Influence of Cation Size on the Structural Features and Interactions in

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Influence of Cation Size on the Structural Features and Interactions in Tertiary Alkylammonium Trifluoroacetates. A Dft Investigation Irina V. Fedorova, and Lyubov P. Safonova J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b04003 • Publication Date (Web): 19 Jun 2018 Downloaded from http://pubs.acs.org on June 20, 2018

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The Journal of Physical Chemistry

Influence of Cation Size on the Structural Features and Interactions in Tertiary Alkylammonium Trifluoroacetates. A DFT Investigation Irina V. Fedorova∗ and Lyubov P. Safonova G. A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, 1 Akademicheskaya Street, Ivanovo 153045, Russia.

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ABSTRACT. In this paper, we present the results of electronic structure calculations based on density functional theory (DFT) in order to investigate the reactions of the interaction of tertiary alkylamines with alkyl groups of different sizes (triethyl, tributyl, dimethylethyl and diisopropylethyl) with trifluoroacetic acid. We have obtained data on the affinity of the studied amines with a proton. It has been shown that amine interaction with the acid leads to proton transfer from the acid to the amine and formation of ions held together in the ion pair by electrostatic interaction and a very strong hydrogen bond. We have also investigated the energy profiles of the proton transfer from the tertiary alkylammonium cation to the trifluoroacetate anion within the ion pair and found different correlations between the geometric characteristics of the H-bond and the parameters obtained by the NBO and QTAIM analysis. It has been established that the interionic interactions in these systems weaken as the length and the degree of cation alkyl chain branching increase. A good qualitative agreement between the theoretical results and the experimental data on physicochemical properties has been obtained.


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INTRODUCTION Protic ionic liquids (PILs) are a comparatively new and so far understudied subclass of ILs.1, 2 Their properties to a great extent depend both on the cation and the anion structure and, by changing the cation – anion combination, it is possible to develop a wide set of PILs with different properties. Quantum chemistry has recently become one of the most effective instruments of studying the structure and predicting the properties of new types of ionic liquids (ILs).3-7 Quantum-chemical simulation allows us to significantly decrease both time and material costs by reducing the number of compounds that should be synthesized and tested experimentally for creating PILs with the required properties. Density functional theory methods8 are most often used in computational studies of these systems as they allow obtaining reasonable evaluations of the structural parameters and cation – anion interaction strengths9-12. And the accuracy of the calculations for this functional can be increased by introducing empirical corrections for dispersion interactions (DFT-D)13-17. The hybrid meta functionals of the M06 family18, 19 with a correction for dispersion interactions are also widely used. The results presented below are a continuation of work20, in which we studied the structures and interionic interactions in the cation – anion pair of alkylammonium-based PILs. The distinguishing feature of the cations in this group is the presence of a sterically accessible proton on the nitrogen atom capable of forming a rather strong H-bond with the acid anion. And depending on the nature of the cation and anion, both H-bonded complexes and H-bonded ion pairs can be formed. Numerous studies have shown that alkylammonium сations with a higher degree of substitution (di- and trisubstituted cations) are more likely to form ion pairs than primary ammonium cations.10, 20-23 In particular, the ion pairs are formed from triethylamine and phosphorous, trifluoroacetic or p-toluenesulfonic acids, while molecular complexes are generated from ethylamine.20 The interaction of diethylamine with


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some acids leads to the formation of ion pairs and molecular complexes with equal probability. The hydrogen bonds formed between the cation and the anion largely determine the physicochemical properties of PILs.24-30 Quite a lot of theoretical and experimental works have been published on the studies of the H-bond in these compounds.31-35 Some of the authors emphasize the important role of the H-bonds in the PILs structure, while others think that their role is limited compared to the Coulomb interactions (electrostatic forces)25, 36-40. In Hayes’s study27, it has been shown that the short and almost linear N-H…X hydrogen bonds between the cation and anion within PILs determine, to a large extent, the “solid-like” character of the physical properties, while the weaker, bent H-bonds have “liquid-like” properties. The tosylate replacement with trifluoroacetate and dihydrogenphosphite anions within the ion pair with the same triethylammonium cation strengthens the interion interaction20, which, in turn, lowers the specific conductivity in a series of proton-conducting gel electrolytes doped with triethylammonium-based PILs41. Among the above-mentioned compounds, triethylammonium tosylate has the highest free energy value associated with the ion pair formation, which agrees well with its higher thermal stability.42 As the size of the alkyl group (methyl, ethyl, and propyl) in trialkylammonium triflate PILs grows, the ions become less mobile.43 Due to additional H-bonding interactions between the three OH protons of the triethanolammonium cation and different oxygen atoms of the dihydrogenphosphite anion, the energetic stability of this compound21 is much higher than in case of the triethylammonium cation20. This may be one of the reasons why the experimental melting point becomes lower at the transition from triethanol-44 to triethylammonium42 based PILs. The aim of this work has been to study the interrelation between the structure and the physicochemical properties of tertiary alkylammonium trifluoroacetate PILs. We used a tertiary cation as the alkylammonium cation and different alkyl groups such as triethyl,


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tributyl, dimethylethyl and diisopropylethyl ones. First of all, we report the results of the quantum-chemical calculations of the proton affinity values of the amines we are studying by using different versions of the density functional method accounting for or without accounting for the dispersion interactions in order to choose (by comparing the calculated and experimental characteristics) the optimal method for further calculations. Then we give the values of the change in Gibbs free energy associated with the formation of the ion pair from isolated amine and acid molecules and discuss the structural features and interionic interactions in the most stable structures. To characterize the hydrogen bond, we use both geometric (interatomic distances in the N-H…O fragment and H-bond angle) and energy (Hbond energies) criteria of hydrogen bond formation45 and parameters obtained by the quantum theory of ‘atoms in molecules’ (QTAIM)46-48 and natural bond orbitals (NBO)49 methods. The calculation results are compared with the data of our experimental study of thermal stability and electric conductivity of alkylammonium trifluoroacetate PILs.

THEORETICAL METHODS The structures of all the compounds considered in this work have been determined with the software package Gaussian0950 via full geometry optimization in the gas phase. All the discussed structures are at the global minima of the corresponding potential energy surface (PES) without imaginary frequencies. When looking for minima on the PES in order to determine stable configurations caused by acid and amine interaction, we use molecules equilibrium geometries arranged in random order. The calculations were made by the electronic density functional method using PBE gradient-corrected functional51, B3LYP hybrid functional52, 53 without and with the Grimme empirical dispersion correction (GD3)14


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and hybrid meta M06 functional (parameterized to evaluate dispersion interactions)18, all of them combined with the 6-31++G(d,p) basis set54. The change in the enthalpy of the reaction of proton addition to amine with the opposite sign (proton affinity) was determined as a difference between the enthalpy values of the cation and the corresponding neutral amine. The change in Gibbs free energy associated with the ion pair formation from amine and acid (at 298 K and atmospheric pressure) was calculated as a difference between the free energies of the cation – anion pair and the optimized acid and amine molecules. The interaction energy (Eint) values were obtained in accordance with the supermolecule approach55, as

E int = E A...B (A...B) A ∪ B − E A...B (A) A − E A...B (B) B

(1)

in which EA...B(A…B)A∪B, EA...B(A)A and EA...B(B)B are the energies of the ion pair and the ions constituting it, respectively, calculated using the basis functions of the whole system (A…B). The binding energy (Ebind) of the cation – anion pair was estimated according to the following

E bind = E int + E def = E A...B (A...B) A ∪ B − E A (A) A − E B (B) B

(2)

where EA(A)A and EB(B)B are the energies of the optimized single ions; Edef is the deformation energy. The Edef value is always positive as the ion conformations obtained by optimizing the ion pair geometry are not within the global minima on the PES. It can be written as

E def = E A...B (A) A + E A...B (B) B − E A (A) A − E B (B) B

(3)

The basis set superposition error (BSSE) was considered by the counterpoise method of Boys and Bernardi56 on all the optimized structures.


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Since B3LYP-GD3 functional includes an additional dispersion correction, the difference between the calculated values of the interaction energies using the “standard” B3LYP and B3LYP-GD3 methods was considered as dispersion energies of the cation – anion pair. AIM calculations were carried out with the AIMAll program (Version 10.05.04)57 on the wave functions obtained at the B3LYP-GD3/6-31++G(d,p) level. The topological properties of electron density at the H…O bond critical points were used as a measure of H-bonding strength. We also employed Espinosa’s equation for the estimation of the H-bond energies (EHB)58, as

E HB =

1 ⋅ V(r) 2

(4)

where V(r) is the potential energy density at the H…O bond critical point. The NBO analysis49 was done by the standard procedure in the software package Gaussian09. The amount of charge transfer (qCT) from the oxygen lone pairs (LP) orbitals of trifluoroacetate anion to the antibonding (BD*) N-H orbital of alkylammonium cation in the investigated ion pairs was calculated according to the equation

q CT

 F  = n ⋅  ij   εi − ε j 

2

(5)

where n is the orbital occupancy; εi, εj are the diagonal elements (orbital energies), and Fij is the off-diagonal NBO Fock matrix element. The stabilization energy (E(2)) associated with LPO→BD*N-H orbital interactions was estimated according to the second-order perturbation approach as follows:

E

(2)

=−

n ⋅ Fij2

(6)

εi − ε j

The simulation of proton transfer from the cation to the anion in cation – anion pairs was made by the method of scanning proton transfer coordinate along the potential energy surface with geometry optimization at every step (0.05 Å). The energies associated with proton


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transfer were determined from the difference between the energies of the transition structure with Ri and δi parameters and the global minimum structure (R, δ), which can be written as ∆E = E i ( R i , δ i ) − E ( R , δ )

(7)

The proton transfer coordinate was represented by the value δ that was calculated by the following relation: δ = rNH − rHO

(8)

where rNH and rHO are the distances from the hydrogen atom to the nitrogen and oxygen atoms in the N–Н…O fragment.

RESULTS AND DISCUSSION The interaction of an acid and a tertiary amine (neutralization reaction1, 59, 60) is not always reduced to complete proton transfer from the acid to the amine and formation of trialkylammonium-based PILs and can be more complicated: (R)3N+HA Molecules

+

−

+

−

↔ [(R)3N…HA] ↔ [(R)3N H…A ] ↔ (R)3N H+A Molecular Neutral H-bonded Dissociated ions H-bonded complex ion pair

where R can correspond to any alkyl radical with the common formula СnH2n+1. The degree of proton transfer from the acid to the amine mainly depends on the acid and amine strength. The calculated proton affinity (РА) values of triethyl-, tributyl-, dimethylethyl- and diisopropylethylamine through density functional theory using different functionals, including B3LYP, PBE, B3LYP-GD3, M06 with the same 6-31++G(d,p) basis set and the experimentally obtained РА values61 and рКа in water62-65 are given in Table 1. It is evident that the calculated РА values in all cases are in good agreement with the experimental ones. The B3LYP-GD3 method produces more accurate results. It can be seen that the рКа value grows with the increase in the energy of amine affinity with the proton. In other words, the higher the PA is, the more probable its protonation is.


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Table 1. Experimental gas-phase and calculated proton affinities of amines (PA in kcal/mol) obtained with different methods and experimental pKa values of amines in water. Amine B3LYP B3LYP-GD3 Dimethylethylamine (DMEA) 227.71 228.76 Triethylamine (TEA) 233.15 234.51 Diisopropylethylamine (DiPrEA) 236.74 238.26 Tributylamine (TBA) 237.16 238.74 a, b, c, d, e are taken from refs. 61, 62, 63, 64, 65, respectively.

M06 225.05 230.86 234.33 234.58

PBE 225.81 231.60 235.38 235.83

Exp.a 229.5 234.7 238.6

pKa 9.99b 10.75c 10.75d 10.89e

The calculation results show that the interaction of the tertiary amine with trifluoroacetic acid leads to proton transfer from the acid to the amine and formation of ions held together in the ion pair by the electrostatic interaction and the hydrogen bond (Figure 1). And the proton position in the N-Н…О hydrogen bonded fragment is asymmetric in all cases; the N-H bond is much shorter than the H…O one. The order of changing geometric parameters of the Hbonds and energy characteristics in the series of the studied compounds does not depend on the calculation method (Table 2). At the same time, it is evident that the PBE functional predicts slightly lower values of the N…O distances in the hydrogen bonded fragments than the “standard” B3LYP method, while the H-bond angle values are close to each other for both methods. Including the GD3 version of the Grimme's dispersion correction in the B3LYP method has almost no effect on the H-bond geometry in the investigated ion pairs, while the M06 functional makes the N…O distances bigger and the N-H…O angles smaller. Taking into account the dispersion interactions in the B3LYP-GD3 and М06 methods strengthens the interion interaction in all the ion pairs. The magnitude of the BSSE obtained by each functional with the 6-31++G(d,p) basis set does not affect the trends in the interaction energies of the ion pairs found in this study. The BSSE for these compounds grows with the increase in the number of carbon atoms in the tertiary amine alkyl chains. Further discussion is based on the B3LYP-GD3 data.


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Figure 1. Optimized structures consisting of hydrogen-bonded ion pairs of alkylammonium cation with trifluoroacetate anion: [DMEA][TFA] (a), [TEA][TFA] (b), [TBA][TFA] (c) or [DiPrEA][TFA] (d) at the B3LYP-GD3/6-31++G(d,p) level of theory. The interatomic distances are given in Å. Table 2. Comparison of some structural and energy parameters of the investigated ion pairs calculated by different methods. B3LYP B3LYP-GD3 M06 PBE Geometric parameters (H-bond lengths in Å, angles in deg.) rNО rNО rNО rNО ∠NHO ∠NHO ∠NHO ∠NHO [DMEA][TFA] 2.535 179.2 2.533 177.6 2.569 177.5 2.523 179.5 [TEA][TFA]а 2.569 174.9 2.562 175.4 2.613 173.8 2.540 174.6 [TBA][TFA] 2.584 175.1 2.574 175.9 2.620 174.1 2.552 174.9 [DiPrEA][TFA] 2.606 175.4 2.589 176.1 2.639 171.1 2.578 175.1 Energy parameters (in kcal/mol) Eint BSSE Eint BSSE Eint BSSE Eint BSSE [DMEA][TFA] -114.45 0.77 -118.35 0.79 -116.41 0.69 -115.61 0.88 [TEA][TFA]а -107.51 0.86 -112.44 0.90 -109.71 0.80 -111.46 0.99 [TBA][TFA] -102.27 1.02 -109.07 1.06 -106.82 0.97 -108.02 1.16 [DiPrEA][TFA] -102.26 0.92 -108.86 0.96 -106.68 0.88 -107.64 1.05 а data obtained at the B3LYP/6-31++G(d,p) level of theory in our previous study, ref. 20. Ion pairs


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Despite the fact that the results of our calculations clearly show that there are ion pairs in trifluoroacetate-based PILs, we have studied the possibility of molecular complex formation +

−

at the proton transfer from the (R)3N H cation to anion A along the hydrogen bond in the ion pair. The potential profiles for proton transfer for all the investigated compounds as a function of the δ coordinate are shown in Figure 2. As it shows, the energy profiles for the proton transfer from the tertiary alkylammonium cation to the trifluoroacetate anion within the ion pair look very similar to each other. The proton transfer energy increases in all cases with the N…H distance growth. The only minimum on the potential curve corresponds to the structures shown above (Figure 1), in which the proton is near the nitrogen atom of the protonated amine. The energy proton transfer in the ion pairs grows in the following series: DMEA

Influence of Cation Size on the Structural Features and Interactions in

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