Gas-phase electronic properties of tri-cationic imidazolium-based ionic liquids in comparison with mono- and di-cationic ionic liquids

Journal of Molecular Graphics and Modelling 96 (2020) 107529

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Gas-phase electronic properties of tri-cationic imidazolium-based ionic liquids in comparison with mono- and di-cationic ionic liquids Azim Soltanabadi a, *, Maryam Bahrami b a b

Department of Physical Chemistry, Faculty of Chemistry, Razi University, Kermanshahm, Iran Department of Chemistry, Shiraz University, Shiraz, 71946, Iran

a r t i c l e i n f o

a b s t r a c t

Article history: Received 7 September 2019 Received in revised form 28 December 2019 Accepted 28 December 2019 Available online 30 December 2019

The optimized geometries, electronic structures, and gas-phase properties of widely applicable nonlinear trigeminal tri-cationic ILs (TT-X3) were investigated using density functional theory (DFT) calculations and compared with mono- (M-X) and di-cationic (D-X2) ionic liquids. The studied ILs are based on the imidazolium cation containing halide (X) anions, where X ¼ Cl, Br and I. Inter-molecular hydrogen bonds were studied by atoms in molecules (AIM) and natural bond orbital (NBO) analyses. Accordingly the most significant cation-anion charge transfer is related to C1eH1 … X (X ¼ Cl, Br, I) interaction which strongly occurs in TT-X3 ILs and especially in TT-Cl3. Among ILs under investigation, TT-Cl3 has the strongest cation-anion interaction. Also M  I IL has the largest and D-Cl2 has the smallest electrical dipole moment. © 2019 Elsevier Inc. All rights reserved.

Keywords: Mono-cationic di-cationic Non-linear trigeminal tri-cationic ILs DFT NBO analysis Interaction energy HOMO-LUMO energy gap Dipole moment Charge density

1. Introduction Ionic liquids (ILs) are salts that are liquid at room temperature. They have many applications in the laboratory and industry. They are powerful solvents and electrically conducting fluids (electrolytes). Most ionic liquids are composed of only one imidazolium or pyridinium cation with different anions. Different properties of ionic liquids can be changed by modifying their cations and the substitution of cation and anion. Di-cationic ionic liquids (DILs) [1] are a new family of ILs which consist of a doubly charged cation that is composed of two separately charged cations linked by an alkyl chain (also called a spacer) and paired with two individually charged anions. It has been found that the di-cationic ILs possess a wider liquid range and higher thermal stability compared to the traditional mono cationic ILs [2e5]. DILs are applied as stationary phases for gas chromatography [6e9], solvents for hightemperature organic reactions [10], high-temperature lubricants

* Corresponding author. E-mail addresses: [email protected] (A. Soltanabadi), maryam.bahrami@ shirazu.ac.ir (M. Bahrami). https://doi.org/10.1016/j.jmgm.2019.107529 1093-3263/© 2019 Elsevier Inc. All rights reserved.

[11e13], electrolytes in secondary batteries [14,15], and dyesensitized solar cells [16e18]. Due to the variation of the anion and cation, the properties of di-cationic ILs can be made to compare with those of mono ionic liquids. Tri-cationic ionic liquids (TTILs) are a special class of ILs. They are made of three imidazolium or pyridinium cations linked to each other linearly or triangularly. Trigeminal tri-cationic ionic liquids (TTILs) are a particular class of ILs with extensive applications in the laboratory and industry. TILs have trigonal or linear geometry. They are thermally highly stable, and their liquid temperature range is more than about 300  C [19,20]. TTILs have been used in all areas of separation science, including extractions, gas and liquid chromatography, and supported liquid membranes [21e24]. They have also shown excellent performance as ion-pairing reagents for the ultra-trace detection of anions [25] and in electrowetting applications [19]. To date, most theoretical researches in the field of ILs are related to monocationic ionic liquids (MILs) and to some extent, to di-cationic ionic liquids (DILs) [26,27]. As far as we know, there are two simulation studies on the linear tri-cationic ionic liquids [28,29]. Moosavi et al. [28] applied the MD simulations to determine the dynamic properties of TTILs. The effects of temperature and alkyl chain length on the physiochemical, transport, and structural

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properties of LTILs have been investigated by Moosavi et al. using density functional theory (DFT) and also classical molecular dynamics simulation (MDS). They studied some unusual properties such as viscosities and melting points of LTILs. Tri-cationic ionic liquids can be used as electrolytes in the electrochemical processes and devices [30]. In most practical electrolyte applications, the relative contributions of the charged species to the transfer of the total charge are also significant. Unlike mono cationic ionic liquids, in di-cationic ILs, the transfer number of the anion is more considerable than the cation, which makes these materials (di-cationic ILs) perform well as electrolytes, and anions have a large share in the diffusion of electric current. Therefore, by studying the interactions of anion and cation in tri-cationic ionic liquids, it is possible to use certain specific anions with better efficiency for the design of the electrolytic cells. To the best of our knowledge, no research has been performed on the electronic structure and geometry optimization of the trigonal tri-cationic ionic liquids. In this work, we have chosen non-linear trigeminal tri-cationic imidazolium-based ILs combined with the halide anions (Cl, Br, and I) to study their gas-phase electronic properties using quantum chemical calculations in the framework of density functional theory (DFT) and ab initio methods. The comparison was made with the mono- and di-cationic ILs. The electronic structure, cation-anion interaction energy, HOMO-LUMO energy gap, and partial atomic charges are investigated. The natural bond orbital (NBO) and AIM analysis have also been employed to study the H-bonding in the studied mono cationic ionic liquids (MILs), di-cationic ionic liquids (DILs) and non-linear trigeminal tri-cationic ionic liquids (TILs). 2. Computational method The quantum chemical calculations were used to predict the equilibrium geometry of MILþ, DILþ2, and TT3þ cations. In this regard, the initial structures of each cation, established with the molecular mechanics, were used as the input for full optimization with the density functional theory (DFT) method. The geometry optimizations were performed at the B3LYP/6-31þþG(d,p) [31,32] level for all atoms, and DGDZVP [33] for the iodine atom. Due to large atomic number of iodine atom, 6-31þþG (d,p) basis set is found to be incapable of predicting accurate structure and vibrational spectrum of ILs containing iodine (I⁻) anion [33e35]. Grimme-D3 dispersion corrections performed in all DFT calculations [36]. The optimized structure of the MILþ, DILþ2 and TT3þ in the gas phase are shown in Fig. 1. To determine the final structures of these ionic liquids containing the halide anions, we put the studied halides (Cl, Br and I) in different positions of the MILþ, DILþ2 and TT3þ and optimized them at B3LYP/6-31þþG(d,p)-DGDZVP level, where 6-31þþG(d,p) basis set was used for C, N, O, H, Cl, Br atoms and DGDZVP for I atom. The interaction energies (DEint)), enthalpy   (DH int) and Gibbs free energy (DG int) of the ion pairs can be defined by equation (1): 

DF



int

¼F 

a-c-





F a- F

(1)

c 



Where F int denotes internal energy (E ), enthalpy (H ) and Gibbs     free energy (G ). The symbols F a-c, F a, and F c stand for the ionpair (ion-triplet), the purely anionic and the cationic species, respectively. The zero-point vibrational energy corrections (ZPE) were considered within the harmonic approximation. The basis set superposition error (BSSE) [37] was corrected using the counterpoise method. The ion-pair interactions were calculated for all the optimized structures at the same level of theory and basis set. All

calculations were carried out using the Gaussian 09 program [38]. The optimized structures of cation, anion and ion pair were verified as local minima by the absence of imaginary vibrational frequencies. The natural bond orbital (NBO) [39] and atoms in molecules (AIM) analyses were also carried out to better clarify the nature of the intermolecular H-bonding interactions in the MILs, DILs and TTILs. Both methods have been widely and successfully used to study hydrogen bonding in various systems [39]. For the NBO analysis, the orbital interactions between the proton donor and proton acceptor can be estimated through the second-order perturbation theory. For the AIM analysis [40], the nature of the H-bonding interaction can be predicted from the topological parameters, such as the electron density, Laplacian of electron density and the bond critical point (BCP). For each donor NBO(i) and acceptor NBO(j), the stabilization energy E(2) associated with the delocalization of the electron pair from the donor orbital (i) to the acceptor orbital (j) is estimated as:

Eð2Þ ¼ DEij ¼

qi Fði; jÞ2 εi  εj

(2)

where qi is the donor orbital occupancy, εi and εj are the diagonal elements of the orbital energies and Fði; jÞ is the interaction element between the donor and acceptor orbitals known as the diagonal NBO Fock matrix element. In this case, the electronic wave function is interpreted in terms of a set of occupied Lewis and a set of unoccupied non-Lewis localized orbital and the delocalization effects can be identified utilizing off-diagonal elements of the Fock matrix. The forces of these delocalization interactions, E(2) (kcal/mol), are estimated by the second-order perturbation theory. E(2) term corresponding to these interactions can also be the total charge transfer energy in the molecule. Atoms in molecules (AIM) analyses were calculated by AIM2000 to provide the topological properties [41,42].

3. Results and discussion 3.1. Geometry optimization Fig. 1 shows the optimized structures of MILþ, DILþ2, and TT3þ. In the cation MILþ, the imidazolium ring is a planar. The alkyl chain is directed to the top of the imidazolium ring. In other words, the dihedral angle between the imidazolium ring and the alkyl chain is 90 . In the DILþ2, two imidazolium rings are positioned so that they have the maximum distance from each other and the cis conformer is more durable than the trans conformer (molecular symmetry may cause the cis conformer to be more stable than the trans conformer). In the cation TT3þ, the three rings are positioned so that they have the maximum distance from each other. Table S1, S2 and S3 reports some important optimized parameters of MILþ, DILþ2, and TT3þ. The NBO analyses of MILþ, DILþ2 and TT3þ cations are shown in Table S4 in supporting information. Accordingly, the oxygen atoms are the most negatively charged. Also, the net atomic charge of the methyl imidazolium connected by the oxygen atoms is more than one. For this reason, the rings are located so that they have the maximum distance from each other. The steric hindrance and positive charges loaded on the rings causes the three rings to have the maximum distance from each other.

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Fig. 1. Structures of (a) mono-, (b) di- and (c) tri-cationic cations of ILs optimized at B3LYP/6-31þþG(d,p) level of theory.

3.2. Thermodynamic interaction of M-X, D-X2 and TT-X3 ILs 

Table 1 reports the calculated internal energy (DU int), enthalpy   (DH int) and Gibbs free energy (DG ) of the M-X, D-X2, and TT-X3 ILs. As can be seen from Table 1, the interaction (internal) energy is in the order TT-X3 > D-X2 > M-X IL. Due to the strong columbic interactions between the anions and cations, these energies are too much negative. Also, the thermodynamic interactions of TT-X3 ILs are more than three times of their corresponding mono-cationic ILs.    For example, for the M  Cl, DU int, DH int and DG int are 398.04, 401.11 and 366.44 kJ/mol, respectively while for    TT-Cl3, DU int, DH int and DG int are 1858.38, 1870.79 and 1749.02 kJ/mol, respectively. Moreover, in our previous work

Table 1 Thermodynamic interaction energies (kJ/mol) of cationeanion species at B3LYP/631þþG(d,p)-DGDZVP level of theory (6-31þþG(d,p) basis set for C, N, O, H, Cl, Br atoms and DGDZVP basis set for I atom) with Grimme-D3 dispersion corrections. 

ILs

DU

TT-Cl3 TT-Br3 TT-I3 D-Cl2 D-Br2 D-I2 M-Cl M-Br M-I

1858.38 1794.61 1671.87 1064.21 1026.02 946.20 398.04 378.25 336.94

int/kJmol

1





DH /kJmol1

DG /kJmol1

1870.79 1986.83 1717.33 1071.30 1142.78 975.60 401.11 414.83 347.69

1749.02 1853.97 1600.48 993.92 1058.73 896.23 366.44 378.26 318.43

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[27], for the C6(mim)Cl, DU int, DH int and DG int are 376.26, 378.74 and 351.97 kJ/mol, respectively. Bending two rings toward each other and placing a halide in the middle of the rings caused more interactions between halides and other atoms. Fig. S2 shows the optimized structures of the MILþ, DILþ2 and TT3þ cations with different halide anions of Cl, Br and I. As can be seen in M-X ILs, the halogen atom is located near the H1 and H7 atom. Therefore, the halide, H1, N1 and H7 atoms are on the same plane. In other words, the dihedral angle between these atoms (halide, H1, N1, and H7) is almost zero. Also, by increasing the atomic weight of the halide, halide-H1 distance increases. In the D-X2 IL, two of the rings bend toward each other and two halides are placed in the middle of the two rings. Bending the two rings toward each other and placing the halides between the rings, cause the halide anions to interact more with other atoms. In the TT-X3, two of the rings bend toward each other and two halides are placed in the middle of the two rings. The third ring is positioned so that the distance from the other rings is maximized. Some essential distances, angles and dihedral angles for M-X, D-X2 and TT-X3 ILs are listed in Tables S1, S2 and S3. Accordingly, the optimized bond lengths for MILþ, M-X, DILþ2, D-X2,TT3þ and TT-X3 ILs are not significantly different except for the bond lengths of C1eH1 for mono-cationic ILs; C1eH1 and Cʹ1-Hʹ1 for di-cationic ILs; C1eH1, Cʹ1Hʹ1, and Cʹʹ1-Hʹʹ1 for TT-X3 ILs. The most significant change observed for the C1eH1 bond in the TT-Cl3 decreased from 1.093 Å in TT-Cl3 to 1.089 Å in TT-I3. The angels between the imidazolium rings did not change dramatically (<1 ). Also, the dihedral angles between the imidazolium rings did not change significantly. However, the dihedral angles in the chain connecting the imidazolium rings may vary more than 30 . 3.3. NBO analysis The Natural bond orbital (NBO) analysis was performed to evaluate the charge distribution and the bonding properties. NBO analysis reveals that the most significant charge transfer between cation and anion is related to C1eH1 … X (X ¼ Cl, Br, I) interaction. Calculated values of stabilization energies, E(2) (kcal/mol), for all ILs are tabulated in Table 2. The E(2) values indicate the intensity of the interaction between the electron donor and acceptor orbitals. The higher the value of E(2), the more electrons tend to transfer from donor orbitals to acceptor orbitals. The order of E(2) for C1eH1 … X is TT-X3 > M-X > D-X2 (see Table 2). In each series of ILs, C1eH1/Cl

has the largest and C1eH1/I has the smallest E(2) value. We have also calculated total E(2) for cation-anion interaction, E(2)tot, (see Table 2). The order of E(2)tot is TT-X3 > D-X2 > M-X. In TT-X3 ILs series, TT-Br3 has the largest and TT-I3 has the smallest E(2)tot values, Whereas in M-X and D-X2 ILs the order of E(2)tot is M  Cl, D-Cl2 > M  Br, D-Br2 > M  I, D-I2 which is in good agreement with literature data [43]. The most significant E(2)tot for TT-Br3 ILs is likely due to the different stable molecular geometry and packing of bromide anions. This has already been reported in literature [43e45]. Also, Table 3 show that the donoreacceptor NBO charges on anions of mono-, di- and tri-cationic ILs. From this table, it can be seen that the chlorine atom has the most negative charge. From data presented in Tables 2 and 3, it is evident that NBO charge transfer from halide anion to imidazolium cation is maximum in

Table 3 Donoreacceptor NBO charges on anions of mono-, di- and tri-cationic ILs. ILs

NBO charge on X (anion)

TT-Cl3 TT-Br3 TT-I3 D-Cl2 D-Br2 D-I2 M-Cl M-Br M-I

Cl ¼ 0.88115, Clʹ ¼ 0.87737, Clʹʹ ¼ 0.85743 Br ¼ 0.85972, Brʹ ¼ 0.86714, Brʹʹ ¼ 0.84329 I ¼ 0.87661, Iʹ ¼ 0.87744, Iʹʹ ¼ 0.85745 Cl ¼ 0.88180, Clʹ ¼ 0.88167 Br ¼ 0.87587, Brʹ ¼ 0.87708 I ¼ 0.89348, Iʹ ¼ 0.88752 Cl ¼ 0.83623 Br ¼ 0.82859 I ¼ 0.84473

Table 4 Optimized distance (Å), bond and dihedral angles (degree) for H1 … X, Hʹ1 … X and Hʹʹ1 … X, (X ¼ Cl, Br, and I) in TT-X3 ILs at B3LYP/6-31þþG(d,p)-DGDZVP level of theory (6-31þþG(d,p) basis set for C, N, O, H, Cl, Br atoms and DGDZVP basis set for I atom) with Grimme-D3 dispersion corrections. R, A, and D denote distance, angle, and dihedral angle.

R (C1eH1 … X) A (C1eH1 … X) D (N1eC1eH1 … X) R (Cʹ1-Hʹ1 … X) A (Cʹ1-Hʹ1 … X) D (N1-Cʹ1-Hʹ1 … X) R (Cʹʹ1-Hʹʹ1 … X) A (Cʹʹ1-Hʹʹ1 … X) D (Nʹʹ1-Cʹʹ1-Hʹʹ1 … X)

TT-Cl3

TT-Br3

TT-I3

2.265 149.0 173.6 2.300 151.5 0.47 2.192 164.6 120.9

2.423 149.6 169.1 2.420 152.4 8.4 2.388 157.9 30.5

2.723 149.9 170.34 2.737 152.1 4.3 2.616 162.5 130.8

Table 2 Some significant donoreacceptor NBO interactions in different ILs along with their second order stabilization energies. ILs TT-Cl3

TT-Br3

TT-I3

D-Cl2 D-Br2 D-I2 M-Cl M-Br M-I

Donor (i) LP LP LP LP LP LP LP LP LP LP LP LP LP LP LP LP LP LP

(4) (4) (4) (4) (4) (4) (4) (4) (4) (4) (4) (4) (4) (4) (4) (4) (4) (4)

Cl Cl’ Cl" Br Br’ Br" I I0 I00 Cl Cl’ Br Br’ I I0 Cl Br I

BD*(1) BD*(1) BD*(1) BD*(1) BD*(1) BD*(1) BD*(1) BD*(1) BD*(1) BD*(1) BD*(1) BD*(1) BD*(1) BD*(1) BD*(1) BD*(1) BD*(1) BD*(1)

C1 e H1 C0 1 e H0 1 C00 1 e H00 1 C1 e H1 C0 1 e H0 1 C00 1 e H00 1 C1 e H1 C0 1 e H0 1 C00 1 e H00 1 C1 e H1 C0 1 e H0 1 C1 e H1 C0 1 e H0 1 C1 e H1 C0 1 e H0 1 C1 e H1 C1 e H1 C1 e H1

Acceptor (j)

E(2)/kcalmol1

E(j)-E(i) a.u.

F(i,j) a.u.

qCT

13.06 20.66 15.52 13.41 15.87 13.90 8.77 15.68 11.17 14.90 14.98 10.10 13.65 8.62 11.59 36.04 29.16 19.37

0.73 0.72 0.72 0.72 0.71 0.71 0.68 0.68 0.67 0.70 0.70 0.69 0.69 0.65 0.66 0.66 0.65 0.62

0.087 0.109 0.095 0.088 0.095 0.089 0.069 0.092 0.077 0.091 0.092 0.075 0.087 0.067 0.078 0.139 0.123 0.098

0.029 0.046 0.034 0.030 0.036 0.031 0.021 0.037 0.027 0.034 0.034 0.023 0.032 0.021 0.028 0.087 0.071 0.050

109.46

118.57

91.54

65.52 65.3 47.32 51.01 49.11 30.37

E(2)tot/kcalmol1

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Table 5 Some important AIM analysis of TT-Cl3, TT-Br3 and TT-I3 ILs at B3LYP/6-31þþG(d,p)-DGDZVP level of theory (6-31þþG(d,p) basis set for C, N, O, H, Cl, Br atoms and DGDZVP basis set for I atom) with Grimme-D3 dispersion corrections. TT-Cl3

r(R) BCP

V2 rðRÞ

TT-Br3

r(R) BCP

V2 rðRÞ

TT-I3

r(R) BCP

V2 rðRÞ

CleH1 CleH4 Cl-Hʹʹ3 Cl-Hʹʹ7 Clʹ-Hʹ1 Clʹ-Hʹʹ7 Clʹ-Hc2 Clʹ-Hʹʹ4 Clʹ-H7 Clʹʹ-Hʹʹ1 Clʹʹ-Hc3 Clʹʹ-Hʹ4

0.0244 0.0160 0.0177 0.0138 0.0225 0.0139 0.0125 0.0103 0.0086 0.0275 0.0114 0.0111

0.0588 0.0440 0.0500 0.0416 0.0560 0.0400 0.0360 0.0344 0.0292 0.0640 0.0352 0.0364

BreH1 BreH4 Br-Hʹʹ3 Br-Hʹʹ7 Brʹ-Hʹ1 Brʹ-Hʹ7 Brʹ-Hc2 Brʹ-Hʹʹ4 Brʹ-H7 Brʹʹ-Hʹʹ1 Brʹʹ-Hc3 Brʹʹ-Hʹ4

0.0214 0.0155 0.0182 0.0131 0.0213 0.0134 0.0120 0.0113 0.0094 0.0224 0.0121 0.0120

0.0480 0.0402 0.0468 0.0368 0.0493 0.0348 0.0330 0.0332 0.0296 0.0512 0.0340 0.0348

IeH1 IeH4 I-Hʹʹ3 I-Hʹʹ7 Iʹ-Hʹ1 Iʹ-Hʹ7 Iʹ-Hc2 Iʹ-Hʹʹ4 Iʹ-H7 Iʹʹ-Hʹʹ1 Iʹʹ-Hc3 Iʹʹ-Hʹʹ4

0.0165 0.0135 00000 0.0119 0.0159 0.0125 0.0100 0.0085 0.0072 0.0195 0.0106 0.0050

0.0324 0.0303 0.0000 0.0280 0.0323 0.0280 0.0236 0.0224 0.0208 0.0360 0.0240 0.0132

bromide derivatives. Table 6 Calculated dipole moments (m0 in Debye) of mono-, di- and tri-cationic ILs at B3LYP/ 6-31þþG(d,p)-DGDZVP level of theory (6-31þþG(d,p) basis set for C, N, O, H, Cl, Br atoms and DGDZVP basis set for I atom) with Grimme-D3 dispersion corrections. TT ILs

m0 /Debye

DILs

m0 /Debye

M ILs

m0 /Debye

TT-Cl3 TT-Br3 TT-I3

8.67 8.90 11.17

D-Cl2 D-Br2 D-I2

0.70 2.13 1.44

M-Cl M-Br M-I

11.78 12.33 12.63

3.4. H-bonding interaction Hydrogen bonding (H-bonding) plays an important role in the formation of cationeanion pairs of ionic liquids in the gas phase and effectively determines ILs properties. When an H-bond is formed, the bond distance is less than the sum of the van der Waals radii of H and halide atoms ½RCl/H  2:81
A; RBr/H  2:91
A; RI/H  3:04
A (threshold

Fig. 2. Calculated dipole moment vector of mono-, di- and tri-cationic ILs obtained at B3LYP/6-31þþG(d,p)-DGDZVP level of theory (6-31þþG(d,p) basis set for C, N, O, H, Cl, Br atoms and DGDZVP basis set for I atom) with Grimme-D3 dispersion corrections.

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Fig. 3. MEP plots of the optimized mono-, di- and tri-cationic ILs calculated at B3LYP/6-31þþG(d,p)-DGDZVP level of theory (6-31þþG(d,p) basis set for C, N, O, H, Cl, Br atoms and DGDZVP basis set for I atom) with Grimme-D3 dispersion corrections.

distance)] x and the angle between them is greater than 90 . The distances of H-bonding interactions can be seen in Fig. S2 and the bond lengths, bond angles and dihedral angles are reported in Table 4. According to Table 4 and Fig. S2, we conclude that each halide can form a strong H-bond with H1, Hʹ1, Hʹʹ1 atoms and some week H-bond with other hydrogens. 3.4.1. AIM analysis The theory of AIM has been applied theoretically to a wide variety of structures containing different types of hydrogen interactions, ranging from hydrogen bonds to van der Waals interactions. The interactions can be successfully investigated using topological properties of electron density distribution r(R) which were analyzed by AIM2000. The AIM analysis was used to have a better insight into the hydrogen bonding. The existence of the intermolecular H-bonds was further confirmed by the location of the corresponding bond critical points (BCP). The BCPs and bond paths for halide and hydrogen from AIM calculations are shown in Fig. S3. According to the aim theory, an hydrogen bond is formed when the electron density at BCP and the Laplacian of the electron density V2r(R) must be within the 0.002e0.035 and 0.024e0.139 ranges (in atomic units), respectively [46]. The AIM results for various pairs in the gas phase are shown in Fig. S3 and Table 5. As can be seen, for the X … H

Table 7 Energies of HOMO and LUMO, HOMO-LUMO energy gap (Egap), chemical hardness (h), chemical potential (m) and electrophilicity (u) of all ILs calculated at B3LYP/631þþG(d,p)-DGDZVP level of theory (6-31þþG(d,p) basis set for C, N, O, H, Cl, Br atoms and DGDZVP basis set for I atom) with Grimme-D3 dispersion corrections. ILs

EHOMO/eV

ELUMO/eV

Egap/eV

h/eV

m/eV

u/eV

TT-Cl3 TT-Br3 TT-I3 D-Cl2 D-Br2 D-I2 M-Cl M-Br M-I

5.76 5.41 5.15 5.89 5.51 5.23 5.41 5.17 4.87

0.99 1.09 1.35 1.10 1.05 1.27 1.27 1.37 1.49

4.77 4.33 3.81 4.80 4.46 3.96 4.15 3.80 3.38

2.38 2.16 1.90 2.40 2.23 1.98 2.07 1.90 1.69

3.37 3.25 3.25 3.49 3.28 3.25 3.34 3.27 3.18

2.39 2.44 2.77 2.55 2.42 2.66 2.69 2.81 3.00

bonds in all pairs, BCP, and the Laplacian of the electron densities are in the range 0.005e0.024 and 0.013e0.058, respectively. Therefore, an H- bonding is formed for all XeH in the gas phase. Also, r(R) in the bond of halide with the H1 atom is higher than in the other atoms and decreases with increasing halide atomic weight. According to this theory, it can be concluded that interaction of halide and H1 is stronger than halide and other atoms, and this interaction decreases with increasing atomic weight of halide. This result can be compared with the range of 0.002e0.0274

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recommended by Kuch and Popley [47].

3.4.2. Electric dipole moment It is well known that the electric dipole moment (m0) of a molecule is an important parameter which characterizes its response to a polar medium. Also, the m0 is a useful concept in dielectrics and other applications in solid and liquid materials. Thus, it is of great importance to study the electric dipole moments of TTHalides ILs. The calculated values of m0 (in Debye) for all studied ionic liquids (see Table 6 and also Fig. 2 for calculated dipole moment vector of ILs), show that the electric dipole moments of TT-X3 ILs are considerably higher than those of similar di-cationic ILs. Furthermore, the values of m0 increase as I > Br > Cl for di-cationic ILs. Dipole moments can indicate to what extent some structures will interact with some other molecules through electrostatic interactions. The large dipole moment of one structure can induce the charge separation in other molecules, so electrostatic interactions occur. Besides, large dipole moments can also indicate excellent adsorption properties towards CO2 molecules, for which various ILs turn out to have significant potential Namely, the dipole moment of TT-Cl3 is 8.67D, while dipole moment of TT-I3 is 11.17D, which indicate severely different reactive properties when it comes to the interaction with water. As a result of the medium electric dipole moment and high dipolar bonds of TT-X3 ILs, these kinds of ionic liquids can be used both as polar and non-polar compounds.

7

3.5. Charge density calculations Molecular electrostatic potential (MEP) plots of TTILs, which reveal the charge distribution within the ILs, are shown in Fig. 3. All the plots are formed by mapping the electrostatic potential of the systems onto their constant electron density surface (isovalue ¼ 0.0004). The different values of the electrostatic potential (ESP) at the surface are represented by different colors. Red parts of the surface refer to the sites for electrophilic reactions with negative ESP, blue parts represent nucleophilic sites with positive ESP and the green parts correspond to zero ESP, i.e., the neutral portions of the surface. Accordingly, the anion atoms are the most electrophilic sites. By increasing the anion size, the electrophilicity of the anionic sites in TTILs decreases.

3.6. Frontier molecular orbitals The molecular orbital theory is a powerful theoretical tool for the investigation of stability and reactivity of molecules. Several quantities such as HOMO-LUMO gap (Egap), global (or chemical) hardness (h), chemical potential (m) and electrophilicity (u) can be calculated within this framework, which are known as the global quantum molecular descriptors [48]:

Fig. 4. Topology of HOMO orbitals of mono-, di- and tri-cationic ILs calculated at B3LYP/6-31þþG(d,p) level of theory with Grimme-D3 dispersion corrections.

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4. Conclusions

h¼

ðELUMO  EHOMO Þ 2

m¼ 

u¼

ðEHOMO þ ELUMO Þ 2

m2 2h

(3)

(4)

(5)

The calculated values of the highest occupied molecular orbital (HOMO) energies, the lowest unoccupied molecular orbital (LUMO) energies and the gap between them for all the studied TT-ILs are reported in Table 7. Also, the calculated values of chemical hardness (h), chemical potential (m) and electrophilicity (u) are listed in Table 7. Accordingly, the energy gap (EHOMO-ELUMO) decreases in the order TT-Cl3 > TT-Br3 > TT-I3. Furthermore, we know that the spatial distribution of the HOMO and the LUMO molecular orbitals are important in describing the electrical properties of ILs. Thus, the spatial distribution of the HOMO and the LUMO orbitals are visualized in Figs. 4 and 5. The HOMO is the non-bonding orbital which is localized on the halide ion (due to the presence of the lone pair electron) while the LUMO is anti-bonding in nature (p*) and is mainly localized on the imidazolium ring. The HOMO represents the ability to donate an electron and the LUMO represents the ability to obtain an electron (as an electron acceptor). Therefore, the charge transfer can be occurred from the HOMO of halide anion to the LUMO of imidazolium cation in all studied TT-X3 ILs.

In this work, we calculated gas-phase electronic structures and properties of trigeminal tri-cationic ILs (TTILs) with halide anions (Cl, Br, I) and compared with mono- (MIL) and di-cationic ILs (DILs) in the framework of density functional theory (DFT) calculations. B3LYP exchange-correlation functional with 6e31þþg(d,p) and DGDZVP (for iodine atom) basis sets was used for geometrical optimizations and calculation of various properties. In all three types of ILs, the cation-anion interaction weakened by increasing the anion size. The cation-anion interaction energies of ILs are in the order TT-X3 > D-X2 > M-X. Global reactivity was assessed using molecular orbital theory and quantum molecular descriptors. By increasing the anion size, the calculated HOMO-LUMO energy gap decreases in all three ILs types; the D-X2 ILs shows the highest energy gap and the M-X ILs shows the lowest energy gap. Accordingly, the calculated chemical hardness has the trend D-X2 > TT-X3 > M-X, and decreases by increasing the anion size. TT-X3 > D-X2 > M-X is the obtained trend for the chemical potential and decreases by increasing the anion size. The observed trend for the electrophilicity of ILs is M-X > TTX3 > D-X2 and increases by increasing the anion size. The calculated gas-phase electric dipole moment increases by increasing the anion size in all three types of ILs, found in the order M-X > TT-X3 > D-X2. Molecular electrostatic potential (MEP) surfaces were created in order to elucidate the charge distribution of the investigated ILs. From MEP analysis we found the following trend in charge density: M-X > TT-X3 >D-X2. Intermolecular hydrogen bonding analysis was performed using NBO and AIM calculations. According to NBO analysis and E(2)

Fig. 5. Topology of LUMO orbitals of mono-, di- and tri-cationic ILs calculated at B3LYP/6-31þþG(d,p) level of theory with Grimme-D3 dispersion corrections.

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values the most significant charge transfer between cation and anion is related to C1eH1 … X (X ¼ Cl, Br, I) interaction. The order of E(2) for C1eH1 … X is TT-X3 > M-X > D-X2. Also, in each series of ILs, C1eH1/Cl has the largest and C1eH1/I has the smallest E(2) values. The order of E(2)tot is TT-X3 > D-X2 > M-X. In TT-X3 and DX2 ILs series, bromide derivatives (TT-Br3 and D-Br2) have the largest and iodide derivatives (TT-I3 and D-I2) have the smallest E(2)tot values, whereas in M-X ILs the order of E(2)tot is M  Cl > M  Br > M-I. The largest E(2)tot for bromide derivatives of TT-X3 and D-X2 ILs is likely due to the different stable molecular geometry and packing of bromides. Due to the low duplex momentum and bending of the rings, it is possible to use three-cationic ionic liquids in cell building or as suitable solvent for non-polar materials. Also, due to the presence of three anions, three-cationic ionic liquids can be used as a dielectric in aqueous solutions, and the results show that the chlorine atom is less effective than bromine.

[14]

[15]

[16]

[17]

[18]

[19]

Declaration of competing interest

[20]

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

[21] [22]

Acknowledgements [23]

Authors are indebted to the research council of Razi University for the financial supports. Computer time provided by High Performance Computing research laboratory of Institute for Research in Fundamental Sciences (IPM) is greatly acknowledged.

[24]

[25]

Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.jmgm.2019.107529.

[26]

[27]

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