Corrosion Inhibition Properties of Phenyl Phthalimide Derivatives against Carbon Steel in the Acidic Medium: DFT, MP2, and Monte Carlo Simulation Studies.

The effectiveness of phenyl phthalimide and its derivatives at preventing corrosion of carbon steel has been tested experimentally using gravimetric and electrochemical measurements. However, experimental studies have not thoroughly explained the structural patterns and coating mechanisms of phenyl phthalimide and its derivatives during corrosion inhibition. In this study, the density functional theory (DFT), ab initio MP2, and Monte Carlo simulation are applied to study phenyl phthalimide (PP) and its derivatives as corrosion inhibitors of carbon steel. The geometry, quantum parameters, and reactive site of the inhibitors were determined by DFT and ab initio MP2 methods. The real environment conditions of corrosion inhibition in the solution phase can be replicated by the Monte Carlo simulation. The corrosion inhibition efficiency of phthalimide derivatives is PP-OCH3 > PP-CH3 > PP-H > PP-Cl > PP-NO2. The theoretical study is consistent with previously reported experimental results.

Introduction

Carbon steel has been widely used in various applications, such as structural components, industrial pipes, and kitchen utensils.[1] Carbon steel is highly susceptible to corrosion in the oil and gas industry.[2] Corrosion of carbon steel in the environment can harm the economy.[3] Therefore, corrosion inhibition in carbon steel is desirable because of its excellent mechanical properties and low cost but feeble corrosion resistance.[4,5] Corrosion inhibition is often used with the addition of an inhibitor.[6] Inhibitors are one of the most efficient ways to prevent corrosion from attacking carbon steel.[7−9] A suitable inhibitor requires heteroatoms like sulfur, nitrogen, and oxygen and π-bonds that can be used to form complexes with metals.[10−12] Organic inhibitors have high corrosion inhibition efficiency values and are environmentally friendly.[13−15]

Phenyl phthalimide is an aromatic organic compound that has oxygen and nitrogen heteroatoms. These atoms act as electron donors in the corrosion inhibition process. Experimental studies have previously reported the corrosion inhibition of phthalimide derivatives on copper in nitric acid using weightloss and polarization techniques. The highest inhibition efficiency value was obtained for the N-(3-methoxyphenylaminomethyl) phthalimide at 67.8%.[16] Zaafarany tested the corrosion inhibition of phenyl phthalimide and its derivatives on carbon steel in sulfuric acid media using weightloss and polarization techniques. The highest inhibition efficiency value with the addition of an OCH3 substituent was obtained at 92.36%. An OCH3 substituent acts as an electron donor so that the adsorption is stronger, increasing the value of the inhibition efficiency.[17]

Experimental studies have accurately determined the efficiency of corrosion inhibition, but the detailed explanation of why OCH3 contributes the most to corrosion inhibition has not been explained in detail. Research time and costs are high. The theoretical study, which is now supported by adequate software and hardware, becomes a bridge for these problems. The corrosion inhibition efficiency depends on the molecule’s electron density, which can be calculated with high accuracy by theoretical studies. Theoretical studies are as critical as experimental ones in testing corrosion inhibition in a molecule. The use of quantum chemical calculations can predict the adsorption site during the corrosion inhibition process.[18,19] Quantum chemical calculations can provide answers to questions about experimental findings based on the interactions of organic inhibitors with metal surfaces.[20,21] The approaches of density functional theory,[22,23] ab initio,[24,25] and molecular dynamic simulation[26−28] can provide a thorough explanation of each inhibitor’s performance in relation to its orientation and structure, as well as the process by which an inhibitor adheres to metal surfaces. Hadisaputra et al. used density functional theory (DFT) at different theoretical levels, ab initio, and Monte Carlo simulation to predict caffeine and hydrocoumarin derivatives’ copper corrosion inhibition performance.[29,30] Donor- and electron-withdrawing groups, as well as the orientation of the molecule, all affect how strongly organic corrosion inhibitors interact with the surface of metals.[31−33] In this study, the effects of quantum parameters and the molecule’s adsorption process on the corrosion inhibition of phenyl phthalimide derivatives on metal surfaces are tested.

Methods

Quantum Chemical Calculations

Calculations based on quantum chemistry were used to predict the molecular geometry, electron distribution, and transfer from corrosion inhibitors. Figure depicts the structure of a targeted inhibitor molecule. The molecular geometry calculation is accelerated by first optimizing the geometry using the DFT method B3LYP/6-31G(d). DFT and ab initio MP2 methods at 6-311++G (d,p) were used to re-optimize the structures of 4PP-H, PP-CH3, PP-OCH3, PP-Cl, and PP-NO2 in the gas phase. The influence of solvents is incorporated into the computation using a polarized continuum model built on the Gaussian code. The dielectric constant of water is 78.4. For solvent phase energetics, single-point computations of gas-phase geometries are sufficient. Previous research found that it had a minor impact on structure and energy.[34−36] The Gaussian 09 program calculates all quantum chemical and geometric parameters.[37]

Figure 1

2D and 3D structure of PP-H, PP-CH3, PP-OCH3, PP-Cl, and PP-NO2.

Based on DFT and ab initio methods, quantum chemistry characteristics including electron affinity (A), electronegativity (χ), hardness (η), energy of highest occupied molecular orbitals (EHOMO) and energy of lowest unoccupied molecular orbitals (ELUMO), gab energy (E), ionization potential (I), and the number of electron transfers (N) were computed. The ionization potential (I) and electron affinity (A) are correlated with the HOMO and LUMO energy values in each organic inhibitor.[38]

The electronegativity (χ) and hardness (η) of the inhibitor can be determined using eqs and 4.[39]

Equation can be used to determine the number of electrons transferred (N) from the inhibitor to the metal.[40]where χFe and χInh are the absolute electronegativity values of Fe and organic inhibitors. ηFe and ηInh are the absolute hardness values of Fe and organic inhibitors, respectively. The number of electrons transferred was calculated using theoretical values of χFe = 7.00 eV and ηFe = 0 eV.[41,42]

Equations and 7 can be used to calculate the Fukui index to determine nucleophilic (fK+) and electrophilic (fK–) attacks.[43]In organic inhibitors, qk (N + 1) is the atomic charge (+1), qk (N) is the atomic charge (neutral), and qk (N – 1) is the atomic charge (−1).[43]

Monte Carlo Simulation

Material Studio 7.0 from Accelrys Inc. was used to perform the Monte Carlo simulation.[44,45] Monte Carlo simulation was used to help find the inhibitor’s reactive site for adsorption at the lowest energy on the metal surface.[46] The following weight percentages apply to the carbon steel type (L-52): 0.26% C, 1.35% Mn, 0.04% P, 0.05% S, 0.05% Nb, 0.02% V, 0.03% Ti, and 98.2% Fe.[7] Thus, the Fe(110) plane can represent the surface of carbon steel. The Fe(110) crystal plane was the most stable for simulating the adsorption process.[47] Supercells were used (8 × 8) to provide a large surface for interacting with organic inhibitors. These simulations were carried out in a grid (19.859002 × 19.859002 × 34.187956) with periodic boundary conditions and a representative interface portion to be simulated without arbitrary boundary effects. The Fe(110) plane is used to build a vacuum slab with a thickness of 20 along the C axis. To optimize the structure of every system component under study, the COMPASS force field is used in all simulations.[30] Phenyl phthalimide derivatives (PP-H, PP-CH3, PP-OCH3, PP-Cl, and PP-NO2) and Fe(110) with 100 water molecules were used. Water molecules are essential in the simulation to imitate the conditions of the corrosion process in the environment.[48,49]

Results and Discussion

Quantum Chemical Parameters

Phenyl phthalimide and its derivatives as a corrosion inhibitor against carbon steels in sulfuric acid media have been reported previously.[17]Figure depicts phenyl phthalimide’s corrosion inhibition efficiency values and its derivatives in the KI synergic effect environment. Experimental studies show that OCH3 provides the maximum contribution to the corrosion inhibition performance of phthalimide derivatives. Theoretical studies can complement experimental studies by explaining why OCH3 contributes significantly. The electronic properties and the reactive site of the inhibitor and the adsorption mechanism of the inhibitor on the metal surface can be explained theoretically.

Figure 2

Inhibitory efficiency of phenyl phthalimide and its derivatives in the KI synergic effect environment.

Due to the selection of DFT and ab initio, method validation is carried out first to test the need for the method and basis set according to the system under study. The method and basis set at the DFT and MP2 levels 6-111++G (d,p) show the agreement between the experimental[50] and theoretical geometric parameters. Table shows that the difference in the bond length is 0.0128, and the bond angle is 1.3236°. The difference is low, so the method and basis set can be used to calculate quantum chemical parameters and Fukui functions in the studied system.

Table 1

Crystal Structures of Phenyl Phthalimide Derivatives Experimentally[50] and DFT/6-311++G (d,p)

bond length (Å)	exp[50]	theory	bond angle (°)	exp[50]	theory
N1–C1	1.4089	1.42832	C1–N1–C9	124.34	125.25679
N1–C2	1.4148	1.42832	C2–N1–C9	123.42	125.25679
N1–C9	1.4214	1.43919	N1–C9–C10	119.38	120.51544
C1–O1	1.2093	1.21393	N1–C9–C14	119.11	120.51544
C2–O2	1.2053	1.21393

Energy parameters provide important information about the electronic properties and reactivity of the corrosion inhibitors studied. The EHOMO value is associated with the electron-donating ability of the corrosion inhibitor. A high EHOMO value indicates that it is easier to donate electrons to empty d orbitals in metals. A high EHOMO value facilitates good adsorption to increase the value of corrosion inhibition efficiency by influencing the electron transport process through the adsorbed layer.[51,52] The EHOMO values obtained using the DFT and ab initio MP2 methods are displayed in Tables 345. PP-OCH3 has the highest EHOMO value, −8.3408 eV (ab initio MP2). The order of EHOMO values is PP-OCH3 > PP-CH3 > PP-H > PP-Cl > PP-NO2. This explains that PP-OCH3 can adhere more strongly than other inhibitors to the carbon steel surface. PP-OCH3 has a lone pair of electrons that acts as an electron-donating group so that it can transfer more electrons to the carbon steel surface to form complex compounds.

Table 2

Phenyl Phthalimide and Its Derivatives’ Quantum Chemical Properties with B3LYP/6-311++G(d,p) and MP2/6-311++G(d,p) in Gaseous Media

inhibitors	EHOMO eV	ELUMO eV	ΔE eV	I eV	A eV	χ eV	η eV	ΔN eV
PP-H
B3LYP	–6.5914	–2.7639	–3.8276	6.5914	2.7639	4.6776	1.9138	0.6067
MP2	–8.6094	0.8376	–9.4470	8.6094	–0.8376	3.8859	4.7235	0.3296
PP-CH3
B3LYP	–6.3558	–2.7149	–3.6409	6.3558	2.7149	4.5353	1.8204	0.6769
MP2	–8.3313	0.8506	–9.1819	8.3313	–0.8506	3.7403	4.5910	0.3550
PP-OCH3
B3LYP	–5.9944	–2.6942	–3.3002	5.9944	2.6942	4.3443	1.6501	0.8047
MP2	–8.0815	0.8514	–8.9330	8.0815	–0.8514	3.6150	4.4665	0.3789
PP-NO2
B3LYP	–7.3286	–3.1783	–4.1503	7.3286	3.1783	5.2534	2.0751	0.4208
MP2	–9.5292	0.5157	–10.0448	9.5292	–0.5157	4.5068	5.0224	0.2482
PP-Cl
B3LYP	–6.5933	–2.9051	–3.6882	6.5933	2.9051	4.7492	1.8441	0.6103
MP2	–8.7033	0.7714	–9.4747	8.7033	–0.7714	3.9659	4.7374	0.3202

Table 3

Phenyl Phthalimide and Its Derivatives’ Quantum Chemical Properties with B3LYP/6-311++G(d,p) and MP2/6-311++G(d,p) in Aqueous Media

inhibitors	EHOMO eV	ELUMO eV	ΔE eV	I eV	A eV	χ eV	η eV	ΔN eV
PP-H
B3LYP	–6.7280	–2.7658	–3.9623	6.7280	2.7658	4.7469	1.9811	0.5686
MP2	–8.8149	0.9723	–9.7871	8.81498.800[59]	–0.9723	3.9213	4.8936	0.3146
PP-CH3
B3LYP	–6.5030	–2.7484	–3.7546	6.5030	2.7484	4.6257	1.8773	0.6324
MP2	–8.5487	0.9848	–9.5335	8.5487	–0.9848	3.7820	4.7668	0.3375
PP-OCH3
B3LYP	–6.1745	–2.7426	–3.4319	6.1745	2.7426	4.4586	1.7160	0.7405
MP2	–8.3408	0.9837	–9.3245	8.3408	–0.9837	3.6786	4.6623	0.3562
PP-NO2
B3LYP	–7.2176	–3.1538	–4.0638	7.2176	3.1538	5.1857	2.0319	0.4465
MP2	–9.4252	0.6063	–10.0315	9.4252	–0.6063	4.4095	5.0157	0.2582
PP-Cl
B3LYP	–6.6880	–2.8044	–3.8836	6.6880	2.8044	4.7462	1.9418	0.5803
MP2	–8.8494	0.9344	–9.7839	8.8494	–0.9344	3.9575	4.8919	0.3110

Table 4

Phenyl Phthalimide and Its Derivatives’ Quantum Chemical Properties with B3LYP/6-311++G(d,p) and MP2/6-311++G(d,p) in Gaseous Media

inhibitors	EHOMO eV	ELUMO eV	ΔE eV	I eV	A eV	χ eV	η eV	ΔN eV
protonated PP-H
B3LYP	–10.9199	–7.4010	–3.5190	10.9199	7.4010	9.1604	1.7595	–0.6139
MP2	–13.0125	–3.5331	–9.4794	13.0125	3.5331	8.2728	4.7397	–0.1343
protonated PP-CH3
B3LYP	–10.6095	–7.3171	–3.2923	10.6095	7.3171	8.9633	1.6462	–0.5963
MP2	–12.7953	–3.4613	–9.3341	12.7953	3.4613	8.1283	4.6670	–0.1209
protonated PP-OCH3
B3LYP	–9.9401	–7.2872	–2.6528	9.9401	7.2872	8.6136	1.3264	–0.6083
MP2	–12.4008	–3.4648	–8.9360	12.4008	3.4648	7.9328	4.4680	–0.1044
protonated PP-NO2
B3LYP	–11.1833	–7.7283	–3.4550	11.1833	7.7283	9.4558	1.7275	–0.7108
MP2	–13.8008	–3.9040	–9.8968	13.8008	3.9040	8.8524	4.9484	–0.1872
protonated PP-Cl
B3LYP	–10.5950	–7.4924	–3.1026	10.5950	7.4924	9.0437	1.5513	–0.6587
MP2	–13.0299	–3.6548	–9.3751	13.0299	3.6548	8.3423	4.6876	–0.1432

Table 5

Phenyl Phthalimide and Its Derivatives’ Quantum Chemical Properties with B3LYP/6-311++G(d,p) and MP2/6-311++G(d,p) in Aqueous Media

inhibitors	EHOMO eV	ELUMO eV	ΔE eV	I eV	A eV	χ eV	η eV	ΔN eV
protonated PP-H
B3LYP	–7.8353	–3.9304	–3.9048	7.8353	3.9304	5.8828	1.9524	0.2861
MP2	–9.9466	–0.0501	–9.8965	9.9466	0.0501	4.9983	4.9483	0.2023
protonated PP-CH3
B3LYP	–7.5974	–3.9138	–3.6836	7.5974	3.9138	5.7556	1.8418	0.3378
MP2	–9.7860	–0.0365	–9.7496	9.7860	0.0365	4.9112	4.8748	0.2142
protonated PP-OCH3
B3LYP	–7.0771	–3.9116	–3.1655	7.0771	3.9116	5.4944	1.5828	0.4756
MP2	–9.5085	–0.0414	–9.4671	9.5085	0.0414	4.7749	4.7336	0.2350
protonated PP-NO2
B3LYP	–8.3667	–4.0273	–4.3394	8.3667	4.0273	6.1970	2.1697	0.1851
MP2	–10.4846	–0.1521	–10.3324	10.4846	0.1521	5.3183	5.1662	0.1628
protonated PP-Cl
B3LYP	–7.7131	–3.9663	–3.7467	7.7131	3.9663	5.8397	1.8734	0.3097
MP2	–10.0690	–0.0909	–9.9781	10.0690	0.0909	5.0800	4.9891	0.1924

Therefore, the theoretical study concluded the same as the experimental study that PP-OCH3 contributed maximally to the corrosion inhibition efficiency. In contrast, a low ELUMO value indicates that the inhibitor prefers to accept electrons from the metal.[53,54]Tables –5 show the lowest ELUMO value for PP-NO2 at 0.6063 eV. PP-NO2 is more likely to be electron-withdrawing and accepts more electrons from carbon steel than other inhibitors, so it is not strongly adsorbed on the carbon steel surface. Figure depicts the electron distribution in molecular orbitals of PP-OCH3, PP-CH3, PP-H, PP-Cl, and PP-NO2. The difference in electron distribution between the three compounds is noticeable, with PP-OCH3 having a more extensive electron distribution. This improves inhibitor performance by strengthening the predicted EHOMO-related sequence.

Figure 3

HOMO, LUMO, MEP, and ESP orbitals of PP-H, PP-CH3, PP-OCH3, PP-Cl, and PP-NO2.

The value of the ionization potential is directly related to EHOMO.[55] The ionization potential value is the least amount of energy needed for electrons to attach to the surface of the metal and shield it from the corrosive medium. As a result, the low ionization potential (I) indicates the ease with which the atom can release its outer electron. It can donate electrons to the metal surface, thus increasing corrosion inhibition efficiency.[56,57]Equation can be used to calculate the ionization potential value. Table shows the quantum chemical parameters of phenyl phthalimide and its derivatives in aqueous media. Table shows that PP-OCH3 has the lowest ionization potential value (8.3408 eV) compared to PP-CH3, PP-H, PP-Cl, and PP-NO2, the values of which are 8.5487, 8.8149, 8.8494, and 9.4252 eV, respectively. In comparison to PP-CH3, PP-H, PP-Cl, and PP-NO2, PP-OCH3 is anticipated to have a better inhibitory efficiency value. This also explains why PP-NO2 has the lowest corrosion inhibition efficiency, with the lowest 9.4252 eV. This ionization potential value can also be used to validate the theoretical calculation methods. The DFT ionization potential value is far below the standard experimental value.[58] Experimentally, the PP-H ionization potential is 8.80 eV,[59] whereas DFT/6-311++G(d,p) yields a value of 6.7280 eV. DFT/potential B3LYP’s ionization value is 2 eV lower than the experimental results. This demonstrates DFT’s weakness in imitating the energy of experimental results. We therefore advise against using DFT to determine the energy of a molecule’s quantum parameter.

High electronegativity values indicate that organic corrosion inhibitors are electron acceptors, while low ones indicate corrosion inhibitors as electron donors. This is because corrosion inhibitors with low electronegativity values will be easier to donate electrons or more reactive.[60−62] Electronegativity values can be calculated using eq . Tables –5 depict that the order of electronegativity values is PP-OCH3 < PP-CH3 < PP-Cl < PP-H < PP-NO2. PP-OCH3 has the lowest electronegativity value of 3.6786 eV calculated by MP2/6-311++G(d,p). The electronegativity of PP-OCH3 is lower than that of iron, 7 eV. PP-OCH3 will donate its electrons to carbon steel. Therefore, PP-OCH3 acts as the most effective corrosion inhibitor than other inhibitors. The theoretical value of electronegativity has a linear correlation with the efficiency of corrosion inhibition (Figures and 5).

Figure 4

Correlation between the effectiveness of inhibition and quantum chemical properties of phenyl phthalimide and its derivatives, including electronegativity, ionization potential, and electron transfer in the gas phase.

Figure 5

Correlation between the effectiveness of inhibition and quantum chemical properties of phenyl phthalimide and its derivatives, including electronegativity, ionization potential, and electron transfer under protonated conditions.

A high electron transfer value, according to Koopmans, enhances the value of corrosion inhibition efficiency.[38]Tables –5 show the fraction of electrons, and the electron transfer values can be calculated using eq . Table shows the N of the inhibitors using the MP2/6-311++G (d,p) method. The highest electron transfer value in PP-OCH3 is 0.3562 eV. The order of electron transfer values is PP-OCH3 > PP-CH3 > PP-H > PP-Cl > PP-NO2. This electron transfer value is consistent with the previously published corrosion inhibition efficiency analysis (Figures and 5).

The adsorption of organic corrosion inhibitors on the carbon steel metal surface occurs through donor–acceptor interactions, which can be analyzed by local reactivity, namely, the Fukui function. Fukui’s function measures chemical reactivity and shows the nucleophilic and electrophilic attack of organic inhibitors. Nucleophilic and electrophilic attacks can occur in the presence of maximum f+ and f– values.[63−65] The greater the value of the Fukui function, the more reactive the active site of a molecule.

The fK+ value indicates the preferable sites for nucleophilic attack or when the molecule receives electrons, whereas the fK– value indicates the preferable sites for electrophilic attack or when the molecule donates electrons.[66,67]Equations and 7 can be used to calculate the Fukui function’s value. Table shows that the most reactive sites of PP-H and PP-CH3 for nucleophilic attack are in N8 and C13 atoms, PP-OCH3 in N8, C14, and O26 atoms, respectively, PP-Cl on N8 and Cl18 atoms, and PP-NO2 in N8 and C15 atoms. The atom shows that it is most likely to accept electrons from the surface of Fe(110), thus forming a back bond. The maximum fK– values of PP-H, PP-CH3, and PP-OCH3 for electrophilic attack are located in O16 and O17 atoms. PP-Cl and PP-NO2 are located at C3 and C6 atoms and O19 and O20 atoms, respectively. This demonstrated a propensity for donating electrons to an open d orbital on the surface of Fe(110) in order to create a coordinate bond.

Table 6

Functional Analysis of PP-H, PP-CH3, PP-OCH3, PP-NO2, and PP-Cl

PP-H	qk (N – 1)	qkN	qk (N + 1)	fK+	fK–
C1	–0.3744	–0.331	–0.3135	0.0175	0.0435
C2	–0.3744	–0.331	–0.3135	0.0175	0.0435
C3	–0.3700	–0.3314	–0.3387	–0.0073	0.0386
C4	0.1598	0.1933	0.2231	0.0298	0.0335
C5	0.1598	0.1933	0.2231	0.0298	0.0335
C6	–0.3700	–0.3314	–0.3387	–0.0073	0.0386
C7	0.1021	0.1815	0.1802	–0.0013	0.0794
N8	0.0310	0.0827	0.1919	0.1092	0.0517
C9	0.1021	0.1815	0.1802	–0.0013	0.0794
C10	0.3984	0.3569	0.4130	0.0561	–0.0415
C11	–0.0856	–0.0679	0.0011	0.0690	0.0177
C12	–0.3225	–0.3072	–0.2736	0.0337	0.0153
C13	–0.402	–0.3843	–0.2669	0.1174	0.0177
C14	–0.3225	–0.3072	–0.2736	0.0337	0.0153
C15	–0.0856	–0.0679	0.0011	0.0690	0.0177
O16	–0.4713	–0.3116	–0.2521	0.0595	0.1596
O17	–0.4713	–0.3116	–0.2521	0.0595	0.1596

Monte Carlo simulations can be used to demonstrate the mechanism of corrosion inhibition by organic inhibitors on metal surfaces. The Monte Carlo simulation tries to find the lowest energy for all systems.[68,69] Monte Carlo simulations were carried out on inhibitors (PP-H, PP-CH3, PP-OCH3, PP-Cl, and PP-NO2), 100 water molecules, and a carbon steel surface represented by Fe(110). Figure shows the Monte Carlo simulation of the most stable adsorption conformation of each organic inhibitor (PP-H, PP-CH3, PP-OCH3, PP-Cl, and PP-NO2) on the surface of Fe(110) and 100 water molecules. The distance between the atoms in the organic inhibitor and the metal surface can help understand the adsorption process’s nature. A distance value less than 3.5 indicates chemical adsorption (chemisorption), while a distance value greater than 3.5 indicates physical adsorption (physisorption).[70,71] A higher negative adsorption energy value indicates a more stable and stronger interaction between organic inhibitors of carbon steel.[72,73]Table shows that the highest adsorption energy value for the organic inhibitor PP-OCH3 was obtained at −173.5912 kcal mol–1. The order of adsorption energy is PP-OCH3 > PP-CH3 > PP-H > PP-Cl > PP-NO2. This sequence is the same result of MP2/6-311++G (d,p) quantum chemistry calculations in the solution phase. Table shows that the adsorption energies of the corrosion inhibitors are higher than the adsorption energies of the water molecules. This demonstrates how water molecules can be gradually replaced by inhibitor molecules on the carbon steel surface, forming a stable layer that protects the carbon steel from aqueous corrosion. The experimental results of the previously reported corrosion inhibition efficiency are linearly correlated with the Monte Carlo simulation studies that have been carried out. PP and its derivatives have a lone pair of electrons, such as nitrogen and oxygen atoms, so it is possible to donate electrons to the empty d orbital on the Fe(110) surface to form a stable coordination bond. Therefore, PP and its derivatives can cover and form a protective layer of carbon steel from corrosive substances in the solution. A short bond distance <3.5 Å between the inhibitor and metal often indicates chemisorption, while a higher bond length >3.5 Å suggests physisorption. The average bond length of all inhibitors was Fe–O 2.850–2.980 Å, Fe–N 2.900–2.998 Å, and Fe–C 2.970–3.00 Å. This indicates the occurrence of chemical interactions between N, O, and C-benzene atoms and the Fe(110) surface. Figures and 8 show a linear correlation between the adsorption energy and quantum chemical parameters of phenyl phthalimide and its derivatives under neutral circumstances. Adsorption is widely accepted as the primary mechanism of corrosion inhibitors interacting with carbon steel. As a result, the adsorption energy can be used to rank inhibitory molecules directly. The most stable and strong adsorption system has high negative adsorption energy.[74,75]

Figure 6

Adsorption of phenyl phthalimide and its derivatives on the surface of ferrous metals in the Monte Carlo Fe(110)/inhibitor/100H2O system.

Table 7

Energy of Phenyl Phthalimide Adsorption and Fe(110)/Inhibitor/100H2O System Derivatives Based on Monte Carlo Simulation

systems	energy adsorption (inhibitor) kcal mol–1	adsorption energy (water) kcal mol–1
neutral inhibitor
Fe(110)/PP-H/100H2O	–150.40607559	–13.26304026
Fe(110)/PP-CH3/100H2O	–162.60596435	–12.28170340
Fe(110)/PP-OCH3/100H2O	–173.59120922	–11.90185293
Fe(110)/PP-Cl/100H2O	–138.72615845	–12.81391923
Fe(110)/PP-NO2/100H2O	–130.48848970	–12.81391923
protonated inhibitor
Fe(110)/PP-H/100H2O	–157.30443499	–12.09552923
Fe(110)/PP-CH3/100H2O	–167.05417030	–10.65878790
Fe(110)/PP-OCH3/100H2O	–172.29703093	–14.46829434
Fe(110)/PP-Cl/100H2O	–148.12364859	–14.62546890
Fe(110)/PP-NO2/100H2O	–129.66083150	–15.48199690

Figure 7

Phenyl phthalimide and its derivatives under neutral inhibitor conditions: correlation of adsorption energy and quantum chemical parameters.

Figure 8

Phenyl phthalimide and its derivatives under protonated inhibitor conditions: correlation of adsorption energy and quantum chemical parameters.

Conclusions

Theoretical studies have been carried out to elucidate the corrosion inhibitory mechanism of phenyl phthalimide and its derivatives as corrosion inhibitors against carbon steels. DFT and ab initio MP2 explain quantum parameters’ influence on corrosion inhibition efficiency. In addition, the reactive site of the inhibitor, which contributes maximally to the corrosion inhibition process, has also been described. Fukui function analysis showed that nitrogen, oxygen, and phenyl carbon atoms became the main reactive sites of corrosion inhibitors; the reactive site can donate electrons to the carbon steel surface. The Monte Carlo simulation can also provide an overview of the mechanism between the organic inhibitor, 100 water molecules, and the carbon steel surface. The highest negative adsorption energy was obtained from the organic inhibitor PP-OCH3 of −173.5912 kcal mol–1. In an aqueous solution, all the organic inhibitors studied were able to compete with water so that they could be adsorbed on the metal surface. PP-OCH3 contributes very well to inhibiting corrosion of carbon steel. The result follows the corrosion inhibition efficiency test conducted previously. This theoretical study can be a bridge in solving problems related to the electronic properties of corrosion inhibitors.