**2. Computational section**

#### **2.1 Overview of computational quantum chemistry**

Density functional theory (DFT) is one of the most commonly employed methods to solve Schrödinger's equation by proposing a few justifiable approximations. In contradiction to the wave function methods used earlier, this method is the perfect adaptation for solving large systems involving a huge network of atoms and molecules. Since many rudimentary terms are overlapping in both the methods, the most primitive Hartree-Fock (HF) theory is used to explain the terms in a more elegant manner.

The energy computed from this method will take into account the potential energy of electrons and nuclei based on the relative positions with respect to each other as well as the average kinetic energy of electrons in every orbital. Assuming Born-Oppenheimer approximation, the relative velocity of nuclei is considered insignificant and so does its contribution in the kinetic energy of the system. The columbic interaction of electrons with respect to each other is brought about by assuming a mean field wherein each electron interacts with the averaged field of all the other electrons.

Kohn and Sham's work, in particular, attracted many researchers working in the field of DFT as they attempted to use the standard self-consistent field method to obtain the exchange-correlation energies as well apart from the basic Columbian energies obtained from HF theory [9]. Therefore, owing to their contribution, DFT is also colloquially referred to as Kohn-Sham (KS) formalism. Perdew et al. [10] proposed the advancements in the field of DFT functionals to that of a ladder, where every step leads to a better approximation and, hence, accuracy. The drawback of DFT method is that it can be used only for ground state computations as well as does not, by itself, reveal a detailed picture of electronic distribution owing to which, the optimized structure may not show any key resemblance when compared with other higher accurate methods. However, HF assumes linear combination of atomic orbital (LCAO) which helps to elucidate primitive picture

**97**

*DFT Study on Interaction of Estrone and Imidazolium-Based Hydrophobic Ionic Liquids*

of electrons in the molecule and, hence, can be used as an input for the method of higher accuracy, such as the configuration interaction method, which are collec-

DFT methods used in the present scenario describe the changes in total energy of the system, via exchange and correlation of electrons and electrons and nuclei using hybrid functionals. These sets of mathematical functions utilize a subset of exact exchange from HF, while the remaining uses predefined functions from each individual pure functional [11]. The most commonly used hybrid functional, obtained as a result of this implementation, is the B3LYP hybrid functional. As for the basis is concerned, standard 6-31G(d) basis set is invoked though higher accurate ECP sets are available [12] simply due to the fact that various literature studies in ionic liquids akin to that of ours have obtained better results using this model

The interacting monomers, namely, estrone and each of the three ionic liquids

Gaussview6 [13] and were optimized separately at the B3LYP/6-31G(d) level using Gaussian16 program [14] to find the corresponding geometry and energy at the ground state. Since all the bonding parameters of the monomers are unknown,

The estrone is then introduced selectively to various regions in the vicinity of the ionic liquid such as near the electropositive and electronegative moieties, the imidazolium ring, and the cation and anion groups of ionic liquid to search for all possible interaction sites of the EDC. All these optimized systems can be visualized as various minima in the potential energy surface (PES), and only the properties and structure corresponding to the global minimum are presented for discussion. The absence of imaginary frequencies at all optimized ground states justified that the proposed geometry is a minimum in the PES and not a transition state (TS)

The keyword "output = wfn" is invoked along with the default settings to create. wfn extension file which is then used in multiwfn package to calculate topological

Optimized structures of estrone/ionic liquid complexes are depicted in **Figure 1**. Estrone was found closer to the anion species, especially just near the electronegative atoms having most negative partial charges in all the three cases. For instance,

tions which are visible from the proximity of the groups at the optimized structure, it can be seen that there is a substantial difference in the partial atomic charges of S(1.125e) and C(−0.394e) at one end followed by partial atomic charges 0.6e and −0.49e on the carbon-bearing fluoride and hydrogen atoms on [NTF2]<sup>−</sup> and

the vicinity of the bromine and fluoride is not justified by oppositely polarized moieties in estrone, however, also not indicative of an open-shell or covalent interaction as well simply because all the outer shell electrons of the atoms involved

[NTF2]<sup>−</sup> and estrone, apart from O▬H and F▬H interac-

[BF4]<sup>−</sup> and estrone,

**3.1 Optimized structures of the complex at the B3LYP/6-31G(d) level**

estrone, respectively. While in the other case such as [BMIM]<sup>+</sup>

[BF4]<sup>−</sup>, were constructed using

[PF6]<sup>−</sup>, and [BMIM]+

*DOI: http://dx.doi.org/10.5772/intechopen.86821*

tively termed as post-HF methods.

chemistry in conjunction with B3LYP.

[NTF2]<sup>−</sup>, [BMIM]+

properties at all bond critical points.

**3. Results and discussion**

in the case of [BMIM]+

[BMIM]+

intermediate.

**2.2 Computational details and methodology**

none of them were restricted under optimization.

*DFT Study on Interaction of Estrone and Imidazolium-Based Hydrophobic Ionic Liquids DOI: http://dx.doi.org/10.5772/intechopen.86821*

of electrons in the molecule and, hence, can be used as an input for the method of higher accuracy, such as the configuration interaction method, which are collectively termed as post-HF methods.

DFT methods used in the present scenario describe the changes in total energy of the system, via exchange and correlation of electrons and electrons and nuclei using hybrid functionals. These sets of mathematical functions utilize a subset of exact exchange from HF, while the remaining uses predefined functions from each individual pure functional [11]. The most commonly used hybrid functional, obtained as a result of this implementation, is the B3LYP hybrid functional. As for the basis is concerned, standard 6-31G(d) basis set is invoked though higher accurate ECP sets are available [12] simply due to the fact that various literature studies in ionic liquids akin to that of ours have obtained better results using this model chemistry in conjunction with B3LYP.

### **2.2 Computational details and methodology**

*Advances in Quantum Communication and Information*

et al. [5] presents a theoretical study of quantum mechanical continuum solvation models which is developed to overcome computational costs which attribute via explicit introduction of solvent molecules over the solute phase. Multiple articles have been presented using hydrophobic ionic liquids and DES for extraction of potential endocrine descriptors such as diethylstilbestrol, bisphenol-A, and dichlorodiphenyltrichloroethane (DDT) [6]. However, less emphasis is shed toward compounds such as estrone and other estrogen-based endocrine-disrupting compounds, in general. Ab initio-based quantum chemistry methods attempt to solve the Schrödinger

equation to extract intricate details such as electron distribution, underlying molecular interaction, as well as reactivity in a proposed virtual environment. Recent advancements in computational facilities have paved way to run these simulations in a much faster means and have also enabled theoretical chemists to solve a range of problems in disciplines ranging from spectroscopy [7] to solvent extraction [8]. In this work, we use ab initio calculations using benchmarked computational procedures to study the interacting behavior of estrone and ionic liquids such as

[PF6]<sup>−</sup>, and [BMIM]+

a primer for understanding the affinity of estrone so as to theoretically validate if the solvent is a potential extractor when commercially employed in standard liquid-

Density functional theory (DFT) is one of the most commonly employed methods to solve Schrödinger's equation by proposing a few justifiable approximations. In contradiction to the wave function methods used earlier, this method is the perfect adaptation for solving large systems involving a huge network of atoms and molecules. Since many rudimentary terms are overlapping in both the methods, the most primitive Hartree-Fock (HF) theory is used to explain the terms in a more

The energy computed from this method will take into account the potential energy of electrons and nuclei based on the relative positions with respect to each other as well as the average kinetic energy of electrons in every orbital. Assuming Born-Oppenheimer approximation, the relative velocity of nuclei is considered insignificant and so does its contribution in the kinetic energy of the system. The columbic interaction of electrons with respect to each other is brought about by assuming a mean field wherein each electron interacts with the averaged field of all

Kohn and Sham's work, in particular, attracted many researchers working in the field of DFT as they attempted to use the standard self-consistent field method to obtain the exchange-correlation energies as well apart from the basic Columbian energies obtained from HF theory [9]. Therefore, owing to their contribution, DFT is also colloquially referred to as Kohn-Sham (KS) formalism. Perdew et al. [10] proposed the advancements in the field of DFT functionals to that of a ladder, where every step leads to a better approximation and, hence, accuracy. The drawback of DFT method is that it can be used only for ground state computations as well as does not, by itself, reveal a detailed picture of electronic distribution owing to which, the optimized structure may not show any key resemblance when compared with other higher accurate methods. However, HF assumes linear combination of atomic orbital (LCAO) which helps to elucidate primitive picture

[BF4]<sup>−</sup>. This study is meant to be

**96**

[BMIM]+

[NTF2]<sup>−</sup>, [BMIM]+

**2.1 Overview of computational quantum chemistry**

liquid extraction procedures.

**2. Computational section**

elegant manner.

the other electrons.

The interacting monomers, namely, estrone and each of the three ionic liquids [BMIM]+ [NTF2]<sup>−</sup>, [BMIM]+ [PF6]<sup>−</sup>, and [BMIM]+ [BF4]<sup>−</sup>, were constructed using Gaussview6 [13] and were optimized separately at the B3LYP/6-31G(d) level using Gaussian16 program [14] to find the corresponding geometry and energy at the ground state. Since all the bonding parameters of the monomers are unknown, none of them were restricted under optimization.

The estrone is then introduced selectively to various regions in the vicinity of the ionic liquid such as near the electropositive and electronegative moieties, the imidazolium ring, and the cation and anion groups of ionic liquid to search for all possible interaction sites of the EDC. All these optimized systems can be visualized as various minima in the potential energy surface (PES), and only the properties and structure corresponding to the global minimum are presented for discussion.

The absence of imaginary frequencies at all optimized ground states justified that the proposed geometry is a minimum in the PES and not a transition state (TS) intermediate.

The keyword "output = wfn" is invoked along with the default settings to create. wfn extension file which is then used in multiwfn package to calculate topological properties at all bond critical points.
