Ab Initio Study of Structural Features and H-Bonding in

Oct 2, 2017 - For all systems, the proton transfer between ion pairs and molecular complexes has been examined. ... Its viscosity,(39) density,(40, 41...
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Ab Initio Study of Structural Features and H‑Bonding in Alkylammonium-Based Protic Ionic Liquids Irina V. Fedorova,* Michael A. Krestyaninov, and Lyubov P. Safonova G. A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, 1 Akademicheskaya Street, Ivanovo 153045, Russia S Supporting Information *

ABSTRACT: The structural and energetic characteristics of protic ionic liquids (PILs) based on ethyl-, diethyl-, or triethylammonium cations with anions of phosphorus, trifluoroacetic, or p-toluenesulfonic acids have been investigated by density functional theory calculations at the B3LYP/ 6-31++G(d,p) level of theory. As a result of the interaction between acid and alkylamine, the H-bonded molecular complexes or H-bonded ion pairs have been obtained. The increasing number of ethyl groups attached to the nitrogen atom of amine and H-bond donor ability of acid causes a stronger H-bonding interaction leading to the formation of ion pairs. For all systems, the proton transfer between ion pairs and molecular complexes has been examined. Solvation effects have been also investigated using the solvent polarizable continuum model (CPCM).

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different experimental methods. Its viscosity,39 density,40,41 conductivity,42,43 and phase transition41 have been reported. It has been shown that the H-bonding between the ammonium hydrogen atoms and the oxygen atoms of the nitrate leads to the formation of three-dimensional networks structure which is similar to those observed in water.44,45 Similar H-bond networks have been found for neat propyl- and butylammonium nitrate and their solutions in methanol, iso-propanol, and acetonitrile.46 The cation−anion interactions in these systems are stronger than those between the solvent molecules and ions.47 The correlations between physical properties and Hbond geometry have been obtained for PILs composed of ethylammonium cation and anions of different acids.48 It has been established that a short and nearly linear N−H···X H bonds in these PILs reflect “solid-like” character of physical properties, whereas weaker, bent H bonds display more “liquidlike” properties. The latter kind of cation−anion binding is preferred. Computational study of ethyl-, propyl-, and butylammonium nitrate cluster structures by Bodo et al.49 has indicated that the H-bonds geometry slightly depend on the alkyl chain length. For such systems, the distance between the hydrogen and oxygen atoms in the H bond is between 1.8 and 1.9 Å. These distances are usually classified to lie between moderate and strong H bonds.50 The highest values of the binding energies per a single H bond are observed for clusters involving two ion pairs, while these values change slightly with further increasing the size of the cluster. These results agree

INTRODUCTION Protic ionic liquids are one of the promised materials with wide practical applications such as catalysis,1,2 extraction/separation,3−5 electrolyte devices,6−8 and soft materials.9−11 PILs are a subclass ILs formed by the proton transfer from a Brønsted acid (AH) to a Brønsted base (B)12,13 according to the following AH + B ↔ A− + BH+

(1)

One of the structural features of PILs is the formation of strong H bonds between protonated base cations and acid anions that define their unique physicochemical properties.14−16 Because of the wide range of cations and anions constituting PILs, the determination of the structures and properties of all PILs one by one by experimental methods is unfeasible. In principle, the use of computational chemistry methods could be a valuable tool to simulate all possible combinations of cations and anions or their proportions and, most importantly, to examine structural features of PILs. Numerous studies have been performed to investigate the Hbonding characteristics within the PILs.16−27 Some of them indicate a significant role of H-bonding, whereas others show its minor importance when compared to the electrostatic interactions (Coulomb force).14,28−33 There are also a number of quantum chemical studies describing the crucial role of dispersion forces in ILs.24,34−37 In particular, they have a major contribution to the interaction energies in PILs that are caused by the formation of a larger system (cluster size)37 or presence of a longer alkyl chain of the cation.34 Among all PILs, neat liquid ethylammonium nitrate, which is also the first known IL,38 has been widely investigated by © XXXX American Chemical Society

Received: June 2, 2017 Revised: October 2, 2017 Published: October 2, 2017 A

DOI: 10.1021/acs.jpca.7b05393 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A well with the outcomes of Fumino et al.29 who have studied of the H-bonding features in clusters of tetramethyl- or trimethylammonium nitrate consisting up to six ion pairs. The steric effects of alkyl groups on strength of H bonds in triflate-51 and fluorous52-based PILs have been also investigated. The H-bonding interactions within these ion pairs become stronger with increasing number and size of cation alkyl groups, leading to lower mobility of ions. The replacement of the methylsulfonate anion by nitrate and chloride in PILs with trimethylammonium cation causes the decreasing of the H-bonding interactions.29 In a mixture of two different PILs having the same triethylammonium cation, the two different anions compete with each other for a hydrogen bond to this cation.53 As a result, the H-bonding interaction of the cation with the methylsulfonate anion is much more favorable than the interaction with the triflate anion. Several studies54−57 have shown that not only ion pairs but also neutral components that form as a result of proton backtransfer from cation to anion exist in liquid and gaseous PILs. In particular, the transition state structures for proton transfer in acetate-based PILs have been examined with density functional theory.57 Stoimenovski et al.58 have indicated that the degree of proton transfer in PILs having similar value of ΔpKa (the difference between the pKa values of acid and protonated base) mainly depends on whether the alkylammonium ion is a primary, secondary, or tertiary. The proton transfer in ethylammonium acetate is more complete than in the case with triethylammonium cation. For the latter case, the presence of neutral nonconducting species, possibly the neutral ion pairs or H-bonded clusters, has been demonstrated. Also, the authors suggest that the effect of the environment influences significantly the process of proton transfer in PILs. The present work aims to study the structural features and H-bonding interaction in the series of PILs which contain ethyl-, diethyl-, or triethylammonium cations and dihydrogen phosphite, trifluoroacetate, or tosylate anions using B3LYP approximation. The influence of both the anion nature and steric effects of the cation alkyl groups on the H-bonding strength are also examined. The paper is organized as follows. First of all, we determine the Gibbs free energy change for reaction of the interaction between acid and alkylamine molecules. We investigate the features of the H-bonding interaction in the most stable structures. The following criteria as a way of identifying H bonds are used, that is, (i) geometric characteristics for X···H (where X = O and N) fragment,50 (ii) energy of the H bonds based on Espinosa’s equation,59 and (iii) topological properties electron density and its Laplacian at (3, −1) bond critical point (BCP).60 Finally, we present the potential energy curves for proton transfer that allow us to find all the local minima and saddle points along the path connecting the molecular complexes and ion pairs. To study the solvation effects on the stabilities of PILs, we employed the implicit solvent polarizable continuum model, CPCM (conductor-like polarizable continuum model). 61,62 We are convinced that the obtained results will be important for understanding the behavior of PILs, especially for prediction of their physicochemical properties and their suitability for the particular application.

Gaussian-0966) and the 6-31++G(d,p) basis set,67 which allows one to estimate adequately structures and energies of the Hbonded systems.68 Three acids of varying H-bond donor strength such as phosphorus (PA) (pKa = 2.0), trifluoroacetic (TFA) (pKa = 0.23), and p-toluenesulfonic (PTSA) (pKa = −6.56) acids and three amines with different number of ethyl groups attached to nitrogen atom were selected for our study. The optimized geometries of single molecules (see Figure S1) were employed to construct the initial starting structure of different configurations in the AH−B systems. Both H-bonded molecular complexes and H-bonded complexes where the proton is transferred to the alkylamine nitrogen forming ion pairs (further referred to as ion pairs) were considered in these systems. The possibility of formation of different H-bonded structures in the AH−B systems in terms of Gibbs free energies (at 298 K and atmospheric pressure) was estimated as the difference between the free energy of the H-bonded complex and separately optimized molecules. The interaction energy (ΔEint) of all the H-bonded complexes was estimated according to the so-called supermolecular approach. For H-bonded molecular complexes, the ΔEint value was obtained by subtracting the sum of neutral acid and base energies from the total energy of complex, while the interaction energy in the H-bonded ion pair was defined by subtracting the sum of cation and anion energy from the total energy of ionic complex. Furthermore, the interaction energies were corrected for the basis set superposition error (BSSE),69 using the full counterpoise method of Boys and Bernardi.70 Some test calculations were carried out by applying another basis set, in particular the 6-311++G(d,p),71 and no qualitatively different result was observed. Also, the interaction energies of the H-bonded complexes calculated at the “standard” DFT level with both basis sets were compared with the results obtained by the dispersion-corrected DFT method (B3LYP+GD3 method).36 As will be extensively discussed later, both B3LYP functionals give the same qualitative trends for PILs studied here. The results of all these calculations can also be found in Tables S1−S3. In order to better understand the H-bond properties, we employed the “atoms in molecules” theory (AIM).60 In accordance with the Bader theory, the existence of (3, −1) the critical point of the electron density (ρ(r)) on the bond path is a sufficient condition that the two atoms be bonded to one another. This kind of BCP has one positive (λ3) and two negative (λ1 and λ2, λ1 ≥ λ2) eigenvalues. The sum of the eigenvalues of the density Hessian at this point is equal to the Laplacian of electron density (∇2ρ(r)) value. As a rule, the electron density at BCP is used to characterize the intensity of bond. Herein, greater electron density at BCP corresponds to a stronger bond. The ∇2ρ(r) determines the nature of the bond. Any pair of atoms is regarded as covalently bonded if ∇2ρ(r) < 0 and hydrogen bonded if ∇2ρ(r) > 0. The AIM calculations are performed using the AIMAll software (version 10.05.04).72 In addition, we estimated the hydrogen bond energy (EHB) according to Espinosa’s equation:59 E HB =

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1 × V (rCP) 2

(2)

The energy curves along the proton transfer coordinate, δ = rN···H−rO···H for the H-bonded complexes was determined using the potential energy surface (PES) scan method. A hydrogen atom was transferred between N and O atoms of alkylammonium cation and acid anion with an increment of

THEORETICAL METHODS The results reported here were obtained by quantum-chemical calculations based on density functional theory (DFT)63 level by using the B3LYP functional64,65 (as implemented in B

DOI: 10.1021/acs.jpca.7b05393 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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Figure 1. Optimized structures of molecular complexes and ion pairs at the B3LYP/6-31++G(d,p) level of theory. Dashed lines indicate H bonds.

Table 1. Gibbs Free Energy (ΔG, kJ/mol) Associated with the Formation of Different H-Bonded Complexes Determined with the B3LYP/6-31++G(d,p) Level at 298 K and Atmospheric Pressure EA

DEA

TEA

type reactions

PA

TFA

PTSA

PA

TFA

PTSA

PA

TFA

PTSA

AH + B → A−H···B AH + B → A−···BH+

−17.33 −3.32

−26.76 −

−17.77 −9.32

−15.60 −5.81

−22.99 −15.99

− −17.63

−5.84 −0.38

− −10.47

− −13.23

representing the solvent. The ε = 1 within the inner cavity. The cavity is constructed from the overlapping van der Waals spheres of the atoms. This approach allows us to describe the distinctions between proton transfer processes in the gas phase and solvated phase.

0.05 Å, and the geometry optimization was performed at each point. The energies associated with proton transfer were defined from the difference of the energies of the transition structure with Ri and δi parameters and the global minimum structure (R, δ), which can be expressed as ΔE = E i(R i , δi) − E(R , δ)

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(3)

RESULTS AND DISCUSSION With dependence on the nature of acid and base, the formation of both H-bonded molecular complexes AH···B (Figure 1I) and H-bonded ion pairs A−···BH+ (Figure 1II) are possible in the systems studied here. Our attempt to obtain the H-bonded molecular complexes of PTSA with diethyl- and triethylamines as well as H-bonded complex of TFA with triethylamine was unsuccessful: molecular configuration, which was preassigned

The harmonic frequencies were calculated after optimizing all of the possible geometries. This allows us to identify a minimum (without any imaginary frequency) and saddle point (with only imaginary frequency). The solvent effects on the PES for proton transfer were studied by employing the CPCM model. Here, the investigated system is placed in a cavity surrounded by a polarizable continuum with a dielectric constant (for PILs ε = 25), C

DOI: 10.1021/acs.jpca.7b05393 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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Table 2. Geometric (Interatomic Distances in Angstroms and Bond Angles in Degrees) and Energetic (Energies of H-Bonds and Interaction Energies in kJ/mol) Characteristics of Different H-Bonded Complexes Calculated at the B3LYP/6-31++G(d, p) Level of theory type molecular complexes PA−EA PA−DEA PA−TEA TFA−EA TFA−DEA PTSA−EA ion pairs [PA][EA] [PA][DEA] [PA][TEA] [TFA][DEA] [TFA][TEA] [PTSA][EA] [PTSA][DEA] [PTSA][TEA] a

Figure 1

RON

(I-a) (I-d) (I-f) (I-b) (I-e) (I-c)

2.618 2.600 2.565 2.620 2.590 2.589

(II-a) (II-c) (II-f) (II-d) (II-g) (II-b) (II-e) (II-h)

2.556; 2.635; 2.543 2.567 2.569 2.551; 2.657; 2.602

ROHa

RNH 1.586 1.540 1.485 1.571 1.515 1.525

2.713 2.726

2.725 2.718

1.109; 1.052; 1.128 1.117 1.125 1.108; 1.063; 1.093

1.045 1.060 1.085 1.051 1.075 1.067 1.048 1.075

1.497; 1.626; 1.417 1.475 1.446 1.479; 1.674; 1.512

1.038 1.047

∠NHO 168.8 177.4 172.5 175.8 179.5 174.9

1.825 1.807

1.906 1.819

157.5; 154.0; 174.8 164.2 174.9 160.7; 151.6; 174.0

140.1 143.6

133.2 141.7

ΔEint (BSSE)

EHB 80.82 99.32 126.76 86.00 110.83 103.74

−81.36 (5.29) −85.67 (5.96) −100.43 (7.34) −83.81 (4.57) −92.31 (4.74) −88.89 (5.88)

99.33; 37.03 61.85; 38.46 138.05 111.59 124.46 106.40; 31.81 53.32; 37.78 92.33

−543.60 −501.07 −482.51 −473.58 −449.78 −502.89 −462.34 −439.97

(4.37) (5.31) (6.37) (3.26) (3.60) (4.49) (5.87) (6.67)

The length of the O−H bond is 0.969, 0.973, and 0.973 for PA, TFA, and PTSA molecules, respectively.

B3LYP/6-311++G(d,p) calculations lead to results similar to those obtained with the 6-31++G(d,p) basis set (Table S2). Although the O···N distances in all the H-bonded complexes are slightly longer at the B3LYP/6-311++G(d,p) level, the calculated H-bond angles show no significant difference in the values. Among the considered amines, it may be seen that triethylamine demonstrates a marked ability to act as a proton acceptor (due to single site) in the H-bonding interactions with the considered acids. The presence of strong and directional H bond provides the successful proton transfer from the hydroxyl group of TFA and PTSA to the nitrogen atom of TEA, leading to the dominant formation of ion pairs (Table 1). In like manner, PTSA is a better hydrogen donor in the interaction with amines than the other investigated acids. The calculated RON value between PTSA and EA molecules is smaller than the ones in the molecular complexes of PA and TFA with the same alkylamine. For latter cases, the intermolecular O···N distances are very closely in value. The H-bond strength in the molecular complexes (e.g., with phosphorous acid) increases when passing from primary to secondary and tertiary ethylamine. For these systems, there is good correlation between interaction energies (ΔEint) and geometric parameters of the H bonds. Among them, the highest values of ΔEint and the smallest value of RON are observed for PA−TEA (Table 2). The calculated values of the interaction energies between acid and base in the molecular complexes agree fairly well with the energies of the H bond (EHB) evaluated by the Espinosa’s method. The high EHB values reflect the significant strength of the H bonds in these systems. The results of our computations show that the different configurations having either one H bond or two H bonds depending on cation and anion are possible upon formation of ion pairs. A similar conclusion was drawn by Hayes et al.,48 who found that the formation of more than one H bond is possible in PILs composed of ethylammonium cation and anions of different acids. As can be seen from Table 2, the one H bond is formed between triethylammonium cation and anions of all the investigated acids (Figure 1II, panels f, g, and h), and parameters of this bond fall into the strong hydrogen bond criteria. The two hydrogen atoms attached to the nitrogen atom

for the initial complex, transformed upon optimization of the geometry in the ionic structure in which the proton is fully transferred from the acid molecule to base forming two ions which strongly hydrogen bond, as we shall discuss later. We also found that TFA, on the contrary, is able to form only one molecular complex with ethylamine. From Table 1, one can see that the Gibbs free energies (ΔG) associated with the formation of all the other investigated H-bonded complexes are negative, supporting their energetic stability (spontaneous process). The calculated ΔG values for the H-bonded ion pairs formed by the triethylammonium cation with anions of the aforementioned acids increases in the following order: [PA]− < [TFA]− < [PTSA]−. This sequence is consistent change in thermal stability of the same ionic liquids.73 Here, the greater the energy value, the higher is the decomposition temperature. It is worth noting that the B3LYP computations with 6-311+ +G(d,p) (Table S1) predict less negative ΔG values for investigated systems (with the exception of [PTSA][DEA] and [PA][TEA] ion pairs) compared to those obtained with the 631++G(d,p). Nevertheless, the same trend of increase in the energetic stability for PILs with the same cation and acid anions in the order [PA]− < [TFA]− < [PTSA]− is observed. Geometries and Interaction Energies. The geometrical and energetic parameters of the H bonds as well as interaction energies both between molecules in the A−H···B complex and between cation and anion in the A−···BH+ ion pairs for the most stable structures are summarized in Table 2. As one sees, the H-bonding interactions in all of the molecular complexes lead to the lengthening of the proton-donating O−H bond of acid with respect to its molecule. The proton in the hydrogen bond is close to the oxygen atom belonging to the hydroxyl group of acid than to the nitrogen belonging to the alkylamine (i.e., ROH < RNH). On the contrary, the value of ROH in the Hbonded fragment for the ion pairs becomes larger than the value of RNH. As a first estimation, it is possible to relate the strength of the H bond to the interatomic distance between the oxygen and nitrogen atoms in the H bond (RON).74−76 All optimized structures of the molecular complexes have mainly strong H bonds with RON smaller than 2.65 Å in an almost linear arrangement. Here, it is important to note that the D

DOI: 10.1021/acs.jpca.7b05393 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A Table 3. Topological Parameters at the Corresponding Bond Critical Points for Different H-Bonded Complexesa type molecular complexes (see Figure 1I) PA−EA PA−DEA PA−TEA TFA−EA TFA−DEA PTSA−EA ion pairs (see Figure 1II) [PA][EA] [PA][DEA] [PA][TEA] [TFA][DEA] [TFA][TEA] [PTSA][EA] [PTSA][DEA] [PTSA][TEA] a

bond

ρ(r)

O−H N···H O−H N···H O−H N···H O−H N···H O−H N···H O−H N···H

0.2720 0.0733 0.2598 0.0837 0.2398 0.0977 0.2731 0.0763 0.2544 0.0900 0.2567 0.0857

N−H O···H N−H O···H N−H O···H N−H O···H N−H O···H N−H O···H N−H O···H N−H O···H

0.2625; 0.0795; 0.2923; 0.0577; 0.2525 0.0965 0.2598 0.0867 0.2558 0.0923 0.2624; 0.0828; 0.3027; 0.0513; 0.2789 0.0756

0.3125 0.0369 0.3131 0.0385

0.3217 0.0310 0.3176 0.0372

∇2ρ(r)

λ1

−1.2861 0.0916 −1.1489 0.0708 −0.9607 0.0266 −1.2987 0.0869 −1.1010 0.0542 −1.1253 0.0664

−1.2912 −0.1476 −1.1861 −0.1796 −1.0258 −0.2262 −1.3065 −0.1578 −1.1465 −0.2000 −1.1701 −0.1874

−1.2778; −1.6795 0.1532; 0.1015 −1.5173; −1.6772 0.1473; 0.1045 −1.1740 0.1328 −1.2397 0.1393 −1.1999 0.1321 −1.2733; −1.7432 0.1526; 0.0893 −1.5982; −1.7100 0.1382; 0.1039 −1.3934 0.1620

−1.0178; −0.1670; −1.1557; −0.1010; −0.9555 −0.2281 −0.9916 −0.1956 −0.9689 −0.2165 −1.0194; −0.1821; −1.1258; −0.0862; −1.1002 −0.1583

λ2 −1.2778 −0.1465 −1.1744 −0.1794 −1.0174 −0.2254 −1.2903 −0.1574 −1.1317 −0.1999 −1.1481 −0.1863

−1.2613 −1.0178 −1.2512 −0.0540

−1.2957 −0.0403 −1.2720 −0.0528

−1.0087; −0.1644; −1.1566; −0.0992; −0.9548 −0.2234 −0.9864 −0.1913 −0.9680 −0.2114 −1.0117; −0.1760; −1.2068; −0.0831; −1.0992 −0.1530

λ3 1.2829 0.3856 1.2115 0.4299 1.0825 0.4782 1.2980 0.4021 1.1773 0.4541 1.1929 0.4401

−1.2447 −0.0503 −1.2383 −0.0535

−1.2781 −0.0393 −1.2601 −0.0515

0.7486; 0.4846; 0.8051; 0.3476; 0.7364 0.5843 0.7383 0.5262 0.7370 0.5600 0.7577; 0.5107; 0.8245; 0.3075; 0.8060 0.4732

0.8266 0.2027 0.8123 0.2120

0.8305 0.1689 0.8221 0.2082

All values in a.u.

the calculated ΔEint values for, for example, the [PA][EA], [PA][DEA], [PA][TEA] ion pairs at the B3LYP+GD3 level are −556.62, −519.15, −502.71 kJ/mol, respectively. Also, the strength of interactions between triethylammonium cation and acid anions becomes smaller when passing from [PA]− to [TFA]− (−470.45 kJ/mol) and [PTSA]− (−467.44 kJ/mol). Topological Properties. As mentioned before, Bader’s theory of “atoms in molecules” is a useful tool to analyze bonding properties since the characteristics of bond critical point indicate the nature of these interactions. For all considered systems, there are two (3, −1) BCPs in a hydrogen bond, one between hydrogen and oxygen atoms within acid and one between acidic proton and nitrogen atom of alkylamine. Results of the AIM analysis are given in Table 3. The Hbonding in the molecular complexes has a low value of the electron density at the N···H BCP and positive value of its Laplacian. These characteristics are in good agreement with the H-bonding criteria proposed by Koch and Popelier.79,80 Among investigated molecular complexes, the maximum of the ρ(r) is observed for PA−TEA that has the strongest H bond and minimal N···H distance (Table 2). By contrast, the smallest ρ(r) value at the N···H bond and the greatest value of RNH are obtained for PA−EA, which reflects the weakest H-bonding interaction. A relatively large ρ(r) values and negative values of ∇2ρ(r) at the O···H BCPs show that the O−H bonds within acids have covalent character. For the ion pairs, the electron density at the N···H BCP in the H-bonded fragment is much larger than at the O···H. The Laplacian of the electron density

of ethyl- (Figure 1II, panels a and b) and diethylammonium (Figure 1II, panels c and e) cations participate in the Hbonding with different oxygen atoms in the POO− group of dihydrogen phosphate anion as well as in the SOO− group of the tosylate anion. In such systems, the N−H···O−(−X) (where X = P and S) H-bond lengths are shorter than the ones in the N−H···O(X) fragment. The deviations of the H-bond angle from its idealized value (180°) are observed for both H bonds. On the basis of these data, the H bonds may be classified as the moderate-strength hydrogen bond. The calculated values of the interaction energies for all the investigated ion pairs are very large (much larger than the strong hydrogen bond energy 60÷160 kJ/mol77,78) that indicates the existence of strong electrostatic interactions between ionic species. As a result, the O···N distances in the ion pairs, especially in the structures with one H bond is smaller than ones in the molecular complexes. The increasing number of ethyl groups on the ammonium cation for PILs with the same anion causes the decreasing of the interaction energy but not the energy of the H bond. Similar results were found for the series of PILs containing the same cations and heptafluorobutyrate anion.52 Obviously, the larger the ions, the weaker the interaction energy turns out. Changing the anion at the same cation in all of the considered systems has the same effect. It is important to note that the dispersion correction to B3LYP functional significantly increases the ΔEint values (Table S3). Nevertheless, we obtained the same qualitative trends for PILs as calculations without dispersion correction. For comparison, E

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transfer from the acid in the H-bonded molecular complex to the nitrogen atom of the amine was considered. It is important to note that all the H-bonded structures represented by Figure 1 are real minima on the corresponding PES. Our computations show that for ethylammonium trifluoroacetate the proton transfer from A−···BH+ to AH···B (Figure 2a) takes place without an activation barrier, whereas in the case of ethylammonium dihydrogen phosphate and tosylate, the energy barrier for proton transfer was found. The barrier height for transfer is lower for ethylammonium tosylate compared to dihydrogen phosphate. For both cases, the potential energy of the molecular complexes is lower than for the ion pairs. Compared to the systems considered above, spontaneous proton transfer A−···BH+ → AH···B for PILs with triethylammonium cation and anions of the aforementioned acids is very unlikely (Figure 2c). Although the curve for triethylammonium dihydrogen phosphate has an asymmetric double-well form, the ion pair has a higher potential energy in the proton transfer process than the molecular complex. As can be seen, the energies associated with proton transfer in PILs with triethylammonium cation become higher when passing from [PA]− to [TFA]− and [PTSA]−. These results correlate well with the energy characteristics of the formation of these Hbonded ion pairs, as mentioned earlier in Table 1. Since the existence of activation barrier for proton transfer between A−··· BH+ and AH···B is sufficient to cause a change in curve shapes, no such correlation is observed for other investigated PILS. For the diethylammonium cation cases (Figure 2b), the situation seems to lie between the ones described above. Herein, the calculated energy profiles for proton transfer strongly depend on the nature of the acid anion. The curves for diethylammonium dihydrogen phosphate and trifluoroacetate have two asymmetric minima with respect to the activation barrier. These minima correspond to energetically stable positions of the proton along the hydrogen bond; that is, the proton can be bound to either the nitrogen atom of DEA or the oxygen atom defining a hydroxyl group of the acid. This indicates that the proton transfers incompletely; the molecular complexes could coexist with ion pairs. The energy barrier height of proton transfer for diethylammonium trifluoroacetate is lower than for dihydrogen phosphite anion. Proton transfer from diethylammonium tosylate to its molecular complex is not observed. Also, changing the cation (for the same anion) in the analyzed systems has a significant effect on the process of proton transfer. All potential curves for proton transfer from A−···BH+ to AH···B, where A− is dihydrogen phosphate anion represent a double-well form, pointing out that the molecular complexes could coexist with ion pairs. The energy barrier height for proton transfer from alkylammonium cation to dihydrogen phosphate anion decreases in the following order: [EA]+ (7.71 kJ/mol) > [DEA]+ (4.78 kJ/mol) > [TEA]+ (2.19 kJ/mol). Solvation Effects. As the gas phase calculations cannot always correctly describe the real liquids’ behavior, it is worth making a comparison of the results obtained in the gas phase and solvent environment, to evaluate the solvation effects on the energy profiles for proton transfer and describe the distinctions between these processes. In general, the overall structures of all our ion pairs obtained from the B3LYPCPCM/6-31++G(d,p) calculation are close to those found in the gas phase. The environmental conditions influence mainly the H-bond geometries in these systems. Results in Table S4

at the N−H bonds have negative values, and consequently, these bonds become covalent in nature. The calculated ρ(r) and ∇2ρ(r) values indicate that the O···H binding in these cases mainly originates from the H bond between the cation and the anion. For ion pairs with two H bonds, the different ρ(r) and ∇2ρ(r) values at the BCP for both H bonds are observed, which is consistent with the aforementioned results (Table 2). Proton Transfer Process. The study of the potential energy surface and energy barriers is of great interest,81−84 especially for understanding the shape and proton dynamics in the H-bonded complexes. The potential profiles for proton transfer between A−···BH+ and AH···B along the hydrogen bond as a function of the δ coordinate are shown in Figure 2

Figure 2. Potential energy profiles for proton transfer from A−···BH+ to AH···B, where BH+ is (a) ethyl-, (b) diethyl-, and (c) triethylammonium cation in the gas phase (filled symbols) and solvent environment modeled by the CPCM model (open symbols) calculated at the B3LYP/6-31++G(d,p) level. The curves for each acid anion are assigned in the legend.

(panels a−c). In all of the considered systems (with the exception of ethylammonium trifluoroacetate), the proton transfer from alkylammonium cation in the H-bonded ion pair to oxygen atom in X−O− (where X = P, C, and S) group of acid anion was investigated. Since no energetically stable ion pair for ethylammonium trifluoroacetate was found, proton F

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with triethylammonium cation and the same acid anions is very unlikely. The energy profiles for proton transfer in the cases with diethylammonium cation strongly depend on the participating acid anion, and potential curves (with the exception of tosylate anion) show asymmetric double minima, corresponding to the molecular complexes and ion pairs. In the solvent model, on the contrary, the probability of proton transfer from alkylammonium ion in the investigated ion pairs to acid anion is negligibly small. Although all considered configurations are very small, we believe that we have obtained useful information on the structural features of ionic liquids and interactions between their components. The latter may considerably influence the physical properties of real liquids. In particular, the correlation between our theoretical results and experimental data73 has been found for PILs based on triethylamine with acids studied here indicating that triethylammonium tosylate exhibiting a high thermal stability show a high value of free energy associated with its formation.

show that the O···H and O···N distances in the solvated ion pairs are greater (for example, 1.606 Å and 2.671, respectively, in [PA][TEA]), and the N−H bond lengths are shorter (1.068 Å for the same ion pair) than in the gas phase. Here, weaker interaction that forms between cation and anion within solvated ion pairs is identified from the geometrical criteria of the Hbond formation. Using the CPCM model, we also found that the formation of [TFA][EA] ion pair is possible (Figure S2). In accordance with both methods of the computations, the RES for proton transfer from A−···BH+ to A···BH for all the cases with triethylammonium cation show qualitatively similar shapes, while the calculated curves for all other investigated ion pairs differ markedly from those obtained in the gas phase (Figure S3). For comparison, the potential profiles for the dihydrogen phosphite cases are shown in Figure 2. When the CPCM model is applied, all the curves for proton transfer A−··· BH+ → AH···B have a single minimum corresponding to the initial state where proton is covalently bonded to the nitrogen atom of amine. The energies of all these systems greatly increase with the increasing N···H distances. This indicates that all our ion pairs are definitely energetically more stable than the ones in the gas phase. The probability that the proton is transferring from alkylammonium ion to acid anion forming molecular complexes is negligibly small. As it is noticeable from Figure S3, the energy values associated with proton transfer from the same cation to acid anions in the considered ion pairs increase in the order: [PA]− < [TFA]− < [PTSA]−. In fact, these results agree well with the energetic stable of the Hbonded ion pairs in the gas phase (Table 1).

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b05393. Optimized structures of single molecules are presented in Figure S1, Cartesian coordinates and calculated Gibbs free energies at 298 K and atmospheric pressure for all the investigated structures are also given; results of the B3LYP/6-311++G(d,p) calculations are shown in Tables S1 and S2; Table S3 contains the interaction energies of different H-bonded complexes calculated at the B3LYP/ 6-311++G(d,p) level and B3LYP-GD3 method with 631++G(d,p) and 6-311++G(d,p) basis sets; Cartesian coordinates for optimized [TFA][EA] structure obtained from the B3LYP-CPCM/6-31++G(d,p) level are shown in Figure S2; Figure S3 presents the potential energy curves for proton transfer from alkylammonium cation to acid anion in all the considered systems obtained from the B3LYP-CPCM/6-31++G(d,p) calculations; bond lengths and angles for H-bonded ion pairs calculated at the B3LYP-CPCM/6-31++G(d,p) level of theory in Table S4; the complete text of refs 26 and 66 is also given (PDF)

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CONCLUSIONS Protic ionic liquids based on ethyl-, diethyl-, or triethylammonium cations with anions of phosphorus, trifluoroacetic, or ptoluenesulfonic acids have been examined using quantum chemical gas-phase computations. The structural and energetic characteristics of both H-bonded ion pairs (A−···BH+) and Hbonded molecular complexes (A−H···B) in these systems were investigated. We have shown that the strength of H-bonding interactions considerably depends on the nature of acid and base. The calculated interaction energies between acid and amine molecules in the molecular complexes correlate well with the estimated H-bond energies by the method of Espinosa which increase with increasing the number of the ethyl group attached to the nitrogen atom of amine. The strong acid as PTSA promotes proton transfer leading to the ion pair formation and performs better than the other considered acids. All investigated amines interacting with phosphorous acid can form both molecular complexes and ion pairs with H bonds. The interaction within ion pairs is a result of a subtle balance between Coulomb forces and H-bonding. The Hbonding in all of the systems may be classified as the strong H bonds (with the exception of the ion pairs in which there is two H bonds with moderate strength). The analysis topological parameters derived from the Bader theory supports the obtained results from the DFT calculations. The potential curves for proton transfer from A−···BH+ to AH···B have been investigated using the potential energy surface scan method, and the solvation effect on the PES have been included using the conductor polarized continuum model. In the gas phase, the proton transfer process from ethylammonium cation to anions of all considered acids is much easier than those in other investigated systems. The spontaneous proton transfer A−···BH+ → AH···B for PILs

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AUTHOR INFORMATION

Corresponding Author

*E-mail: fi[email protected]. ORCID

Irina V. Fedorova: 0000-0002-0424-8498 Author Contributions

The manuscript was written through the contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Russian Science Foundation (Grant 16-13-10371). G

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