Computational and Theoretical Chemistry 1037 (2014) 70–79

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Computational and Theoretical Chemistry

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Aggregated ion pairs of [MIM+][N(CN)2�]2 ionic liquid: A quantum

chemical study in solvents with different dielectric constants

http://dx.doi.org/10.1016/j.comptc.2014.03.0352210-271X/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author. Fax: +98 131 3233262.E-mail addresses: hrouhi@gmail.com, hroohi@guilan.ac.ir (H. Roohi).

Hossein Roohi ⇑, Shiva KhyrkhahDepartment of Chemistry, Faculty of Science, University of Guilan, Rasht, Iran

a r t i c l e i n f o

Article history:Received 11 November 2013Received in revised form 21 March 2014Accepted 31 March 2014Available online 13 April 2014

Keywords:Aggregation[MIM+][N(CN)2

�] ILGibbs free energySolvation energyEffect of temperature

a b s t r a c t

The aggregated ion pairs of [MIM+][N(CN)2�] ionic liquid have been studied using MP2, B3LYP, M05-2X

and M06-2X methods in conjunction with the 6-311++G(2d,2p) basis set. Five aggregated ion pairs (2-IP1-5) were characterized on the potential energy surface of interaction of two cations with two anions.The geometrical parameters, Gibbs free energy of formation in gas and solution phases (DG� and DGsln�)and solvation Gibbs free energy were calculated for aggregates of [MIM+][N(CN)2

�]. The range of DG� was3.3 to �10.4 kcal/mol at MP2/6-311++G(2d,2p) level of theory. The DG� value first significantly decreaseswith increasing solvent dielectric constant and then changes smoothly when the dielectric constantbecomes greater than 20.0. The results of the temperature dependence of DG� revealed that the tendencyfor aggregation decreases as the temperature increases. Frequency analysis showed a significant red-shiftin the N–H stretching vibrational wave number of 2-IP1 and 2-IP2 aggregates. Population analysis showsthat the charge transfer (CT) taking place from anion N(CN)2

� to cation MIM+ upon complex formation.� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Ionic liquids (ILs) are usually composed of organic cations andinorganic anions with melting points below 100 �C [1]. They haverecently attracted much interest due to some of their unique prop-erties such as non-volatility, high ionic conductivity, no flammabil-ity, high thermal stability and wide electrochemical window [2–6].Due to their unusual properties, attention of a growing number ofengineers and scientists has been focused on different applicationsof ILs, as shown by the increasing number of published papers inrecent years [7–11].

Some of scientists have shown that ionic liquids can be aggre-gated in aqueous and non aqueous solutions [12]. The aggregationbehaviors of such surface-active ILs have attracted the most atten-tion in the colloid and interface fields; numerous aggregates formedby the surface-active ILs have been investigated over the past years[13]. The aggregation characteristics of ILs based on 1-alkyl (butylto hexadecyl)-3-methylimidazolium in water have been exten-sively studied by using various experimental methods such as sur-face tension, electrical conductivity, fluorescence, H NMR, steadystate fluorescence spectroscopy and isothermal titration calorime-try [14]. There is a relationship between molecular structural

features and micro-structural characteristics of aggregated ILs inaqueous solutions that is always an interesting and an importantsubject area of the investigation in the discipline of colloid andinterface science [14].

Many electrochemical applications of ionic liquids (ILs) dependon ionic conductivities [15–17] which can be changed by theiraggregation. The long-chain imidazolium and pyridinium basedionic liquids consist of charged hydrophilic head group and hydro-phobic tails possess an inherent amphiphilic nature. Therefore, itcan be anticipated that these compounds will exhibit an interfacialand aggregation behavior analogous to that displayed by conven-tional cationic surfactants. Thus, the ability to form self-assembledstructures may have consequences in a variety of areas such as theextractions of products from IL-containing systems, the synthesisand purification of bulk ILs, the solvation properties of the ILs mol-ecules, the formation of dispersed or phase-separated systems,[18]. Evans et al. reported the aggregation behavior of alkyl tri-methyl ammonium bromides, alkyl pyridinium bromides ionic liq-uids [19]. The later attention in this field has been rather focusedon imidazolium based ILs which are composed of 1-alkyl-3-methylimidazolium cation and appropriate anion [20]. Wang et al. [21]studied the aggregation behavior of [BMIM]BF4 and [CnMIM]Br(n = 4, 6, 8, 10 and 12) in aqueous solutions by conductivity mea-surement. Several researchers have demonstrated that some typesof aggregation occur in aqueous solutions of ILs, especially in thecase of imidazolium based ones [22–31].

H. Roohi, S. Khyrkhah / Computational and Theoretical Chemistry 1037 (2014) 70–79 71

As reported, ionic clusters formed by various ions can reflect thearrangement of ions in the bulk phase of ILs [32,33]. These ionicclusters may become microscopic models to describe the struc-tures of the bulk ILs [34,35]. Although, as mentioned above, exper-imental methods have provided a lot of information about theaggregation characteristics of ILs, it is still a great challenge tounderstand the behaviors of these ILs at molecular levels. Recently,Kirchner [36] reviewed the theoretical investigations of ionic liq-uids. In this review, three main categories such as static quantumchemical calculations (electronic structure methods) traditionalmolecular dynamics simulations and first-principles moleculardynamics simulations were discussed. Among all of these reportedmethods, quantum chemistry calculations are receiving more andmore attentions due to its advantage in producing electric struc-ture, anion–cation binding energy, orbital property, and so on. Tothe best of our knowledge, investigation of the physicochemicalproperties of 2-IP aggregated forms of MIM+N(CN)2

� has not beenreported, although such knowledge is of great importance to itsfuture applications. The main aim of this work is to find the clus-ters formed from interaction between 2MIM+ and 2 N(CN)2

� ions,calculation of binding energy, geometrical parameters and topo-logical properties, Gibbs free energy in the different mediumsand characterization of the nature of intermolecular interactionsin the [MIM+]2[N(CN)2

�]2 complex.

2. Computational details

All the structures studied in this work were fully optimizedusing B3LYP [37,38], MP2 [39], M05-2X [40] and M06-2X [41]methods with 6-311++G(2d,2p) basis set [42]. Vibrational frequen-cies calculated using DFT methods have been used to characterizethe stationary points, calculation of zero-point vibrational energy(ZPVE) and thermochemical quantities. The counterpoise proce-dure (CP) [43] was used to correct for basis set superposition error(BSSE) in the calculation of binding energies with all of availablemethods. All calculations were performed using the Gaussian pro-gram package [44]. Solvent effect on conformational stability wasexamined using the polarizable continuum model (PCM) [45] atM05-2X/6-311++G(2d,2p) level. The PCM model creates the solutecavity via a set of overlapping spheres. It was initially devised byTomasi [45] and coworkers and Pascual-Ahuir and coworkers[46]. The standard Gibbs free energy change for solvation of thesolute species M in solvent S (DG�solv) can be separated into:DG�solv = DG�el + DG�noel. The electrostatic contribution DG�el toDG�solv results from the electrostatic interactions between the sol-ute and solvent and can be found from an SCRF calculation [47].The non-electrostatic contribution can be split into DGnoel =DGcav + DGdis + DGrep + DGmm where they are cavitation,dispersion, repulsion and molecular motion contributions to non-electrostatic energy, respectively. The Gibbs free energy changesin gas phase (DG�g) at each temperature were obtained using thedifference between the sum of electronic and thermal free energiesof products and reactants in which were obtained by frequencycalculations. The Gibbs free energy of formation of the aggregatesin solution (DG�sln) was calculated according to the equationDG�sln = DDG�solv + DG�g, where DDG�solv = DG�solv,2-IP � (2DG�1-IP).

3. Results and discussion

In this work, clusters formed by interaction two cations withtwo anions of [MIM+][N(CN)2

�] ionic liquid were modeled. The opti-mized structures of aggregates were illustrated in Fig. 1. As can beseen, anions in five modeled aggregates lie between two cations sothat four hydrogen bonds are formed between terminal nitrogenatoms of the anions and N–H as well as C–H bonds of the cations.

In all aggregates, N–H and C–H bonds of IM rings are involved inhydrogen bonds having different strength, which leads to slightlydifferent intermolecular distances. In clusters 2-IP1-3 and 2-IP5,two C–H and two N–H bonds of IM rings operate as proton donorsand N atoms of two N(CN)2

� anions act as proton acceptors. In 2-IP4, one N–H and three C–H bonds of IM rings are proton donors.2-IP1 and 2-IP2 have C2h and C2v symmetry, respectively. The basicdifference between the two structures arises from the arrangementof the Me groups (anti in 2-IP1 and syn in 2-IP2). The directions ofN–H and C–H bonds of the IM rings in 2-IP1 and 2-IP2 are also dif-ferent. The orientations of the two N–H bonds of the IM rings in 2-IP2 are the same whereas in 2-IP1 are opposite. Each of the anionsin 2-IP1 and 2-IP3 is involved in two NH� � �N and CH� � �N H-bond-ing whereas one anion in 2-IP2 and 2-IP5 participates in twoNH� � �N H-bonding interactions and the other one participates intwo CH� � �N interactions.

3.1. Aggregation energy

The energy changes to form modeled aggregates were calcu-lated by the following equation:

1-IPþ 1-IP ! 2-IP; DE ¼ E2-IP � ð2E1-IPÞ

where EIP and E2-IP are the energy of the ion pair and aggregatespecies, respectively. The calculated formation energy of 1-IP([MIM+][N(CN)2

�]) and the aggregation energies of 2-IP1-5 are givenin Table 1. The Gibbs free energy change, DG�, to form 1-IP at roomtemperature is �79.4 kcal/mol at B3LYP/6-311++G(2d,2p) level,�81.9 kcal/mol at M05-2X/6-311++G(2d,2p), �81.8 kcal/mol atM06-2X/6-311++G(2d,2p) and �80.1 kcal/mol at MP2/6-311++G(2d,2p) level of theory. It is clear that a large negative DG�favors products of reaction. Therefore, 1-IP is favored over free ionsin gas phase.

The BSSE corrected Gibbs free energies of aggregation (DG�BSSE)range from �4.5 to �17.8 kcal/mol at B3LYP/6-311++G(2d,2p), 0.5to �12.5 kcal/mol at M05-2X/6-311++G(2d,2p), 2.4 to �13.6 kcal/mol at M06-2X/6-311++G(2d,2p) and 3.3 to �10.4 kcal/mol atMP2/6-311++G(2d,2p) level of theory. These values show that thesum of the energies of two separated 1-IP species on the potentialenergy surface is close to the energy of 2-IP cluster. The compari-son of DG� of 1-IP with 2-IP1-5 reflects that the formation of 1-IPis favored over 2-IP aggregates in the gas phase.

A comparison of DG� obtained at various levels of theory revealsthat the B3LYP values are bigger than MP2, M05-2X and M06-2Xones. Among the DFT methods, M06-2X and M05-2X energies aresmaller than B3LYP method and are near to MP2 ones, indicatingthat the aggregation energies calculated by M06-2X and M05-2Xmethods are in good agreement with MP2 one. Therefore, MP2and new DFT methods M06-2X and M05-2X give the better andmore reliable results than B3LYP method.

It is possible to estimate the relative stability of aggregatedforms of [MIM+][N(CN)2

�] ionic liquid (2-IPs) by using the DG� val-ues. It is predicted that the 2-IP1 and 2-IP5 are the most and leaststable aggregates at all levels of theory, respectively. Between fiveoptimized structures, greatest DG� value belongs to the 2-IP1. Thissuperiority is due to interaction of N atoms of N(CN)2

� with moreacidic hydrogens bonded with two nitrogens and two carbons onIM rings. One of the H-bonding interactions between cations andanions in 2-IP3 and 2-IP4 and two of them in 2-IP5 occurs throughthe less acidic C4–H bond. Thus, it is expected that the DG� forthese aggregated structures to be smaller than 2-IP1 and 2-IP2.The relative stability order predicted by all present methods afterBSSE correction is: 2-IP1 > 2-IP2 > 2-IP3 > 2-IP4 > 2-IP5. DG� of2-IP2 is close to that of 2-IP1. Thus, most stable aggregates pre-dicted at all levels of theory are 2-IP1 and 2-IP2.

2-IP1 2-IP2

2-IP3 2-IP4

2-IP51-IP

Fig. 1. The optimized structures of aggregated ion pairs (2-IP1-5) at MP2/6-311++G(2d,2p) level of theory.

72 H. Roohi, S. Khyrkhah / Computational and Theoretical Chemistry 1037 (2014) 70–79

The values of DG� at M05-2X/6-311++G(2d,2p) level of theoryfor 2-IP1 (�10.4 kcal mol�1) and 2-IP2 (�12.5 kcal mol�1) arecomparable with standard Gibbs free energy of aggregationreported by Wang et al. [48] for [C8mim][CH3COO] (�5.1 kcal mol�1), [C8mim]Cl (�5.4), [C8mim]Br (�5.6 kcal mol�1),[C8mim][NO3] (�6.0 kcal mol�1), [C8mim][CF3COO] (�6.5 kcal mol�1), 4m-[C8Pyr]Br (�5.9 kcal mol�1), [C8mpyrr]Br (�5.2 kcal mol�1).

3.2. Effect of temperature on the stability of aggregates

The interesting properties of ILs are governed by the type andstrength of interaction between its constituents. It has been shownthat hydrogen bonds play a dominant role in the aggregation of ILsin addition to Coulombic and hydrophobic interactions [21,49].Melting point is an important property of ILs which defineswhether or not it is a room-temperature IL. Besides, it reflectsthe molecular packing and the strength of the intermolecular inter-action between monomers. Therefore, there is a correlationbetween interaction energy and physical properties of ILs. Theresults reported in literature [50–52] show that the melting pointof ILs increases as the BE increases.

To predict the temperature dependence of the Gibbs free energyof aggregation, we have calculated aggregation energies at differ-ent temperatures. Fig. 2 plots DG� versus T for 1-IP + 1-IP ? 2-IP

process. As can be seen, there exists a linear correlation betweenaggregation energy of the 2-IP1-5 and temperature. An increasein temperature is accompanied by a decrease in absolute value ofaggregation energy. The aggregation energy is a measure of melt-ing tendency of ILs. Thus, tendency for aggregation decreases asthe temperature increases. However, the steepness of the slopemeans that the change in DG�-versus-T will be quite small. Becauseof small slope, prediction of temperature in which aggregationdose not occur is difficult.

3.3. Effect of solvent on aggregation

It is a well known fact that the ILs were often used in the pres-ence of different solvents. Also considering the fact that number ofthe ion pairs can be decreased obviously as the polarity of solventincreases or concentration of IL reduces [53–55], it is necessary toinvestigate the effect of different solvents on the physicochemicalproperties of 2-IP1-5 aggregates.

Binding energy (BE) of 2-IP1-5 aggregates in different solvents(BEsln = �DE) with the dielectric constants between 2.0 and 80.0was calculated at M05-2X/6-311++G(2d,2p) level of theory usingequation: DEsln = E2-IP,sln � 2E1-IP,sln. A comparison between elec-tronic BEs calculated in gas and solution phases revealed that theBE decreases on going from gas phase to solution phase. For exam-ple, BE of 2-IP1 in gas phase at M05-2X/6-311++G(2d,2p) level is

Table 1Aggregation energies (kcal/mol) calculated for 2-IP1-5 at various levels of theory. The Gibbs free energies of formation for 1-IP are given in parentheses.

Dimer Method Basis set BSSE DEeaDEe

BSSE bDE0cDE0

BSSE dDG�,BSSE

2-IP1 B3LYP 6-311++G(2d,2p) 0.8 �28.5 �27.3 �28.1 �27.2 �17.8 (�79.4)M05-2X 0.9 �25.2 �24.0 �25.1 �24.3 �10.4 (�81.9)M06-2X 0.9 �25.8 �24.7 �25.7 �24.9 �13.6 (�81.8)MP2 6.1 �26.4 �20.3 �26.0 �19.9 �10.4 (�80.1)

2-IP2 B3LYP 6-311++G(2d,2p) 0.8 �27.9 �26.8 �27.2 �26.4 �16.2M05-2X 0.9 �24.7 �49.8 �23.9 �23.1 �12.5M06-2X 0.9 �25.2 �24.0 �24.6 �18.6 �13.1MP2 6.1 �25.9 �19.8 �25.1 �19.0 �8.9

2-IP3 B3LYP 6-311++G(2d,2p) 0.8 �22.9 �21.9 �22.4 �21.7 �10.9M05-2X 0.8 �21.2 �20.1 �21.1 �20.3 �9.5M06-2X 0.8 �21.5 �20.4 �21.6 �20.7 �10.2MP2 6.6 �23.4 �17.0 �22.9 �16.3 �5.5

2-IP4 B3LYP 6-311++G(2d,2p) 0.8 �16.2 �15.1 �15.4 �14.6 �4.9M05-2X 0.8 �15.2 �14.1 �14.5 �13.6 0.5M06-2X 0.8 �15.6 �14.5 �15.2 �14.3 �1.5MP2 6.1 �16.0 �10.1 �15.2 �9.1 0.6

2-IP5 B3LYP 6-311++G(2d,2p) 0.8 �12.3 �11.4 �12.2 �11.4 �4.5M05-2X 0.8 �11.4 �10.4 �11.7 �11.0 �0.5M06-2X 0.8 �7.4 �6.4 �7.7 �6.9 2.4MP2 5.8 �9.6 �4.0 �9.4 �3.7 3.3

The zero point energy was included in the calculation of Gibbs free energy change.a DEe

BSSE = Electronic binding energy (DEe) + BSSE.b DE0 = DEe + DZPE.c DE0

BSSE = DE0 + BSSE.d DG�,BSSE = DG� + BSSE.

ΔGg/k

cal m

ol-1

T/K

2IP-1

2IP-2

2IP-3

2IP-4

2IP-5

Fig. 2. Correlation between DG�g and temperature for 2-IP1-5 at M05-2X/6-311++G(2d,2p) level of theory.

-BE

sln/k

cal m

ol-1

Dielectric constant (ε)

Fig. 3. The correlation between BEsln of 2-IP1-5 and dielectric constant (e).

H. Roohi, S. Khyrkhah / Computational and Theoretical Chemistry 1037 (2014) 70–79 73

�25.2 kcal/mol that reduces to �6.8 kcal/mol in water. In the sol-vent with the smallest dielectric constant (benzene, e = 2.27), theBE is �15.4 kcal/mol that is 60.1% of BE in gas phase.

Fig. 3 shows correlation between electronic BEsln and dielectricconstant (e). As can be seen, BEsln significantly decreases with e andchanges smoothly when the dielectric constant is larger than 20.0.Thus, association of ions to from the aggregates decreases withincrease in polarity of solvent. Consequently, it is reasonable toimage that the solvent with high dielectric constants will havemuch strong ability to influence the aggregation of IL.

As mentioned above, BE decreases with the increasing dielectricconstant. The reported experimental results indicate that ion asso-ciation of ILs reduces as the dielectric constant or concentration ofwater increases due to the solvent cage effect so that there isapproximately no ion pairs in IL-water solutions when the con-tents of water is 80% [56]. Besides, it has been found that ion pairformation was strongly promoted by dilution of the ILs in chloro-form [57]. There is a question that why the tendency of ionstoward the aggregation reduces as the polarity of solvent increases.

In general, solvation of solutes increases as the polarity of solventincreases. Correlation between dielectric constants and the solva-tion energies of cation, anion, most stable 1-IP and 2-IP1 calcu-lated according to the equation: Esolv = Esln � Eg are shown inFig. 4. As can be seen, solvation energies of all species are negativeand their values reduces by increase in e values. However, Esolv of1-IP and 2-IP1 is smaller than those of separated ions. For example,Esolv for cation, anion, 2-IP1 and 1-IP is �62.0, �53.4, �29.9 and�24.5 kcal/mol, respectively. Hence, stability of separated ions inthe presence of solvent is greater than aggregated forms of IL. Asa result, the strength of interactions between the anions and cat-ions reduces in the environments with greater dielectric constants.

The Gibbs free energy of solvation and the Gibbs free energy offormation of the 2-IP aggregates in various solvents (S) were calcu-lated at M05-2X/6-311++G(2d,2p) level of theory. Tables 2 and S1(supplementary data) show the Gibbs free energy of solvation(DG�solv), electrostatic DG�ele and non-electrostatic DG�noel contribu-tions to the DG�solv, change in Gibbs free energy of solvationDDG�solv, Gibbs free energy of formation of the 2-IP aggregates ingas (DG�g), solution (DG�s ln) media and dipole moments (l) ingas and solution phases.

ESo

lv./k

cal m

ol-1

Dielectric constant (ε)

Fig. 4. Correlation between dielectric constant and the solvation energy of cation,anion, 1-IP and 2-IP1 (Esolv) at M05-2X/6-311++G(2d,2p) level of theory.

74 H. Roohi, S. Khyrkhah / Computational and Theoretical Chemistry 1037 (2014) 70–79

Inspection of these results shows that DG�noel values are nearlyidentical for all aggregates in the same solvent and DG�ele is mainlyresponsible for the changes of relative energy of 2-IP aggregates.For all aggregates in water, DG�noel is greater and positive unlikeanother solvents that have negative and small DG�noel. The orderof DG�solv values in the all solvents is: 2-IP5 > 2-IP4 > 2-IP3 > 2-IP1 � 2-IP2. Since Gibbs free energy of formation in gas phase for2-IP1 and 2-IP2 aggregates is greater than others, it is expectedthat degree of solvation to be smaller than less stable aggregatesin gas phase. The value of DG�solv is a measure of strength of

Table 2The electrostatic, DG�el, and non-electrostatic, DG�nonel, contributions to the Gibbs free eneenergy of formation of the aggregated ion pairs in gas, DG�g, and solution, DG�sln, and dipolenergies are in kcal/mol and dipole moments in Debye (D).

Complex Solvent DG�el DG�nonel DG�solv

2-IP1 Water �33.9 20.1 �13.92-IP2 �33.7 19.7 �13.92-IP3 �37.0 18.8 �18.22-IP4 �41.2 18.8 �22.42-IP5 �53.1 20.1 �33.01-IP �27.3 9.4 �17.9

2-IP1 DMSO �33.6 �8.5 �42.02-IP2 �33.3 �8.0 �41.22-IP3 �36.6 �6.9 �43.42-IP4 �40.7 �6.6 �47.32-IP5 �52.5 �7.5 �60.01-IP �27.0 �2.3 �29.3

2-IP1 Acetonitrile �33.3 �10.8 �44.02-IP2 �33.0 �10.3 �43.32-IP3 �36.2 �9.2 �45.42-IP4 �40.4 �8.9 �49.32-IP5 �52.0 �9.9 �62.01-IP �26.8 �3.6 �30.4

2-IP1 Acetone �32.4 �12.3 �44.72-IP2 �32.1 �11.9 �44.02-IP3 �35.9 �11.0 �46.82-IP4 �39.3 �10.4 �49.62-IP5 �50.5 �11.6 �62.11-IP �26.0 �4.4 �30.4

2-IP1 Ethanol �32.7 1.2 �31.62-IP2 �32.4 1.5 �30.92-IP3 �35.6 1.9 �33.72-IP4 �39.7 2.0 �37.72-IP5 �51.1 1.8 �49.31-IP �26.3 1.4 �24.9

2-IP1 Dichloroethane �30.2 �12.4 �42.62-IP2 �29.9 �12.0 �41.92-IP3 �32.8 �10.7 �43.62-IP4 �36.6 �10.4 �47.02-IP5 �47.0 �11.6 �58.61-IP �24.3 �4.3 �28.7

interaction between solute and solvent. Therefore, it is expectedthat DG�solv for polar solutes to be greater in polar solvents. Ascan be seen in Table 2, DG�solv values for all 2-IP aggregates aregreater than DG�g. The difference between DG�g and DG�solv isgreater in water than other solvents.

Also the Gibbs free energy of formation of the aggregates insolution (DG�sln) was calculated according to the equation:DG�sln = DDG�solv + DG�g, where DDG�solv = DG�solv,2-IP� (2DG�1-IP).As can be seen from Table 2, it is significant that the Gibbs freeenergy of aggregates (DG�sln) in the polar solvents is positive, indi-cating that the tendency for aggregation in these solventsdecreases compared with the gas phase. The results also show thatpositive value of DG�sln decreases as the polarity of solventdecreases. Consequently, tendency for aggregation and formationof 2-IP clusters increases as the polarity of solvent decreases.Fig. 5 shows the correlation between DG�sln and e. As can be seen,DG�sln decreases with increase in e and then in polar solventsbecomes constant.

3.4. Elucidation of potential energy curve (PEC)

We have also calculated separation profile for 2-IP1 cluster ingas and solution phases. The analysis of these profiles can providethe important information regarding the effect of various environ-ments on the separation of ions and charge distribution betweenthem. The potential energy scan in gas phase and different envi-ronments was performed at the B3LYP/6-311++G(2d,2p) level by

rgy of solvation, DG�solv, change in Gibbs free energy of solvation, DDG�solv, Gibbs freee moments in gas and solution phases at M05-2X/6-311++G(2d,2p) level of theory. All

DDG�solv DG�g DG�sol l (g) l (sln)

22.0 �10.4 11.6 0.0 0.021.9 �12.5 9.4 0.1 0.217.6 �9.5 8.1 3.7 4.313.5 0.5 14.0 2.4 3.6

2.9 �0.5 2.4 4.2 8.5

16.5 �10.4 6.1 0.0 0.017.3 �12.5 4.8 0.1 0.215.2 �9.5 5.7 3.7 4.311.3 0.5 11.8 2.4 3.6�1.4 �0.5 �1.9 4.2 8.5

16.8 �10.4 6.4 0.0 0.017.5 �12.5 5.0 0.1 0.215.4 �9.5 5.9 3.7 4.311.5 0.5 12.0 2.4 3.5�1.2 �0.5 �1.7 4.2 8.5

16.1 �10.4 5.7 0.0 0.016.9 �12.5 4.4 0.1 0.214.0 �9.5 4.5 3.7 4.311.2 0.5 11.7 2.4 3.5�1.3 �0.5 �1.8 4.2 8.4

18.3 �10.4 7.9 0.0 0.018.9 �12.5 6.4 0.1 0.216.1 �9.5 6.6 3.7 4.312.2 0.5 12.7 2.4 3.5

0.5 �0.5 0.0 4.2 8.4

14.8 �10.4 4.4 0.0 0.015.5 �12.5 3.0 0.1 0.213.8 �9.5 4.3 3.7 4.310.3 0.5 10.8 2.4 3.5�1.2 �0.5 �1.7 4.2 8.3

ΔGso

l /kc

al m

ol-1

Dielectric constant (ε)

Fig. 5. Correlation between DGsol and dielectric constant (e) for 1-IP and 2-IP1-5 atM05-2X/6-311++G(2d,2p) level of theory.

ΔGso

lv/k

cal m

ol-1

Distance/Å

water

acetonitrile

ethanol

Fig. 7. The variation of DG�solv against the distance between cations in threesolvents.

H. Roohi, S. Khyrkhah / Computational and Theoretical Chemistry 1037 (2014) 70–79 75

fixing C1–C1 distance between two cations of cluster and optimiz-ing the remaining degree of freedom in each step of the energyscan using a 0.1 decline (Fig. 6). As can be seen, energy of aggrega-tion in gas phase increases as the distance between cationsincreases. There is a significant difference between the behaviorof 2-IP1 in solution and gas phase. In the solvents with dielectricconstant 78.4, 35.7 and 24.9, energy of aggregation first decreasesto a minimum and then increases as the distance between cationsincreases. In other words, the presence of solvent facilitates theseparation of ions.

Fig. 7 shows the variation of DG�solv against the distancebetween cations (C1–C1). Inspection of Fig. 7 reveals that the abso-lute values of DG�solv increase when the structure of aggregate isdeformed upon extension.

Table 3Selected geometrical parameters (Å) for 1-IP and [MIM+][N(CN)2

�] aggregates at MP2/6-311++G(2d,2p) level of theory.

Bond 1-IP 2-IP1 2-IP2 2-IP3 2-IP4 2-IP5

C1–H10 1.074 1.079 1.081 1.073 1.080 1.073N2–H11 1.009 1.070 1.062 1.067 1.073 1.062

3.5. Structural parameters

The selected geometrical parameters including the bondlengths and bond angels of 2-IP aggregates in gas phase at MP2/6-311++G(2d,2p) level of theory are given in Table 3 and the restin Table S2. In each of five clusters, four N� � �H H-bonds existbetween two cations MIM+ and two anions N(CN)2

�. In general,intermolecular distances of N� � �HN hydrogen bonds are shorterthan N� � �HC ones. This emphasizes that the N� � �HN hydrogenbonds are stronger than the N� � �HC ones. In both aggregates 2-IP1 (C2h point group) and 2-IP2 (C2v point group) point group,two NH and two acidic CH bonds of cations are bonded to the

0.0

5.0

10.0

15.0

20.0

25.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.00 0.40 0.80 1.20 1.60 2.00 2.40 2.80

Rel

ativ

e E

nerg

y(g)

/kca

l mol

-1

Rel

ativ

e E

nerg

y(s)

/kca

l mol

-1

Distance/Å

water

acetonitrile

ethanol

gas

Fig. 6. The potential energy curves in gas phase and different environments using a0.1 decline at B3LYP/6-311++G(2d,2p) level.

nitrogen atoms of anions but directions of these groups are oppo-site to each other in these aggregates. In the most stable aggregates(2-IP1 and 2-IP2) these distances are smallest, in good agreementwith their greater BE. The N� � �HN distances in 2-IP1 and 2-IP2 arerespectively, 1.578 Å and 1.607 Å which are shorter than those ofN� � �HC distances in 2-IP1 (2.100 Å) and 2-IP2 (2.064 Å). TheN� � �HN H-bond distances in 2-IP1 are shorter than 2-IP2 whilethe N� � �HC distances are longer than 2-IP2. Thus, N� � �HN interac-tions in 2-IP1 are stronger than those of 2-IP2 and N� � �HC interac-tions are weaker than those of 2-IP2. In addition, CN groups ofanions in 2-IP1 complex can form two H-bonds (2.270 Å) withCH groups of the methyl. It seems that these additional H-bondscan play an important role in greater stability of 2-IP1 complex.

While in the 2-IP3 and 2-IP5 aggregates exist two N� � �HN andtwo N� � �HC H-bonds, in 2-IP4 exists three N� � �HC and one N� � �HCH-bonds. A striking feature of the 2-IP3 complex is that nitrogen ofCN groups can form H-bonds with C–H of methyl groups, in addi-tion of two N� � �HN and two N� � �HC H-bonds. In 2-IP5 complex,although two NH groups contribute in H-bonding, but acidic CHgroup (C1(19)–H) does not contribute in H-bonding. The mean

C3–H12 1.073 1.073 1.073 1.073 1.073 1.087C4–H13 1.074 1.073 1.073 1.072 1.073 1.074C15–N16 1.187 1.184 1.182 1.186 1.187 1.182C15–N14 1.318 1.298 1.302 1.300 1.307 1.302C17–N14 1.318 1.309 1.302 1.310 1.311 1.302C17–N18 1.187 1.184 1.182 1.185 1.186 1.182H29–N20 1.009 1.070 1.062 1.064 1.006 1.062C19–H28 1.074 1.079 1.081 1.079 1.089 1.073C22–H31 1.074 1.073 1.073 1.073 1.081 1.074C21–H30 1.073 1.073 1.073 1.073 1.072 1.087N36–C35 1.187 1.184 1.186 1.188 1.184 1.186C35–N32 1.318 1.298 1.306 1.297 1.312 1.309N32–C33 1.318 1.309 1.306 1.318 1.297 1.309N34–C33 1.187 1.184 1.186 1.185 1.185 1.186N16���H 1.578 1.607 1.588 2.092 1.611N18���H 2.100 1.607 2.081 1.901 1.611N34���H 2.100 2.064 2.348 1.566 1.953N36���H 1.578 2.064 1.604 2.065 1.953N16���HN(C) 179.2 179.5 168.7 147.4 172.1N18���HN(C) 145.6 179.5 147.2 161.8 172.1N34���HN(C) 145.6 145.9 147.6 147.6 165.1N36���HN(C) 179.2 145.9 175.2 153.4 165.1

Table 4NBO data calculated at MP2/6-311++G(2d,2p) level of theory.

N(CN)2� MIM+ 2-IP1 2-IP2

Natural charge (au)C1 0.409 0.399 0.400N2 �0.551 �0.594 �0.594H10 0.235 0.272 0.278H11 0.452 0.504 0.503C19 0.409 0.399 0.400N20 �0.551 �0.594 �0.594H28 0.235 0.272 0.278H29 0.452 0.504 0.503N14 �0.864 �0.817 �0.810C15 0.588 0.724 0.714N16 �0.656 �0.745 �0.726C17 0.588 0.661 0.714N18 �0.656 �0.714 �0.726N32 �0.864 �0.817 �0.825C33 0.588 0.661 0.670N34 �0.656 �0.714 �0.738C35 0.588 0.724 0.670N36 �0.656 �0.745 �0.738CT(anion ? cation) (au) 0.221 0.206Occupancy (au)r(N2–C1) 1.988 1.986 1.987p(N2–C1) 1.900 1.901r(H10–C1) 1.988 1.984 1.984r(H11–N2) 1.990 1.984 1.985r(N20–C19) 1.988 1.986 1.987p(N20–C19) 1.900 1.901r(H28–C19) 1.988 1.984 1.984r⁄(1)C1–H10 0.008 0.019 0.021r⁄(1)N2–H11 0.010 0.097 0.088r⁄(N20–H29) 0.010 0.097 0.088r⁄(H28–C19) 0.008 0.019 0.021r⁄(1)N14–C15 0.022 0.020 0.020r⁄(1)C15–N16 0.022 0.016 0.016r⁄(1)N14–C17 0.022 0.021 0.020r⁄(1)C17–N18 0.022 0.018 0.016r⁄(1)(N32–C33) 0.022 0.021 0.021r⁄(1)(C33–N34) 0.022 0.018 0.018r⁄(1)(C35–N32) 0.022 0.020 0.021r⁄(1)(C35–N36) 0.022 0.016 0.018E(2) (kcal mol�1)LP(1)N16 ? r⁄(1)N2–H11 67.5 59.8LP(1)N34 ? r⁄(1)C1–H10 6.1 7.2LP(1)N14 ? r⁄(1)C15–N16 12.1 7.9 8.0LP(1)N14 ? r⁄(1)C17–N18 12.1 9.9 8.0LP(1)N16 ? r⁄(1)N14–C15 16.1 11.4 11.7LP(1)N18 ? r⁄(1)N14–C17 16.2 14.4 11.7LP(1)N18 ? r⁄(1)C–H 6.1 59.8LP(1)N36 ? r⁄(1)N–H 67.5 7.2LP(1)N32 ? r⁄(1)C33–N34 12.1 9.9 9.8LP(1)N32 ? r⁄(1)C35–N36 12.1 7.9 9.8LP(1)N34 ? r⁄(1)N32–C33 16.1 14.4 14.3LP(1)N36 ? r⁄(1)N32–C35 16.2 11.4 14.3

76 H. Roohi, S. Khyrkhah / Computational and Theoretical Chemistry 1037 (2014) 70–79

N� � �HN H-bond distance value in 2-IP3 and 2-IP5 aggregatesequals 1.596 and 1.611 Å while mean value of N� � �HC bond dis-tance is 2.214 and 1.953 Å, respectively. In addition, CN groups ofanions in 2-IP3 can form two H-bonds (2.300 and 2.304 Å) withCH groups of methyl, so that these additional H-bonds can make2-IP3 complex more stable than 2-IP5 one. From three CH groupsparticipating in H-bonding in 2-IP4, two of them are acidic ones.The N� � �HN distance value in the 2-IP4 is 1.566 Å and mean valueof three N� � �HC bond distances is 2.019 Å.

As can be seen, mean value of H-bond distances in 2-IP5 com-plex is greater than that of 2-IP4 one, in good agreement withthe greater BE of 2-IP4 with respect to the 2-IP5.

In all 2-IP aggregates, N2-H11 bond of MIM+ is involved in thehydrogen bonds with differing strengths, which leads to slightlydifferent intermolecular distance. Each of the two N-H bonds(1.009 Å in MIM+) involved in H-bonding are elongated by 0.061and 0.053 Å upon formation of 2-IP1 and 2-IP2 aggregates, respec-tively. The change in C–H (1.074 in MIM+) bond length involved ininteractions for 2-IP1 and 2-IP2 is 0.005 and 0.007 Å, respectively.There is two additional H-bonding between CN group and CHgroup of Me in 2-IP1 and 2-IP2 aggregates. The C–H bond lengthof Me in MIM+ is 1.083 Å that was elongated to the 1.085 Å in bothaggregates. In 2-IP3 and 2-IP5 aggregates, N–H11(29) bonds werestretched by 0.058 (0.055 Å) and 0.053 (0.053 Å). The C–H13 bondin 2-IP3 was shortened by 0.002 Å, while C–H28 bond in the 2-IP3and C–H12(30) bonds in the 2-IP5 were stretched by 0.005 Å and0.014 (0.014 Å), respectively. In 2-IP4 complex, N–H11 and C–H11(31,28) bonds were stretched by 0.053 Å and 0.014 (0.007,0.015 Å), respectively. As can been seen, the number of H-bondsand the value of change in proton donor N–H and C–H bondlengths in most stable aggregates 2-IP1 and 2-IP2 is greater thanothers, in good agreement with the greater stability of theseaggregates.

Complex formation also change the structural parameters inN(CN)2

�. In general, CN bonds involved in H-bond interactionsand middle NC bonds are shortened upon complex formation.

The H-bond strength depends on its length and angle. Never-theless, small deviations from linearity in the bond angle havemarginal effect on H-bond strength. Due to the formation of cyclichydrogen bonds, the hydrogen-bond angles deviate from linearity.The N-H� � �N angle values are 179.2� and 179.5� and C-H� � �N anglevalues are 145.6� and 145.8� in 2-IP1 and 2-IP2 aggregates, respec-tively. In all of the aggregates, deviation from linearity for N-H� � �N16 angle is smaller than C-H� � �N18 one, in good agreementwith the greater change in NH bond length with respect to theCH ones upon complex formation.

We have also studied the effect of theoretical methods on thestructural parameters of aggregates. The structural parametersobtained at M06-2X/6-311++G(2d,2p) level are given as supple-mentary data (Table S3). As can be seen in Table S3, the M06-2Xfunctional as a DFT method overestimates the structural parame-ters with respect to the MP2 one. The N–H and C–H bond lengthvalues in 2-IP1 are 1.080 and 1.081 Å, respectively, that are greaterthan corresponding values calculated at MP2/6-311++G(2d,2p)level (1.070 and 1.079 Å). N-H� � �N and C-H� � �N H-bond distancevalues in 2-IP1 are 1.563 and 2.136 Å, respectively, which are big-ger than H-bond distances obtained at MP2/6-311++G(2d,2p) level(1.563 and 2.136 Å). The longer bond distance calculated by usingDFT method is due to the overestimation of electron–electronrepulsions [58].

3.6. Vibrational frequencies analysis

IR technique can be a direct probe for studying the strength ofinteraction between cations and anions in ionic liquids. The struc-tural changes induced by the formation of the H-bonding are often

accompanied by shifts in vibrational frequencies with respect tothe monomers. Because of the more stability of 2-IP1 and 2-IP2aggregates in the gas phase, hereinafter vibrational frequencies inthese aggregates are discussed.

The C–H and N–H groups in the imidazolium ring are character-istic groups interacting with anion. An increase in the strength ofthe hydrogen bond C(N)–H� � �N is accompanied by a lengtheningof the covalent bonds C(N)–H and a shortening of the hydrogenbonds C(N)–H� � �N. The weaker force constants for the C(N)–Hbonds lead to lower wave numbers and thus red-shifted vibra-tional bands. This was shown for the region in which the C(N)–Hstretch vibrations of imidazolium-based ionic liquids appear. Thescaling factor for the calculated frequencies is 0.955 [59]. The IRfrequency data for 2-IP1 and 2-IP2 complexes at M06-2X/6-311++G(2d,2p) level of theory are listed in Table S4. The bands cal-culated above 3050 cm�1 at M06-2X/6-311++G(2d,2p) level are

Fig. 8. Frontier molecular orbital (HOMO and LUMO) energy diagram of 2-IP1 and 2-IP2.

H. Roohi, S. Khyrkhah / Computational and Theoretical Chemistry 1037 (2014) 70–79 77

attributed to the C–H stretching vibrations on the imidazoliumring. The vibrational bands observed at 3096.1 cm�1 (2-IP1) and3068.4 cm�1 (2-IP2) can be assigned to the C–H stretching modesof cation, in good agreement with the experimental wave numberof 3104 cm�1 [60]. Red-shift in stretching vibrational wave numberof C–H bond involved in H-bonding is 53.3 cm�1 for 2-IP1 and81.0 cm�1 for 2-IP2 with respect to the corresponding free cationvibrational mode at 3149.4 cm�1. The red-shifted frequency valuesreflect the strength of H-bond interaction between MIM+ andN(CN)2

�. Thus, C–H� � �N interaction in 2-IP2 complex is strongerthan that of 2-IP1 one, in good agreement with the greater changeof C–H bond length upon formation of 2-IP2 with respect to the 2-IP1.

A significant red-shift is observed in the N–H stretching vibra-tional wave number. The red-shifts of N–H stretching vibrationalwave number of MIM+ involved in N� � �H–N interaction upon for-mation of 2-IP1 and 2-IP2 aggregates at the M06-2X/6-311++G(2d,2p) level are 1129.6 cm�1 for 2-IP1 and 990.6 cm�1

for 2-IP2 with respect to the corresponding free cation vibrationalmode at 3478.9 cm�1, indicating N� � �H–N interaction in 2-IP1 clus-ter is stronger than that of 2-IP2 one. These dramatic red shifts forN–H stretching vibrational wave number as one of the most signif-icant features of results obtained reflect the strength of H-bondinteraction between MIM+ and N(CN)2

�.

3.7. Natural bond orbital (NBO) analysis

The formation of a hydrogen bond implies that a certain amountof electronic charge is transferred from the proton acceptor to theproton donor molecule [61,62]. The results of NBO analysis includ-ing charge transfer energy, natural charge, charge transfer valueand the occupancy of NBOs in the 2-IP1-2 clusters at MP2/6-311++G(2d,2p) level of theory are given in Table 4. Here, the chargetransfer has been defined as the difference between sum of atomiccharges on complexed and isolated N(CN)2

� anions. The NBO resultsshow that the LP(N) ? r⁄(N(C)–H) donor acceptor interactions aremost important intermolecular ones.

Sum of charge transfer energy E(2) corresponding to the twoLP(N(anion)) ? r⁄(N–H(cation)) interactions is, respectively,135.1 and 119.5 kcal/mol in 2-IP1 and 2-IP2 aggregates, and thatof LP(N) ? r⁄(C–H) interactions is 12.1 kcal/mol in 2-IP1 and14.4 kcal/mol in 2-IP1, respectively, indicating the N(anion)� � �H–N (cation) H-bonds are stronger than N(anion)� � �H–C(cation) ones.As can be seen, sum of two LP(N(anion)) ? r⁄(N–H(cation)) andtwo LP(N) ? r⁄(C–H) charge transfer energies in 2-IP1(147.18 kcal/mol) is greater than 2-IP2 (133.9 kcal/mol). A com-parison between the charge transfer energies calculated for[MIM+][N(CN)2

�] [8] and ([MIM+][N(CN)2�])2 revealed that the E(2)

energy increases as the size of complex increases. This increase

78 H. Roohi, S. Khyrkhah / Computational and Theoretical Chemistry 1037 (2014) 70–79

can be attributed to the cooperative effects in the cyclic tetramer ofIL.

Owing to the electron lack in the imidazolium ring, carbon C1 ispositively charged, making hydrogen of C1(19)–H the most acidichydrogen atom among the H atoms of the imidazolium ring. Fromthe results of NBO analysis at MP2/6-311++G(2d,2p) level, positivecharge of H is 0.235 au in free cation that increases to 0.272 au and0.278 au in 2-IP1 and 2-IP2 aggregates, respectively. As can beseen, increase in positive charge of the H atom is accompaniedby the decrease in positive charge of C atom involved in H-bonding.Increase in positive charge on the bridging H atoms involved in H-bonds is a common observed feature of proper H-bonds. The posi-tive charge of H atom in N–H bond is 0.452 au that increases to0.504 au in 2-IP1 and 0.503 au in 2-IP2. The negative charges ofN2 and N5 atoms of cation increase upon formation of both 2-IP1 and 2-IP2 aggregates.

For anion, the negative charge of N atom involved in N� � �HC andN� � �HN interactions increases and negative charge of central Natom (N14) decreases upon formation of 2-IP1 and 2-IP2 aggre-gates. Besides, positives charge of C atoms increase upon formationof both ion pairs.

Change in the atomic charges is accompanied by the transfer ofthe some charge from anion to cation upon complex formation.Population analysis shows that the charge transfer (CT) takingplace from anion N(CN)2

� to cation MIM+ upon complex formation.The shift of electron charge causes the positive charge on the eachof the cations decreases from 1 to 0.890 au in 2-IP1 and 0.834 au in2-IP2 and total negative charge of N(CN)2

� anions decreases by0.221 au and 0.206 au, respectively, in good agreement with thegreater E(2) energy obtained for 2-IP1 with respect to the 2-IP2.

3.8. Frontier molecular orbitals

The results obtained and hence the conclusion drawn from theanalysis of the CT, energetic and structural parameters can furtherbe supported from the analysis of the MOs (HOMO and LUMO)along the approaching of anion to the cation to form the aggre-gates. Fig. 8 shows Frontier molecular orbital (HOMO and LUMO)energy diagram of 2-IP1 and 2-IP2 aggregates when anionsapproach cations to form the clusters. As can be seen, the HOMOof anion includes three deformed p orbitals (EHOMO = �4.84 eV)localized on the three N atoms. The LUMO of cation is p⁄ in nature.From the electronic charge distribution of LUMO (ELUMO =�2.35 eV) within IM ring, the C3–C4, N2–H and C1–H bonds havebonding character, whereas other bonds have antibonding one.When anions approach the cations to form the 2-IP1 cluster,HOMO of cluster shows the bonding character across the N2–C1–N5, C3–C4 and C–Nanion bonds and antibonding character acrossthe N2–C3, C4–N5 and N32–Canion bonds. As observed, the HOMOof ion pairs comprises a low electron density projection along theN2–H bond. Besides electron density over the N atoms of aniondecreases upon aggregation, indicating the CT occurs from theanions to cations. The formation of the 2-IP2 results in the moresignificant reduction of the electron density of one of the anions.

4. Conclusions

In this work, clusters formed by interaction two cations withtwo anions of [MIM+][N(CN)2

�] ionic liquid were modeled. We havefound five clusters with four hydrogen bonds in each of them. Thestructural and electronic properties of the clusters of [MIM+][N(CN)2

�] were studied using quantum chemical calculations atvarious levels of theory.

The DG� of the aggregates changes depending on interactionsite. The results showed 2-IP1 and 2-IP2 aggregates have the most

stability by all studied methods. BSSE effect on DG� leads to stabil-ity order: 2-IP1 > 2-IP2 > 2-IP3 > 2-IP4 > 2-IP5.

Among the DFT methods, M06-2X and M05-2X energies aresmaller than B3LYP method and are near to MP2 ones.

The results show that the tendency for aggregation decreases asthe temperature increases. It is estimated that the association ofions to from the aggregates decreases with increase in polarity ofsolvent. The order of DG�solv values in the all solvents is as: 2-IP5 > 2-IP4 > 2-IP3 > 2-IP1 � 2-IP2 and difference between DG�g

and DG�solv is greater in water than other solvents. The potentialenergy curves show that the presence of solvent facilitates the sep-aration of ions.

The results reveal that change in proton donors N–H and C–Hbond lengths in most stable aggregates 2-IP1 and 2-IP2 is greaterthan others, in good agreement with the greater stability of theseaggregates. Frequency analysis showed that a significant red-shiftin the N–H stretching vibrational wave number of 2-IP1 and2-IP2 aggregates. NBO results show that the charge transfer (CT)taking place from anion N(CN)2

� to cation MIM+ upon complexformation.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.comptc.2014.03.035.

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