Theoretical Probing of Weak AnionâCation Interactions in Certain

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Theoretical Probing of Weak Anion-Cation Interactions in Certain Pyridinium based Ionic Liquid Ion-Pairs and the Application of Molecular Electrostatic Potential in their Ionic Crystal Density Determination : A Comparative Study Using Density Functional Approach Aswathy Joseph, Vibin Ipe Thomas, Gawe# #y#a, Padmanabhan Sridharan Alapat, and Suresh Mathew J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b09189 • Publication Date (Web): 07 Nov 2017 Downloaded from http://pubs.acs.org on November 9, 2017

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The Journal of Physical Chemistry

Theoretical Probing of Weak Anion-Cation Interactions in Certain Pyridinium based Ionic Liquid Ion-pairs and the Application of Molecular Electrostatic Potential in their Ionic Crystal Density Determination: A Comparative Study Using Density Functional Approach Aswathy Joseph1, Vibin Ipe Thomas2, Gaweł Żyła3, A. S. Padmanabhan 1,4, Suresh Mathew*1,5

1

School of Chemical Sciences (SCS), Mahatma Gandhi University, Kottayam 686560, Kerala,

India 2

Department of Chemistry, CMS College of Arts and Science, Kottayam, 686001, Kerala,

India 3

Department of Physics and Medical Engineering, Rzeszow University of Technology,

Rzeszow, 35-905, Poland 4

Centre for High Performance Computing (CHPC), Mahatma Gandhi University, Kottayam

686560, Kerala, India 5

Advanced Molecular Materials Research Centre (AMMRC), Mahatma Gandhi University,

Kottayam 686560, Kerala, India Correspondences to: Prof. Dr. Suresh Mathew (E-mail: [email protected]*)

Abstract: A comprehensive study on the structure, nature of interaction and properties of six ionic pairs of 1-butylpyridinium and 1-butyl-4-methylpyridinium cations in combination with tetrafluoroborate (BF4-), chloride (Cl-) and bromide (Br-) anions have been carried out using Density

Functional

Theory

(DFT).

The

anion-cation

interaction

energy

(∆Eint),

thermochemistry values, theoretical band gap, molecular orbital energy-order, DFT-based chemical activity descriptors: chemical potential (µ), chemical hardness (η) and electrophilicity index (ω) and distribution of density of states (DOS) of these ion-pairs were investigated. The

1 ACS Paragon Plus Environment


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ascendancy of –CH3 substituent at the 4th position of the 1-butylpyridinium cation ring on the values of ∆Eint, theoretical band gap and chemical activity descriptors was evaluated. The ∆Eint values were negative for all the six ion-pairs and were highest for Cl- containing ion-pairs. The theoretical band-gap value after –CH3 substitution increased from 3.78 to 3.96 eV (for Cl-) and from 2.74 to 2.88 eV (for Br-) and decreased from 4.9 to 4.89 eV (for BF4-). Ion-pairs of BF4were more susceptible to charge transfer processes as inferred from their significantly high η values and comparatively small difference in ω value after -CH3 substitution. The change in η and µ values due to the –CH3 substituent is negligibly small in all cases except for the ion-pairs of Cl-. Critical point (CP) analyses were carried out to investigate the AIM topological parameters at the inter-ionic bond critical points (BCPs). The RDG isosurface analysis indicated that anion-cation interaction was dominated by strong Hcat….Xani and Ccat….Xani interactions in ion-pairs of Cl- and Br- whereas weak van der Waal’s effect dominated in ionpairs of BF4-. The molecular electrostatic potential (MESP) based parameter ∆∆Vmin measuring the anion-cation interaction strength showed a good linear correlation with ∆Eint for all 1butylpyridinium ion-pairs (R2 = 0.9918). The ionic crystal density values calculated using DFT based MESP showed only slight variations from experimentally reported values. 1. Introduction The utility of ionic liquids (ILs), pure salts that are liquid under ambient conditions1, now encompasses all areas of industrial and molecular research2. The flourishing, highly innovative and ever-increasing research on these materials is driven by their wide potential applicability as performance chemicals in numerous fields of research3-10 . The pyridinium based ILs posses an important position in the field of industrial research for applications such as nuclear separation techniques, electrolytes in batteries and supercapacitors and for removal of sulphur compounds 2 ACS Paragon Plus Environment

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from fuels11

12-14

. Derivatives of pyridinium cations have been particularly suggested for the

purpose of separation applications based on many experimental and theoretical studies because of its tunable aromatic nature 15 16-18 11 19 13. However, there have been only very less theoretical literatures reported so far on the anion-cation interactions in pyridinium based ionic liquids,20-22 while more extensive studies are being focused on the molecular structure modeling, electronic properties and hydrogen-bonding interactions of pyridinium and imidazolium based ones23 20, 25-27

24

. The interaction between N-butylpyridinium hydrogen sulfate IL and certain derivatives

of sulphur compounds have been reportedly studied using a dispersion corrected hybrid functional ωB97X-D for analysing its suitability for sulphur extraction process28. The structure characteristic and long-range ordered arrangement of anions and cations in 1-butylpyridinium tetrafluoroborate have been previously studied using DFT and molecular dynamic (MD) simulations21. In another reported literature, the electronic structure and reactivity of 1ethylpyridinium trifluoroacetate have been studied using DFT calculations29. The effect of temperature on the microstructure and microscopic dynamics of certain N-alkylpyridinium tetrafluoroborate ionic liquids have been investigated and recently reported using MD simulation30. Also, a combined MD and experimental study on certain pyridinium based ILs to study the thermodynamic and transport properties were also reported31. Recent literature reports reveal that density functional theory (DFT) based quantum chemistry methods have been widely employed to analyze the anion-cation interaction and binding energies of many ILs22, 32 29. These quantum chemical calculations could successfully account for the observed nature of these interactions within ILs. The cation-anion interactions in ILs are mainly coulombic in nature though interactions such as hydrogen bondings may also have crucial roles in defining their physical and chemical nature22. From electron density and wave 3 ACS Paragon Plus Environment


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function analysis, more detailed molecular-based understanding of the chemical nature of anion-cation interaction in them and prediction of certain macroscopic properties are also possible33. Herein, we have analysed the quantitative nature of non-covalent anion-cation interaction from the view point of donor(D)-acceptor(A) interactions from the electron density and wavefunction analysis to obtain more insights into the correlation between its electronic structure and bulk physiochemical properties. The anions and cations composing ILs generally have poor molecular symmetry and low charge density which prevents them from forming a stable crystal lattice34. In pyridinium based ILs also, similar to the other ILs, altering the type of anion moiety accompanying the cation causes profound variation in its observed physicochemical properties. So far not much theoretical probing has been done on the anioncation interactions in the ion-pairs of pyridinium based ionic liquids (ILs) from wave function analysis. Therefore, our present work theoretically investigates the anion-cation interactions among 1-butylpyridinium and 1-butyl-4-methylpyridinium cations with the anions such as BF4, Cl- and Br- that have been widely employed in many organic as well as inorganic reactions. Using DFT, we investigated the effect of these anions and methyl substituent of 4th position of 1-butylpyridinium cation ring on the anion-cation interaction energy (∆Eint), theoretical bandgap value, nature of the chemical activity descriptors: chemical potential (µ), chemical hardness (η) and electrophilicity index (ω), distribution of density of states (DOS), topological parameters and molecular electrostatic potential (MESP). The present study will therefore be a valuable addition to the DFT based quantum chemical understanding of these pyridinium based ionic liquids. We have also probed into the theoretical aspects of MESP and its applicability for the determination of ionic crystal density using general interaction properties function (GIPF)33. The six pyridinium based ionic liquid ion-pairs theoretically investigated and their


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representations used here are: (A) 1-Butylpyridinium tetrafluorborate (1-BuPyBF4), (B) 1Butylpyridinium chloride (1-BuPyCl), (C) 1-Butylpyridinium bromide (1-BuPyBr), (D) 1Butyl-4-methylpyridinium

tetrafluorborate

(1-Bu-4-MePyBF4),

(E)

1-Butyl-4-

methylpyridinium chloride (1-Bu-4-MePyCl) and (F) 1-Butyl-4-methylpyridinium bromide (1Bu-4-MePyBr). 2. Computation and Theory The DFT simulation have been carried out using the B3LYP (Becke’s three parameter exchange functional in combination with the Lee, Yang, and Parr correlation functional) in Gaussian 09 suit of programme35. The gas-phase geometries of different conformers of the six pyridinium-based IL ion-pairs have been optimized using 6-311++G (d,p) basis set without any symmetry constraint. The vibrational frequency analysis of the most stable ion pair structures shown in Fig.1 was carried out to ensure that the conformer represented the true energy minima containing no imaginary frequencies, but only real frequencies. The most stable conformers of the six ion-pairs were selected and their anion-cation interaction energies (∆Eint) were calculated after correcting the basis-set superposition error (BSSE) according to the Boys and Bernardi counterpoise method36-37. Multiwfn 3.3.9 programme38 (MWF) was used for AIM topological analysis of the IL ion-pairs to study the following: electron density (ρ), Laplacian (∇2ρ), electron localization function (ELF), reduced density gradient (RDG), critical points (CP), total density of states (DOS), partial density of states (PDOS) and molecular electrostatic potential (MESP). Geometry of optimized ion-pair structures and HOMO-LUMO orbital structures were elucidated using GassView 5.0 and for the RDG isosurface visualization, MWF and Visual Molecular Dynamics (VMD) 1.9.3 softwares were used.



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The anion-cation interaction energy (∆Eint) of ion-pairs obtained from DFT calculation using 6311(++)G (d,p)/ B3LYP level of theory were estimated using equation: ∆Eint = (Ecat + Eani) EIL where EIL, Ecat and Eani represents the energies of the optimized geometries of IL (anioncation complex), cations and anions, respectively. The values of chemical activity descriptors: chemical potential (µ), chemical hardness (η) and electrophilicity index (ω) shown in Table 1 was determined from the DFT based energy values of HOMO (εHOMO) and LUMO (εLUMO) from the following equations28 39: µ = - (I+A)/2, η = (I-A) and ω = (µ2/2η ) where I ≈ -εHOMO and A ≈ -εLUMO. The energy lowering of the IL molecules due to maximal electron flow between an electron donor and an electron acceptor in the excited state (ωvs) was calculated using the equations proposed by Paar et. al. 40 in terms of I and A given as: ωvs= (I+A)2/4(I-A) where, ωvs = 2ω. Bader’s “atoms in molecules” (AIM) topological analysis of the most stable conformers of the six ion-pairs have been carried out to study the non-covalent hydrogen (H) and halogen (X) bond interactions among the ion-pairs. The values of electron density (ρ), Laplacian (∇2ρ), potential energy density (V(r)), electron localization function (ELF) and reduced density gradient (RDG) at the bond critical points (BCPs) was analysed. The strength of hydrogen bond interactions ( ) between pyridinium H atoms and anionic X atoms was determined from the topological analysis of electron densities ρ(r) at the BCPs41. The MESP analysis of the ILs and its constituent ions was carried out for two purposes: a) for verifying the linear correlation between ∆∆V

min

and ∆Eint proposed for H-, X- and dihydrogen bonds42 and b) for the

estimation of ionic crystal densities using the set of statistically based indices introduced by Murray et al.: ∏ (indicator of charge separation), σ2tot (the variability of the potential on the


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molecular surface), and ν (degree of charge balance) which relates the MESP to the macroscopic properties for deriving general interaction properties function (GIPF)33. 3. Results and discussion 3.1. Analysis of band-gap, anion-cation interaction energy, chemical activity descriptors and thermochemistry values The gas-phase optimized geometries of A, B, C, D, E and F is shown in Fig.1. The structure of HOMO and LUMO of these six ion-pairs and its constituent ions is shown in the frontier molecular orbital (FMO) energy-order diagram in Fig.2. The quantum descriptor, HOMOLUMO energy band-gap can account for the electronic properties and reactivity of A, B, C, D, E and F. The methyl substituent on the 4th position of 1-butylpyridinium cation increased the band-gap value from 3.78 to 3.96 eV for Cl- ion-pairs (B and E) and from 2.74 to 2.88 eV for Br- ion-pairs (C and F). In the case of BF4- anion ion-pairs (A and D), the band gap showed a decreased value from 4.9 to 4.89 eV. The anions had discernible influence on the interaction energy (∆Eint) of different ion-pairs. The DFT based ∆Eint values for A, B, C, D, E and F have been estimated and their chemical activity descriptors have been comparatively studied which is shown in Table 1. All the ionpair structures showed negative interaction energies. Negative ∆Eint values indicated that such anion-cation complex are thermodynamically stable due to the ionic size and geometric orientation of these ions in their distorted lattice sites.43 The highest negative ∆Eint among 1butylpyridinium cation (1-BuPy+) ion-pairs was calculated to be -92.4 kcal/mol for B and that among 1-butyl-4-methylpyridinium cation (1-Bu-4-MePy+) ion-pairs was calculated to be -87.3 kcal/mol for E in which the accompanying anion was Cl- in both cases. The second highest



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negative ∆Eint was for Br- ion pairs (-89.7 kcal/mol for C and -82.9 kcal/mol for F) and the least was for BF4- ion-pairs (-78.6 kcal/mol for A and -79.1 kcal/mol for D). The difference in ∆Eint value caused by a methyl substituent at the 4th position of the 1-butylpyridinium cation ring are approximately -0.5 kcal/mol (for A and D), -5.1 kcal/mol (for B and E) and -6.8 kcal/mol (for C and F). The smaller anion-cation interaction energy, greater inter ionic separation and larger anionic size also leads to a lower melting point in A and D compared to the other ILs. The computed inter ionic distances in the optimized gas-phase ion-pair structures can be seen in Fig. 1. The chemical hardness (η) of ILs that can be calculated as the energy band-gap between the HOMO and LUMO levels accounts for the resistance to charge redistribution and chemical potential (µ) measures the ability of a system to donate electron density.44 In ILs, when a cation (electron acceptor) and an anion (electron donor) approaches each other, there is a slight redistribution of electron density from the anion to the cation. However, the bond formed between them remains electrostatic in nature rather than covalent. If η ˃ 0, then the energy change due to the transfer of electron is less than zero i.e, the charge transfer process is energetically favourable40. The theoretically computed values of η are positive for all the ionpairs and its constituent ions indicating that electron transfer process can easily occur in such systems. However, the constituent ions in the independent state had larger η value when compared to the anion-cation bound state as can be observed from Table 1. Among the two sets of ion-pairs with similar cations, A and D having BF4- anions are most favourable to charge transfer processes showing only slight difference in their η values (0.1804 and 0.18 respectively). The η values calculated for anions alone varies in the order BF4- > Cl- > Br-. Similar trend is observed in the ILs irrespective of the nature of the cation. Therefore, charge


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transfer process can easily occur in BF4- ion-pairs. This is experimentally valid in our previous work stating the electron transfer between 1-butylpyridinium tetrafluoroborate and polyvinyl pyrrolidone can lead to the formation of free radical species45. In the cations, methyl substitution increases the η value from 0.2094 (for 1-BuPy+) to 0.2199 (for 1-Bu-4-MePy+). The change in η value as a result of the -CH3 substituent is negligible except in the case of B and E probably due to the influence of Cl- hard base. The theoretical value of chemical potential (µ) for 1-BuPy+ and 1-Bu-4-MePy+ cations are lower than that of BF4-, Cl- and Branions which implies that the electron will flow from these anions to cation during the anioncation complex formation. Similar to the trend observed in η values, the change in µ values as a result of the -CH3 substituent is also small here except in the case of B and E. The global chemical reactivity descriptor defined by Parr et al., electrophilicity index (ω) quantifies the electrophilic nature of the molecular species within a relative scale39. This descriptor measures the energy lowering of a chemical species due to maximal electron flow between an electron donor and an electron acceptor. The computed values of ω for various ion-pairs and its constituent ions are given in Table 1. In the cations (1-BuPy+ and 1-Bu-4-Me-Py+), this energy lowering is greater than that in the anions. Among the anions, the theoretically calculated ω varies in the order: Cl- > Br- > BF4-. However, the computed values of this DFT based descriptor for the six ion-pairs varies in the order: C > F > B > E > A > D. In the anion-cation bound state, Br- ion-pair exhibit greater energy lowering than that of Cl- ion-pair. The least energy lowering is calculated for anion-cation bound state of BF4-. This order of change in ω value is the same for the IL ion-pairs in the excited state also, i.e., ωvs as shown in Table 1. Another observed fact was that the ω values of all the anion-cation complex decreased after CH3 substitution indicating that the electron flow from these complexes is slightly less favored



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after the presence of the inductive electron donating effect of -CH3 group. The total electron density at the centre of 1-butylpyridinium cationic ring for A, B and C was found to be 0.0223, 0.0216 and 0.0211 respectively whereas, the total electron density at the ring centre of 1-butyl4-methylpyridinium cation for D, E and F was found to be 0.02322, 0.02240 and 0.02245 respectively.

Due to the partial electron density withdrawal through C5….X25 path, the

electron density inside the ring in B and C is quantitatively low when compared to that in A. Also, the decrease in energy lowering due to the flow of electrons after -CH3 substitution was the least (~0.005) for ILs of BF4- (A and D).

Thermochemistry data obtained for the formation

of all the six ion-pairs at 298.15 K and 1 atm pressure is shown in Table 2. The enthalpy (ΔH) and free energy (ΔG) of formation of all the ion-pairs were positive where as the entropy change (∆S) was calculated to be negative for D and E which indicates that the formation of these ion-pairs is never spontaneous. All the other ion-pairs can be formed spontaneously if the temperature is high enough. 3.2. Topological analysis of electron density at inter-ionic BCPs The critical points (CPs) in the selected conformers of A, B, C, D, E and F have been mapped as shown in Fig. 3. CPs of electron density are those at which gradient norm of function value is zero (except at infinity) denoted as (ω,σ) where, ω, the rank of a CP is the number of nonzero curvatures and σ, its signature is the sum of their algebraic signs. With a fewer exceptions, the CPs of energetically stable molecules have a rank three (ω =3) for the charge distribution on it. According to Bader’s QTAIM theory46, CPs with ω < 3 is said to be degenerate and unstable. Therefore, a small change in the topology of electron density caused by a nuclear displacement in such cases can cause it either disappear or to bifurcate into a number of nondegenerate stable CPs with ω =3 as stated by Bader. There are four types of CPs with ω=3: (3,-3), (3,-1), (3,+1) 10 ACS Paragon Plus Environment

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and (3,+3), depending on the number of eigenvalues of Hessian matrix of real space function which are negative. The number of CPs of each type identified in A, B, C, D, E and F is given in Table 3. The position of (3,-3) local maximum is called nuclear critical point (NCP) as they are nearly identical to nuclear positions. In (3,-3), all three eigen values of Hessian matrix of function (λ1, λ2 and λ3) are negative. The CP type (3,-1) called the bond critical point (BCP) with one positive (+1) and two negative (-1) curvatures is the focus of study here. (3,-1) usually appears in chemical bond path or between atom pairs that have weak attractive interaction. The (3,+1) CP is in the case of a centre of a ring in cyclic molecules having one negative and two positive curvatures and is called the ring critical point (RCP) which displays steric effect. The (3,+3) CP which known as the cage critical point (CCP) has the minimum of electron density and generally appears in the center of cage system. Only two such CCPs have been identified in D. The Table 3 and Fig. 3 depicts the number of different kinds of CPs observed in the six IL ion-pairs and the CP paths connecting (3,-3) to (3,-1) and (3,+1) to (3,+3). A and D consisting of BF4- anion has greater number of CPs connecting the anion and cation while the pairs B and C and E and F have same number of CPs detected. The numbers and types of CPs that can coexist in a system with a finite number of nuclei are governed by the Poincaré-Hopf relationship

47

expressed in the equation: n(3,-3) – n(3,-1) + n(3,+1) – n(3,+3) = 1 where, n represents

the number of CPs of each type. For all the ion-pairs, this relationship was verified using MWF indicating that all CPs may have been found. The (3,-1) BCPs formed between the anions-cation complex are of two types which have been labeled in Fig.3, one through Hcat….Xani interactions and the other through Ccat….Xani interactions. For example, in A, three of the four fluorine atoms (F26, F27 and F29) in BF4anion (shown in Fig.1.) is connected to two H atoms either one on the butyl chain and 11 ACS Paragon Plus Environment


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pyridinium ring. In B and C, the halogen ions (X = Cl- or Br-) are connected to the H17 atom on the butyl chain and to C5 atom on the ring. The BCPs are represented as A1, A2, A3 etc. where A represents the IL ion-pair and the numbers 1, 2, 3 etc represents the label of inter-ionic BCP shown in Fig. 3. Further probing into the weak bonding interactions in these ion-pairs was done by analysing the values of topological descriptors: electron density (ρ), Laplacian of electron density ( ) , potential energy density (V(r)), electron localization function (ELF), reduced density gradient (RDG), total electrostatic potential (ESPtotal) and hydrogen bond strength (EHB) at these CPs to obtain a quantitative picture of the nature and extent of interaction. These results are shown in Table 4. The values of ρ and at all the CPs fall in the typical range proposed for ρ (0.002-0.035 a.u.) and (0.024-0.139 a.u.) in hydrogen bond complexes42. However, the ρ and values at A4, B1, C1, D4, E1 and F1 were conspicuously high signifying stronger inter-ionic interactions through their representative atoms. Here, A4 and C1 are BCPs of Hcat….Xani interaction and B1, D4, E1 and F1 are BCPs of Ccat….Xani interactions. The strength of intramolecular hydrogen bond interactions ( ) between cationic H atoms and anionic X atoms at inter-ionic BCPs was estimated using equation41 : = ( )/2 where, ( ) represents the electronic potential energy density at that specific (3,-1) BCP. The calculated DFT based values in kJ/mol at these CPs are also shown in Table 4. The ESPtotal was highly positive for (3,-1) inter-ionic BCPs with high electron density (ρ) values. Among such BCPs, A4 and C1 exhibited highest negative values of -27.58 and -21.62 kJ/mol respectively demonstrating strongest Hcat….Xani interactions. 3.3. Electron localization function (ELF) analysis


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The ELF analysis was performed using MWF on geometry optimized structures. The values of ELF at inter-ionic BCPs for the six ion-pairs are given in Table 4. ELF depends on the kinetic energy density which is excess kinetic energy density (D(r)) caused by Pauli repulsion and the Thomas-Fermi kinetic energy density (D0(r)) as interpreted by Savin et. al.48-49 Therefore ELF, which can be expressed as 1 + (()⁄ ()) indicate the relative localization of electron density and its value is within the range of 0 and 1. ELF = 0.5 corresponds to uniform electron gas. ELF value is closer to 1 for localized electron pairs, whereas small values less than 0.5 correspond to highly delocalized electron density50. The ELF can have several maxima, denoted as ‘attractors’ the position of which between the centers can provide a quantitative idea of the extent of bond polarity and all points in space which reach this attractor form its domain49. According to Bader, the regions which have large ELF values have large magnitudes of Fermi hole integration51. The disparity in the electron density distribution between anions and cations can be clearly understood from the two dimensional ELF map of A, B, C, D, E and F shown in Fig. 4 with a colour scale on the right side of the plot. The region of closer anion-cation interactions are marked using dashed white circles in the figure. The region of large ELF value greater than 0.5 represented by the colour ranging from light green to red indicates that electrons are greatly localized due to the presence of a covalent bond, a lone pair or inner shells of the atom involved. The ELF plots of B, C, E and F shows closer anion-cation interaction visible as light blue region inside the white circle. The ELF values for B1, C1, E1 and F1 ranges from 0.19 to 0.26 approximately. The ELF plots of A and D reveals greater inter-ionic distance between the F atoms of the BF4- anions and the cationic H atoms on the butyl tail denoting a weaker anion-cation interaction. This is characterized by the dark or navy blue region corresponding to an ELF of zero. Since the attractors between anionic



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and cationic groups are more spherically distributed around the atom cores, either a more ionic or a van der Waals interaction is present49. In the ELF plots of B, C and E, the localization of electron density (ELF~0.2) between the single carbon atom of the pyridinium ring and the Cl- or Br- anion indicates the possibility of migration of electron density from anion to cation. Due to the smaller size of the halide anions, this kind of interaction is always possible to occur unlike in the one with larger anion (BF4-) which does not provide a closer interaction with cation. The ELF plot of F shows that stronger anion-cation interaction is possible through the H atom of the pyridinium ring also. Previously reported simulation studies on imidazolium based ILs suggests that the size of the anion greatly influence the mutual position of the anion and cation in an IL network. The larger anions with more diffused negative charge would prefer the positively charged ring whereas smaller anions are more closer to the most acidic Hs on the cation52. Among the ion-pairs investigated here, the optimized ion-pair structure of D with larger anion (BF4-) occupied the position above the positively charged 1-butyl-4-methylpyridinium ring. In all the other ion-pair structures, the anions preferred closer interaction with the cationic Hs either on the ring or on the butyl tail. 3.4. RDG isosurface analysis To gain more insights into the weaker cation-anion interactions in these ion-pairs, reduced density gradient (RDG) analysis was performed. Region of weaker interaction between the anion and cation can be distinguished from other regions from the value of reduced density gradient (RDG) function (RDG= | |/2(3 )

! ( ) ).

RDG isosurface analysis is a very

useful method for studying weaker interactions for which the range of values of electron density (ρ), gradient norm of electron density ( | |) and RDG(r) will be small, 0 ~ small and 0 ~ medium respectively. The RDG isosurface of the six ILs plotted using the molecular 14 ACS Paragon Plus Environment

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modeling software VMD53 shown in Fig. 5 demonstrates the region of weaker van der Waal’s interaction, steric repulsion and strong attraction between the anions and cations. From the color scale shown below in the figure, it can be seen that the anion-cation interactions in A and D are dominated by weak van der Waal’s interaction represented in green colour. The stronger Ccat….Xani and Hcat….Xani interactions in B, C, E and F shown in the ELF plots in Fig. 4 are represented as blue isosurface regions in Fig. 5. All the structures exhibits red colored isosurface region at the centre of the pyridinium ring which indicates steric effect. The scatter diagram in Fig. 6 shows a plot of sign(λ2)ρ

i.e., sign of the second largest

eigenvalue of electron density Hessian matrix verses and RDG value for A, B, C, D, E and F. The spikes in the scatter diagram corresponds to three kinds of interactions in the molecule: strong attraction regions (H- and X-bondings), van der Waals (vdW) region and strong repulsive region (steric effect). In D, the characteristic spike of strong interaction is absent. In B and C, due to the difference in the anionic constituent, the position of the RDG spike corresponding to strong attraction region is slightly different. The position of the spike near 0.04 in B is shifted to -0.03 in C, similar to E and F. The vdW interaction between anion and cation is greater in A and D when compared to the other ion-pairs as observed from the scatter diagram and RDG isosurfaces in Fig.5. 3.5. Study of Density of States (DOS) Fig. 7 shows the plots of the total density of states (TDOS) and overlap density of states (OPDOS) for A, B, C, D, E and F. The DOS curves were plotted using Gaussian function with the corresponding full width at half maximum (FWHM) of 0.05 a.u. The plots of broadened partial DOS (PDOS) and overlap DOS (OPDOS) for the cation and anion obtained after



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defining fragments 1 (as 1-BuPy+ in A, B and C and as 1-Bu-4-MePy+ in D, E and F) and fragment 2 (as BF4- in A and D, Cl- in B and E, and Br- in C and F). The plots help in visualizing the orbital composition and density of states in these ion-pairs. From the curves corresponding to TDOS, PDOS (red line for fragment 1 corresponding to cation, blue line for fragment 2 corresponding to anion) and OPDOS (green line) the characters of each orbital can be identified. The height of black curve (TDOS) in the plots clearly shows how dense the energy levels are distributed. The region in the plot where red curve is high nearly approaching black line in the region indicates that the orbitals in the cation have significant contribution to corresponding MO of the ion-pair. The vertical dashed line in these six plots indicates the HOMO energy level whose right end corresponds to the higher energy antibonding orbitals. As can be seen in Fig. 7, for A, B, C, D, E and F, PDOS curve height of anions approached the TDOS line, indicating that most of the contributions to the HOMO of the ion-pair came from the anion orbitals. Also, the antibonding MOs have a major contribution from the cation. The OPDOS curves in these plots lying in the negative region confirms that the possibility of chemical bond formation between the anion and cation in A, B, C, D, E and F is so less. These conclusions further confirm the weak interaction between anion and cation in Fig. 5. 3.6. Quantitative analysis of Molecular electrostatic potential (MESP) a) Investigating the correlation between MESP minimum and ∆Eint Changes in MESP values during accociative interaction between the anions and cations are indicative of a shift in the electron density distribution between them. The value of MESP minimum (Vmin) is a sensitive descriptor that helps to understand this shift of electron density from one atom to another in a non-covalent binding interaction. From the analysis of Vmin of


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the optimized gas-phase ion-pair structures and its constituent ion structures, the correlation between the ∆∆V min and ∆Eint for all the six ion-pairs was studied as proposed by N. Mohan et. al according to the equation (4) given below: 42 ∆∆ "#$ = ∆ "#$& − ∆ "#$( …………..(4) where, ∆ "#$& = "#$&′ − "#$& for the IL anion which is the electron donor (D) and ∆ "#$( = "#$(′ − "#$( for the IL cation which is the electron acceptor (A). "#$&′ and "#$& represents the "#$ of anion (BF4-, Cl- or Br-) in the ion-pair and in isolated gas-phase state. Similarly, "#$(′ and "#$( represents the "#$ of cation (1-BuPy+ or 1-Bu-4-MePy+) in the ion-pair state and in isolated gas-phase state. The highest negative valued MESP was chosen as "#$ for the calculation of ∆∆ "#$ in all these ion-pairs. The calculated values of ∆Eint, ∆ "#$& , ∆ "#$& and ∆∆ "#$ is shown in Table 5. For 1-Butylpyridinium based ILs, ∆∆ "#$ showed a good correlation with ∆Eint with an R2 value of 0.9918. But, the correlation was poor (R2=0.6185) for 1-Butyl-4-methylpyridinium based ILs. This can be a result of greater steric interaction due to the -CH3 substituent at 4th position of 1-Butylpyridinium cation ring. The correlation fitting for the ion-pairs is shown in Fig.8. On the other hand, the computed values of ∆∆ $ from the MESP of the nuclei (Vn) of the interacting atoms at the inter-ionic CPs were not sensitive to ∆Eint. b) Calculation of ionic crystal density from MESP In this section, we studied the suitability of molecular electrostatic potential (MESP) of the optimized gas-phase IL ion-pair structures to predict their ionic crystal densities. The anions and cations of ILs generally have poor molecular symmetry and low charge density which prevents them from forming a stable crystal lattice34. Therefore, theoretically determined values



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of ionic crystal densities can be useful. The prediction of crystal densities of molecular and ionic compounds from the computed volume (Vm) of the isolated geometry-optimized gas phase molecule from the equation M/Vm (where M is the molecular mass) have been previously investigated by Rice et al.54 This equation did not take into consideration the intermolecular interactions within the crystal. In order to rectify this, Politzer et al.55 introduced an interaction correction term which is the product of the variance of the computed electrostatic potential on the molecular surface and a parameter that indicates the degree of balance between positive and negative regions. This is useful especially for molecular crystals. For ionic crystals, Rice et al.54, after recognizing that the sum of the ionic volumes of the optimized gas phase geometries is too large to be applied in the equation M/Vm, modified Vm by introducing a negative correction term for each ion. However, since Vm of the isolated gas phase ions do not consider the strong electrostatic attractions between positive and negative ions, leading to the less accurate estimation of ionic crystal density, electrostatic potentials on the surfaces of the cations and anions have been used for this purpose by Politzer et al.56 The electrostatic potential (ESP) analysis on IL molecules can extract details about the strength and orientation of weak interaction such as coulombic interaction, hydrogen-bonding, halogen-bonding etc. This can be further understood by analyzing the magnitude and positions of ESP minima and maxima on the molecular surface. The ESP on van der Waals surface of IL molecules can be related to many of its condensed phase properties like density, boiling point, diffusion constant, viscosity, surface tension etc through a set of molecular descriptors based on ESP. Using Multiwfn57, we calculated the theoretical ionic crystal densities of A, B, C, D, E and F (shown in Table 6) from the ESP data based on the expression proposed by Politzer et al. which is given in equation (5) below56: 18 ACS Paragon Plus Environment

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5 67 (89:;

Theoretical Probing of Weak AnionâCation Interactions in Certain

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