Quantum chemical study of heterocyclic organic compounds on the corrosion inhibition Chimica Techno Acta REVIEW published by Ural Federal University 2022, vol. 9(2), No. 20229203 eISSN 2411-1414; chimicatechnoacta.ru DOI: 10.15826/chimtech.2022.9.2.03 1 of 11 Quantum chemical study of heterocyclic organic compounds on the corrosion inhibition Dyari Mustafa Mamand a, Awat Hamad Awla a, Twana Mohammed Kak Anwer b, Hiwa Mohammad Qadr a* a: Department of Physics, College of Science, University of Raparin, 46012 Sulaymaniyah, Iraq b: Department of Physics, College of Science Education, Salahaddin University, Erbil, Iraq * Corresponding author: hiwa.physics@uor.edu.krd This paper belongs to a Regular Issue. Β© 2021, the Authors. This article is published open access under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Abstract Corrosion damages all materials, necessitating replacement and inspection related expenses. Thus, the demand has increased for new corrosion inhibitor materials. The ratios of corrosion inhibition of materials are different, but organic compounds have high efficiency in aqueous corrosion inhibition for various alloys and metals. This efficiency can increase in the presence of O, N and S. The molecule provides great inhibition with the presence of both S and N atoms in the same compound. This paper investigates the 1, 3, 4-thiadiazole molecule and electronic structure of several organic compounds such as R1 and R2 which consist of different substituent groups. They were united to the ring of 1, 3, 4-thiadiazole to provide nine different de- rivatives. Quantum computations (density functional theory, DFT) at 6-311G++ (d, p) basis set and Becke’s three parameters hybrid (B3LYP) level were performed using Gaussian program. The purpose of this study is to determine the chemical behaviour of several heter- ocyclic organic compounds and to understand the process of the cor- rosion inhibition. Keywords DFT HUMO LUMO corrosion inhibition 1, 3, 4-thiadiazole Received: 25.10.21 Revised: 07.04.22 Accepted: 09.04.22 Available online: 17.04.22 1. Introduction Corrosion is the degradation of the material and it is gen- erally a slow process [1]. But it can accelerate if incompat- ible materials are combined, e.g. when two materials with different electrochemical activity are in electrical contact with each other. In this process, more passive metal drives the corrosion of the active metal at the same time as the passive metal remains unharmed [2–4]. This process keeps going until the active metal has been completely gone or the electrical connections between the two metals have been broken. Using corrosion inhibitors is one of the best and most effective ways to protect the surface of ma- terials from corrosion in acid environments [5]. Watery corrosion of metallic surfaces can be hindered with organ- ic materials [6]. Nowadays, these compounds have a good capability for the prevention of metallic surface abuse, which has caused their widespread usage [7]. Decreasing the cathode reaction with the anodic process of destruc- tion of the mineral in acid solution, these factors all stem from the inhibitors adsorbed on the surface of the met- als [8]. This leads to the creation of a diffusion barrier between two sides. The electrical conductivity is drastical- ly decreased due to forming a diffusion barrier that sur- rounds the reaction sites [9]. There are many ways to pre- vent metallic material from corrosion. Some materials , such as those containing heteroatoms, are beneficial for preventing corrosion. Organic compounds containing Ο€ bonds and N, O, S have been widely used [10]. In previous years, theoretical methods have been wide- ly used in various fields [11]. Quantum computational method is realized in the Gaussian Program [12]. A theo- retical calculations in the Gaussian Program can be used to estimate corrosion inhibition performances of molecules [13]. The corrosion inhibition efficiencies are determined by the experimental method and allowed to estimate the corrosion inhibition mechanisms of composites in terms of weight loss [14]. Nitrogen and sulfur are two important atoms for inhibition. It would be beneficial, if the two of them came together in the same molecule [14]. However, if the compounds consist of oxygen or nitrogen, the effect will be reduced. So, it will not provide an excellent inhibi- tion [15]. The ability of these compounds to inhibit corro- http://chimicatechnoacta.ru/ https://doi.org/10.15826/chimtech.2022.9.2.03 mailto:hiwa.physics@uor.edu.krd http://creativecommons.org/licenses/by/4.0/ https://orcid.org/0000-0001-5585-3260 https://crossmark.crossref.org/dialog/?doi=https://doi.org/10.15826/chimtech.2022.9.2.03&domain=pdf&date_stamp=2022-4-17 Chimica Techno Acta 2022, vol. 9(2), No. 20229203 REVIEW 2 of 11 sion depends on the structure of the molecular [16]. The adsorption of these molecules on metallic surfaces is im- portant in this regard, and it is possible to estimate it, as it depends on the lone electron pairs in the heteroatoms [17]. The computational method in quantum chemistry is able to predict some parameters such as hardness and softness [18, 19]. This paper investigates the molecular structure and electronic behaviour of some organic compounds by using quantum computational method based on DFT. Hardness, softness, electronegativity and chemical potential are im- portant parameters for quantum chemical method. 2. Computational Details Density functional theory (DFT) is a computational quantum mechanical modelling method used in this study to calculate the electronic structure of atoms and molecules [20]. The quantum chemical calculations based on DFT at 6-311G++ (d, p) basis set were used because this basis set is very popular for determining the electronic and molecular geometry accurately. All computations were performed with Gaussian 09 package program. The 6-311G is the standard, split- valence and double-zeta basis set use to describe the core and valence orbitals, (d, p) are polarization function to describe the chemical bonds and ++ are diffuse functions [21]. 6- 311G++ (d, p) basis set is very useful and can accurately cal- culate high occupied molecular orbital (HOMO), lower unoc- cupied molecular orbital (LUMO), hardness, softness, elec- tronegativity, chemical reaction, electrophilicity, proton af- finity and nucleophilicity [22]. The use of Fukui indices can predict the local molecular reactivity [23]. The Fukui function 𝑓(π‘Ÿ) can be written with the following expression [24]: 𝑓(π‘Ÿ) = ( 𝜌(π‘Ÿ) πœ•π‘ ) 𝑣(π‘Ÿ) , (1) where 𝜌 is the electronic density of the system under con- sideration, 𝑁 is the number of electrons and 𝑣(π‘Ÿ) is the external potential. Removal or addition of an electron in the relaxation ef- fects is not measured approximately from the Fukui func- tion. The removal and addition of an electron can be ex- pressed as follows: πœŒβˆ’(π‘Ÿ) β‰ˆ πœŒπΏπ‘ˆπ‘€π‘‚ (π‘Ÿ), (2) 𝜌+(π‘Ÿ) β‰ˆ πœŒπ»π‘‚π‘€π‘‚ (π‘Ÿ), (3) where πœŒπΏπ‘ˆπ‘€π‘‚ (π‘Ÿ) is the density for the lowest unoccupied molecular orbital and πœŒπ»π‘‚π‘€π‘‚ (π‘Ÿ) is the density of the high- est occupied molecular orbital [25]. Condensed Fukui functions are used for the local activity sites which are determined by using the infinitesimal change, limited var- iation and approximations of quantum computational chemistry from the Mulliken population analysis of atoms, which depend on the direction of electron transfer of at- oms in molecules [26]. There are two types of local active sites - the nucleophilic and the electrophilic. In the nucle- ophile site, the electrons will transfer from the nucleo- phile to the electrophile. But, in the electrophile site, the electron will transfer to the end site of electrophile [27]. Each of R1 and R2 consist of different substituent groups, which are united to the ring of 1, 3, 4-thiadiazole to pro- vide nine various derivatives as shown in Figure 1, where R1 consists of (H), hydrogen, and (–CH3), methyl, while R2 consists of a variety of substituents united to 1, 3, 4- thiadiazole. The substituent groups consist of ethyl (–C2H5), methyl (–CH3), propyl (–C3H7), chloroethyl (–C2H5–Cl), hydroxyethyl (–C2H5–OH), tioethyl (–C2H5–SH), carboxyethyl (–C2H5–COOH) and aminoethyl (–C2H5–NH2). Figure 2 shows the chemical structure of 1, 3, 4-thiadiazole derivatives 1–9. Figure 1 Chemical structure of 1, 3, 4-thiadiazole ring with R1 and R2 substituents. 3. Computational Results Quantum computational chemistry method optimized ge- ometries of the compounds withnine various substitutions of the ring (1, 3, 4-thiadiazole) by using Gaussian program with 6-311G++ (d, p) basis set as shown in Figure 2 [28, 29]. The structures of these derivatives are presented in Figure 3: (1) 2-methyl-1,3,4-thiadiazole (2) 2-propyl-5- methyl-1,3,4-thiadiazole (3) 2,5-dimethyl-1,3,4-thiadiazole; (4) 2-ethyl-5-methyl-1,3,4-thiadiazole (5) 2-(2-hidroxy ethyl)-5-methyl-1,3,4-thiadiazole; (6) 2-aminoethyl-5-methyl- 1,3,4-thiadiazole; (7) 2-(2-chloroethyl)-5-methyl-1,3,4- thiadiazole; (8) 2-(2-carboxy ethyl)-5-methyl-1,3,4- thiadiazole; and (9) 2-(2-tioethyl)-5-methyl-1,3,4-thiadiazole. 4. Quantum chemical calculations HOMO, LUMO and frontier orbital gap are significant param- eters in quantum computational chemistry. They are im- portant for the kinetic stability and chemical reactivity of the molecules [30, 31]. Table 1 shows the bandgap energies of nine different derivatives. The charge-transfer interaction inside the molecule is explained by the energy gap of HOMO and LUMO [32]. They are two popular parameters in quan- tum chemistry. Frontier orbitals are the main factors to de- scribe the molecule's interaction with other species. Chimica Techno Acta 2022, vol. 9(2), No. 20229203 REVIEW 3 of 11 inh 1 HOMO LUMO inh 2 HOMO LUMO inh 3 HOMO LUMO inh 4 HOMO LUMO inh 5 HOMO LUMO inh 6 HOMO LUMO inh 7 HOMO LUMO inh 8 HOMO LUMO inh 9 HOMO LUMO Figure 2 The optimized structures of LUMO and HOMO using DFT/B3LYP/6-31++G (d, p) of non-protonated inhibitor molecules 1 to 9 in gas phase. Chimica Techno Acta 2022, vol. 9(2), No. 20229203 REVIEW 4 of 11 Figure 3 Chemical structure of 1, 3, 4-thiadiazole derivatives 1–9. The chemical interaction between HOMO and LUMO decides the formation of transition states [33]. The ability of molecules to donate electrons can be found with the energy of EHOMO [34]. The tendency to donate electrons in the molecules is related to the energy of EHOMO [35]. If the molecule has a high EHOMO, the tendency to donate an elec- tron will increase to allow acceptor molecules with low energy and empty molecular orbital. Facile adsorption of molecules (i.e. the inhibition) will increase with the in- crease in the value of EHOMO due to adsorbed layer which influences the transportation process [36]. The probability of accepting electrons by the molecules is related to the value of ELUMO, the tendency of accepting electrons by molecules will increase with the lower value of ELUMO. Ma- terials have a good inhibition efficiency if they have lower bandgap energy. In this case, more energy is required to transfer the electron from the last lowest occupied orbital and the surface of the material [37]. In recent years, quan- tum chemical approaches have shown to be particularly beneficial in the assessment of prospective corrosion in- hibitors. Quantum chemical parameters based on the DFT, such as chemical potential, chemical hardness, electro- philicity, electronegativity, and nucleophilicity, have been used to investigate the results of the computational chem- istry works' consistency with experimental data [38]. In- deed, Koopmans theorem is one of the most significant contributions to the computational chemistry research. Following that, it is possible to explain hard and soft acid- base (HSAB) theory in detail. Pearson developed the HSAB theory as a result of studies on Lewis acid bases in the 1960 [39]. Bases and Lewis acids were characterized as hard or soft, based on this hypothesis. The hard acids choose to correlate with hard bases, but soft acids prefer to associate with soft bases. The description for these pur- poses is that the soft-soft interactions are frequently cova- lent, but hard-hard interactions are electrostatic. Because the corrosion inhibitors are Lewis bases, the HSAB theory should be included in corrosion research [13]. Further- more, the HSAB theory is a significant advancement in quantum chemistry, which is useful in a variety of theoret- ical and experimental research involving corrosion inhibi- tors, chemical equilibrium, complex stability, precipitation 2-methyl-1, 3,4-thiadiazol 2-propyl-5-methyl-1,3,4-thiadiazole 2,5-dimethyl-1,3,4-thiadiazole 2-ethyl-5-methyl-1,3,4-thiadiazol 2-(2-hidroxyethyl)-5-methy1-1,3,4-thiadiazole 2-aminoethyl-5-methyl-1,3,4-thiadiazole 2-(2-chloroethyl)-5-methyl-1, 3,4-thiadiazole 2-(2-carboxyethyl)-5-methyl-1,3,4-thiadiazole 2-(2-tioethyl)-5-methyl-1, 3,4-thiadiazole Chimica Techno Acta 2022, vol. 9(2), No. 20229203 REVIEW 5 of 11 titrations and gravimetry. The chemical potential (ΞΌ), chemical hardness (Ξ·) and reactivity indexes electronega- tivity (Ο‡) are described as derivatives of the number of electrons (N) of the electron energy (E) at external poten- tial (v) in the conceptual DFT. The expression for the mathematical operations can be obtained as: 𝐼 = βˆ’πΈπ»π‘‚π‘€π‘‚ , (4) 𝐴 = βˆ’πΈπΏπ‘ˆπ‘€π‘‚ , (5) πœ’ = ( 𝐼 + 𝐴 2 ), (6) πœ‚ = ( 𝐼 βˆ’ 𝐴 2 ), (7) 𝜎 = 1 πœ‚ , (8) πœ” = πœ‡2 2πœ‚ , (9) where I is the ionization energy, A is the electron affinity, Οƒ is the softness and Ο‰ is the electrophilicity. 5. Mulliken atomic charges and Fukui function calculations in the gas phase The value of bandgap energy of each derivative reduces, evidencing the increase of corrosion inhibition of 1, 3, 4- thiadiazole with substituents. The hardness and softness of molecules are related to ELUMO and EHOMO. Reactivity wards chemical species depends on the bandgap energy, where high reactivity wards chemical species indicates a small bandgap [40]. A hard molecule has lower reactivity than a soft molecule because a soft molecule has a small bandgap energy [41]. Reactivity and stability of molecules are two parameters that can be determined by measuring the softness and hardness properties of molecules [42, 43]. The harness properties of the materials in a low per- turbation of the reactions are the resistance to prevent deformation, preventing the polarization of the electron cloud of the molecules. Inhibition properties of the mole- cules will rise with an increase in the value of softness. Inhibition efficiency will be highest when the softness is the highest, which is in agreement with our conclusions [44]. All calculations were performed with quantum compu- tational chemistry for the derivatives of 1, 3, 4-thiadiazole in the gas phase, as shown in Tables 1 and 2. For each of derivatives of 1, 3, 4-thiadiazole molecule, Fukui indices have been calculated. Tables 1 and 2 are expressed in terms of ionization energy, where βˆ†πΈ, CP and πœ€ are the energy gap, the chemical potential and the nucleophilicity. Table 1 shows the calculated values of EHOMO and ELUMO for the investigated derivatives 1–9 in non-protonated gas. The order of inhibition efficiency of the investigated inhib- itors corresponds to the order established from theoretical data based on EHOMO, which is 1<9<8<3<4<5<6<7<2. However, based on the results obtained for ELUMO in the gas phase, the value of ELUMO changes follows: 1>9>8>3>4>5>6>7>2. As a function of the reaction of the inhibitor molecule towards adsorption on the metal sur- face, the energy gap is an important descriptor. The reac- tivity of the molecule increases due to the reduction of βˆ†πΈ. It is known that corrosion inhibitors with small energy gaps are effective because the ionization energy needed to remove the electron from the final occupied orbital is low. according to Bereket et al., organic compounds do not only donate electrons to empty metal orbitals, but also accept free electrons from metals [45]. Furthermore, a molecule with a lower energy gap appears to be more polarizable and typically characterized by low kinetic stability and strong chemical activity. The results in Table 1 shown that inhibitor 1 has the smallest energy gap under all condi- tions, which means the molecule can perform better as a corrosion inhibitor. Absolute hardness and softness are well-known quali- ties to determine molecule stability and reactivity. Accord- ing to Obi-Egbedi, chemical hardness is defined as the re- sistance to deformation or polarization of the electron cloud of atoms, ions, or molecules under minor perturba- tions of chemical reactions [46]. A soft molecule has a tiny energy gap, whereas a hard molecule has a big energy gap. As a result, molecules in the lowest global hardness values are supposed to be effective corrosion inhibitors for bulk metals in acidic environments. Table 1 Gas phase calculations with 6-311++(d, p) basis set and B3LYP level for molecular characteristics of compounds 1–9. No. HOMO (eV) LUMO (eV) I A βˆ†π‘¬ (eV) 𝜼 𝝈 𝝌 CP 𝝎 𝜺 1 –6.2861 –2.1850 6.28615 2.18509 4.1010 2.05053 0.48767 4.235 62 –4.235628 4.3745 0.22859 2 –6.8684 –6.4850 6.86847 6.48506 6 0.3834 0.19170 5.21632 6.676 77 –6.6767 116.27 0.00860 3 –7.1555 –3.5951 7.15556 3.59519 3.5603 1.78018 0.56174 5.375 37 –5.37537 8.1156 0.12321 4 –7.5808 –5.5582 7.58087 5.55824 2.0226 1.01131 0.98880 6.569 56 –6.56956 21.338 0.04686 5 –7.1955 –6.1615 7.19556 6.16152 1.0340 0.51702 1.93415 6.678 54 –6.6785 43.134 0.02318 6 –7.3011 –6.3490 7.30114 6.34901 0.9521 0.47606 2.10054 6.825 07 –6.8250 48.923 0.02044 7 –6.4091 –5.6156 6.40914 5.61565 0.7934 0.39674 2.52050 6.012 40 –6.01240 45.556 0.02195 8 –7.5982 –5.1299 7.59829 5.12993 2.4683 1.23418 0.81025 6.364 11 –6.36411 16.408 0.06094 9 –6.6184 –3.9364 6.61840 3.93643 2.6819 1.34098 0.74571 5.277 41 –5.27741 10.384 0.09629 Chimica Techno Acta 2022, vol. 9(2), No. 20229203 REVIEW 6 of 11 Table 2 Gas phase calculations of Fukui functions and Mulliken atomic charges at 6-311G++ (d, p) basis set at B3LYP level for deriva- tives 1–9. No. Atoms 𝒒𝑡 𝒒𝑡+𝟏 π’’π‘΅βˆ’πŸ π’‡π’Œ + π’‡π’Œ βˆ’ π’‡π’Œ 𝟎 1 N4 –0.106 –0.030 –0.130 0.076 0.024 0.050 N5 0.065 0.166 –0.034 0.101 0.099 0.100 S6 0.082 0.228 –0.124 0.146 0.206 0.176 2 N4 0.025 0.061 0.011 0.036 0.014 0.025 N5 –0.315 –0.215 –0.329 0.100 0.014 0.057 S6 0.235 0.349 0.209 0.114 0.026 0.070 3 N4 –0.227 –0.148 –0.254 0.079 0.027 0.053 N5 –0.296 –0.218 –0.299 0.078 0.003 0.0405 S6 0.402 1.035 0.332 0.633 0.070 0.3515 4 N4 0.034 0.039 0.008 0.005 0.026 0.0155 N5 –0.354 –0.317 –0.362 0.037 0.008 0.0225 S6 0.266 0.359 0.235 0.093 0.031 0.062 5 N4 0.070 0.075 0.016 0.005 0.054 0.0295 N5 –0.303 –0.294 –0.312 0.009 0.009 0.009 S6 0.194 0.226 0.179 0.032 0.015 0.0235 O16 –0.353 –0.307 –0.365 0.046 0.012 0.029 N4 0.070 0.075 0.016 0.005 0.054 0.0295 6 N4 –0.144 –0.129 –0.181 0.015 0.037 0.026 N5 –0.318 –0.297 –0.331 0.021 0.013 0.017 S6 0.309 0.396 0.290 0.087 0.019 0.053 N16 –0.378 –0.290 –0.479 0.088 0.101 0.0945 7 N4 0.056 0.058 –0.012 0.002 0.068 0.035 N5 –0.237 –0.230 –0.240 0.007 0.003 0.005 S6 0.116 0.200 0.109 0.084 0.007 0.0455 Cl12 0.764 0.822 0.639 0.058 0.125 0.0915 8 N4 –0.016 –0.011 –0.066 0.005 0.05 0.0275 N5 –0.250 –0.211 –0.256 0.039 0.006 0.0225 S6 0.195 0.298 0.181 0.103 0.014 0.0585 9 N4 –0.193 –0.191 –0.239 0.002 0.046 0.0240 N5 –0.356 –0.321 –0.365 0.035 0.009 0.0220 S6 0.253 0.286 0.213 0.033 0.040 0.0365 Inhibitor adsorption occurs on a metal surface in the softest part of the molecule. Table 1 shows the calculated values of the gas phases for the analysed derivatives 1–9. Compared with other inhibitors, 1, 3, 9 and 8 have the highest levels of hardness. Compared with the derivatives, the data for B3LYP/6-311++G (d, p) show that inhibitor 1 has the highest stiffness value of 2.05 eV in the non- protonated gas phase. Table 2 shows the gas phase calculations of Fukui func- tions and Mulliken atomic charges at 6-311G++ (d, p) basis set at B3LYP level for derivatives 1–9, where π‘“π‘˜ +, π‘“π‘˜ βˆ’ and π‘“π‘˜ 0 are the nucleophilic attack, the electrophilic attack and the radical attack. A high value of the nucleophilic attack site indicates the increased ability of the molecules to accept electrons, and the molecule will be more able to stabilize additional electrons [47]. The tendency of a molecule to donate electrons is defined by the high electrophilic site value. The ability of the metal surface to donate electrons increases with an increase in the inhibition efficiency [40]. Figure 3 shows the optimized structures LUMO and HOMO using DFT/B3LYP/6-31++G (d, p) of non- protonated inhibitor molecules 1–9. 6. Mulliken atomic charges and Fukui function for derivatives 1–9 in the presence of water Only four atoms O, N, S, and Cl were shown in Mulliken charge and Fukui function calculations to determine the effect of each of the atoms on the molecule because of the existence of electrochemical corrosion in the liquid phase. It is obvious that quantum computational calculations in the aqueous phase are necessary to show the effect of solvents on corrosion inhibition of organic compounds. For this pur- pose, Gaussian program can describe the properties of or- ganic compounds. In this case, the polarized continuum method PCM was used [48]. The solute is placed in a cavity of a roughly molecular shape. For determining the effect of solvent on geometry optimization calculations, the solvent in these models is defined by a continuum that interacts with charges on the cavity surface [49]. Table 3 shows the aqueous phase calculations with 6-311++ (d, p) basis set and B3LYP level for molecular characteristics of the com- pounds 1–9. Table 4 shows the aqueous phase calculations of Fukui functions and Mulliken atomic charges at 6-311G++ (d, p) basis set at B3LYP level for the derivatives 1–9. Chimica Techno Acta 2022, vol. 9(2), No. 20229203 REVIEW 7 of 11 Table 3 Aqueous phase calculations with 6-311++ (d, p) basis set and B3LYP level for molecular characteristics of compounds 1–9. No. HOMO (eV) LUMO (eV) I A βˆ†π‘¬ (eV) 𝜼 𝝈 𝝌 CP 𝝎 𝜺 1 –8.26307 –4.0488 8.26307 4.04881 4.21426 2.10713 0.47457 6.15594 –6.1559 8.992 0.11120 2 –7.59611 –7.1969 7.59611 7.19692 0.39919 0.19959 5.01009 7.39652 –7.3965 137.04 0.00729 3 –7.23093 –5.7757 7.23093 5.77579 1.45514 0.72757 1.37443 6.50336 –6.5033 29.065 0.03440 4 –6.82249 –4.9440 6.8224 4.94407 1.87841 0.93920 1.06472 5.88328 –5.8832 18.426 0.05426 5 –6.44425 –5.4951 6.4442 5.49511 0.94914 0.47457 2.10716 5.96968 –5.9696 37.546 0.02663 6 –6.59527 –5.5862 6.59527 5.58626 1.00900 0.50450 1.98214 6.09077 –6.0907 36.766 0.02719 7 –6.40914 –5.6156 6.4091 5.6156 0.7934 0.3967 2.5205 6.01240 –6.0124 45.556 0.02195 8 –6.81324 –4.4303 6.8132 4.4303 2.3829 1.1914 0.8393 5.6217 –5.6217 13.262 0.07539 9 –6.61840 –3.9364 6.6184 3.9364 2.6819 1.3409 0.7457 5.2774 –5.2774 10.384 0.09629 Table 4 Aqueous phase calculations of Fukui functions and Mulliken atomic charges at 6-311G++ (d, p) basis set at B3LYP level for de- rivatives 1–9. No. Atoms 𝒒𝑡 𝒒𝑡+𝟏 π’’π‘΅βˆ’πŸ π’‡π’Œ + π’‡π’Œ βˆ’ π’‡π’Œ 𝟎 1 N4 –0.288 –0.114 –0.333 0.174 0.045 0.1095 N5 –0.219 –0.205 –0.238 0.014 0.019 0.0165 S6 0.633 1.189 0.575 0.556 0.058 0.307 2 N4 0.033 0.061 0.011 0.028 0.022 0.025 N5 –0.212 –0.215 –0.329 –0.003 0.117 0.057 S6 0.248 0.349 0.209 0.101 0.039 0.07 3 N4 –0.511 –0.441 –0.535 0.07 0.024 0.047 N5 –0.519 –0.430 –0.535 0.089 0.016 0.0525 S6 0.804 1.450 0.761 0.646 0.043 0.3445 4 N4 0.034 0.039 0.008 0.005 0.026 0.0155 N5 –0.354 –0.317 –0.362 0.037 0.008 0.0225 S6 0.266 0.359 0.235 0.093 0.031 0.062 5 N4 0.070 0.075 0.016 0.005 0.054 0.0295 N5 –0.303 –0.294 –0.312 0.009 0.009 0.009 S6 0.194 0.226 0.179 0.032 0.015 0.0235 O16 –0.353 –0.307 –0.365 0.046 0.012 0.029 6 N4 –0.144 –0.129 –0.331 0.015 0.187 0.101 N5 –0.318 –0.297 –0.181 0.021 –0.137 –0.058 S6 0.309 0.369 0.290 0.06 0.019 0.0395 N16 –0.378 –0.290 –0.479 0.088 0.101 0.0945 7 N4 0.056 0.058 –0.012 0.002 0.068 0.035 N5 –0.237 –0.230 –0.240 0.007 0.003 0.005 S6 0.116 0.200 0.109 0.084 0.007 0.0455 Cl12 0.764 0.822 0.639 0.058 0.125 0.0915 8 N4 –0.016 –0.011 –0.066 0.005 0.05 0.0275 N5 –0.250 –0.211 –0.256 0.039 0.006 0.0225 S6 –0.195 0.298 0.181 0.493 –0.376 0.0585 9 N4 –0.193 –0.191 –0.239 0.002 0.046 0.024 N5 –0.356 –0.321 –0.365 0.035 0.009 0.022 S6 0.253 0.286 0.213 0.033 0.04 0.0365 The bond distance from the analyses of the optimized geometry at 6-311++G (d, p) basis set between C2 and R2 remained unchanged and equal to 1.54 Γ…. The bond angle of the 1, 3, 4-thiadiazole internal ring for S6–C2–N4 and S6–C2–N4 is 111.10865–111.108660, respectively. At the first derivative, the difference between them is very small, but at the second derivative it is 0.0060. The bond angle between C1-N4 and C2–N4 is in the same range for all de- rivatives, about 1.349830 and 1.349820. The bond length between C1–N4 and C2–N4 shows just small variations. For this purpose, it is reasonable to arrange all the deriva- tives which showed a length of C1–N4 and C2–N4 bond of 1.34 Γ…. The bond angle between S6–C1 and S6–C2 is 1.758050 for each of the optimized geometry calculations, indicating the formation of single bonds between these atoms. N4, N5, S6, O16 and Cl12 have a high electronic densi- ty, which was calculated by Mulliken population analysis for each derivative. Due to the high electronic density, these atoms are nucleophilic when they interact with the metallic surface. The HOMO calculations in the presence of solvents (water) are shown in Figure 3. In all com- pounds, HOMO is placed on both sides of the functional groups attached to the 1, 3, 4-thiadiazole ring. This calcula- tion shows the positions of the approved active sites for an electrophilic attack. The active region is distributed around the molecule belonging to the 1, 3, 4-thiadiazole ring. The inhibitor with the lowest global hardness (and thus the highest global softness) is likely to have the best inhibition efficiency. The following anticorrosion efficien- cy was predicted in our study: the inhibitor 2 is more effi- cient than the inhibitor 7, 5 – than 6, 9 – than 1. According Chimica Techno Acta 2022, vol. 9(2), No. 20229203 REVIEW 8 of 11 to Hasanov et al., adsorption can occur in the part of the molecule where softness is at maximum [50]. An electrophile is a chemical species that accepts a pair of electrons. The molecule with the larger electrophilicity value has the greater ability to receive electrons, and its opposite will behave as a good nucleophile. Tables 1 and 2 shows the compounds with low electrophilic values (good nucleophiles). Table 3 shows both the electrophilic and nucleophilic data. The corrosion inhibition efficiency rat- ing of the investigated compounds can be defined as fol- lows: 1<9<8<4<3<6<5<7<2. When electronegativity and chemical potentials are equal, electrons flow from the lower-electronegative site to the higher as the inhibitor and iron come close to each other. The fraction of electrons transferred can be calcu- lated from the following equation: Ξ”π‘π‘šπ‘Žπ‘₯ = πœ’πΉπ‘’ βˆ’ πœ’π‘–π‘›β„Ž 2(πœ‚πΉπ‘’ βˆ’ πœ‚π‘–π‘›β„Ž ) . (10) The electronegativity of the inhibitor and the metal are represented by πœ’πΉπ‘’ and πœ’π‘–π‘›β„Ž. The chemical hardness of the inhibitor is πœ‚π‘–π‘›β„Ž and that of the metal – πœ‚πΉπ‘’. Pearson has been demonstrated that electron transfer is driven by electronegativity differences and the aggregation of πœ‚ factors acts as a barrier [51]. As a result, the electronega- tivity of Fe = 7 eV and a global πœ‚ of Fe = 0 were used to calculate the ratio of electrons transferred assuming that for the metallic mass I is equal to A because it is softer than the neutral metal atoms [52]. Tables 5 and 6 shows quantum chemical parameters of derivatives 1–9 in the gas and aqueous phases with 6-311++ (d, p) basis set and B3LYP level. The positive number Ξ”π‘π‘šπ‘Žπ‘₯ indicates that the molecules are electron acceptors, while the negative number of Ξ”π‘π‘šπ‘Žπ‘₯ indicates that the molecules are elec- tron donors. As a result of that as the electron-donating capacity of these inhibitors increases on the metal sur- face, the inhibition efficiency also increases. Moreover, as the electron-donating ability at the metal surface in- creases, the inhibition efficiency also increases if Ξ”π‘π‘šπ‘Žπ‘₯<3.6. The inhibitor molecules' capacity to accept electrons changes in the sequence 7>2>1>9>3>5>8>4>6 in the gas phase and in the aqueous phase – as follows: 7>8>9>6>4>8>3>1>2. The inhibitor 2 is a donor com- pound in the aqueous phase. Figure 5 shows the opti- mized structures, HOMOs of non-protonated inhibitor molecules using DFT/B3LYP/6-31++G (d, p) in the aque- ous phase. A study by Gomez et al. postulated that an electronic back-donation mechanism can control the interaction be- tween the metal surface and the inhibitor molecule, based on the charge transfer model for back-donation and dona- tion of charges [53, 54]. According to this theory, if back- donation transfers from the molecule and electron to the molecule at the same time, the energy change Ξ”πΈπ‘βˆ’π‘‘ is proportional to the molecule's hardness. That is, Ξ”πΈπ‘βˆ’π‘‘ = βˆ’ πœ‚ 4 . (11) From the molecule to the metal, the back donation is strongly preferred when πœ‚ > 0 or Ξ”πΈπ‘βˆ’π‘‘ < 0 . It indicates that charge transfer to the molecule is accompanied by the back donation from the molecule, which is energetically beneficial on the metal surface, if the higher adsorption of the molecule enhances inhibition effectiveness. Then, the inhibition efficiency should arise with the increase in the stabilization energy induced by the contact between the inhibitor and the metal surface. In this study, the calculat- ed Ξ”πΈπ‘βˆ’π‘‘ values exhibit the tendency: 2>7>5>6>4>8>9>3>1 in the gas phase, and in the aque- ous phase the tendency is: 2>7>5>6>3>4>8>9>1, as shown in Tables 5, 6. Tables 1 and 3 show aqueous phase calculations with 6- 311++ (d, p) basis set and B3LYP level for molecular charac- teristics of compounds 1–9. It is an important parameter that can predict the chemical reactive ratio of the molecule. Con- sequently, the reactivity sequence for the derivatives in the liquid phase are: 1<9<8<4<3<6<5<7<2 liquid phase, 1<9<8<3<4<5<6<7<2 gas phase. 2-methyl-1, 3, 4-thiadiazole has a high hardness in the gas phase and aqueous phase, besides 2-propyl-5-methyl- 1, 3, 4-thiadiazole has the lowest value of hardness. Tables 2 and 4 describe the Fukui indices which are more signifi- cant to predict the lowest and highest susceptible site for electrophilic attack. The most susceptible sites are N4 and S6. N4 and N16 have the highest amount in 2-aminoethyl- 5-methyl-1, 3, 4-thiadiazole in the aqueous phase which are equal to 0.187 and 0.101. In the gas phase calculations, Cl atom in 2-(2-chloroethyl)-5-methyl-1, 3, 4-thiadiazole and N16 in 2-aminoethyl-5-methyl-1, 3, 4-thiadiazole have the maximum value of electrophilic attack which are equal to 0.125 and 0.101 respectively. Figure 4 Variation of quantum chemical parameters with the nature of the inhibitor. Chimica Techno Acta 2022, vol. 9(2), No. 20229203 REVIEW 9 of 11 Table 5 Quantum chemical parameters of derivatives 1–9 in the gas phase with 6-311++ (d, p) basis set and B3LYP level. Inhibitors 1 2 3 4 5 6 7 8 9 Δ𝑁 0.674 0.843 0.456 0.212 0.310 0.183 1.244 0.257 0.642 Ξ”πΈπ‘βˆ’π‘‘ –0.512 –0.047 –0.445 –0.252 –0.129 –0.119 –0.099 –0.308 –0.335 Table 6 Quantum chemical parameters of derivatives 1–9 in the aqueous phase with 6-311++ (d, p) basis set and B3LYP level. Inhibitors 1 2 3 4 5 6 7 8 9 Δ𝑁 0.200 –0.99 0.341 0.594 1.085 0.901 1.244 0.578 0.642 Ξ”πΈπ‘βˆ’π‘‘ –0.526 –0.049 –0.18 –0.23 –0.118 –0.126 –0.099 –0.297 –0.335 1 2 3 4 5 6 7 8 9 Figure 5 The optimized structures, HOMOs of non-protonated inhibitor molecules using DFT/B3LYP/6-31++G (d, p) in aqueous phase. 7. Conclusions Quantum computational chemistry approach with 6-311++ (d, p) basis set and Becke’s three- parameters hybrid ex- change-correlation functional (B3LYP) using DFT was used to perform the theoretical calculations. We carried out the geometry optimization of the investigated compounds resulting from the substitution of the ring of 1, 3, 4- thiadiazole with various groups. HOMO and LUMO are extremely useful to determine such parameters as bandgap energy, hardness, softness, ionization energy, electrophilicity, nucleophilicity and electronegativity of molecules to indicate chemical reactive behaviour. Low bandgap and high softness indicate the interaction between inhibitor substituent and 1, 3, 4-thiadiazole. Moreover, we predicted the adsorption abilities of the 1, 3, 4-thiadiazole surface of inhibitor molecules by considering Eg and harness. In the gas phase and the aqueous phase, dynamic simulation approximations to demonstrated the corrosion inhibition performance of the studied inhibitors against the corrosion of 1, 3, 4-thiadiazole. The relative performance in the gas and aqueous phases can be given as 1<9<8<3<4<5<6<7<2, 1<3<9<8<3<4<5<6<7<2, respectively. The Mulliken population analysis was used to determine the Fukui indices to detect the reactive sites. In conclusion, the study shows that N4 has a more reactive site in the gaseous and aqueous phases of these deriva- tives. If these atoms – O, N, S – are present in the mole- cule, the corrosion inhibition increases. The highest value was found in the aqueous phase in the N4 atoms in 2- aminoethyl-5-methyl-1, 3, 4-thiadiazole, which has a sus- ceptible site for electrophilic attack. Supplementary materials No supplementary materials are available. Funding This research had no external funding. Acknowledgments None. Author contributions Conceptualization: D.M.M., H.M.Q. Data curation: D.M.M. Chimica Techno Acta 2022, vol. 9(2), No. 20229203 REVIEW 10 of 11 Formal Analysis: D.M.M, A.H.A., T.M.K. Funding acquisition: D.M.M., H.M.Q. Investigation: D.M.M., H.M.Q. Methodology: D.M.M., H.M.Q. Project administration: D.M.M. Resources: D.M.M., H.M.Q. Software: D.M.M. Supervision: D.M.M. Validation: D.M.M. Visualization: H.M.Q. Writing – original draft: H.M.Q., D.M.M. Writing – review & editing: H.M.Q. Conflict of interest The authors declare no conflict of interest. Additional information Websites of University of Raparin, https://www.uor.edu.krd/en; Salahaddin University, https://su.edu.krd. References 1. Potthast A, Henniges U, Banik G. Iron gall ink-induced corro- sion of cellulose: aging, degradation and stabilization. Part 1: model paper studies. Cellulose. 2008;15(6):849–859. doi:10.1007/s10570-008-9237-1 2. Kim D-K, Muralidharan S, Ha T-H, Bae J-H, Ha Y-C, Lee H-G, Scantlebury J. 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