A density functional theory study on the water aggregation behaviour of fatty acid-based anionic surface active ionic liquids

The hydrogen bond interactions between methyl-imidazolium cation (MIM+) and fatty acid anions (CmHnCOO–, where m = 1–6; n-3–13) of ionic liquids are studied in both gas phase and water phase using density functional theory. The structural properties show that the presence of N–H···O and C–H···O hydrogen bonds between [MIM]+ and [CmHnCOO]– (m = 1–6; n-3–13) ionic liquids. From the vibrational frequency analysis, it was found that the hydrogen bond interaction between [MIM]+ and [CmHnCOO]– (m = 1–6; n-3–13) ionic liquids are red-shifted in frequency. The natural bond orbital analysis show that the N–H···O hydrogen bond associated with the large charge transfer which has the higher stabilization energy (i.e. E(2) ~ 38 kcal/mol). Further, the cation/anion–water cluster (H2O)1–3 interactions show that the water molecules are preferred to interact with anions. In the case of ionic liquid–water cluster interaction, the water molecules occupies the interstitial space between cation and anion of ionic liquids which results in weakening the cation–anion interaction.

The presence of hydrogen bond (H bond) between cation and anion of ILs plays a vital role in the behaviour of ILs [44][45][46][47][48]. In general, the H bond is denoted as X-H···Y interaction in which X (usually, C, N and O) and Y (usually, N and O) are strong electronegative atoms. It was found that the cations are the active H bond donors and anions are the active H bond acceptors. Based on the strength of the H bond, the ILs are divided into two types: (i) protic ILs and (ii) aprotic ILs. In protic ILs, H bond is formed by proton transfer from a Brønsted acid to a Brønsted base; whereas in aprotic ILs, the cationic C-H unit is the major H bond donor unit [48]. Since ILs have large numbers of cations and anions, the H bonding in ILs is highly system dependent. Unlike the H bonding in traditional neutral system, the H bonding present in the ILs has different interesting behaviours.
Nowadays, the water aggregation or micellization properties of SAILs are actively studied by both experimental and theoretical studies [38,49,50]. Experimentally, surface tension, conductivity, steady state fluorescence spectra, viscosity and dynamic light scattering measurements are used to determine the water aggregation properties of SAILs. Theoretically, density functional theory (DFT) is used to study the water aggregation properties of SAILs. Mostly, the studies are performed on water aggregation properties of imidazolium cations with sulfonate anions of SAILs [39,51]. It promoted us to study the water aggregation properties of SAILS. Here, we have studied the water aggregation properties of the methyl-imidazolium cation with six fatty acid anion of SAILs with different water molecules (1-3) using DFT. This study will be useful to understand the interactions of cation-water, anion-water, cation-anion and ionic liquid-water towards the water aggregation properties of SAILs.

Computational details
The hybrid M06-2X density functional [52] along with 6-311++G (d,p) basis set [53] is used to optimize the structures of methyl-imidazolium cation [MIM] + , fatty acidbased anions [C m H n COO] -(where m = 1-6; n = 3-13) and ILs [MIM + -C m H n COO -] (m = 1-6; n = 3-13) and ILs with water molecules (H 2 O) x (where x = 1-3) respectively. The solvent effects on the stability of ILs are examined through self-consistent reaction field (SCRF) using polarizable continuum model (PCM) in water [54,55]. Vibrational frequency analysis used to found the global minimum structures with no imaginary frequency values. The strength of H bond between cation and anion of ILs is studied by atoms in molecule (AIM) analysis using the MORPHY98 program package [56,57]. Further, the natural bond orbital (NBO) analysis is used to understand the charge transfer between ILs [58]. All of the above calculations are performed with Gaussian09 Rev. A.02 package [59].

Structures of [MIM] + cation and [C m H n COO]anions
The optimized structures of methyl-imidazolium cation [MIM] + and fatty acid anions [C m H n COO] -(where m = 1-6; n = 3-13) are shown in Fig. 1. In the case of [MIM] + cation, a three-center (N1-C2-N3) four-electron ∏ system is observed [60]. The bond lengths of N1 = C2 and C2 = N3 are predicted to be 1.327 and 1.333 Å and the bond lengths of N3-C4 and C5-N is to be 1.376 and 1.381 Å respectively, while for C4 = C5, it is of 1.357 Å. From the NBO charge analysis, it is found that the negative charge is located on the    [1][2][3] . Figure 4 shows the optimized structures of interactions between fatty acid anion with different water molecules (H 2 O) 1  . In this study, four different interaction sites are considered (site i) C2-N3, (site ii) N3-C4, (site iii) N3 and (site iv) N1-C2 (Figs. 5 and S1-S3). Further, the optimized structures of ion pairs in water phase and ion pair without proton transfer is shown in Figs. S4 and S5. Among that, the C2-N3 site of MIM + cation is the preferred site for the interaction of fatty acid anions (Fig. 5). From the NBO natural charge analysis, it is evident that the C2 atom in the

Structures of ILs-water cluster interactions
The optimized structures of cation-anion of ILs are further investigated for the water aggregation property with different numbers of water molecules (H 2 O n , n = 1-3). The optimized structures of ILs with water molecules are shown in Figs. 6, 7, and 8 respectively. From Figs. 6, 7, and 8, we found that the water molecules preferentially interact with ILs via C2 site of [MIM] + cation and COOregion of fatty acid anions. The addition of water molecules to the ILs occupies the interstitial part of cation-anion which further weakened the interaction between cation-anion. Previous study also mentioned that the introduction of water molecules reduced the interaction of cation and anion of ILs [48]. Both

Vibrational frequency analysis
The strength of interaction between cation and anions in ILs can be identified by infrared (IR) spectra analysis. The frequency analysis of X-H···Y H bond is important to characterize their nature, whether the X-H bonds are proper or improper i.e. red-shifted or blue-shifted. The H bond formation leads to increase in the X-H bond length because

Interaction energy
One of the advantages of theoretical methods is that the calculation of interaction energy of ILs which plays a vital role in understanding the structure-energetic properties of ILs. The basis set superposition error (BSSE)-corrected [67] interaction energy using the counterpoise method of Boys and Bernardi [68] can be calculated as the difference between the energy of a total system E AB (example, Cation-Anion of ILs and ILs-Water) and the energy of isolated systems E A and E B (example, cation, anion, water).
In this study, the BSSE-corrected interaction energy between cation-water, anion-water, cation-anion and ILs-water are calculated and shown in Figs. 9-11. The total E int = E AB − E A + nE B + BSSE interaction energy ranges from −1 to −140 kcal/mol for the systems considered in this study. In the case of cation-water and anion-water interactions, the total interaction energy is increased by the addition of 1 to 3 water molecules. Especially, the total interaction energy is large in the anion-water interaction than the cation-water interaction which infers that the water molecules prefer to interact with the anion systems (i.e. [C m H n COO] -(m = 1-6; n = 3-13)) ( Fig. 9). In general, the fatty acid anion with carboxyl functional group (COO -) is preferred interaction site for the water molecules.  Table 2. From Table 2, it is found that the changes in enthalpy corresponds to ILs-Water interaction are negative (i.e. ΔH < 0) which indicates the above interaction is an exothermic in nature. The changes in Gibbs' free energies corresponding to the interactions of

AIM analysis
To investigate about the nature of H bond in the selected ILs, we employ the electron density-based topological parameter within the framework of Bader's quantum theory of atoms in molecule (QTAIM) using MORPHY 98 program [56,57]. The QTAIM method examines the topology of electron density ρ(r) (in a.u.), Laplacian of electron density ∇ 2 ρ(r) (in a.u.) at bond critical point (BCP) and Hessian (H BCP = G BCP + V BCP ) values and based on the above values the strength of the H bond can be identified. In general, if the both ∇ 2 ρ(r) and H BCP values are positive then the H bond is weak interaction and if ∇ 2 ρ(r) is positive and H BCP is negative then the H bond is strong. Also, the H BCP > 0 indicates the electrostatic interaction and the  Table 1. From Table 1

NBO analysis
The H bond formation is associate with certain amount of charge is transferred from the proton acceptor to the proton donor molecule [48]. The NBO analysis is used to understand the charge transfer corresponds to the H bond formation. In a system with X-H···Y H bond interaction, the charge transfer takes place between the lone pair of proton acceptor/electron donor (Y) to the anti-bonding orbital σ* (X-H) of proton donor/ electron acceptor. The stabilization energy E (2) corresponds to Y(LP) σ* (X-H) H bond can calculated by E (2) j) is the off-diagonal or coupling NBO fock matrix element, and E i and E j are the diagonal elements. In this study, the calculated occupation number of donor and acceptor of ions and  Table 3 preferentially interact with fatty acid-based anions rather than methyl-imidazolium cation. Further, the ILs-water molecule interactions show that the addition of water molecule reduces the interaction between methyl-imidazolium cation and fatty acid-based anions of ILs. The AIM and NBO analysis also confirms the presence of one strong (N-H···O) and one weak (C-H···O) H bond interactions between methyl-imidazolium cation and fatty acid-based anions of ILs. The stabilization energy E (2) corresponding to the proton transfer process (i.e. N-H···O interaction) is calculated as 36.98-38.51 kcal/mol.

Author contribution The authors Suresh Sampathkumar and Vijayakumar
Subramaniam have contributed to the development of this manuscript and the associated research work and deserve authorship.

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