ DAPTDH+ Exp (%) Pred (%) |Deviation| 78.1 85.5 83.1 88.6 98.1 78.045 85.352 83.182 88.501 98.208 0.055 0.148 0.082 0.099 0.108 78.1 85.5 83.1 88.6 98.1 78.092 85.510 83.100 88.586 98.094 0.008 0.010 0.000 0.014 0.006 Fig. 5. Relationship between predicted and experimental inhibition efficiencies of (a) neutral and (b) protonated inhibitors. 14 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work. ISSN 1466-8858 Volume 22, Preprint 8 first submitted 26 February 2019 4. Conclusion The performances of five thiadiazole derivatives (ATD, ATDT, ABTD, APTD, and DAPTD) as corrosion inhibitors are investigated by means of the B3LYP/6-31++G(df,p) level in PCM (aqueous phase). We examine their inhibition performances through the calculation of several quantum chemical parameters, Fukui functions, and QSAR models. Based on our findings, the following conclusions can be drawn: • Results of proton affinities, basicities, and total energies show that the nitrogen atom (N3) of the thiadiazole ring is the favourable site to accept H+ and be protonated in all investigated inhibitors. • Strong correlations are found between the performance of the studied inhibitors (neutral and protonated species) and most of their calculated quantum parameters. • For both neutral and protonated inhibitors, dipole moment results are found to be inconsistent with the experimental inhibition efficiencies. • Fukui indices show that the sites susceptible to nucleophilic attacks are located in the thiadiazole ring and those susceptible to electrophilic attacks are located outside the ring. • We obtained two linear QSAR equations that fit the experimentally determined corrosion inhibition efficiencies well; one is for the neutral inhibitor species and the other is for the protonated inhibitor species. Acknowledgement The authors are grateful to Compute Canada, the Western Canadian Research Grid (WestGrid), and the Atlantic Computational Excellence Network (ACEnet) for providing the computational facilities. Supporting Information Condensed Fukui functions (𝑓𝑓𝑘𝑘+ and 𝑓𝑓𝑘𝑘− ) for all atoms of the investigated inhibitors. References [1] ‘Theoretical evaluation of the corrosion inhibition performance of 1,3-thiazole and its amino derivatives’, L. Guo, X. Ren, Y. Zhou, et al. Arab. J. Chem., 10, 121–130, 2017. [2] ‘Adsorption and corrosion inhibition properties of 5-amino 1,3,4-thiadiazole-2-thiol on the mild steel in hydrochloric acid medium: Thermodynamic, surface and electrochemical studies’, H. Ouici, M. Tourabi, O. Benali, et al. J. Electroanal. Chem., 803, 125–134, 2017. 15 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work. ISSN 1466-8858 Volume 22, Preprint 8 first submitted 26 February 2019 [3] ‘Theoretical studies on the corrosion inhibition performance of three amine derivatives on carbon steel: Molecular dynamics simulation and density functional theory approaches’, M. Shahraki, M. Dehdab, S. Elmi, J. Taiwan Inst. Chem. Eng., 62, 313–321, 2016. [4] ‘Anodic Polarization Behaviour of Nickel-Based Alloys in Neutral and Very Acidic Solutions’, A. Mohamed, J. R. Cahoon, W. F. Caley, Journal of Corrosion Science and Engineering, 15, 1– 30, 2012. [5] ‘Quantum chemical calculations, molecular dynamics simulation and experimental studies of using some azo dyes as corrosion inhibitors for iron. Part 1: Mono-azo dye derivatives’, L. H. Madkour, S. Kaya, C. Kaya, et al. J. Taiwan Inst. Chem. Eng., 68, 461–480, 2016. [6] ‘Application of corrosion inhibitors for steels in acidic media for the oil and gas industry: A review’, M. Finšgar, J. Jackson, Corros. Sci, 86, 17–41, 2014. [7] ‘Evaluation of some thiadiazole derivatives as acid corrosion inhibitors for carbon steel in aqueous solutions’, A. S. Fouda, K. Shalabi, R. Ezzat, J. Mater. Environ. Sci., 6, 1022–1039, 2015. [8] ‘Experimental and molecular dynamics studies on corrosion inhibition of mild steel by 2-amino5-phenyl-1,3,4-thiadiazole’, Y. Tang, X. Yang, W. Yang, et al., Corros. Sci., 52, 242–249, 2010. [9] ‘Influence of 2,5-bis(4-dimethylamino phenyl)-1,3,4-thiadiazole on corrosion inhibition of mild steel in acidic media’, F. Bentiss, M. Traisnel, M. Lagrenee, et al., J. Appl. Electrochem., 31, 41– 48, 2001. [10] ‘Experimental and theoretical studies of thiazoles as corrosion inhibitors for mild steel in sulphuric acid solution’, A. Döner, R. Solmaz, M. Özcan, et al., Corros. Sci., 53, 2902–2913, 2011. [11] ‘Emerging Corrosion Inhibitors for Interfacial Coating’, M. Taghavikish, N. Dutta, Roy N. Roy Choudhury, Coatings, 7, 217–244, 2017. [12] ‘Density functional theory and molecular dynamics simulation study on corrosion inhibition performance of mild steel by mercapto-quinoline Schiff base corrosion inhibitor’, S. K. Saha, P. Ghosh, A. Hens, et al., Phys. E Low-Dimensional Syst. Nanostructures, 66, 332–341, 2015. [13] ‘Density Functional Theory and Electrochemical Studies: Structure-Efficiency Relationship on Corrosion Inhibition’, R. L. Camacho-Mendoza, E. Gutiérrez-Moreno, E. Guzmán-Percástegui, et al., J. Chem. Inf. Model, 55, 2391–2402, 2015. [14] ‘Density functional theory (DFT) as a powerful tool for designing new organic corrosion inhibitors: Part 1: An overview’, I. B. Obot, D. D. Macdonald, Z. M. Gasem, Corros. Sci., 99, 1– 30, 2015. [15] ‘The discussion of descriptors for the QSAR model and molecular dynamics simulation of benzimidazole derivatives as corrosion inhibitors’, L. Li, X. Zhang, S. Gong, et al., Corros. Sci., 99, 76–88, 2015. [16] ‘A theoretical approach to understand the inhibition mechanism of steel corrosion with two aminobenzonitrile inhibitors’, S. K. Saha, P. Banerjee, RSC Adv., 5, 71120–71130, 2015. [17] ‘Corrosion inhibition efficiency of thiophene derivatives on mild steel: A QSAR model’, B. Usman, H. Maarof, H. H. Abdallah, et al., Int. J. Electrochem. Sci., 9, 1678–1689, 2014. [18] ‘Theoretical evaluation of corrosion inhibition performance of some pyrazine derivatives’, Corros. Sci., 83, 359–366, 2014. 16 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work. ISSN 1466-8858 Volume 22, Preprint 8 first submitted 26 February 2019 [19] ‘Quantum chemical study of the inhibition of the corrosion of mild steel in H2SO4 by some antibiotics’, N. O. Eddy, U. J. Ibok, E. E. Ebenso, et al., J. Mol. Model., 15, 1085–1092, 2009. [20] ‘Quantum chemical studies on the corrosion inhibition of some sulphonamides on mild steel in acidic medium’,T. Arslan, F. Kandemirli, E. E. Ebenso, et al., Corros. Sci., 51, 35–47, 2009. [21] ‘The use of quantum chemical methods in corrosion inhibitor studies’, G. Gece, Corros. Sci., 50, 2981–2992, 2008. [22] M. J. Frisch, G. W. Trucks, H. B. Schlegel, et al., Gaussian 16, Revision A.03, 2016. [23] ‘Density-functional thermochemistry. III. The role of exact exchange’, A. D. Becke, J. Chem. Phys., 98, 5648–5652, 1993. [24] ‘Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density’, C. Lee, W. Yang, R. G. Parr, Phys. Rev. B, 37, 785–789, 1988. [25] ‘Electrostatic interaction of a solute with a continuum. A direct utilization of AB initio molecular potentials for the prevision of solvent effects’,S. Miertus, E. Scrocco, J. Tomasi, Chem. Phys., 55, 117–129, 1981. [26] ‘The Molecular Orbital Theory of Organic Chemistry’, J. S. Michael, F. R. S. Dewar, New York: McGrawHill, Inc.; 1969. 17 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work. ISSN 1466-8858 Volume 22, Preprint 8 first submitted 26 February 2019 Supporting Information for: The inhibition performance of thiadiazole derivatives on the steel corrosion: DFT and QSAR assessment Aezeden Mohamed1,3, Ahmad I. Alrawashdeh2*, and John Pumwa3 1 Faculty of Engineering and Applied Sciences; 2Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John’s, NL, Canada A1B 3X7 3 Mechanical Engineering Department, PNG University of Technology, Lae, MP 411, Papua New Guinea *E-mail: ahmd.raw@mun.ca 18 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work. ISSN 1466-8858 Volume 22, Preprint 8 first submitted 26 February 2019 Table S1 Condensed Fukui functions (𝑓𝑓𝑘𝑘+ and 𝑓𝑓𝑘𝑘− ) for the atoms of ATD and ATDH+ inhibitors obtained using the B3LYP/6-31++G(df,p) level with PCM in aqueous phase. The labelling of atoms is shown in Figs. 1 and 2. Number Atom 1 2 3 4 5 6 7 8 9 10 S C N N C N H H H H Neutral Protonated 𝒇𝒇− 𝒌𝒌 𝒇𝒇+ 𝒌𝒌 0.2616 0.1003 0.0716 0.1599 0.1886 0.0599 0.0860 0.0387 0.0335 0.1664 0.0744 0.1616 0.1018 0.1225 0.1952 0.0481 0.0649 0.0650 - - 𝒇𝒇𝒌𝒌+ 0.2703 0.1343 0.0564 0.1127 0.1448 0.0907 0.0625 0.0475 0.0433 0.0377 𝒇𝒇− 𝒌𝒌 0.2251 0.0577 0.0916 0.1311 0.1062 0.1881 0.0434 0.0583 0.0580 0.0406 Table S2 Condensed Fukui functions (𝑓𝑓𝑘𝑘+ and 𝑓𝑓𝑘𝑘− ) for the atoms of ATDT and ATDTH+ inhibitors obtained using the B3LYP/6-31++G(df,p) level with PCM in aqueous phase. The labelling of atoms is shown in Figs. 1 and 2. Number Atom 1 2 3 4 5 6 7 8 9 10 11 S C N N C S N H H H H Neutral 𝒇𝒇+ 𝒌𝒌 0.24307 0.09610 0.06978 0.14051 0.13147 0.15903 0.05690 0.03502 0.03675 0.03138 - Protonated 𝒇𝒇− 𝒌𝒌 0.11484 0.06656 0.13565 0.09967 0.07278 0.24212 0.13276 0.04072 0.04760 0.04729 - 𝒇𝒇𝒌𝒌+ 0.24591 0.13064 0.05563 0.09224 0.10284 0.13314 0.08752 0.02877 0.04542 0.04139 0.03650 𝒇𝒇− 𝒌𝒌 0.09848 0.04181 0.07243 0.12572 0.05731 0.37200 0.08311 0.05765 0.03032 0.02905 0.03213 19 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work. ISSN 1466-8858 Volume 22, Preprint 8 first submitted 26 February 2019 Table S3 Condensed Fukui functions (𝑓𝑓𝑘𝑘+ and 𝑓𝑓𝑘𝑘− ) for the atoms of ABTD and ABTDH+ inhibitors obtained using the B3LYP/6-31++G(df,p) level with PCM in aqueous phase. The labelling of atoms is shown in Figs. 1 and 2. Number Atom 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 S C N N C C C C C N H H H H H H H H H H H H Neutral 𝒇𝒇+ 𝒌𝒌 0.24058 0.06537 0.03156 0.02727 0.02677 0.00220 0.00324 0.00373 0.00352 0.09410 0.00346 0.00417 0.00318 0.00396 0.00371 0.00482 0.00386 0.00427 0.00375 0.39375 0.07272 - Protonated 𝒇𝒇− 𝒌𝒌 0.13370 0.07731 0.15901 0.09453 0.08868 0.00886 0.00711 0.01351 0.01277 0.18125 0.00966 0.01157 0.00975 0.01508 0.01058 0.00978 0.00948 0.01454 0.01051 0.06181 0.06052 - 𝒇𝒇𝒌𝒌+ 0.24005 0.14770 0.06391 0.08067 0.08762 0.00810 0.00748 0.01197 0.01200 0.09665 0.00925 0.01133 0.00925 0.01455 0.01060 0.01239 0.01244 0.01457 0.01059 0.05091 0.04663 0.04134 𝒇𝒇− 𝒌𝒌 0.16756 0.05543 0.09495 0.12514 0.07853 0.01069 0.00747 0.01624 0.01633 0.16865 0.01037 0.01264 0.01037 0.01597 0.01226 0.01081 0.01085 0.01601 0.01226 0.05383 0.05274 0.04092 20 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work. ISSN 1466-8858 Volume 22, Preprint 8 first submitted 26 February 2019 Table S4 Condensed Fukui functions (𝑓𝑓𝑘𝑘+ and 𝑓𝑓𝑘𝑘− ) for the atoms of APTD and APTDH+ inhibitors obtained using the B3LYP/6-31++G(df,p) level with PCM in aqueous phase. The labelling of atoms is shown in Figs. 1 and 2. Number Atom 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 S C N N C C C C C C C N H H H H H H H H Neutral 𝒇𝒇+ 𝒌𝒌 0.13200 0.05279 0.04488 0.10725 0.07721 0.05869 0.05921 0.04540 0.08463 0.04393 0.06260 0.03594 0.03144 0.02511 0.03795 0.02458 0.03600 0.02068 0.01970 - Protonated 𝒇𝒇− 𝒌𝒌 0.10096 0.06043 0.12317 0.08268 0.06917 0.03827 0.04254 0.03416 0.06569 0.02981 0.04606 0.11800 0.01993 0.01875 0.02519 0.01782 0.02199 0.04278 0.04260 - 𝒇𝒇𝒌𝒌+ 0.15057 0.10077 0.05561 0.03001 0.04696 0.00677 0.02078 0.01318 0.01711 0.01124 0.01709 0.01317 0.00409 0.00407 0.02085 0.04844 0.02674 0.04674 0.02723 0.04802 𝒇𝒇− 𝒌𝒌 0.03242 0.01170 0.02075 0.05193 0.01356 0.06962 0.03198 0.06257 0.03310 0.05576 0.03170 0.10337 0.02456 0.02441 0.01750 0.01154 0.01690 0.01253 0.01476 0.01102 21 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work. ISSN 1466-8858 Volume 22, Preprint 8 first submitted 26 February 2019 Table S5 Condensed Fukui functions (𝑓𝑓𝑘𝑘+ and 𝑓𝑓𝑘𝑘− ) for the atoms of DAPTD and DAPTDH+ inhibitors obtained using the B3LYP/6-31++G(df,p) level with PCM in aqueous phase. The labelling of atoms is shown in Figs. 1 and 2. Number Atom 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 S C N N C C C C C C C N C C C C C C C C N C C H H H H H H H H Neutral 𝒇𝒇+ 𝒌𝒌 0.14906 0.07458 0.05919 0.05919 0.07458 0.01835 0.03776 0.01891 0.03215 0.01799 0.03253 0.01869 0.00636 0.00639 0.01835 0.03776 0.01891 0.03215 0.01799 0.03253 0.01869 0.00636 0.00639 0.02135 0.01099 0.01070 0.01873 0.00518 0.00754 0.00754 0.00522 Protonated 𝒇𝒇− 𝒌𝒌 0.04012 0.01994 0.04349 0.04349 0.01995 0.04075 0.02459 0.03729 0.02593 0.03254 0.02436 0.05647 0.01388 0.01379 0.04075 0.02459 0.03729 0.02593 0.03254 0.02436 0.05647 0.01388 0.01379 0.01365 0.01635 0.01520 0.01439 0.01019 0.01672 0.01672 0.01021 𝒇𝒇𝒌𝒌+ 0.15057 0.10077 0.05561 0.03001 0.04696 0.00677 0.02078 0.01318 0.01711 0.01124 0.01709 0.01317 0.00409 0.00407 0.02085 0.04844 0.02674 0.04674 0.02723 0.04802 0.03408 0.01045 0.01046 0.01258 0.00719 0.00667 0.00967 0.00332 0.00480 0.00480 0.00336 𝒇𝒇− 𝒌𝒌 0.03242 0.01170 0.02075 0.05193 0.01356 0.06962 0.03198 0.06257 0.03310 0.05576 0.03170 0.10337 0.02456 0.02441 0.01750 0.01154 0.01690 0.01253 0.01476 0.01102 0.02323 0.00589 0.00584 0.01861 0.02561 0.02402 0.01945 0.01751 0.02914 0.02914 0.01754 22 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work. ISSN 1466-8858 Volume 22, Preprint 8 32 33 34 35 36 37 38 39 40 41 42 43 44 H H H H H H H H H H H H H 0.00767 0.00767 0.02135 0.01099 0.01070 0.01873 0.00518 0.00754 0.00754 0.00522 0.00767 0.00767 - 0.01674 0.01674 0.01365 0.01635 0.01520 0.01439 0.01019 0.01672 0.01672 0.01021 0.01674 0.01674 - first submitted 26 February 2019 0.00487 0.00487 0.02423 0.01551 0.01564 0.02234 0.00828 0.01228 0.01228 0.00828 0.01225 0.01224 0.03018 0.02913 0.02913 0.00662 0.00748 0.00697 0.00599 0.00440 0.00692 0.00692 0.00441 0.00691 0.00691 0.01059 23 © 2019 University of Manchester and the authors. This is a preprint of a paper that has been submitted for publication in the Journal of Corrosion Science and Engineering. It will be reviewed and, subject to the reviewers' comments, be published online at http://www.jcse.org in due course. Until it has been fully published it should not normally be referenced in published work.