Theoretical modeling and molecular level insights into the corrosion

Journal of Molecular Liquids 221 (2016) 579–602

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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq

Theoretical modeling and molecular level insights into the corrosion inhibition activity of 2-amino-1,3,4-thiadiazole and its 5-alkyl derivatives Nuha A. Wazzan a, I.B. Obot b,⁎, Savaş Kaya c a b c

King Abdulaziz University, College of Science, Chemistry Department, Jeddah, Saudi Arabia Centre of Research Excellence in Corrosion, Research Institute, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia Cumhuriyet University, Faculty of Science, Department of Chemistry, Sivas 58140, Turkey

a r t i c l e

i n f o

Article history: Received 12 April 2016 Accepted 5 June 2016 Available online 11 June 2016 Keywords: 2-Amino-5-alkyl-1,3,4-thiadiazole Corrosion inhibitors DFT calculations NBO analysis Molecular dynamic simulation

a b s t r a c t Density functional theory (DFT) with two functionals, namely B3LYP and CAM-B3LYP with the 6-311++G(d,p) basis set was performed on six 2-amino-5-alkyl-1,3,4-thiadiazole derivatives (IC-2 to IC-13) used as corrosion inhibitors for steel in 1.0 M H2SO4 solution, along with the calculations on the parent compound 2-amino-1,3,4thiadiazole (IC). The computations were carried out in non-protonated and protonated forms. The results obtained found a relationship between the molecular structures of the studied IC inhibitors and their experimental inhibition efficiencies. The order of the experimental inhibition efficiencies was matched with the order of a good number of the calculated global and local reactivity descriptors but with varying degrees of correlation. Supported by the Mulliken population analysis and natural population analysis, molecular electrostatic potential plots, and natural bond orbital analysis, the active sites in the inhibitors responsible for their adsorption on a steel surface have been predicted. Molecular dynamic simulations were further carried out on the protonated forms of IC2 to IC-13 with an Fe (110) surface. Results obtained were in reasonable agreement with experimental data. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Corrosion of metals is a big concern in industry and results in a huge waste of both resources and money. Nowadays, it is crucial to control metal corrosion in order to extend the life of metallic equipment and to reduce the leaking of toxic metals to the surrounding. Organic compounds with hetero atoms (mainly N, S, P and O) and an aromatic ring are widely used as metal corrosion inhibitors [1–11]. Organic compounds such as 2-amino-5-mercapto-1,3,4-thiadiazole [1], polyvinylpyrollidone and polyacrylamide [3], 2,3-diaminonaphthalene [4], and 2-amino-5-(ethylthio)-1,3,4-thiadiazole [10], have been reported to be effective metal corrosion inhibitors in various media. The adsorption layer formed between the compounds, acting as an inhibitor, and the metal surface is one of main factors that control inhibition efficiency. Other factors responsible for the formation of a strong adsorption layer on the metal surface are inhibitor's molecular structure and size, the number and type of substituents on the inhibitor molecules, the nature and the surface charge of the metal, and the type of adsorption (whether it is physisorption or chemisorption), and in addition of course to other important factors such as inhibitor concentration, temperature and the corrosive medium [10–11]. ⁎ Corresponding author. E-mail address: [email protected] (I.B. Obot).

http://dx.doi.org/10.1016/j.molliq.2016.06.011 0167-7322/© 2016 Elsevier B.V. All rights reserved.

Electrochemical experiments were extensively carried out to determine the influence of these factors. However, experiments are usually time consuming, expensive, and deficient in elucidating the inhibition mechanism of the system at the sub-atomic and 3D-molecular levels [4]. Therefore, quantum chemical calculation and molecular dynamic simulation were recommended as potent and fast tools to assist in the interpretations of experimental findings and to answer such chemical ambiguities [12–14]. The molecular geometry and vibrational frequencies of a derivative of this class of compounds, namely 2-amino-5-phenyl-1,3,4-thiadiazole, in the ground state has been calculated using the density functional method (DFT/B3LYP) and Hartree–Fock (HF) with 6-31G(d) basis set. Good agreement between the optimized geometry and the experimental data was obtained. The calculated vibrational frequencies by B3LYP showed greater agreement with the experiment compared to those calculated by the HF method [12]. Also, the corrosion inhibition potentials of 2-amino-5-(ethylthio)-1,3,4-thiadiazole (ATD) for copper in two phases, i.e. de-aerated, aerated and oxygenated 3% NaCl solutions and an aerated acidic pickling solution of 0.5 M HCl, using gravimetric and electrochemical techniques were investigated. The study showed that ATD is a good mixed-type inhibitor for copper corrosion with its inhibition efficiency increasing in the order of oxygenated N aerated N de-aerated 3% NaCl solutions; also it is a good inhibitor for copper in the other phase and its inhibition efficiency increased with its concentration [10,

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N.A. Wazzan et al. / Journal of Molecular Liquids 221 (2016) 579–602

15]. The detailed FT-IR and FT-Raman spectra of the solid phase 2amino-5-ethyl-1,3,4-thiadiazole (IC-2) have been recorded, also the 1 H and 13C NMR spectra of IC-2 were obtained in DMSO-d6. The calculations at DFT/B3LYP and DFT/B3PW91 with 6-31G(d) and 6311 ++G(d,p) basis sets were carried out on eight conformers of this compound in order to obtain the conformational energy and vibrational frequencies. Also the calculations of the 1H and 13C NMR chemical shifts were also carried out using a GIAO approximation at the same method/ basis set with solvent effects using the PCM method. A complete vibrational assignment of the observed infrared and Raman bands along with NMR chemical shifts has been proposed [16]. The corrosion inhibition of 2-amino-5-mercapto-1,3,4-thiadiazole on a mild steel surface in 0.5 M HCl solution was investigated by different methods, such as potentiodynamic polarization, electrochemical impedance spectroscopy (EIS) and linear polarization resistance (LPR) etc. Results showed that this compound provided an excellent inhibiting effect with an inhibition efficiency higher than 99% after 120 h at 1.0 × 10−2 M. This was attributed to the strong adsorption of inhibitor molecules on the metal surface [1]. The corrosion inhibition efficiency of 2-amino-5-alkyl-1,3,4thiadiazole (IC) compounds with different alkyl chain lengths, namely: 2-ethyl (IC-2), 3-n-propyl (IC-3), 5-n-pentyl (IC-5), 7-heptyl (IC-7), 11undecyl (IC-11) and 13-tridecyl (IC-13), were evaluated for steel in 1 M H2SO4 by Palomar-Pardave [11]. Palomar-Pardave et al. synthesised, characterized by FT-IR and NMR spectroscopy analysis and evaluated these compounds as corrosion inhibitors for steel in 1 M H2SO4 using electrochemical impedance spectroscopy (EIS) and SEM analysis. They concluded from the obtained results that “the inhibition mechanism involves isolating of the steel surface by the inhibitor molecules from corrosion by the process of Langmuir-type adsorption”. Also they concluded that “the alkyl chain length plays an important role in the inhibition efficiency of the synthesised inhibitors, in such a way that the inhibition efficiency first increased up to undecyl spacer chain, IC-11, and then decreased with the length of the spacer for tridecyl chain, IC13”. They attributed this dependence due to “the flexibility and folding of the alkyl chain”. They suggested that this hypothesis could be supported by theoretical explanation. Thus, their result can be divided into two series: Series I: IC-2 to IC-11 and series II: containing IC-11 and IC-13. Their results are summarized in Table 1 and represented in Fig. 1. To the best knowledge of the present authors, these experimental findings were not combined with any theoretical calculations. The six inhibitors (including also the title molecule IC) are rather a good number to carry out extensive quantum mechanical calculations and molecular dynamics simulations. This can assist in giving a clear correlation between the geometrical, electronic structures and the binding energies calculated theoretically with the inhibition efficiencies for these compounds. Also, the correlation between experimental spectral data and the calculated ones were carried out. The present study uses a high level of computational theory to assist in the interpretation of the experimental findings earlier carried out by Palomar-Pardave et al. [11].

Table 1 Percentage inhibition efficiencies (%IEs) of the IC as corrosion inhibitors for mild steels determined by EIS with concentrations ranging from 5 to 100 ppm in 1.0 M sulfuric acid solutions [11]. Concentration/inhibitor

IC-2

IC-3

IC-5

IC-7

IC-11

IC-13

5 10 20 30 50 80 100 Average %IE

79 73 75 74 62 55 49 67

72 79 80 80 – 81 81 79

64 71 72 75 76 – 83 74

54 70 75 82 82 84 86 76

57 78 86 91 94 – 95 84

65 74 77 79 79 80 82 77

Fig. 1. Percentage inhibition efficiencies of IC inhibitors in 1 M H2SO4 solutions. Data from reference [11] and the plotting is by the present authors.

2. Computational details 2.1. DFT calculations DFT calculations were performed using the Gaussian 09 (G09) suite of programs [17]. Geometry optimizations were conducted using Becke's three parameter exchange functional, the Lee–Yang–Parr correlation functional (B3LYP) [18,19]. To include the long-range correction, which is essential to describe electron excitations to high orbitals, the hybrid exchange–correlation functional (CAM-B3LYP) proposed by Yanai et al. was used [20]. This was combined with the split-valence triple zeta basis set 6-311++G(d,p), with two polarized basis functions (d- and p-orbitals), where a d-type orbital was added to all atoms except the hydrogen atoms, and a p-type orbital was added to all hydrogen atoms. In addition to this, two diffuse functions, where a sp-type diffuse function was added to all atoms except the hydrogen atoms, and one stype diffuse function were added to all hydrogen atoms. Adding higher angular momentum orbitals (polarization orbitals) in the basis set that are empty in the separated atoms was essential for improved representation of the electron density of the molecule; and adding the diffuse functions was also essential for better representation of the broad electron distributions. In geometry optimizations every bond length, bond angle and dihedral angle were allowed to relax, free of constraints. The nature of the stationary points (i.e. minima points on the potential energy surface) was confirmed by vibrational frequency analysis, to verify that only real frequency (i.e. no imaginary frequency) values were obtained for all geometries.† Visual inspection was carried out using the GuassView program (version 5.0.8) [21]. The optimized geometries have been used to calculate all parameters reported in this study. The solvation effects were studied by applying the implicit solvation model, vis. the polarized continuum model (PCM). In the PCM model of solvation, the solvent is treated as a continuum dielectric medium and the solute is considered as a trapped molecule in a cavity surrounded by solvent [22]. The Freq option in G09 software allowed the calculations of vibrational modes. 1H and 13C NMR chemical shifts (δ) were calculated with a gauge including an atomic orbital (GIAO) approach by applying B3LYP/6-311++G(d,p). The natural bond orbital (NBO) calculations have been performed using the NBO 3.1 program implemented in the G09 package at the B3LYP/6-311++G(d,p) functional/basis set.

†

Optimized geometries with negative frequencies were discarded.


The binding energy is the negative of the interaction energy and is given as:

2.2. Molecular dynamics simulations The Forcite module in the Material Studio Software 7.0 from BIOVIAAccelrys, USA was adopted in performing the molecular dynamics (MD) simulations. The simulation was carried out with an Fe (110) crystal with a slab of 5 Å. The Fe (110) plane was enlarged to a (10 × 10) supercell to provide a large surface for the interaction of the inhibitors. After that, a vacuum slab with 30 Å thickness was built above the Fe (110) plane. The condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field was used to optimize the structures of all components of the system of interest. The inhibitor molecules designated as IC-2 to IC-13 were optimized in the protonated form before each of them were placed on top of the Fe (110) surface. This was done since the experiment data were obtained in 1.0 M H2SO4 solution and the molecules are expected to be protonated in this highly acidic solution. The MD simulations were then performed in an NVT canonical ensemble at 298 K with a time step of 1.0 fs and a total simulation time of 1000 ps using an Anderson thermostat. The interaction energy (Eint) of an inhibitor molecule with an Fe surface was obtained using the following equation: Eint ¼ Etotal – EFe

surface

þ Emolecule

581

ð1Þ

where Etotal is the total energy of the molecules and the metal surface system; Esurface is defined as the energy of a metal surface without adsorption of molecules and Emolecule is the energy of isolated molecules.

Ebinding ¼ −Eint

ð2Þ

3. Results and discussion 3.1. Molecular geometries The title molecule IC and its six 5-alkyl derivatives (IC-2 to IC-13) are optimized with B3LYP and CAM-B3LYP with the 6-311++G(d,p) basis set. The optimized geometries obtained at the B3LYP/6-31+G(d) along with atomic numbering used in this study are shown in Fig. 2. Table 2 and Supplementary data Table 1 summarise the main geometrical parameters, i.e. those of the thiadiazole ring of IC inhibitors at B3LYP/6-311++G(d,p) and CAM-B3LYP/6-311++G(d,p), respectively. The optimized geometries are compared with the crystal structure of 2-amino-5-phenyl-1,3,4-thiadiazole derivative [12]. The optimized geometries of ICs at the two functionals are generally in excellent agreement with the experimental crystal structure. The average percent errors in the bond length and bond angle are: 〈%Error〉 = 1.40 and 0.74 at B3LYP and 〈%Error〉 = 1.33 and 0.63 at CAM-B3LYP, respectively. In addition, for IC-2 as a representative example, the calculated and experimental geometrical parameters correlated very well with excellent correlation coefficients of R2 = 0.9912 and 0.9957 at B3LYP and R2 = 0.9902 and 0.9966 at CAM-B3LYP for the bond lengths and bond angles, respectively, (Fig. 3). The B3LYP method shows more agreement with the experiment in reproducing the bond lengths, while the CAM-

Fig. 2. The optimized geometries of the IC inhibitors at B3LYP/6-311++G(d,p) along the numbering scheme used in this study.

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Table 2 Geometrical parameters of the thiadiazole ring of IC inhibitors calculated at DFT with B3LYP/6-311++G(d,p). Note: values in parentheses are calculated values at the same method/basis set from [13], experimental data is for the crystal structure of C8H7N3S from [1]. Geometrical parameter

IC

Bond length (Å) C1\ \S3 C1\ \N5 C1\ \H9/C9 C2\ \S3 C2\ \N4 C2\ \N6 N4\ \N5 N6\ \H7 N6\ \H8 〈%Error〉

1.758 1.289 (1.289) 1.081 (1.081) 1.761 (1.761) 1.303 (1.302) 1.372 (1.372) 1.373 (1.369) 1.011 1.008 (1.008)

Bond angle (o) S3\ \C1\ \N5 S3\ \C1\ \H9/C9 N5\ \C1\ \H9/C9 S3\ \C2\ \N4 S3\ \C2\ \N6 N4\ \C2\ \N6 C1\ \S3\ \C2 C2\ \N4\ \N5 C1\ \N5\ \N4 C2\ \N6\ \H7 C2\ \N6\ \H8 H7\ \N6\ \H8 〈%Error〉

114.312 (114.0) 121.652 (121.7) 124.035 (124.0) 113.987 (114.3) 122.490 (122.5) 123.404 (123.4) 85.431 112.816 113.450 (113.5) 113.430 (113.5) 117.585 (117.6) 114.252

Dihedral angle (o) N5\ \C1\ \S3\ \C2 H9/C9\ \C1\ \S3\ \C2 S3\ \C1\ \N5\ \N4 H9/C9\ \C1\ \N5\ \N4 N4\ \C2\ \S3\ \C1 N6\ \C2\ \S3\ \C1 S3\ \C2\ \N4\ \N5 N6\ \C2\ \N4\ \N5 S3\ \C2\ \N6\ \H7 S3\ \C2\ \N6\ \H8 N4\ \C2\ \N6\ \H7 N4\ \C2\ \N6\ \H8 C2\ \N4\ \N5\ \C1

0.587 −179.154 (179.2) −0.777 178.958 (179.0) −0.260 −176.419 (176.5) −0.096 176.024 (176.1) −171.211 −34.200 12.994 150.004 0.563

IC-2

IC-3

IC-5

IC-7

IC-11

IC-13

1.779 1.289 1.502 1.760 1.299 1.375 1.372 1.012 1.009

1.780 1.290 1.501 1.760 1.299 1.375 1.372 1.012 1.009

1.780 1.289 1.501 1.760 1.299 1.376 1.372 1.012 1.009

1.780 1.289 1.501 1.760 1.299 1.376 1.372 1.012 1.009

1.780 1.290 1.501 1.760 1.299 1.376 1.372 1.012 1.009

1.780 1.290 1.501 1.760 1.299 1.376 1.372 1.012 1.009

112.731 121.817 125.452 114.036 122.316 123.528 85.875 112.728 114.626 113.126 117.172 113.947

112.698 121.785 125.517 114.040 122.331 123.510 85.886 112.736 114.635 113.102 117.141 113.928

112.671 121.742 125.587 114.016 122.321 123.541 85.913 112.744 114.651 113.108 117.131 113.927

112.679 121.717 125.604 114.026 122.317 123.536 85.900 112.743 114.647 113.101 117.125 113.927

112.679 121.717 125.604 114.026 122.317 123.536 85.900 112.743 114.647 113.101 117.125 113.927

112.668 121.721 125.611 114.028 122.327 123.523 85.900 112.746 114.653 113.088 117.115 113.915

0.598 −179.203 −0.829 178.963 −0.237 −176.365 −0.153 175.921 −171.057 −35.388 13.186 148.855 0.648

0.572 −179.221 −0.806 178.978 −0.212 −176.355 −0.171 175.921 −170.989 −35.413 13.236 148.813 0.644

0.608 −179.215 −0.839 178.976 −0.245 −176.357 −0.149 175.910 −170.984 −35.415 13.277 148.846 0.652

0.575 −179.246 −0.808 179.005 −0.217 −176.341 −0.167 175.904 −171.010 −35.453 13.238 148.795 0.643

0.575 −179.246 −0.808 179.005 −0.217 −176.341 −0.167 175.904 −171.010 −35.453 13.238 148.795 0.643

0.606 −179.260 −0.836 179.024 −0.245 −176.356 −0.147 175.911 −171.074 −35.564 13.187 148.697 0.649

Exp. [1] 1.751 (2) 1.300 (2) – 1.749 (2) 1.320 (2) 1.337 (2) 1.384 (2) – – 1.40

113.55 (11) – – 113.30 (11) – 124.42 (5) 87.01 (7) 112.21 (13) 113.94 (12) – – – 0.74 – – – – – – – – – – – – –

Fig. 3. Correlations between calculated and experimental geometrical parameters of IC-2 as a representative example calculated at DFT with 6-311++G(d,p).


B3LYP method agrees more with the experimental bond angles. In general, the two methods underestimate the bond lengths except for the C2\\N6 bond length, since the calculated values are slightly larger than the experimental value by ~ 0.4 Å. The bond angles are in some cases overestimated and in other cases underestimated by the two methods. The difference between the calculated and experimental data is due to the fact that the experimental data was carried out in the solid phase, while the calculated parameters are for the molecules in the gas phase. On the other hand, the agreement between the calculated and experimental data shows the effectiveness of the two methods in reproducing the experimental parameters and the insignificant effect of substitution since the comparison is made between different derivatives. At the B3LYP method, the changes in the optimized bond lengths between the six derivatives (IC-2 to IC-13) are minor, indicating an insignificant effect of the extent of the alkyl series on geometries. On the other hand, the length of the alkyl chain affects in some ways the optimized bond angles and dihedral angles. The changes in the optimized bond lengths between the title molecule IC and its derivatives (IC-2 to IC-13) show the effect of the alkyl chain substitution. For instance, a slight change in the bond lengths of C2\\N4 and C2\\N6 upon substitution is observed, i.e. the C2\\N6 bond increases in length by ~0.004 Å, while the C2\\N4 bond length decreases by ~0.005 Å. The most significant change is in the bond length of C1\\S3, since upon substitution it increases by ~0.021 Å. In contrast, the effect of the alkyl chain on the optimized bond angles and dihedral angles are more significant, as the two dihedral angles, N4\\C2\\N6\\H7 and N4\\C2\\N6\\H8 change by ~0.28 and 1.30°. 3.1.1. FT-IR spectra With the C1 point group, the IC-2 inhibitor as a representative example has 39 normal modes of vibrations, corresponding to 3N-6 degree of freedom. The vibrational modes are calculated at the B3LYP/6311++G(d,p) method/basis set. The experimental [11], and calculated

583

frequencies are compared in Table 3, along with tentative mode assignments. The disagreement between the calculated and experimental values are due to two factors: (1) the calculated values are derived from the harmonic oscillator model point of view, while the experimental data were always deviated from anharmonicity; and (2) the experimental data were carried out in the solid state of the compounds which takes into account the intermolecular interactions, while the calculated data are carried out in the gas phase that exclude such interactions. Vibrational frequencies were scaled by 0.983 at wavenumbers higher than 1700 cm−1 and by 0.958 at wavenumbers lower than 1700 cm−1 to correct the theoretical error [23,24]. The simulated FT-IR spectrum and the correlation between the scaled calculated and experimental frequencies are presented in Table 3. 3.1.1.1. NH2 group vibration. The stretching modes of vibrations (symmetric and asymmetric) of NH2, typically appeared at 3500– 3300 cm−1. Only one band was observed in this region at 3289 cm−1, while theoretically two medium bands appeared near this region at 3608 and 3501 cm−1. With the aid of vibration animation capability of Guassveiw software these two frequencies are unambiguously assigned to asymmetric and symmetric stretching modes of NH2, respectively. The experimental band (3289 cm− 1) corresponds with the band appearing at 3501 cm− 1, and is assigned to the NH2 symmetric stretching with a significant difference of 212 cm−1. This is attributed to the high chance of intramolecular H-bonding in the solid state of the experiment which is not described in the gas phase of the calculated values. The strong band with an intensity of 156 located theoretically at 1573 cm−1 is unambiguously assigned to the NH2 in-plane scissoring mode of vibration, and this corresponds with the experimental frequency of 1638 cm−1, with a difference of 65 cm−1. Three calculated bands at 610, 520 and 500 cm− 1 are assigned without any difficulty to the out-of-plane wagging mode of the vibration of NH2, the most intense band at 610 cm−1 (IIR = 101) corresponding with the observed band appearing at 529 cm−1.

Table 3 Experimental and calculated unscaled and scaled frequencies (at B3LYP/6-311++G(d,p)) of the IC-2 inhibitor as a representative example along with the plots of the calculated FT-IR spectrum and correlation between experimental [11] and calculated scaled frequencies.

Exp./cm−1

– 3289 3113 – 3102 2980 2941 1638 1526 1508 1498 – – 1027 – – 529 – – IIR: IR band intensity.

Selected calc./cm−1 Unscaled

Scaled

3670 3561 3119 3109 3043 3038 3017 1642 1504 1476 1415 1373 1287 1105 976 792 636 543 522

3608 3501 3066 3056 2991 2987 2966 1573 1441 1414 1356 1315 1233 1059 935 759 610 520 500

IIR

Tentative assignments

39 48 20 23 29 10 17 156 5 5 5 22 0 1 8 3 101 81 62

NH2 asy stretching NH2 sym stretching CH3 asy stretching CH3 asy stretching CH3 sym stretching CH2 asy stretching CH2 sym stretching NH2 scissoring CH3 & CH2 scissoring CH2 scissoring CH3 wagging CH2 wagging CH3 & CH2 twisting CH3 & CH2 twisting \CH2 stretching CH3\ CH3 & CH2 rocking NH2 wagging NH2 wagging NH2 wagging

584


3.1.1.2. CH3 and CH2 group vibrations. The stretching mode of vibration (symmetric and asymmetric) of the methyl and methylene groups is typically in the range 3000–2850 cm−1. Four bands were observed near/in this region, i.e. at frequencies of 3113, 3102, 2980 and 2941 cm− 1, while the simulated spectrum shows five bands near/in this region, i.e. at frequencies of 3066, 3056, 2991, 2987 and 2966 cm−1. The assignment of calculated and observed frequencies is as follows: two calculated frequencies at 3066 and 3056 cm− 1 and one frequency observed at 3113 cm−1 are assigned to the CH3 asymmetric stretching modes, the calculated frequency at 2991 cm−1 and the one observed at 3102 cm− 1 are assigned to the CH3 symmetric stretching mode, the CH2 asymmetric stretching is calculated at 2987 cm−1 and observed at 2980 cm−1, and finally the CH2 symmetric stretching is calculated at 2966 cm−1 and observed at 2941 cm−1. Thus, the differences between the two data are of the order of tens of wavenumbers. The C\\H in-plane scissoring appeared typically at 1470–1450 cm−1, and the observed bands at 1526 and 1508 cm−1 correspond to the calculated values at 1441 and 1414 cm−1 with differences of 85 and 94 cm− 1, respectively. The out-of-plane twisting mode is typically at ~ 1250; it was observed at 1027 cm−1 and corresponds to the calculated value at 1059 cm−1. The calculated and observed data correlated very well with excellent correlation coefficient (R2 = 0.9914) (Table 3). 3.1.2. NMR spectra The calculated 1H and 13C isotropic chemical shifts of the IC-2 inhibitor as a representative example in the gas phase, CDCl3 and DMSO solvents at B3LYP/6-311 ++G(d,p) are collected in Table 4, along with graphical correlations between the experimental and calculated values in DMSO-d6. The scheme numeration of atoms is as shown in Fig. 2. The isotropic shielding values were used to calculate the isotropic δ values with respect to tetramethylsilane (TMS). In all cases, the correlation between the experimental chemical shifts and the calculated

shielding constants is better for 13C than for 1H. This may be attributed to the fact that protons are located on the border of the molecule and thus they are believed to precipitate more in intermolecular (solvent– solute) effect than carbon atoms [25].

3.1.2.1. 1H assignments and error analysis. Generally, the electronic atmosphere of the proton will affect to a great extent the proton chemical shift (1H NMR) of organic molecules. Proton attached/close to an electron-withdrawing atom/group is less shielded and thus, δ will move to higher values. On the other hand, the proton attached/close to an electron-donating atom/group is more shielded and thus, δ will move to lower values [26]. The protons of an IC-2 molecule are of three types: two protons of the amine group, the two protons of the methylene group and the three protons of the methyl group. The two amine protons (H7 and H8) are less shielded, thus their chemical shift values are considerably larger, than the two methylene protons (H10 and H11) and the three methyl protons (H13, H14 and H15), and this is attributed to the electronic charge density and the electron-donating properties of the nitrogen atom. On the other hand, the methylene protons are less shielded, thus their chemical shift values are considerably larger than the methyl's protons. This is attributed to the fact that a carbon atom is slightly more electronegative than a hydrogen atom. Experimentally, the protons were not assigned clearly one by one due to overlapping bands. For instance, the experimental chemical shift value of the amine protons is 6.99 ppm; this is compared to the average value of the two chemical shift values (4.58 ppm) obtained theoretically with an unambiguous assignment in a DMSO solvent. The experimental chemical shift values of the seven protons of the IC-2 compound (H7, H8, H10, H11, H13, H14 and H15) are in the range of 1.18–6.99 ppm in the DMSO solvent [11], while the calculated values are in the range of 1.43–4.10, 1.39–4.45 and 1.37–4.58 ppm in gas, CDCl3, and DMSO phases, respectively.

Table 4 Calculated and experimental 1H and 13C NMR isotropic chemical shift, δ, (ppm) with respect to TMS of IC-2 inhibitor as a representative example at B3LYP/6-311++G(d,p) in gas, DMSOd6, and CDCl3, along with graphical correlations between the experimental and calculated values in DMSO-d6.

Calculated Gas

Experimental Average

CDCl3

Average

DMSO-d6

Average

Assignment; integration

DMSO-d6

1

H atoms H(7) H(8) H(10) H(11) H(13) H(14) H(15) R2

4.49 3.71 2.94 2.86 1.05 1.64 1.63

4.098 2.899 1.438

4.70 4.19 3.04 2.97 1.17 1.51 1.50

0.9067

4.447 3.004 1.394

4.76 4.40 3.09 3.03 1.23 1.44 1.43

0.9208

4.58

6.99

NH2; 2H

3.06

2.78

CH2; 2H

1.37

1.18

CH3; 3H

0.9209

13

C atoms C(1) C(2) C(9) C(12) R2

171.34 175.76 29.43 12.29

174.67 178.49 29.29 12.15 0.9952

176.39 179.73 29.23 12.11 0.9957

168.34 160.11 23.25 13.92 0.9960

Thiadiazole ring; 2C Methylene C; 1C Methyl C; 1C


Good correspondences between the experimental and calculated chemical shifts were shown, i.e. linear relationships for 1H chemical shifts were obtained in the gas phase, CHCl3 and DMSO solvents as represented by Eqs. (3)–(5). The correlation coefficients become better as the phase is changed from gas to CDCl3 to DMSO, since the experimental data is in the DMSO solvent; this indicates that the solvation model used in the calculations, i.e. the PCM model, is able to describe the solvation process quite precisely. Gas : δcal ðppmÞ ¼ 0:4227δ exp ðppmÞ þ 1:2689; R2 ¼ 0:9067 CHC13 :

δcal ðppmÞ ¼ 0:4882δ exp ðppmÞ þ 1:1663;

ð3Þ

R2 ¼ 0:9208 ð4Þ

DMSO : δcal ðppmÞ ¼ 0:5143δ exp ðppmÞ þ 1:1259;

R2 ¼ 0:9209 ð5Þ

3.1.2.2. 13C assignments and error analysis. The carbon atoms in this molecule are classified into three types: the two carbon atoms in the thiadiazole ring, the methylene carbon and the methyl carbon. Experimentally and theoretically these carbons are unambiguously assigned. The divergence in the chemical shift values between the different sets of carbon groups is due to the positioning of these carbons with respect to electronegative substituents (i.e. N and S atoms) that polarize the electron cloud in their bonding to carbon [27]. The typical values for the methyl and methylene carbons are 13–16 and 16–25 ppm, respectively. The chemical shifts in DMSO-d6 solvent are experimentally 13.92 and 23.25 and theoretically are 12.11 and 29.23 with few ppm differences for methyl and methylene carbons, respectively. In the DMSO solvent, the thiadiazole carbons are assigned experimentally at 168.34 and 160.11 and theoretically assigned at 176.39 and 179.73 for C1 and C2, respectively. Thus, the calculated chemical shifts show similar values and slightly smaller than the experimental ones (few ppms) in the gas and solvents. This is also the case with 1H NMR even when better correspondences between the experimental and calculated chemical shifts were shown, i.e. the linear relationships for 13C chemical shifts were obtained in the gas phase, CHCl3 and DMSO solvents as represented by Eqs. (6)–(8), respectively. The performance of the B3LYP functional with the 6-311++G(d,p) basis set in the prediction of the chemical shift values is excellent. In addition, the PCM model of solvation calculates better chemical shifts and a slightly larger correlation coefficient (R2 = 0.9960) in DMSO than in the gas phase (R2 = 0.9952). Gas : δcal ðppmÞ ¼ 1:0475δ exp ðppmÞ þ 1:4602;

CHC13 :

R2 ¼ 0:9952

δcal ðppmÞ ¼ 1:0693δ exp ðppmÞ þ 0:9076;

ð6Þ

R2 ¼ 0:9952 ð7Þ

DMSO : δcal ðppmÞ ¼ 1:0799δ exp ðppmÞ þ 0:6641;

R2 ¼ 0:9960 ð8Þ

585

3.2. Frontier molecular orbital analysis Frontier molecular orbitals (FMOs), HOMO and LUMO, i.e. the highest occupied molecular orbital and the lowest unoccupied molecular orbital, respectively, were used to predict the adsorption active site/s of the inhibitor molecules using two DFT functionals with the 6311 ++G(d,p) basis set. Table 5 summarizes the calculated values of the FMOs, i.e. EHOMO and ELUMO, and the energy gap (ΔEL − H) of IC inhibitors along with the experimental inhibition efficiencies [11]. Figs. 4 and 5 show graphical representations of the (in/de)creasing trend of these parameters, and correlations between inhibition efficiencies and these parameters of IC inhibitors, respectively. The adsorption process of a corrosion inhibitor molecule onto a metal surface increases with an increase of the HOMO energy (EHOMO) and a decrease of the LUMO energy (ELUMO). This is because, from the HOMO orbital the inhibitor molecule will donate the electrons to the d-orbital of the metal molecule, and to the LUMO orbital the inhibitor will receive the electrons from the d-orbital of the metal molecule, in an electron-donation and electron-back-donation process. Thus, EHOMO is often associated with the electron donating ability of a molecule; the high value of EHOMO indicates the tendency of the inhibitor to donate electrons to the acceptor metal. On the other hand, ELUMO indicates the ability of the inhibitor to receive electrons, and the lower value of ELUMO indicates more tendency of the inhibitor to receive electrons from the donor metal [28,29]. At the B3LYP/6-311 ++G(d,p) level of theory, the trend of increase of HOMO energies is consistent with the increase of the inhibition efficiencies, i.e. the %IEs of IC inhibitors increase in the following order: IC-2 (49%) b IC-3 (81%) b IC-5 (83%) b IC-7 (86%) b IC-11 (95%); and the HOMO energies increase with same order: IC-2 (− 6.57976 eV) b IC-3 (− 6.56942 eV) b IC-5 (− 6.56181 eV) b IC-7 (− 6.55881 eV) b IC-11 (− 6.55718 eV). Thus, IC-11 with the largest inhibition efficiency has a higher HOMO energy, while IC-13 with an inhibition efficiency lower than IC-11 (82%) has the highest HOMO energy (− 6.55691 eV). On the other hand, at CAM-B3LYP/6-311++G(d,p) the same trend is observed. In addition, when comparing the %IEs and HOMO energies of IC-11 with IC-13, we conclude that they are somehow different from what was obtained by the B3LYP method with the same basis set, i.e. IC-13 with a smaller %IE has an equal HOMO energy (− 8.06552 eV) as IC-11 with %IE = 95%. Also, the HOMO energies obtained by B3LYP and CAM-B3LYP methods are all negative values and the LUMO energies are negative values from B3LYP and positive values with CAM-B3LYP. The trend at which the LUMO energies decrease with the inhibition efficiencies at the two methods is not as expected, since the LUMO energies increase and not decrease as the %IEs increase. This suggests that the electrondonating process from the inhibitor to the metal surface is predominant over the electron-back-donation from the Fe surface to the inhibitor molecule [5], (Fig. 4). The correlations between the %IE values and the HOMO (at B3LYP and CAM-B3LYP) and LUMO (at B3LYP) energies of the IC inhibitors are good with very good correlation coefficients (0.81 b R2 b 0.85), Fig. 5. Energy gap (ΔEL − H) is an important parameter of a reactive inhibitor toward the adsorption on the steel surface; an efficient inhibitor is characterized by a small energy gap [30]. From Table 5, at CAM-B3LYP,

Table 5 Calculated energy levels of the HOMO, LUMO, and ΔEL − H (in eV), along with the experimental inhibition efficiencies [11] for the IC inhibitors calculated at DFT with the 6-311++G(d,p).

B3LYP

CAM-B3LYP

%IE

EHOMO ELUMO ΔEL−H EHOMO ELUMO ΔEL−H

IC

IC-2

IC-3

IC-5

IC-7

IC-11

IC-13

−6.84208 −1.06452 5.77757 −8.34961 0.06041 8.41002 –

−6.57976 −0.85417 5.72559 −8.09110 0.14858 8.23967 49

−6.56942 −0.84356 5.72586 −8.07749 0.15266 8.23015 81

−6.56181 −0.83594 5.72586 −8.06960 0.15538 8.22498 83

−6.55881 −0.83404 5.72478 −8.06688 0.15619 8.22307 86

−6.55718 −0.83240 5.72478 −8.06552 0.15728 8.22280 95

−6.55691 −0.83186 5.72505 −8.06552 0.15728 8.22280 82

586


Fig. 4. Graphical representations of the trend of (in/de)creasing of HOMO and LUMO energies of IC inhibitors at DFT with 6-311++G(d,p).

the trend of decreasing the energy gap with increasing %IEs is consistent with the experiment, i.e. the energy gaps decrease as the %IEs increase from IC-2 to IC-11. At B3LYP the trend is not consistent, but the better inhibitor IC-11 is the one with almost the smallest energy gap (ΔEL − H = 5.72478 eV); also by comparing the two inhibitors IC-11 and IC13 it is revealed that IC-11 with a better inhibition efficiency has an energy gap of 5.72478 eV, which is smaller than that of IC-13 (ΔEL − H = 5.72505 eV). Fig. 6 shows the distributions of the LUMO and HOMO molecular orbitals at CAM-B3LYP/6-311++G(d,p) of some of the studied IC inhibitors (note: for more figures, see Supplementary data Fig. 1). The LUMO and HOMO orbitals of IC inhibitors are spread almost on the entire part of the molecules except the substituted alkyl group, thus, the part of the molecule in which electrons will be donated is undistinguished from the part of the molecule in which the electrons will be received. In addition, from IC-2 to IC-13 the HOMO orbitals are delocalized on C9 and its H atoms, while the LUMO orbitals are not, indicating that due to C9's position (attached to the thiadiazole ring) this carbon will have some of the electron density from the electron-rich thiadiazole ring, and for IC-3 to IC-13, C9 will receive electrons from the carbon atoms of the substituted alkyl groups as they are electron-donating groups (EDGs). This suggests that the electron-donation and electron-back-donation from this site is possible. Also, very significant distributions of the LUMO orbitals are on the amine group (\\NH2 group), an evidence that this group acts as an electron-back-donating group rather than an electron-donating group. This is attributed to the fact that the amine group is in the para-position

with respect to the alkyl group, which results in high conjugation across the ring, i.e. the lone pair of electrons on the amine's nitrogen and the electron-releasing property of the alkyl group (Fig. 6). 3.3. Global reactivity descriptors The energies of the HOMO and the LUMO orbitals of the inhibitor molecule are related to the ionization potential, IE, and the electron affinity, EA, respectively, according to Eqs. (9) and (10): IE ¼ −EHOMO

ð9Þ

EA ¼ −ELUMO

ð10Þ

Global electronegativity, χ, and global hardness, η, are given by Eqs. (11) and (12), respectively [31]:

χ¼

IE þ EA 2

ð11Þ

η¼

IE−EA 2

ð12Þ


587

Fig. 5. Correlations between inhibition efficiencies, EHOMO, energy gap at CAM-B3LYP, and ELUMO values of IC inhibitors calculated at DFT with 6-311++G(d,p).

According to Koopman's theorem, the global softness, σ, is the inverse of the hardness [31,32]: σ¼

1 η

ð13Þ

The number of transferred electrons,ΔN, was also calculated by using Eq. (14) [32]: ΔN ¼

χ Fe −χ inh 2 ηFe þ ηinh

ð14Þ

where χFe and χinh denote the absolute electronegativity of copper and the inhibitor molecule, respectively, and ηFe andηinhdenote the absolute hardness of iron and the inhibitor molecule, respectively. In this study, the theoretical values of χFe = 7.0 eV/mol and ηFe = 0 eV/mol were used for the computation of the number of transferred electrons [32]. The absolute electrophilicity index is given by Eq. (15) [33] ω¼

μ2 2η

ð15Þ

The total energy change describes the energy change associated with the electron-donation and the electron-back donation processes

occurring during the adsorption process, and is given by Eq. (16) [29, 34]: ΔEtot ¼ −η=4

ð16Þ

The global reactivity descriptors calculated at B3LYP and CAM-B3LYP methods with the 6-311++G(d,p) basis set are summarized in Table 6. 3.3.1. Global hardness and softness Table 6 presents the hardness and softness values obtained for the seven IC inhibitors. Hardness and softness are chemical concepts introduced in the literature in early 1952. The hardness of the molecule is a qualitative indication of its polarizability, i.e. how much its electron cloud is distorted in an electric field [29,35,36]. An IC inhibitor with a large hardness value (2.88878 and 4.20501 eV at B3LYP and CAMB3LYP, respectively) is expected to be a weaker inhibitor compared to its derivatives (2.8623 b η b 2.8629 eV and 4.111 b η b 4.119 eV at B3LYP and CAM-B3LYP, respectively). Additionally, an IC inhibitor has the largest softness (the inverse of hardness), σ = 13.041 and 0.23781 eV−1 at B3LYP and CAM-B3LYP, respectively, compared to its derivatives (0.3492 b σ b 0.3494 and 0.242 b σ b 0.244 eV−1 at B3LYP and CAM-B3LYP, respectively). Thus, the IC inhibitor is the hardest and the least soft molecule, parameters that make the molecules less

588


Fig. 6. Distributions of HOMO and LUMO molecular orbitals of some IC inhibitors calculated at CAM-B3LYP/6-311++G(d,p).

reactive as a corrosion inhibitor. With respect to the IC derivatives, IC-2 to IC-13, the trends in which the hardness and softness values change with the inhibition efficiencies are consistent with an experiment at

the CAM-B3LYP, but not quite consistent with an experiment at the B3LYP level. As the %IE values increase from IC-2 to IC-11, the hardness values decrease and the softness values increase, while, this trend is not

Table 6 Global reactivity descriptors of IC inhibitors at DFT with 6-311++G(d,p). η/eV

σ/eV−1

IE/eV

EA/eV

χ/eV

ΔN/e

Etot/eV

ΔEtot/eV

ω/D2 ⋅ eV−1

μ/D

B3LYP IC IC-2 IC-3 IC-5 IC-7 IC-11 IC-13

2.88878 2.86280 2.86293 2.86293 2.86239 2.86239 2.86252

0.34617 0.34931 0.34929 0.34929 0.34936 0.34936 0.34934

6.84208 6.57976 6.56942 6.56181 6.55881 6.55718 6.55691

1.06452 0.85417 0.84356 0.83594 0.83404 0.83240 0.83186

3.95330 3.71697 3.70649 3.69887 3.69642 3.69479 3.69438

0.5273 0.5734 0.5752 0.5765 0.5771 0.5774 0.5774

−640.52 −719.18 −758.51 −837.16 −915.80 −1073.10 −1151.75

−0.72220 −0.71570 −0.71573 −0.71573 −0.71560 −0.71560 −0.71563

36.578 31.554 30.281 29.655 29.440 29.293 29.267

3.8831 3.3196 3.1859 3.1200 3.0968 3.0813 3.0787

CAM-B3LYP IC IC-2 IC-3 IC-5 IC-7 IC-11 IC-13

4.20501 4.11984 4.11507 4.11249 4.11154 4.11140 4.11140

0.23781 0.24273 0.24301 0.24316 0.24322 0.24323 0.24323

8.34961 8.09110 8.07749 8.06960 8.06688 8.06552 8.06552

−0.06041 −0.14858 −0.15266 −0.15538 −0.15619 −0.15728 −0.15728

4.14460 3.97126 3.96242 3.95711 3.95534 3.95412 3.95412

0.3395 0.3676 0.3691 0.3700 0.3703 0.3704 0.3704

−640.40 −719.01 −758.31 −836.91 −915.51 −1072.71 −1151.30

−1.05125 −1.02996 −1.02877 −1.02812 −1.02788 −1.02785 −1.02785

25.779 22.808 21.984 21.575 21.437 21.341 21.322

3.9836 3.4532 3.3245 3.2606 3.2390 3.2244 3.2215


589

Fig. 7. Graphical representations of the trend of in/decreasing of global descriptors of IC inhibitors at DFT with 6-311++G(d,p).

shown at the B3LYP method, Fig. 7. Furthermore, comparing these values for IC-11 and IC-13 shows that as %IEIC-11 N %IEIC-13, the hardness value for IC-13 N IC-11 and identical values are obtained at B3LYP and CAM-B3LYP, respectively.

3.3.2. Global electronegativity When the IC inhibitor is absorbed into an iron surface, a current of electrons will flow from the IC inhibitor because of their lower electronegativity as compared to that of iron (χFe = 7.0 eV/mol), until the

590


chemical potentials becomes equal [37]. According to Sanderson's electronegativity equalization principal, the inhibitor with high electronegativity and hence low electronegativity difference (between the Fe and the inhibitor) will quickly reach equalization and hence will have low reactivity which in turn means low inhibition efficiency [37]. The IC inhibitor has the largest electronegativity values, 3.95330 and 4.14460 eV at B3LYP and CAM-B3LYP, respectively. Again the inhibition efficiency of IC compared to its derivatives is expected to be lower (Table 6). From

Table 6 and Fig. 7, for the series IC-2 to IC-11 at the two methods, the better inhibitor has the lower χ value, i.e. IC-11 (%IE = 95; χ = 3.69479 and 3.95412 eV), and the weaker inhibitor has the higher χ value, i.e. IC-2 (%IE = 49; χ = 3.71697 and 3.97126 eV) all at B3LYP and CAM-B3LYP, respectively. Furthermore, the trend of decreasing the χ values totally agree with the experimental %IEs values with good correlation coefficients (R2 = 0.8162 and 0.8487 at B3LYP and CAM-B3LYP, respectively) (Fig. 8).

Fig. 8. Correlations between inhibition efficiencies and global reactivity descriptors of IC inhibitors at DFT with 6-311++G(d,p).


591

Fig. 8 (continued).

3.3.3. Fraction of electrons transferred (ΔN) This value showed an inhibition effect resulting from electron endowment. If ΔN b 3.6, the inhibition efficiency increased with increasing electron-releasing ability at the metal surface [38]. The calculated ΔN values for the studied inhibitors at the two methods with the 6311++G(d,p) are summarized in Table 6. In this study, ΔN values are smaller than 3.6 for all species at the two levels of theory. The seven

inhibitors are electron donors with varying degrees, and the mild steel surface is the acceptor thereby binding the inhibitor to the Fe surface resulting in an inhibition adsorption layer that prevents the corrosion process. Generally speaking, as the values of ΔN increase, the %IE values will increase and hence the compound will be better as an inhibitor. The order at the two methods show good correlation with the efficiency of corrosion inhibition (R2 = 0.810 and 0.854 B3LYP and CAM-B3LYP,

592


respectively, Fig. 8). This shows that as the strength of the metal-inhibitor bond increased, the degree of corrosion inhibition also increased. A similar observation was also reported elsewhere [29,34]. 3.3.4. Total energy It is expected that as the total electronic energy decreased (more −ve value) the inhibitor is well adsorbed by the active center/s of adsorption on the steel surface [39]. At the two methods, the least efficient inhibitor (IC-2) has the largest total energy. For the series IC-2 to IC-11, the trend in which the total energies change with the %IE values is consistent with the experiment but with poor correlation. However, the change in the total energy does not reflect the fact that IC-11 is a better inhibitor than IC-13. 3.3.5. Total energy change It was reported that there is a direct relationship between the total energy change and hardness of the molecule, if the hardness values are positive then the total energy change values should be negative. This implies that the charge transfer from a molecule followed by back-donation to the molecule is energetically favorable [40]. In this context, Eq. (16) implies that the IC compound and its derivatives are known to donate electrons and then receive charges by back-donation, because then the stabilization will increase as the hardness increases among the members of the family, given that they are interacting with the same metal surface [29]. Better adsorption of the IC inhibitor on the steel surface results in better inhibition efficiency, then the %IE should increase when the stabilization energy that results from the interaction between the metal surface and inhibitor increases [41]. The calculated ΔEtot values (Table 6) show that ΔEtot values for the IC derivatives at the two methods are larger (less −ve) than that of the IC inhibitor; this suggests that the inhibition efficiencies of the IC derivatives are better than that of the title molecule (IC), for instance, the ΔEtot = − 0.71570 and − 1.02996 eV for IC-2, while for IC ΔEtot = −0.72220 and −1.05125 eV at B3LYP and CAM-B3LYP, respectively. Also for the series IC-2 to IC-11 at CAM-B3LYP method, ΔEtot values increase (less −ve) from IC-2 to IC-11 supporting the trend observed for the experimental inhibition efficiencies. At CAM-B3LYP, this series shows an increase in the hardness values as the %IE increased with good correlation coefficient (R2 = 0.8487). It also shows an increase in the total energy change with even better correlation coefficient (R2 = 0.8646). As expected ΔEtotvalues of these species increase as the hardness values increase. Finally, for the two inhibitors IC-11 and IC-13, the B3LYP method was consistent with the experiment while the CAM-B3LYP method was not, i.e., the ΔEtot values decrease (−0.71560 and −0.71563 eV for IC-11 and IC-13, respectively) as the %IE decrease (95% and 82% for IC-11 and IC-13, respectively) at B3LYP, while the two inhibitors have the same total energy change value at CAM-B3LYP (ΔEtot = −1.02785 eV). 3.3.6. Dipole moment The dipole moment values calculated at CAM-B3LYP are generally larger than those calculated at B3LYP, i.e. μ's values range from 3.1 b μ b 3.8 to 3.2 b μ b 4.0 at the B3LYP and CAM-B3LYP methods,

respectively. The dipole moments of the IC derivatives are obviously smaller than the title molecule by a range of 0.5635-to-0.8044 Debye at B3LYP and 0.5304-to-0.7621 Debye at CAM-B3LYP. For instance, the dipole moment for IC-13 is 3.0787 and for IC is 3.8831 Debye at B3LYP, the difference between the dipole moments of the two molecules equals to 0.8 Debye. For the series IC-2 to IC-11, the order of increasing the dipole moments is: IC-2 N IC-3 N IC-5 N IC-7 N IC-11, supporting the trend observed for the experimental %IEs. Thus, a more efficient inhibitor has a smaller dipole moment; this disagrees with the result obtained previously for a different class of corrosion inhibitors, namely, arylisothiocyanates and 1-aryl-2.5dithiohydrazodicarbonamides compounds [39]. In addition, the order of decreasing the dipole moments follows the order of increasing the %IEs of these molecules with good correlation coefficient, R2 = 0.8652 and 0.8648 at B3LYP and CAM-B3LYP, respectively, Fig. 8. Thus, the more reactive inhibitor has a smaller dipole moment value and vice versa. With respect to IC-11 and IC-13, at the two methods the order of the change of the dipole moment is not consistent with the conclusion for the series of IC-2 to IC-11, since, in the former, a better inhibitor has a lower dipole moment. Here however, a better inhibitor has a larger dipole moment; this irregularity in the correspondence between the dipole moment with inhibitor efficiency was observed in literature. An increase in inhibition efficiency with dipole moment could be explained in terms of increased adsorption between the inhibitor and the metal surface; the energy of the deformability increases with the increase in dipole moment, making the molecule easier to adsorb at the metal surface [42]. While, the second observed trend, i.e. the increase of the inhibition efficiency with the decrease of the dipole moment, could be explained by noticing the marked increase in the volume of the inhibitor molecules from IC-2 to IC-11 [43]; this increases the adsorption region between the inhibitor and the surface of steel metal and makes the compound performance as a corrosion inhibitor better.

3.3.7. Global electrophilicity index The tendency of the inhibitor molecule to accept electron/s is measured by this parameter. The decreasing trend with respect to global electrophilicity index ω value, for the studied inhibitors is: IC-2 N IC3 N IC-5 N IC-7 N IC-11 N IC-13 at the two methods with good correlation coefficients (R2 = 0.8656 and 0.8645 at B3LYP and CAM-B3LYP, respectively) (Fig. 8). Thus, for the series IC-2 to IC-11 we find that the inhibitor with higher inhibition efficiency exhibits a lower electrophilicity index; this is in opposition to the concept of complementary processes, i.e. donation and back-donation processes. Since, the donation process involved the transfer of electron/s from the inhibitor molecule to the unoccupied d-orbitals of Fe atom to form a coordinate bond, also in the back-donation process the inhibitor molecule can accept electrons from an Fe atom with its anti-bonding orbitals to form a back-donating bond. These donation and back-donation processes strengthen the adsorption of the inhibitor onto the metal surface [44]. Thus, for the IC inhibitors the correlation between this property and inhibition efficiency is not fulfilled.

Table 7 Fukui functions, local softness and local electrophilicity index of the IC-2 as a representative example calculated at B3LYP/6-311++G(d,p).

C1 C2 S3 N4 N5 N6

ρ(N)

ρ(N+1)

ρ(N−1)

f+

f−

Δf

Δσ

Δω

0.020032 −0.136397 −0.090672 −0.023252 −0.093748 −0.218088

0.089412 −0.120823 0.092281 0.144189 −0.001048 −0.044267

0.114413 0.208326 0.022560 0.134408 −0.201065 −0.321939

0.069380 0.015574 0.182953 0.167441 0.092700 0.173821

−0.094381 −0.344723 −0.113232 −0.157660 0.107317 0.103851

0.1638 0.3603 0.2962 0.3251 −0.0146 0.0700

0.0572 0.1259 0.1035 0.1136 −0.0051 0.0244

5.1673 11.3687 9.3457 10.2581 −0.4612 2.2078

Δf=f+ −f−;Δσ=Δfσglob;Δω=Δfωglob. σglob: global softness = 0.34931 eV−1; ωglob: global electrophilicity index = 31.55366 D2/eV.


Fig. 9. Graphical representations of Fukui functions and local electrophilicity index of some ICs inhibitors (thiadiazole ring only) calculated at B3LYP/6-311++G(d,p).

593

594


Fig. 9 (continued).

3.4. Local reactivity descriptors The local reactivity descriptors of a corrosion inhibitor are best described by the Fukui functions [45]. The Fukui function can be formally defined according to Eq. (17): f ðr Þ ¼

δρðr Þ δN ν

ð17Þ

where ρ(r)is the electron density. Eq. (17) is the typical presentation of the Fukui function. The Fukui function is provoked by the fact that if an electron δ is transferred to anN electron molecule, it will tend to distribute so as to minimize the energy of the resultingN+ δ electron system. The resulting change in electron density is the nucleophilic (f+) and electrophilic (f−) Fukui functions, which can be calculated using the finite difference approximation according to Eqs. (18) and (19), respectively [36,45]: f

f

þ

¼

−

¼

δρðr Þ δN

þ

¼ ρðNþ1Þ −ρðNÞ

ð18Þ

δρðr Þ þ ¼ ρðNÞ −ρðN−1Þ δN ν

ð19Þ

ν

where ρ(N+1), ρ(N), and ρ(N−1) are the Mulliken charges of anionic, neutral, and cationic forms of the atom with N + 1, N, and N − 1 electrons, respectively. The calculated values at B3LYP/6-311 ++G(d,p) of ρ(N + 1), ρ(N), ρ(N − 1),f+, f−, Δf for the IC-2 inhibitor as a representative example is presented in Table 7. Also, Table 7 presents other important local reactivity descriptors, i.e. the local softness (Δσ), and local electrophilicity index (Δω). Fukui functions and the local electrophilicity index of the IC inhibitors calculated at B3LYP/6-311++G(d,p) is summarised in Supplementary data Table 2. The f+ measures the changes of density when the molecule gains an electron and it corresponds to reactivity with respect to nucleophilic attack, thus, the site for nucleophilic attack is the site where the value of f+ is maximum. On the other hand, f− corresponds to reactivity with respect to electrophilic attack or when the molecule loses an electron, thus, the site for electrophilic attack is the site where the value of f− is maximum [46]. The nucleophilic Fukui decreases in the following order: function (f+) S3 N N6 N N5 N C1 N C2, while the electrophilic Fukui function (f−) decreases in the following order: C2 N N4 N S3 N C1 N N6 N N5. The nonidentical correspondence in the order of decrease of f+ and f−, indicates that some sites can act both as a nucleophilic site and an electrophilic site at the same time (donation and back-donation of electrons). Comparing between C1 and C2 atoms shows that f+ and f− unambiguously reveal the order of the nucleophilic attack to be decreased as C1 N C2 and for electrophilic attack as C2 N C1, due to the position of each of

Table 8 Mulliken, regular font, and natural, bold font, charges of heavy atoms in the thiadiazole ring, i.e. C, S and N atoms and TNC for the IC inhibitors calculated at B3LYP/6-311++G(d,p). IC/active site center

C1

C2

S3

N4

N5

N6

TNC

IC

−0.293620 −0.13418 0.020032 0.07656 0.541066 0.08131 0.876620 0.08280 0.964055 0.08305 1.062336 0.08311 1.081592 0.08316

−0.212897 0.23469 −0.136397 0.23918 −0.043223 0.23899 −0.053850 0.23908 −0.108215 0.23911 −0.115901 0.23906 −0.137788 0.23905

0.153839 0.29966 −0.090671 0.28849 −0.147014 0.28823 −0.238035 0.28778 −0.269387 0.28754 −0.280208 0.28748 −0.288541 0.28745

−0.069610 −0.35449 −0.023252 −0.35658 0.028786 −0.35640 0.069175 −0.35639 0.096231 −0.35639 0.113531 −0.35637 0.117712 −0.35635

−0.139485 −0.25367 −0.093748 −0.28436 −0.114390 −0.28400 −0.109020 −0.28403 −0.118856 −0.28398 −0.127026 −0.28395 −0.124761 −0.28393

−0.192328 −0.79209 −0.218088 −0.79452 −0.224715 −0.79462 −0.227423 −0.79473 −0.228301 −0.79476 −0.226845 −0.79479 −0.227154 −0.79479

−0.9079 −1.5344 −0.5622 −1.4355 −0.5293 −1.4350 −0.6283 −1.4352 −0.7248 −1.4351 −0.7500 −1.4351 −0.7782 −1.4351

IC-2 IC-3 IC-5 IC-7 IC-11 IC-13


595

Fig. 10. Graphical representations of (a) the Mulliken charges of atoms of the thiadiazole ring, i.e. C, S and N atoms for the IC inhibitors, (b) Mulliken and NBA charges of IC-2 as a representative example, and (c) TNC with Mulliken and NBA all calculated at B3LYP/6-311++G(d,p).

these atoms. This is because C2 is adjacent to an electron-donating group (NH2) with a lone pair of electrons in conjugation with the π-system, and C1 is also adjacent to the electron-donating group (ethyl chain) but there is no conjugation. The Δf values are mostly positive indicating that most sites of this molecule favor the nucleophilic attack over the electrophilic attack (f+ N f−). Δf, Δσ and Δω values decrease in the following order: C2 N N4 N S3 N C1 b N6 b N5, indicating the order of nucleophilic attack. Thus, N4 is the strongest site for the nucleophilic attack when compared to the other nitrogen atoms (N5 and N6). This supports the fact that this site is the most probable site for protonation as discussed later.

Fig. 9 shows graphical representations of f+, f−, Δω and the corresponding thiadiazole ring atoms for all ICs at B3LYP/6-311++G(d,p). The nucleophilic Fukui functions for all thiadiazole ring atoms for all IC molecules are positive with a varying degree of positive charges. The most positive atoms are S3, N4, N6 and C1; for example, for IC-7 the f+ s values for these atoms are: 0.161810, 0.160567, 0.163455 and 0.092982 e. The extent of the positive charges on these atoms decreases as we move from IC to IC-13 molecules. This is due to increasing electron-donating ability of the alkyl chain. On the other hand, the electrophilic Fukui functions shows a different trend for each specific inhibitor, for example for the IC molecule the f− s values decrease in the following

Fig. 11. (a) TED, (b) ESP and (c) MEP plot surfaces for the IC-2 inhibitor as a representative example at the CAM-B3LYP/6-311++G(d,p). Note: the electron rich region is red and the electron poor region is blue. (For interpretation of the references to in this figure legend, the reader is referred to the web version of this article.)

596


Table 9 Selected natural bond orbital characteristics and second order interaction energies (kcal/mol) between donor and acceptor orbitals of the IC-2 molecule as a representative example at B3LYP/6-311++G(d,p). Numbering schemea,b,c,d

Configuration

C(1) C(2) S(3) N(4) N(5) N(6) H(7) H(8) C(9) H(10) H(11) C(12) H(13) H(14) H(15)

[core] 2s (0.94) 2p (2.95) 4s (0.01) 3d (0.01) 4p (0.02) [core] 2s (0.89) 2p (2.83) 4s (0.01) 3d (0.01) 4p (0.02) [core] 3s (1.67) 3p (4.01) 3d (0.02) 5p (0.01 [core] 2s (1.39) 2p (3.93) 3s (0.01) 3d (0.01) 4p (0.02) [core] 2s (1.38) 2p (3.87) 3p (0.01) 3d (0.01) 4p (0.01) [core] 2s (1.34) 2p (4.44) 3p (0.01) 1s (0.60) 1s (0.61) [core] 2s (1.03) 2p (3.39) 1s (0.79) 1s (0.79) [core] 2s (1.09) 2p (3.47) 4p (0.01) 1s (0.80) 1s (0.79) 1s (0.79) 23.99375 (99.974% of 24) 42.84596 (97.377% of 44) 66.83971 (98.294% of 68) 1.03587 (1.523% of 68) 0.12443 (0.183% of 68) 1.16029 (1.706% of 68)

Core Valance Lewis Total Lewis Valence non-Lewis Rydberg non-Lewis Total non-Lewis Donor NBO (i)

Type of bond

O (i)

Acceptor NBO (j)

Type of bond

O (j)

Stabilization energy E(2)/kcal mol−1

Energy difference εj − εi/a.u.

Polarized energy F(ij)/a.u.

C1\ \S3

σ

1.97671

C1\ \N5

σ

1.93208

C2\ \N4 C2\ \N6 N4\ \N5 C9\ \C12 C1\ \C9 C2\ \N6 C2\ \N4 C9\ \H10 C9\ \H11 C9\ \H10 C9\ \H11 C1\ \N5 N4\ \N5 C9\ \C12 C12\ \H13 C1\ \N5 C1\ \C9 N4\ \N5 N6\ \H7 C1\ \N5 C2\ \N4 N6\ \H8 C1\ \N5 N6\ \H8 C2\ \N4 N4\ \N5 C1\ \C9 C2\ \N6 C2\ \S3 C2\ \N4 C1\ \N5 C1\ \N5 C12\ \H15 C1\ \S3 C1\ \C9 C9\ \H10 C9\ \H11 C1\ \C9 C9\ \H11 C9\ \H11 C1\ \N5 C2\ \N4

σ* σ* σ* σ* σ* σ* σ* σ* σ* σ* σ* σ* σ* σ* σ* σ* σ* σ* σ* σ* σ* σ* π* σ* σ* σ* σ* σ* σ* σ* σ* σ* σ* σ* σ* σ* σ* σ* σ* σ* σ* σ*

0.03073 0.02567 0.01517 0.00676 0.02699 0.02567 0.37312 0.01715 0.01727 0.01715 0.01727 0.02975 0.01517 0.00676 0.00554 0.02975 0.02699 0.01517 0.00963 0.28269 0.37312 0.00794 0.28269 0.00794 0.03073 0.01517 0.02699 0.02567 0.08322 0.03073 0.28269 0.28269 0.00734 0.08955 0.02699 0.01715 0.01727 0.02699 0.01727 0.01727 0.28269 0.03073

1.04 5.60 0.85 1.94 1.97 0.59 9.10 2.31 2.30 1.00 1.01 2.38 3.41 0.63 1.00 1.07 3.86 0.66 2.62 12.59 1.04 1.20 123.11 0.60 1.67 1.95 4.19 5.17 6.48 3.78 4.38 4.39 2.53 4.75 1.34 0.53 0.53 3.08 2.63 2.63 2.16 2.15

1.22 1.08 1.05 1.04 1.32 1.33 0.33 0.72 0.72 0.39 0.38 1.26 1.07 1.05 1.08 1.26 1.08 1.07 1.07 0.34 0.33 0.73 0.01 0.40 1.43 1.26 1.22 1.24 0.84 1.24 0.51 0.51 0.92 0.78 1.02 1.00 1.00 0.91 0.88 0.88 1.27 1.25

0.032 0.070 0.027 0.040 0.046 0.025 0.053 0.037 0.037 0.045 0.045 0.049 0.054 0.023 0.029 0.033 0.058 0.024 0.047 0.061 0.018 0.027 0.062 0.032 0.044 0.044 0.064 0.072 0.067 0.061 0.045 0.045 0.043 0.055 0.033 0.021 0.021 0.047 0.043 0.043 0.047 0.047

π C1\ \C9

σ

1.98169

C2\ \S3

σ

1.97723

C2\ \N4

σ

1.90601

π C2\ \N6

σ

1.99248

N4\ \N5

σ

1.97612

N6\ \H7 N6\ \H8 C9\ \H10 C9\ \H11

σ σ σ σ

1.98083 1.98339 1.96764 1.96707

C9\ \C12

σ

1.98113

C12\ \H13 C12\ \H14 C12\ \H15 S3

σ σ σ n

1.98723 1.98943 1.98940 1.98352


597

Table 9 (continued) Donor NBO (i)

Type of bond

O (i)

N4

n

1.89787

N5

n

1.89247

N6

n

1.82508

a b c d

Acceptor NBO (j)

Type of bond

O (j)

C1\ \N5 C2\ \N4 C1\ \N5 C2\ \S3 C2\ \N6 C1\ \S3 C1\ \C9 C2\ \N4 C2\ \N4

π* π* σ* σ* σ* σ* σ* σ* σ*

0.28269 0.03073 0.28269 0.08322 0.02567 0.08955 0.02699 0.03073 0.03073

Stabilization energy E(2)/kcal mol−1 23.73 27.14 5.06 15.44 2.14 16.95 1.24 5.14 0.96

Energy difference εj − εi/a.u.

Polarized energy F(ij)/a.u.

0.27 0.25 0.97 0.55 0.81 0.55 0.79 0.94 0.88

0.072 0.075 0.064 0.083 0.038 0.086 0.028 0.036 0.027

O: occupancy. E(2): energy of hyperconjugation interaction. εj − εi: energy difference between donor i and acceptor j NBO orbitals. F(ij): Fock matrix element between i and j NBO orbitals.

order: C2 N C1 N N4 N N5 N N6 N S3; for IC-2 the order is: C2 N N4 N S3 N C1 N N6 N N5, and for IC-5 the order is: C2 N N4 N C1 N N5 N N6 N S3. Thus, the general observation for IC molecules is that the C2 atom has the larger f− value compared to all other atoms, and N4 has the larger f− value compared to N5 and N6 atoms. Thus, the electrophilic attack most probably will be to these two sites. Finally, the electrophilicity index as expected is minimum for the atom with the larger nucleophilic Fukui function (S3) (in most cases), and maximum for the atom with the larger electrophilic Fukui function (C2). 3.5. Mulliken population analysis and natural population analysis The inhibitor molecule is believed to be adsorbed through the hetero atoms (as an electron-donor component) into the metal (Fe) surface (as an electron-acceptor component), thus this/these hetero atom/s are called the active site/s of adsorption. So it is important to investigate the electronic charges on these atoms. For this reason, Mulliken population analysis (MPA), the most common type of calculation used to perform such investigations was calculated [29,30]. Table 8 and Fig. 10 shows the Mulliken and natural charges for the C, S and N atoms calculated at the B3LYP/6-311 ++G(d,p) basis set. Good correlations and reasonable correlation coefficients are obtained between the Mulliken charges of the hetero atoms and the inhibition efficiencies of the IC inhibitors (0.747 for N4 atom, 0.812 for N5 and 0.855 for N6 atom at the B3LYP method) (Fig. 8). From Table 8, the Mulliken charge distribution shows that most of the hetero atoms are negatively charged and some are positively charged, thus the negatively charged hetero atoms are the atoms that are considered to be active sites for the adsorption process of the inhibitor molecule into the Fe surface. The N4 atom exhibits a positive charge for all inhibitors except the IC and IC-2 inhibitors, while N5 and N6 atoms are negatively charged for all inhibitors. On the other hand, the natural population analysis (NPA) gives negative charges for all hetero atoms. Also the negative charges of these atoms given by NPA are significantly larger than those given by Mulliken. For IC-2 as an example, the negative charges for N5 are: − 0.093748 and − 0.28436e at Mulliken and NPA, respectively (Fig. 10). With respect to the C atoms, C1 and C2, they are mostly positively charged especially those calculated by NPA; the calculated NPA taking part in intramolecular charge transfer is revealed in the natural bond analysis [47]. C1 and C2 are positively charged and N4 and N5 are negatively charged which indicates the strong bonding between C1\\N5 and C2\\N4 and also the charge transfer from C1\\N5 to C2\\N4 and vice versa. Total negative charge (TNC) is the summation of the total negative charges on the atoms for each inhibitor molecule. If the TNC is large, the inhibitor will be favorably adsorbed on the Fe surface. Generally, the NPA gives higher values than those given by the Mulliken. Considering the two methods, the IC inhibitor gains the largest TNC, −0.908 and

−1.53443 e at B3LYP and CAM-B3LYP, respectively. At the B3LYP method, the series IC-2 to IC-11 is the best inhibitor (IC-11) and has the largest TNG (− 0.74998 e), but the order of decrease of the TNCs do not agree well with the order of decreasing of the experimental %IEs. On the other hand, at CAM-B3LYP, the TNC values are comparable for the derivatives. 3.6. Molecular electrostatic potential The 3D-plots of total electron density (TED), electrostatic potential (ESP) and MEP of the IC-2 inhibitor as a representative example are shown in Fig. 11. The TED plot for IC-2 shows a uniform distribution over the whole molecule. However, the ESP plot shows that the negative charge is localized more over the three nitrogen atoms N4, N5 and N6 and reflected as a red color over N4 and N5 and a yellow color over N6. This result is expected, because ESP correlates with electronegativity and partial charges. Fig. 11 and Supplementary data Fig. 2 illustrate the molecular electrostatic potential (MEP) plots, i.e. the total electron density mapped with electrostatic potential (ESP) of the IC inhibitors at CAM-B3LYP/6311++G(d,p). TED, ESP and MEP plot surfaces for IC and IC-13 inhibitors at the CAM-B3LYP/6-311++G(d,p) level are summarised in SD Fig. 3. The MEP plots were calculated in order to identify the regions of high/ low electron density as well as the molecular size and shape. The high electron density is represented by a red color and the low electron density is represented by a blue color; the electron density decreases in the following order: red N orange N yellow N green N blue. The MEP plots of the IC inhibitors show that the low electron density (green-to-blue color) is delocalized (as expected) on the substituted alkyl groups, and lower electron density is delocalized on the hydrogen atoms of the amine group (blue color). Also the sulphur atoms of the IC inhibitors show low electron density (green color). While the high electron density (yellow-to-red color) is delocalized on the nitrogen atoms of the thiadiazole ring (N4, N5), and N6 is the nitrogen of the amine group, this easily could be attributed to the lone pairs of electrons on these atoms. Moreover, a more negative region was delocalized on N4 and N5 (yellow-to-red color) than the negative region on N6 (yellow color). It may be concluded that these atoms with high-electron densities could be good candidates to be attracted to the Fe surface as a lowelectron density region to form the surface of adsorption. A comparison of the total electron-rich and electron-poor regions on each inhibitor shows that as the substituted alkyl length increases the electron-poor regions increase, while the electron-rich regions remain constant but with noticeable variation in the extent of the distributed negative charges. For instance, the colors for the IC-2 inhibitor line up in the range of − 36.87 (dark red) and + 36.87 kcal/mol (dark blue). The colors line up in different regions and this indicates the effect of the alkyl chain on the electron distribution map. The regions of charge distributions decrease in the following order: IC b IC-13 b IC-11 b IC-5 b IC-

598


Table 10 Influential natural bond orbital characteristics and second order interaction energies (kcal/mol) between donor and acceptor orbitals of the thiadiazole ring of IC inhibitors at B3LYP/6311++G(d,p). NBO/ICs

IC

IC-2

C1\ \S3 → C2\ \N6 σ → σ* C1\ \N5 → C2\ \N4 σ → σ* C1\ \N5 → C9\ \H10 π → σ* C1\ \N5 → C9\ \H11 π → σ* C1\ \C9 → N4\ \N5 σ → σ* C2\ \S3 → C1\ \C9 σ → σ* C2\ \N4 → C1\ \N5 σ → σ* C2\ \N4 → C1\ \N5 π → π* C2\ \N6 → C2\ \N4 σ → σ* C2\ \N6 → N4\ \N5 σ → σ* N4\ \N5 → C1\ \C9 σ → σ* N4\ \N5 → C2\ \N6 σ → σ* N6\ \H7 → C2\ \S3 σ → σ* C9\ \H10 → C1\ \N5 σ → σ* C9\ \H10 → C1\ \N5 σ → π* S3 → C1\ \N5 n → σ* S3 → C1\ \N5 n → π* S3 → C2\ \N4 n → σ* S3 → C2\ \N4 n → π* N4 → C1\ \N5 n → σ* N4 → C2\ \S3 n → σ* N4 → C2\ \N6 n → σ* N5 → C1\ \S3 n → σ* N5 → C1\ \C9 n → σ* N5 → C2\ \N4 n → σ* N6 → C2\ \N4 n → σ* N6 → C2\ \N4 n → π*

5.78

5.60

IC-3 5.62

IC-5 5.61

IC-7 5.61

5.61

5.61

8.98

9.10

9.11

9.11

9.11

9.12

9.12

–

1.00

2.36

2.35

2.36

2.37

2.37

–

1.01

2.35

2.35

2.35

2.34

2.34

–

3.41

3.38

3.39

3.39

3.39

3.38

–

3.86

3.91

3.90

3.90

3.90

3.90

14.48

12.59

12.59

12.56

12.56

12.57

12.57

–

123.11

122.36

121.16

120.67

120.77

120.66

1.64

1.67

1.64

1.66

1.66

1.66

1.66

1.97

1.95

1.97

1.95

1.95

1.95

1.95

2.83

4.19

4.24

4.24

4.24

4.24

4.24

5.14

5.17

5.17

5.18

5.18

5.17

5.17

6.46

6.48

6.48

6.47

6.47

6.48

6.48

–

–

2.61

2.62

2.61

2.59

2.58

–

4.38

4.35

4.37

4.39

4.41

4.42

1.39

??

2.16

2.15

2.15

2.15

2.15

23.47

23.73

23.66

23.64

23.62

23.61

23.60

2.23

??

2.25

2.24

2.25

2.25

2.25

27.5

27.14

27.18

27.16

27.16

27.16

27.16

5.18

5.06

5.06

5.05

5.06

5.07

5.07

15.36

15.44

15.42

15.41

15.42

15.42

15.42

2.06

2.14

2.14

2.14

2.14

2.14

2.14

14.49

16.95

16.99

16.99

17.00

17.00

2.49

1.24

1.14

1.14

1.14

1.13

1.13

5.30

5.14

5.14

5.14

5.14

5.14

5.14

0.87

0.96

0.96

0.96

0.96

0.97

0.97

35.28

33.94

33.86

33.84

33.82

33.79

33.78

17

IC-11

IC-13

Table 11 Total energy (in au), and the relative energy (in kcal/mol) (=EICs − EPICs), are in regular font, calculated at B3LYP/6-311++G(d,p) while total energy (in au), and the relative energy (in kcal/mol) (=EICs EPICs), are in bold font, calculated at CAM-B3LYP/6-311++G(d,p) at different protonated sites of the protonated forms (PICs) of the studied inhibitors. Protonated site/PICs

PIC

PIC-2

PIC-3

PIC-5

PIC-7

PIC-11

PIC-13

N4

−640.89 (226.62) −640.76 (226.20) −640.88 (225.35) −640.84 (197.36)

−719.55 (232.83) −719.38 (232.13) −719.55 (232.72) −719.51 (203.07)

−758.88 (233.38) −758.68 (232.63) −758.88 (233.63) −758.83 (203.58)

−837.53 (233.86) −837.28 (233.07) – – – –

−916.18 (234.03) −915.88 (233.24) – – – –

−1073.47 (234.16) −1073.08 (233.35) – – – –

−1152.12 (234.18) −1151.68 (233.37) – – – –

N5 N6


2 b IC-3 b IC-2, thus the least effective inhibitor (IC-2) has the smallest charge distribution region. IC

IC-2

IC-3

IC-5

IC-7

IC-11

IC-13

−39.00

−36.87

−37.02

−37.19

−37.12

−37.15

−37.27

→ 36.87

→ 37.02

→ 37.19

→ 37.12

→ 37.15

→ 37.27

→ 39.00

Electrostatic potential (kcal/mol)

3.7. Natural bond orbital analysis Natural bond orbital (NBO) analysis is a multistep process [48,49]. In an initial step, orbitals are associated almost entirely with a single atom, e.g., core orbitals and lone pairs, are localized as so-called natural atomic orbitals (NAOs). Next, orbitals involving bonding (or antibonding) between pairs of atoms are localized by using only the basis set atomic orbitals (AOs) of those atoms. Finally, the remaining Rydberg-like orbitals are identified, and all orbitals made orthogonal to one another. The result is that all NAOs and Rydberg orbitals are described using the basis set AOs of a single atom and all NBOs are described using the basis set of AOs of two atoms. Thus, NBO analysis provides an orbital picture that is as close as possible to a classical Lewis structure for a molecule. In addition, population analysis can be carried out using the NBOs to derive partial atomic charges (NPA). This localization scheme permits the assignment of hybridization both to the atomic lone pairs and to each atom's contributions to its bond orbitals. With NBO analysis, the percent s and p, d, f etc. is immediately evident from the coefficients of the AO basis functions from which the NAO/NBO is formed. Another useful chemical concept is hyperconjugation which is defined as the favorable interaction of a filled/partially filled orbital, typically a σ orbital, with a nearby empty orbital, that rationalizes certain chemical phenomena (inhibitor–metal interaction in this study) in terms of filled (donor) orbital-to-empty (acceptor) orbital interactions [50]. Since, the NBOs do not diagonalize the Fock operator (or Kohn–Sham operator as in the case of DFT instead of Hartree–Fock (HF)), when the Fock matrix is formed in the NBO basis, off-diagonal elements will in general be nonzero. Second-order perturbation theory indicates that these off-diagonal elements between donor and acceptor NBOs can be interpreted as the stabilization energies deriving from hyperconjugation. The stabilization energy (E(2)) associated with i (donor) → j (acceptor) delocalization is estimated from the second order perturbation approach as given by Eq. (20): Eð2Þ ¼ ΔEij ¼ qi

F 2 ðijÞ ε j −ε i

ð20Þ

where qi is the donor orbital occupancy, εi and εj are diagonal elements (orbital energies) and F(ij) is the off-diagonal NBO Fock matrix element [50]. The results of the NBO analysis of IC-2 inhibitor as a representative example at the B3LYP/6-311++G(d,p) level are collected in Table 9. 3.7.1. NBO analysis of IC-2 A number of donor–acceptor interactions are observed in the IC-2 molecule and among the strongly occupied NBOs. The most important interaction sites are the orbital overlap between bonding (σ/π) and antibonding (σ*/π*) of C\\S/C\\N orbitals. This is in addition to the orbital overlap between the lone pairs of electrons of S3, N4, N5 and N6 and the antibonding (σ*/π*) of C\\C/C\\N/C\\S orbitals. Those intramolecular interactions result in intramolecular charge transfer (ICT) causing stabilization of the system. NBO analysis shows the ICT from the σ C1\\S3 and C2/S3 to σ* C2\\N6 and C1\\C9 with stabilization energies of 5.60 and 3.86 kcal/mol, respectively. Also, ICT from σ C1\\N5 and σ C2\\N4 to σ* C2\\N4 and σ* C1\\N5 with E(2) = 9.10 and 12.59 kcal/mol, respectively, indicates that each one of these orbitals is

599

acting as an electron-donor and electron-acceptor at the same time. In addition, this transition enhances further conjugation from the π C2\\N4 orbital to the π* C1\\N5 orbital with very strong intramolecular hyperconjugative interaction, E(2) = 123.11 kcal/mol, indicating that this ICT is probably one of the most important reason for the stability of the molecule. On the other hand, the NBO analysis does not give any indication of ICT from the opposite direction, i.e. from π C1\\N5 orbital to the π* C2\\N4 orbital, indicating that the C1\\N5 is acting as an acceptor more than a donor. The NBO analysis also shows the ICT from the σ C2\\N6 orbital to the σ* C2\\N4 orbital with a stabilization energy of 1.67 kcal/mol. There is also an exchange of ICT between σ and σ* of C2\\N6 and N4\\N5 orbitals, i.e. the σ C2\\N6 orbital is donating an electron to σ* N4\\N5 with an E(2) value of 1.95 kcal/mol, and the σ N4\\N5 orbital is donating an electron to σ* C2\\N6 with a higher E(2) value of 5.17 kcal/mol. Therefore these two orbitals are also acting as donors and acceptors at the same time resulting in more stabilization of the molecule. The stabilization energy values due to ICTs from the lone pairs of electrons of S3, N4, N5 and N6 are high. The ICT from n S3 orbital to π* C1\\N5 and C2\\N4 have E(2) values of 23.73 and 27.14 kcal/mol, respectively, while as expected the transitions from this lone pair to the σ* of these orbitals are the result of lower E(2) values, 2.16 and 2.15 kcal/mol, respectively, indicating the important role that the π electrons play in the stabilization of any molecule. The lone pair of electrons on the N4 and N5 atoms are acting as donors mainly to the acceptors σ* C2\\S3 and C1\\S3 with E(2) values of 15.44 and 16.95 kcal/mol, respectively. Finally, the ICT occurs from an N6 orbital to σ* C2\\N4 and π* C2\\N4 with stabilization energy values of 0.96 and 33.94 kcal/mol, respectively. Comparing the electron-occupancy of the nitrogen atoms N4, N5 and N6 show that the N4 atom has the higher occupancy (1.89787) while the occupancy of the other atoms decreases in the following order: N5 (1.89247) N N6 (1.82508) supporting that N4 is the electron-rich atom which explains also why N4 is the more probable site for protonation. 3.7.2. NBO analysis of all ICs The important natural bond orbital characteristics and second order interaction energies (kcal/mol) between donor and acceptor orbitals of the thiadiazole ring of all IC inhibitors are calculated at B3LYP/6311++G(d,p) and the results are summarized in Table 10. 3.7.2.1. The title molecule and its derivatives. Generally, the effect of the substituted alkyl chain on the modes of hyperconjugation and values of E(2) is significant. The major differences in the E(2) values for the characteristic NBOs are between the title molecule (IC) and its derivatives (IC-2 to IC-13). In some cases the E(2) values for the IC molecule are larger than those of its derivatives and in other cases the reverse is true. For instance, the hyperconjugation energies of σ C1\\S3 → σ* C2\\N6, σ C1\\N5 → σ* C2\\N4, σ N4\\N5 → σ* C1\\C9 of the IC inhibitor are smaller than those of the derivatives. The larger differences in the E(2) values between the IC and its derivatives are in the NBOs in which the lone pairs of electrons of S3, N4, N5 and N6 atoms are acting as donors. For instance, the differences in E(2) values between the IC and IC-2 inhibitors of the transitions n S3 → π* C1\\N5, n N5 → σ* C1\\S3, n N6 → σ* C2\\N4 and n N6 → π* C2\\N4 are 0.26, 2.46, 0.09 and 1.34 kcal/mol. It is important to note that the major ICT from π C2\\N4 → π* C1\\N5 with the largest E(2) values for all the derivatives (120.66 b E(2) b 123.11 kcal/mol) is absent for the title molecule (IC), so the effect of the alkyl chain on the NBOs is demonstrated by this ICT. 3.7.2.2. The derivatives together. Generally, the effect of the substituted alkyl chain on the modes of hyperconjugation and values of E(2) is less significant. The major differences are found in the ICTs from π C2\\N4 → π*C1\\N5, since the E(2) values decrease in the following order: IC-2 N IC-3 N IC-5 N IC-7 N IC-11 N IC-13 with differences in the range of 0.75-to-2.45 kcal/mol. It can also be seen that the E(2) values

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Fig. 12. Top and side views of the most stable low energy adsorption configurations of the protonated form of (a) IC-2, (b) IC-3, (c) IC-5, (d) IC-7, (e) IC-11 and, (f) IC-13 on an Fe (110) surface using MD simulations:


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inhibitors increased from IC-2 to IC-13. Therefore, the trend of the binding energies is as follows: IC-2 b IC-3 b IC-5 b IC-7 b IC-11 b IC-13. Thus, IC-11 with the highest experimental inhibition efficiency has a lower binding energy than IC-13. This result does not follow the experimentally determined inhibition efficiency probably due to the fact that the simulations was conducted in the gas phase. However, the ordering is in agreement with the experimentally determined inhibition efficiency for most of the corrosion inhibitors investigated. All the binding energies were high and negative, indicating a strong interaction between the inhibitor molecules and the Fe (110) surface [51,52]. 4. Conclusions

Fig. 13. Binding energies of protonated IC-2 to IC-13 with increasing alkyl chain.

of ICTs of the IC-2 show significant differences from those of the other derivatives; and from IC-3 to IC-13 the effect of the length of the alkyl chain on these values are insignificant. Also, the effect of the alkyl chain appears on the ICTs from n N5 → σ* C1\\C9, showing a significant difference between that of IC-2 and those of the other derivatives, i.e. E(2) value for IC-2 is 1.24 kcal/mol, while the E(2) value of the other derivatives is ~1.14 kcal/mol. 3.8. Effect of protonation In H2SO4 medium, the IC inhibitors are very likely to be protonated at several sites, namely, N4, N5 and N6. In this section, calculations similar to those carried out on the non-protonated forms (ICs) were carried out on the protonated forms (PICs) and the obtained results are collected in Table 11. Also, this table summarizes the relative energies (in kcal/ mol). These are the differences in energies between the protonated and non-protonated forms at B3LYP and CAM-B3LYP with 6-311++G(d,p). The protonated forms (PICs) are energetically more favorable than the non-protonated forms (ICs), since generally the total energies of PICs are larger (more negative) than those of ICs, and the relative energies are in the range of 226–234 kcal/mol. In general, the most favorable protonated site for all ICs is the N4 atom. This is because, this atom is positioned between the two other nitrogen atoms, i.e. N5 and N6. N4 will be most affected by the expected conjugation between the lone-pairs of electrons on these nitrogen atoms and the thiadiazole ring; and this may also explain the privilege of this nitrogen to be the most probable protonated site. Supplementary data Table 3 summarizes the global reactivity descriptors of the PIC inhibitors (at the N4 atom). 3.9. Molecular dynamics (MD) simulations results Electronic properties alone are not sufficient to predict the trend of the inhibition performance of the investigated inhibitors in spite of its success in exploring the mechanism of inhibitors. Therefore, it is imperative to carry out rigorous modeling of the direct interaction of the inhibitors with an Fe surface (since the steel used in the wet laboratory experiment has a 98.3% weight of Fe). It is generally believed that the primary mechanism of corrosion inhibition is by adsorption. The protonated forms of the inhibitors were adopted because the DFT results presented above indicate that the protonation of IC primarily occurs at the N4 atom. In this study, protonated IC-2 to IC-13 at the N4 atom were used for the molecular dynamics simulation studies. The most stable low energy adsorption configurations of IC-2 to IC-13 on Fe (110) surface using MD simulations are depicted in Fig. 12. The plot of the binding energies of protonated IC-2 to IC-13 is presented in Fig. 13. It is quite clear from Fig. 13 that the binding energies of the inhibitors on an Fe (110) surface increased as the size of the alkyl chain on the

In this study, the following goals have been achieved at the DFT using two functionals, B3LYP and CAM-B3LYP with the 6311 ++G(d,p) basis set: (1) the geometries of the IC inhibitors were successfully calculated, (2) the capabilities of these compounds to act as corrosion inhibitors of mild steel in 1.0 M H2SO4 were demonstrated theoretically, (3) global and local descriptors and NBO analysis were calculated and used to identify the reactivity of these molecules toward corrosion inhibition, (4) the protonated forms of the studied inhibitors are proved to be more stable than the non-protonated forms, and (5) furthermore, MD simulations carried out in the gas phase indicate that the binding strength of IC-2 to IC-13 protonated at the N4 atom on an Fe (110) surface was high and negative and also increases with the size of the alkyl chain present on the inhibitors. Acknowledgements Ime Obot would like to acknowledge the support and fruitful collaboration between the Center of Research Excellence in Corrosion (COREC), at King Fahd University of Petroleum & Minerals (KFUPM) and the Chemistry Department of King Abdulaziz University all in Saudi Arabia. Nuha Wazzan acknowledges King Abdulaziz University’s High Performance Computing Center (Aziz Supercomputer) (http://hpc.kau.edu. sa) for supporting the computation for the work described in this paper. Appendix A. Supplementary data Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.molliq.2016.06.011. References [1] R. Solmaz, G. Kardaş, B. Yazıcı, M. Erbil, Adsorption and corrosion inhibitive properties of 2-amino-5-mercapto-1,3,4-thiadiazole on mild steel in hydrochloric acid media, Colloids Surf. A Physicochem. Eng. Asp. 312 (1) (2008) 7–17. [2] J.M. Roque, T. Pandiyan, J. Cruz, E. García-Ochoa, DFT and electrochemical studies of tris(benzimidazole-2-ylmethyl)amine as an efficient corrosion inhibitor for carbon steel surface, Corros. Sci. 50 (3) (2008) 614–624. [3] S.A. Umoren, I.B. Obot, Polyvinylpyrollidone and polyacrylamide as corrosion inhibitors for mild steel in acidic medium, Surf. Rev. Lett. 15 (3) (2008) 277–286. [4] I.B. Obot, N.O. Obi-Egbedi, Inhibitory effect and adsorption characteristics of 2.3diaminonaphthalene at aluminum/hydrochloric acid interface: experimental and theoretical study, Surf. Rev. Lett. 15 (6) (2008) 903–910. [5] R.M. Issa, M.K. Awad, F.M. Atlam, Quantum chemical studies on the inhibition of corrosion of copper surface by substituted uracils, Appl. Surf. Sci. 255 (5) (2008) 2433–2441. [6] H. Ju, Z.-P. Kai, Y. Li, Aminic nitrogen-bearing polydentate Schiff base as corrosion inhibitors for iron in acidic media: a quantum chemical calculation, Corros. Sci. 50 (3) (2008) 865–871. [7] N.A. Wazzan, F.M. Mahgoub, DFT calculations for corrosion inhibition of ferrous alloys by pyrazolopyrimidine derivatives, Open. J. Phys. Chem. 4 (1) (2014) 6–14. [8] F.M. Mahgoub, B.A. Abdel-Nabey, Y.A. El-Samadisy, Adopting a multipurpose inhibitor to control corrosion of ferrous alloys in cooling water systems, Mater. Chem. Phys. 120 (1) (2010) 104–108. [9] M.K. Awad, F.M. Mahgoub, M.M. El-iskandarani, Theoretical studies of the effect of structural parameters on the inhibition efficiencies of mercapto-1,2,4-triazoline derivatives, J. Mol. Struct. (THEOCHEM) 531 (1) (2000) 105–117. [10] E.S. Sherif, Effects of 2-amino-5-(ethylthio)-1,3,4-thiadiazole on copper corrosion as a corrosion inhibitor in 3% NaCl solutions, Appl. Surf. Sci. 252 (24) (2006) 8615–8623.

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