**2. Computational method**

The B3LYP method of density functional theory in Gaussian 09 software package [31] is utilized to optimize the geometric configuration and analyze the frequency of ionic liquid. The 6-311++G(d, p) basis set was used in this paper, which is same as the literature [26–28]. The geometry optimization and frequency analysis of the studied ionic liquid molecules were performed, and the stable geometry was obtained. There are seven interaction sites of 1-alkyl-3-methylimidazolium cations to interact with anions, as shown in **Figure 1**, where 1–5 represent the five positions of anions in the plane of imidazole ring, and 6 and 7 are respectively located on both sides perpendicular to the plane of imidazole ring. As confirmed by many authors, position 2 is the most active site and the anions are always located in this position, so we just discuss the anions' contact with cations at position 2. The *E*HOMO and *E*LUMO, energy gap (Δ*E*), electronegativity (*χ*), the softness (*S*), dipole moment (*μ*), polarizability (*α*), electrophilic index (*ω*), hardness (*η*), Fukui index and other structural and property parameters were calculated. Distribution of Fukui index was drawn by Multiwfn software [32, 33].

According to the frontier molecular orbital theory, the molecules' reactivity is related to their lowest unoccupied molecular orbits (LUMO) and the highest occupied molecular orbital (HOMO). In general, the level of the *E*HOMO value determines the ability to deliver electrons to the outside. The level of the *E*LUMO value represents the ability to obtain electrons. Therefore, the higher the *E*HOMO value, the lower the *E*LUMO value can reflect the reactivity of a molecule. [34] As for the adsorption of a molecule on the carbon steel surface, a higher *E*HOMO value will make them have a stronger electronic supply capacity and can form an adsorption with the d orbital on the surface of iron. A lower *E*LUMO value will make them have a stronger electronic acceptance capacity, which becomes more easily accepted electrons from the surface of iron and form an antibond orbital to promote the adsorption. Therefore, the energy gap difference Δ*E* = *E*HOMO-*E*LUMO can be used to assess

**Figure 1.** *Anions can form ionic liquids with [Emim]<sup>+</sup> in several different sites.*

*Theoretical Study of the Structure and Property of Ionic Liquids as Corrosion Inhibitor DOI: http://dx.doi.org/10.5772/intechopen.92768*

the bonding ability of a molecule with iron. The smaller Δ<sup>E</sup> is, the stronger bonding ability with iron is, and the easier adsorption on the iron surface [35].

In the concept density functional theory, according to Koopmans theorem [36], ionization potential *I* under vacuum condition can be approximated to the negative value of *E*HOMO *I* ¼ �*E*HOMO. Similarly, the electron affinity a is approximately negative for *E*LUMO *A* ¼ �*E*LUMO. The dipole moment (*μ*), electronegativity (*μ*), softness (*S*) and polarizability (*α*) of a molecule are generally referred to as the global reactivity of a molecule [37, 38]. Molecular polarity is always described by dipole moment (*μ*), which is defined as the product of atomic distance *R* and atomic charge *q* as *μ* ¼ *qR* [39]. Generally, the higher *μ* will make the molecules more easily adsorbed on the surface of carbon steel [40], and the efficiency of the molecular inhibitor will increase accordingly. However, the dipole moment reflects the global polarity of molecules rather than the polarity of the bond in the molecule. According to the concept density functional theory, the electronegativity (*χ*) of the system with n electrons is defined as follows when the external field *ν*(*r*) is fixed [38]:

$$\chi = -\left(\frac{\partial E}{\partial N}\right)\_{\nu(r)}\tag{1}$$

Hardness (*η*) is defined as the second derivative of the system energy *E* to *N* [41]

$$\eta = \frac{1}{2} \left( \frac{\partial^2 E}{\partial \mathbf{N}^2} \right)\_{\nu(r)}. \tag{2}$$

Using the finite difference approximation, the global hardness (*η*) and electronegativity (*χ*) are related to ionization energy *I* and affinity energy *A* as follows [42]:

$$
\chi = \frac{I + A}{2},
\tag{3}
$$

$$
\eta = \frac{I - A}{2} \tag{4}
$$

According to Koopmans theorem [36], the electronegativity (*χ*) and global hardness (*η*) can be calculated from *E*HOMO and *E*LUMO as

$$\chi = -\frac{E\_{\text{HOMO}} + E\_{\text{LUMO}}}{2},\tag{5}$$

$$\eta = \frac{E\_{\rm LUMO} - E\_{\rm HOMO}}{2} \,\text{.}\tag{6}$$

Global softness (*s*) is usually defined as the reciprocal of global hardness [37].

$$\mathcal{S} = \frac{1}{\eta}. \tag{7}$$

Electronegativity (*χ*) is a scale of the ability of atoms in molecules to attract electrons. The larger its value is, the easier it is to attract electrons [38] reflecting a better inhibitor effect. The smaller the global hardness (*η*) or the larger the global softness (*S*) of the molecule means that the stronger the interaction between metal surface and a molecule [43], and a higher corrosion inhibition efficiency. Parr introduced the concept of electrophilic index (*ω*), which is defined as following [37]:

[Omim]Y (n = 2, 4, 6, 8, Y = Cl, BF4, HSO4, Ac and TFO) are studied by quantum chemical calculation. The active region, inhibition efficiency of possible interaction

The B3LYP method of density functional theory in Gaussian 09 software package [31] is utilized to optimize the geometric configuration and analyze the frequency of ionic liquid. The 6-311++G(d, p) basis set was used in this paper, which is same as the literature [26–28]. The geometry optimization and frequency analysis of the studied ionic liquid molecules were performed, and the stable geometry was obtained. There are seven interaction sites of 1-alkyl-3-methylimidazolium cations to interact with anions, as shown in **Figure 1**, where 1–5 represent the five positions of anions in the plane of imidazole ring, and 6 and 7 are respectively located on both sides perpendicular to the plane of imidazole ring. As confirmed by many authors, position 2 is the most active site and the anions are always located in this position, so we just discuss the anions' contact with cations at position 2. The *E*HOMO and *E*LUMO, energy gap (Δ*E*), electronegativity (*χ*), the softness (*S*), dipole moment (*μ*), polarizability (*α*), electrophilic index (*ω*), hardness (*η*), Fukui index and other structural and property parameters were calculated. Distribution of Fukui index was drawn by

According to the frontier molecular orbital theory, the molecules' reactivity is

related to their lowest unoccupied molecular orbits (LUMO) and the highest occupied molecular orbital (HOMO). In general, the level of the *E*HOMO value determines the ability to deliver electrons to the outside. The level of the *E*LUMO value represents the ability to obtain electrons. Therefore, the higher the *E*HOMO value, the lower the *E*LUMO value can reflect the reactivity of a molecule. [34] As for the adsorption of a molecule on the carbon steel surface, a higher *E*HOMO value will make them have a stronger electronic supply capacity and can form an adsorption with the d orbital on the surface of iron. A lower *E*LUMO value will make them have a stronger electronic acceptance capacity, which becomes more easily accepted electrons from the surface of iron and form an antibond orbital to promote the adsorption. Therefore, the energy gap difference Δ*E* = *E*HOMO-*E*LUMO can be used to assess

between ionic liquid molecules and iron surface are preliminaries analyzed.

**2. Computational method**

*Density Functional Theory Calculations*

Multiwfn software [32, 33].

**Figure 1.**

**40**

*Anions can form ionic liquids with [Emim]<sup>+</sup> in several different sites.*

$$
\mu = \frac{\chi^2}{2\eta}.\tag{8}
$$

According to the definition, this parameter is a measure of the capability of electron acceptors. The larger the value is, the stronger the capability of electron acceptor is. As an important parameter of global reaction activity, the molecular polarizability (*α*) is the average value obtained by calculation, and its relationship is as follows [44]:

$$a = \frac{1}{3}(a\_{\text{xx}} + a\_{\text{yy}} + a\_{\text{xx}}). \tag{9}$$

where, *α*xx, *α*yy and *α*zz are molecular polarizability in x, y and z directions, respectively. The higher the molecular polarizability (*α*) is, the easier adsorption on the metal surface is, and the higher corrosion inhibition performance is [44].

The local reactivity of ionic liquid inhibitors was evaluated by their Fukui index. Nucleophilic and electrophilic behavior of the molecule was studied by analyzing its Fukui index distribution. Fukui function is an important concept in density functional theory, which is commonly used to predict the active sites of a molecule [45]. In the case of certain outfield *v*(*r*), the Fukui function is defined as follows [46]:

$$f(r) = \left[\frac{\partial \rho(r)}{\partial N}\right]\_{\nu(r)}.\tag{10}$$

ring of cation is easy to accept electrons from the iron surface and form a feedback bond. According to the distribution of HOMO and LUMO, when the [Xmim]Cl ionic liquid adsorbs on the surface of carbon steel, the imidazole ring of the ionic liquid will interact with the surface of carbon steel and lay parallel to the surface. The *E*HOMO, the *E*LUMO and the energy gap difference (Δ*E*) of four ionic liquid molecules in [Cnmim]Cl system are shown in **Table 1**. It can be seen from **Table 1** that by increasing the length of the alkyl chain, the *E*HOMO becomes larger and larger, indicating the increased capability of electron donor of the molecule. By increasing the length of the alkyl chain, *E*LUMO also has an increasing trend, which shows that the capability of electron acceptor will weaken. However, the smaller (Δ*E*) is, the better the activity of the molecule is, the easier absorption between the carbon steel surface and molecules, and the higher the inhibition efficiency is. The sequence of inhibition efficiency of these four ionic liquids should be [C2mim]Cl < [C4mim]Cl < [C6mim]Cl < [C8mim]Cl. The [C8mim]Cl has the highest inhibition efficiency and the best inhibition performance, which agrees well with the

E*HOMO,* E*LUMO and Δ*E *of [Cnmim]Cl (n = 2, 4, 6, 8) with B3LYP/6-311++G (d, p) method.*

*The equilibrium geometry structures, HOMO and LUMO isosurfaces of [Cnmim]Cl (n = 2,4,6,8) with B3LYP/6-311++G(d,p) method. From left to right, it is [C2mim]Cl, [C4mim]Cl, [C6mim]Cl and [C8mim]*

*Theoretical Study of the Structure and Property of Ionic Liquids as Corrosion Inhibitor*

*DOI: http://dx.doi.org/10.5772/intechopen.92768*

**ILs [C2mim]Cl [C4mim]Cl [C6mim]Cl [C8mim]Cl** *E*HOMO (eV) 5.2672 5.2641 5.2623 5.2608 *E*LUMO (eV) 1.1890 1.1824 1.1820 1.1819 Δ*E* (eV) 4.0782 4.0817 4.0903 4.0789

**Table 2** shows the global activity parameters of [Cnmim]Cl system obtained by B3LYP/6-311++G(d, p) method. It can be seen from **Table 2** that by increasing the length of the alkyl chain, the dipole moment (*μ*) decreases gradually, indicating that the increase in alkyl chain length will reduce the polarity of the whole molecule. Increasing the length of alkyl chain, the electronegativity (*χ*) is also gradually

experimental measurement [29].

*3.1.2 Global activity parameters*

**Figure 2.**

**Table 1.**

**43**

*Cl, respectively.*

Within the finite difference approximation, the nucleophilic attack can be expressed as *f* þð Þ¼ *r* ρ*<sup>N</sup>*þ<sup>1</sup>ð Þ� *r* ρ*N*ð Þ*r* , and electrophilic attack is *f* �ð Þ¼ *r* ρ*N*ð Þ� *r* <sup>ρ</sup>*<sup>N</sup>*�<sup>1</sup> ð Þ*<sup>r</sup>* [29], where *<sup>ρ</sup><sup>N</sup>* + 1(*r*)、 *<sup>ρ</sup>N*(*r*)、 *<sup>ρ</sup>N*�1(*r*) are the charge density of the atom in the molecule with one unit negative charge, uncharged and one unit positive charge, respectively.

#### **3. Results and discussion**
