Organic Corrosion Inhibitors

As a consequence of FMOs theory discussed above, HOMO and LUMO were associated with electron‐donating and electron‐accepting abilities of molecules, respectively. Hence, it can be noted that any inhibitor molecule characterized by high energy of HOMO will be, in most cases, effective in terms of its tendency to transfer the electrons to a metallic surface. On the other hand, low LUMO energy value shows that the molecule is a good electron acceptor.

In addition, Koopmans theorem [34] is a bridge between DFT and MO theory and it can be used in the prediction of ionization potential (IP) and electron affinity (EA) values of molecules. According to this theorem, IP and EA can be expressed via the following equations:

(3.3)

(3.4)

Further, the energy difference between LUMO and HOMO called an energy gap (Δ E ) is also an essential parameter toward the description of reactivity of a molecule.

(3.5)

A large value of Δ E indicates low reactivity of molecules while a molecule with low value of Δ E can be strongly adsorbed on a metal surface.

Parameters such as ɳ, μ , η , and σ are defined as the derivatives of the total electronic energy ( E ) with respect to the number of electrons ( N ) at a constant external potential. The ɳ is defined as the negative value of μ . Within the framework of finite differences approaches, these parameters can be expressed in the form of ground‐state IP and ground‐state EA values of a chemical compound. The theoretical formulas can be expressed as [35]:

(3.6)

(3.7)

(3.8)

The new parameters called ω −and ω +were introduced by Gazquez et al. [36] to predict the propensity of chemical species to accept and to donate electrons. Also, these two parameters are related to IP and EA and are mathematically described via the following equations:

(3.9)

(3.10)

Based on these parameters, we can, again, shed light on the inhibition abilities of chemical compounds based on their ability to accept and receive electrons.

For the prediction of Δ N , which reflects the tendency of an inhibitor molecule to transfer its electron to a metal surface, the hardness and electronegativity indices have been used. This parameter was computed according to Pearson as per the following equation [35]:

(3.11)

In this equation, ∅ is the work function calculated for metal surface and η metalmeans the global hardness of the metal.

The fraction of electrons transferred provides important insight into the adsorption process and the power of the interaction between the metal surface and inhibitor molecule. Consistent with the literature [37–39], an inhibitor can transfer its electron if Δ N > 0 and vice versa if Δ N < 0.

The application of these parameters in evaluating the adsorption and corrosion inhibition behavior of a large number of molecules is extensively reviewed in the following chapters.

Fukui functions offer unique opportunities to increase the fundamental understanding of the local reactivity and selectivity of chemical species. In other words, Fukui function is a local reactivity index proposed to examine the nucleophilic and electrophilic attack regions of inhibitor molecules. In fact, from this important concept (FIs), we can pinpoint the reactive sites in which the electrophilic or nucleophilic attacks are large or small. As discussed above, HSAB theory provides an important contribution in the prediction and interpretation of many CQ parameters, and the judgment of Fukui functions is also an early attempt in this direction. It is necessary here to clarify exactly what is meant by Fukui function f(r) . By definition, f(r) is a first derivative of 𝜌(r) with respect to number of electrons ( N ) at a constant external potential v(r) .

(3.12)

In addition, FIs were identified with respect to hard or soft reagents by involving the HSAB principle. A simple approximation can be used with the aid of finite difference approximation and Mulliken's population analysis in which FIs were determined as per the following equations [40]:

(3.13)

(3.14)

(3.15)

where q k( N ), q k( N + 1), and q k( N − 1) are charge values of neutral, anionic, and cationic forms of atom k, respectively.

Microscopic analyses are methods developed to serve as a basis for the investigation and simulation of physical phenomena on a molecular level. As these methods usually allow such a deep analysis, they became essential tools in generating and designing new functional materials. Macroscopic and microscopic characteristics of species constituting a simulation system, i.e. molecules and fine particles, are generated from analyzing the output of simulations.

Two well‐known atomistic simulation methods are MC and MD. The advantage of the MD method over the MC method is, besides its ability to analyze thermodynamic equilibrium, it can be used to investigate the dynamic properties of a system in a nonequilibrium state.