Quantum chemical parameters for the benzimidazole derivatives.
In the current chapter, recent progress has been described in the field of computational quantum chemistry for the development of corrosion inhibitors. The current chapter is divided into several sections and subdivisions. Recently, the development of green and sustainable technologies for corrosion prevention is highly desirable an increase in ecological awareness and strict environmental regulations. In the last decade, the use of quantum calculation based corrosion inhibitors study has attracted considerable attention. Quantum calculation based density function theory (DFT) has been widely accepted as “green corrosion inhibition technique” because of its theoretical based work. DFT can be used to design corrosion inhibitors to prevent corrosion on mild steel, aluminum, copper, zinc, and magnesium in aqueous media. DFT is the simplest way to study the molecular structure and behavior of corrosion inhibitors. Various quantum chemical parameters such as dipole moment (μ), energy difference (∆E), softness (σ) and global hardness (η), highest occupied molecular orbital (EHOMO) and lowest occupied molecular orbital (ELUMO), etc., of corrosion inhibitors has been calculated using software in order to elucidate the adsorption and corrosion inhibition behavior of inhibitor molecules.
- corrosion inhibition
- aqueous solution
The damage on the material by corrosion produces not only for the high cost inspection, repair, and replacement, but in addition to these formation of a public risk, thus the need for the development of the novel Substances that treat acid in particular, like corrosion inhibitors Media . The use of corrosion inhibitor molecules is one of the most practical ways to protect the materials against corrosion, and it is becoming increasingly popular in industrial applications. The atmosphere is affected by various metals and their alloys strikes due to the use of acid like H2SO4 and HCl for various industrial processes (acid pickling, oil well-acidification, chemical clean-up, etc.) [2, 3], for these reasons the inhibitors is employed as one of the most practical ways to conserve corrosion. Traditionally, corrosion inhibition performance is evaluated experimentally, such as gravimetric analysis, potentiodynamic polarization, and electrochemical impedance spectroscopy (EIS). However, these experimental methods are expensive and laborious, and often decrease in the illuminating corrosion mechanism. With the improvements in software and hardware, computer simulation has become a powerful tool to investigate the complex system of corrosion resistance . By checking the structure, electron distribution, and adsorption of molecules on the metal and oxide surfaces, the corrosion mechanism is now deeply detected. In 1971, Vosta and Eliasek  introduced quantum chemical methods to investigate the prohibition of corrosion and established the field of quantum corrosion electrochemistry. After this, the main objective of quantum chemistry methods was primarily on the discovery and establishment of relations between molecular structure and prohibition, and many valuable results have now been reported. Quantum chemical study has proven itself very long ago useful in determining the structure of the molecules, the reaction as well as the obvious electronic structures . Thus, it has become a common practice to calculate quantum chemical corrosion study concept of assessment of efficiency a corrosion inhibitors with the help of computational chemistry using chemicals to find compounds with desired properties intuition and experience in a mathematical quantitative and a relation between the structure once computerized and activity or property are found, any number of compounds. Those who have not been synthesized so far can be easily tested planning of computational method  and a set of mathematical equations that are capable of displaying correctly chemical incident under study [8, 9].
2. Principles of corrosion
Thermodynamic and electrochemical are two basic principles of corrosion mechanism which describe the transformation of metals and alloys into their stable states like hydroxides, sulfates, oxides and chlorides, etc.
2.1. Thermodynamic principles
Thermodynamics directs the spontaneous direction of a chemical reaction and it is used to determine whether the corrosion on metal surface is theoretically possible or not .
2.2. Electrochemical principles
Basically corrosion is the coupled of two half-cell electrochemical reaction, cathodic and anodic reaction. Anodic reaction involves the leaving of free electron by metal ionization however cathodic reaction involves the up taking of free electrons by dissolved oxygen and/or water molecules in the solution. Previous is oxidation type reaction where free electrons are produced while later is reduction reaction in which electrons can be accepted . Corrosion behavior of metals and alloys can be easily determine using electrochemical principles.
Two half-cell reaction can be divided in to following type as given:
2.2.1. Anodic reaction
Anodic reaction is the loss of metal cations as given in examples:
2.2.2. Cathodic reaction
Reduction of cation(s) from free electrons of oxidation reaction is a cathodic reaction. Formation of hydrogen gas (H2) from the reduction of two hydrogen ions at metal surface is an example of cathodic reaction (Eq. (4)):
Above reactions are shown schematically in Figure 1.
2.2.3. Coupled electrochemical reactions
Figure 2 represents coupled electrochemical reactions in which anodic and cathodic reactions exist on the metal surface at different places. There are four different types of conditions causes to corrosion are: (i) an anodic reaction, (ii) a cathodic reaction, (iii) a metallic path between these two reactions, and (iv) electrolyte. Electrolyte is an ionic aqueous solution in which current can be flow. The coupled reaction for an iron metal dipped in neutral, acidic or basic medium is illustrated in Figure 2.
Heterogeneous nature of a metal surface is reason for the orientation of coupled reaction on the same metal surface. Heterogeneity on metal surface can be arise due to defects like screw, steps, dislocation, point defects and kink sites, etc.
3. Adsorption mechanism of corrosion
Corrosion inhibition properties of metals and alloys can significantly change due to adsorption of inhibitor molecules at metal/solution interface. Inhibition of metal corrosion is a surface phenomenon which involves the adsorption of corrosion inhibitors over the metal surface in electrolytic solution. In corrosive solution inhibitor molecules adsorbed on the metal surface by replacing the H2O molecules at the metal/solution interface according to the given process Eq. (5) :
where Inh (ad) and Inh (sol) are inhibitor molecules in the corrosive medium and adsorbed on the metal surface, respectively, whereas
4. Consequences and economics of corrosion
Corrosion is a global problem, which adversely affects the development of both developed and developed countries. According to a highly cited study conducted by the National Association of Corrosion Engineers (NACE) in 1998, the total annual cost of corrosion in the U.S. is estimated at US $ 276 billion, which is approximately 3.1% GDP (GDP; NACE 2002) . In 2011, the total cost of corrosion in the US increased to $ 2.2 trillion. Since the cost of corrosion in India is a matter of concern, it is about two lakh crores (US $ 45 billion) proposed by the 1st Global Corrosion Summit held in New Delhi in 2011 . However, these estimates are outdated and recently the NACE is being closely examined at the cost of the corrosion, according to which the annual global cost of the corrosion is approximately $ 2.5 trillion, which is equivalent to 3.4% of the global GDP. In India, the cost of annual corrosion is more than 100 billion US dollars, whereas in South Africa, direct corrosion costs are estimated to be around 130 billion (i.e., 9.6 billion US dollars) [16, 17]. By applying the existing methods of prevention of corrosion, this cost of the war can be reduced by 35% (US $ 875 billion) to 15% (US $ 375 billion).
Corrosion is a global problem, which adversely affects the development of both developed and developed countries. According to a highly cited study conducted by the National Association of Corrosion Engineers (NACE) in 1998, the total annual cost of corrosion in the U.S. is estimated at US $ 276 billion, which is approximately 3.1% GDP (GDP; NACE 2002) . In 2011, the total cost of corrosion in the US increased to $ 2.2 trillion. Since the cost of corrosion in India is a matter of concern, it is about two lakh crores (US $ 45 billion) proposed by the 1st Global Corrosion Summit held in New Delhi in 2011 . However, these estimates are outdated and recently the NACE is being closely examined at the cost of the corrosion, according to which the annual global cost of the corrosion is approximately $ 2.5 trillion, which is equivalent to 3.4% of the global GDP [7, 8].
In India, the cost of annual corrosion is more than 100 billion US dollars, whereas in South Africa, direct corrosion costs are estimated to be around 130 billion (i.e., 9.6 billion US dollars) [7, 8]. By applying the existing methods of prevention of corrosion, this cost of the war can be reduced by 35% (US $ 875 billion) to 15% (US $ 375 billion).
5. Basics and computational aspects of density function theory (DFT)
5.1. The basics of DFT: Hohenberg-Kohn theorem
In Moscow, at the Frumkin Institute of Electrochemistry of the Russian Academy of Sciences, the scientific school of Quantum Electrochemistry was to be started in Revaz Dogonadze in the 1960s. Generally, the ideas that are generated in the field include quantum mechanics, electrodymamics, and electrochemistry; and likewise a very large group of different professional academics is studied. The fields of expertise include chemicals, physics, mechanical and electrical engineering. More specifically, quantum electrochemical electrode surfaces  for the study of electrochemical processes, quantum mechanical devices such as DFT are used, including the transfer of electrons from the molecules to the metal electrode surface.
In some previous studies, the basis and importance of DFT [19, 20] has been described. The recent impact of DFT in the development of quantum electrochemistry is significant, and can be linked to achievements in the late 1980s when hybrid functional and gradient-corrected methods were introduced . Based on the famous Hohenberg-Kohn theorem awarded the Nobel Prize in physics for his work on DFT in 1964. DFT concentrates on electron density
Eq. (10) pledges the proper normalization of the electron density.
5.2. Basis sets
The base set, the mathematical description of the orbital within the system used to do theoretical calculations. By putting a low restriction on the location of electrons in large base space, they make a more accurate orbital estimate. When molecular calculation is done, it is common to use sophisticated finite numbers based on the atomic orbitals cantered on each atomic nucleus within this molecule. Most molecular quantum mechanical methods begin calculating with the choice of a set of base functions. The use of a substantial base set for the success of calculation is a mandatory requirement. Standard basis for electronic computation calculation uses linear combinations of geosynchronous functions of set orbit. In order to accurately represent atomic orbitals, we should use a linear combination of several codgers. Gaussian offers a wide range of predefined base sets, which can be categorized from those numbers and types of works, in which they are included.
5.3. Basic parameters derived from DFT and their application to corrosion inhibition design
5.3.1. Frontier molecular orbitals
The frontier orbitals are very important in defining the lowest unoccupied molecular orbital (LUMO) and highest occupied molecular orbital (HOMO) of molecules. Scientist Fukui  recognized the importance of the frontier orbitals of first time because the stereochemistry of the inhibition system and the chemical reactions were key factors in the governing of ease of reaction. A good relationship has been found between
5.3.2. Dipole moment
The dipole moment is a vector quality which is most extensively used for describing the polarity of a molecule. It is a measurement of the separation of the two opposite electrical charges (positive and negative) and represented as given in Eq. (12) :
5.3.3. Electronegativity and the electronic chemical potential
DFT has been found to be successful in providing insight into chemical reactivity and selectivity, in terms of global molecular properties, such as chemical potential (−
According to Iczkowski and Margrave , it should be noted that, when assuming a quadratic relationship between E and N and in a finite difference approximation, than it can be written as represented in Eqs. (14) and (15):
where A and I have the electron affinity and ionization potential, respectively, due to which the electronegative definition of Mulliken can be corrected . In addition, a theoretical justification was provided for the theory of Sanderson’s equation of electronegativity, which states that when two or more atoms join together to form a molecule, then their electro negativities is the same intermediate the value is adjusted from .
5.3.4. Global hardness and softness
There is total hardness (H) and softness properties, which also facilitate analysis of molecular selectivity and reaction. Correlation between quantum chemical quantities and corrosion inhibition is based on Pearson’s hard and soft acids and bases, and the Lewis theory of acid and base . Energy gap, ∆
The reverse of the global hardness is written as the softness,
5.3.5. Mulliken population analysis
To identify the adsorption centers of inhibitors, Mulliken population analysis has been widely reported [39, 40]. All chemical interactions are either covalent or polar (electrostatic). Electric charge in the molecule is obviously responsible for electrostatic interaction. Local electron charge or density is important in the properties of many physical-chemical and chemical reactions of biological molecules. Thus, charge-based parameters have been widely employed as weak intermolecular interaction measures or as chemical reactive indices. Mulliken population analysis  is mostly used to calculate the charge distribution in a molecule. These numerical quantities are easy to obtain and provide at least a qualitative understanding of structural reactions of blocking molecules . In addition, atomic charge is used to describe molecular polarization of molecules.
5.3.6. The fraction of electrons transferred (∆
6. Some recent studies of corrosion inhibitor using density function theory
DFT is widely used software designing new corrosion inhibitors of chemical compounds using energy of the highest occupational molecular orbital (
During the last two decades, computational methods have been developed as important tools in the corrosion resistance, because in the calculation, large amounts of compounds can be provided in large amounts within a reasonable time frame. The results of such studies can be further used as an appropriate starting point for experimental studies. Computational methods can also be important tools in the development of more suitable compounds used for metal protection, starting with the already available compounds and by identifying derivatives with better metal protection efficiencies through structural modifications. Recently, there are many studies in literature on computational studies of useful organic materials for metal protection. The goal of these studies is to gain insights at the molecular level on the contact of these organic matters with metal surfaces. This important approach is particularly important in the design of new and effective corrosion inhibitors for industrial applications in oil and gas fields. A recent review of some of the research has been given below. They are not enough anywhere because excellent reviews are available elsewhere .
6.1. Organic corrosion inhibitors studied using DFT
Using the semi-experimental AM1 method, Mahendra et al. , studied the inhibition efficiency of benzimidazole derivatives. Quantum chemical parameters such as
Quantum chemical calculation of commercially available drug namely grieseofulvin was calculated towards the corrosion inhibition potential of mild steel using Gaussian 9.0 software package . Quantum chemical parameters has confirmed that the presence of heteroatoms and
Verma et al.  describes the effect of ring and ring size of three 3-amino alkylated indoles (AAIs) namely, N-((1H-indol-3-yl)(phenyl)methyl)-N-ethylethanamine (AAI-1), 3-(phenyl(piperidin-1-yl)methyl)-1H-indole (AAI-3) and 3-(phenyl(pyrrolidin-1-yl)methyl)-1H-indole (AAI-2) on mild steel corrosion acidic solution using experimental as well as theoretical calculations such as quantum chemical calculations and molecular dynamics simulations methods. Experimental results revealed that the inhibition efficiency increases with increased concentration of the corrosion inhibitors. Maximum inhibition efficiencies of 94.34% for AAI-1, 96.08% for AAI-2 and 96.95% for AAI-3 were obtained at 0.862 mM concentrations of inhibitors. Both experimental and theoretical calculations show that 3-amino alkylated indole with cyclic amino groups exhibit high corrosion inhibition efficiency compared with open-chain amino groups. Experimental results explains that resistance efficiency increases with increased concentration of the inhibitors. Maximum inhibition efficiency of 94.34% for AAI-1, 96.08% for AA-II and 96.95% for AAI-3 was obtained in 0.862 mm concentrations of inhibitor. Quantum chemical calculations such as dipole moment (
6.2. Plant extracts based corrosion inhibitors studied using DFT
Emeka et al.  studied the Inhibition efficiency of green and sustainable biomass extract of
Anupama et al.  examine the
Raja et al.  investigated Isoreserpiline (Figure 5c) as active molecule against corrosion protection of mild steel. Isoreserpiline is the major component of leaves and bark extracts of
7. Future developments
Density functional theory (DFT) has become an attractive theoretical method, because it provides accurate, basic and important parameters for at least complex and molecules cost. Apart from this, by implementing the DFT methodology, we can understand reactionary behavior conditions of hard and soft acid/base (HSAB) principles that provide a systematic way interrupter/analysis of surface interaction and prediction. Survey of theoretical corrosion literature presented in chapter (Sections 6.1 and 6.2) shows that density function theory (DFT) is a powerful tool to study fundamental, molecular-level processes regarding the corrosion barrier. However, it should be very careful with these calculations, these studies should be taken in planning can easily lead with inaccurate or inadequate data-sets for the wrong findings. Role of quantum chemistry in corrosion focus is likely to increase in future inhibitory studies moves towards the investigation of complex chemical mechanisms. However, due to high computational effort restrictions calculations mean that there will be no quantum chemical methods be able to replace experimental corrosion in the near future less expensive methods of study or computerized procedures regarding the corrosion inhibition.
This chapter focuses on the use of modern quantum chemical methods, primarily to describe the adsorption of corrosion-resistant molecules on a metal surface in the aqueous solution as the functional principle of density. It is evident that DFT can be used as powerful technique with a unique ability to make practical calculations on many complex bodies system, such as large organic molecules, drugs, ionic liquids those are widely used as inhibitor. Hydrophobic/hydrophilic nature of corrosion inhibitor has been identified as an important factor in determining the ability of the resistant to prevent corrosion. Finally, the idea of an important future in the design of new and effective corrosion inhibitors using DFT will identify organic structures, which have less toxicity besides having high corrosion protection capacity.
Author greatly acknowledges Dr. (Mrs) Fahmida Khan and Dr. R.N. Singh, Principal Govt. Digvijay College Rajnandgaon for their support.