All the reagents used such as choline chloride, betaine, 1,2-propanediol, glycerol, urea, ethylene glycol, 1,2 butanediol, 1,4 butanediol, and ILs were commercially available by Sigma-Aldrich, Merck, and IoLITech. The certificate of analysis guarantees purity ≥99%. DESs were prepared by mixing the corresponding components at the desired mole ratio and heating them for 3 h at 70–80°C until a clear liquid appeared. Previously, the reagents choline chloride, urea, and IL were put under vacuum at 70°C for 3 h to ensure the removal of traces of water before being used. HBD such as 1,2-propanediol, glycerol, and 1,2-butanediol were dried with molecular sieves. After preparation, they were stored in a desiccant prior to being used. Betaine monohydrate was used in the formation of the corresponding DES without further drying.

The probe ferrocyphen was purchased from BOC Science and used without further purifying. The probe Cu(acac)(tmen)⁺ClO₄⁻ was synthetized using the procedure indicated in the literature (Kuzmina et al., 2017) and purified through hot filtration and recrystallization.

All calculations were performed using the Gaussian 09 package visualized by the Gaussview 5.0 program. Initially, the calculations were made at the M06/6-31+g(d,p) level of theory. Antimony atom was represented by the pseudopotential core LanL2DZ, and all the calculations were performed using the SMD model of implicit solvation to represent the solvent dichloroethane. An optimization of geometries at the length of interaction followed by a frequency analysis was performed to characterize the thermodynamic parameters of the system. These energies were compared to the energy of the probe and anion/IL at a non-interacting distance to get the binding enthalpy. This was carried out in order to account for the error of superposition of bases by using the same Hamiltonian to represent the complete system in both cases. Later, the calculations were redone in different levels of theory, changing the DFT functional (to B3LYP and ωB-97XD) and the basis size (to 6-311+g(2df,2p) for the elements of the first three rows and cc-pVTZ-PP for antimony), to ensure the independence of the results on the basis set and functional used.

Table 1 shows the experimental values of DN and AN determined by the solvatochromic shift of the probes of copper and iron (Cu(acac)(tmen)⁺ClO₄⁻, ferrocyphen) dissolved in ILs. As expected, most of the ANs fall in a narrow range of variations, or slightly lower when compared to the C₄C₁IM cation with the C₂C₁IM⁺ analogous. We consider, for instance, the slight reduction when C₄C₁IMSCN (AN = 25,6) and C₂C₁IMSCN (AN = 27,1) are compared, or the null effect observed after comparing C₄C₁IMCF₃COO (AN = 27,0) with C₂C₁IMCF₃COO (AN = 27,1). Therefore, the increase in the chain length has a little impact on the capacity of the cation to accept electric charge density from a donor. A more significant effect can be observed when the nature of the cation is changed. For example, going from an imidazolium cation such as C₂C₁IMDCA (AN = 28,4) to a pyrrolidinium cation C₄C₁PYRRDCA (AN = 23,1) with the same counter anion shows a greater decrease in the capacity to accept charge. This fact may be traced to the enhanced ability of imidazolium cation to delocalize electronic charge by the presence of nitrogen atoms and double bonds in comparison to pyrrolidinium cation (see Figure 1).

In ILs, the AN is, in general, associated to the cationic component of the IL. To assess the influence of the type of cation on the AN’s responses, the anion NTf₂⁻ was kept fixed. The cations considered include aromatic heterocyclic ring (imidazolium, AN close to 30, for both chain length); piperidinium and pyrrolidinium cations, both with AN close to 26; quaternary amine (ethyl dimethyl propyl ammonium EDMPA, AN = 28,8); and a sulfonium cation (triethylsulfonium TES, AN = 28,6). The values of AN fall within the range between 25,6 and 30 as shown in Table 1. These values could be either evidence for the low response of the capacity to accept charges in IL or it may be attributable to the probe which could be unsuitable to resolve finer differences of the solvent responses. This fact presents an additional problem when a computational method is used to model the system (IL-probe) because a low variance in the experimental data gives flat curves in the correlation between calculated parameters and experimental data. Then, a careful approach is needed to analyze these data.

On the other hand, the DN is associated with the anion of the ILs. Table 1 shows a significant difference in the values of DN. In this case, the probe chosen has enough sensitivity to give a wide range of values which facilitates the comparison with calculated data. As expected, the presence of an oxygen-containing group or cyanate group increases the value of the DN, while the increase in the side chain length of the imidazolium only has a small decreasing effect on the DN in most of the ILs tested. It is worth noting that several ILs reacted with the probes in such a way that spectrophotometric measures can no longer be used reliably.

To set up a reliable model for the donicity number for ILs, the original definition proposed by Gutmann was slightly adapted to consider the variation in the binding enthalpy of solvent–probe systems, including the presence of the solvent. The calculated results display a qualitative agreement with experimental data. A good linear relationship between them is obtained, as shown in Figure 3.

As it was explained in the methodology section, the geometries of probe–anion and probe–IL pairs were optimized, adding one molecule of dichloroethane as an explicit solvent in the simulation. The stabilization of charges of the anions gave better results which were closely correlated to the experimental data as compared to the same calculation in the gas phase. The choice of solvent was the same as the original work; the focus was to simulate the original experimental conditions in the calculations. However, the computational model treats the IL as a solute which differs from experimental values because in the UV–Vis experiments, the ILs act as solvents. In this case, bulk properties do not appear to influence the donicity of the system, so we conclude that this is good approximation.

All the calculations made supported the original predictions of the change in geometry and coordination number of the antimony atom, going from a trigonal bipyramidal geometry to a more octahedral one. As noted by Gutmann, stronger donors have a smaller antimony–donor distance and longer Sb–Cl distance, as it is shown in Table 2 for the series of anions: MeSO₄⁻, CF₃COO⁻, and CH₃COO⁻. As noted by Gutmann, there is a bigger influence on the Sb–O distance than the Sb–Cl.

Table 2 emphasizes a qualitative agreement with Gutmann’s proposal, in the sense that shorter Sb–O distances are in accordance with a more favorable probe–anion interaction. The results for the calculated DN are contrasted against the experimental values for the cases of single anions of the IL and the cation–anion pair in Figure 3. As expected, the major contribution to the DN is given by the anion which gives good correlation with the experimental values. When the cation is added, less dispersion of the data can be observed, thereby suggesting that even at a very low level of approximation (first-order approximation), the probe–anion pair is qualitatively assessed at lower computational cost. It is worth noting that this methodology treats the ILs as an ion pair which is not necessarily true for this kind of solvents, but we believe that, in this specific case, the addition of extra pairs of IL will not change the results drastically.

An additional problem arises when an anion has multiple possible interaction centers that give different local minima configurations. For example, the anion SCN⁻ could interact with the probe through the sulfur atom or through the nitrogen atom, and both configurations seem to be stable enough to generate a minimum in energy. The configuration that gets closer agreement with the experimental values for the DN and, more importantly, that is consistent with the correlation found for the remaining elements of the series is when the molecule interacts through the nitrogen as it has a bigger binding enthalpy than the other configuration and, thus, gets closer to the trend. The choice of the configuration to be used to model the interaction depends on the nature of molecules that surround the anion, since the different polarizabilities of each interaction site are determinant to decide which side the anion is going to prefer to interact with. In this case, both the antimony probe for the calculation and the experimental probe based on copper seem to prefer to interact with the nitrogen side of the anion, but that is not necessarily the case for all solutes.

Figure 4 shows the behavior of the anion–probe pair when the functional and the basis set are changed. As observed, although there is a small difference in the absolute values and slopes for each method, the placement of each IL does not change and the same order is predicted for all of them. The increase in base size gives a small improvement in accuracy, thereby lowering the dispersion of the data, yet it is not enough to justify the increase in calculation time that this change originates: a smaller base set with the appropriate functional can give similar results at a lower computational cost.

When a similar approach was attempted to model the AN of ILs, no correlation could be found between the calculated data and the experimental data. Since the acceptor scale proposed by Gutmann was established based on the NMR shift of the phosphorus atom of the probe triethylphosphine oxide, this probe was used in the optimization with each IL. Neither binding enthalpies between the probe and solvent nor RMN shifts of the phosphorous atom displayed good correlations with the experimental data, as shown in Figure 5. This could be traced to the fact that, in contrast to the DN scale, in the AN scale, the IL acts as a solvent in which the probe is dissolved. Since the addition of an implicit solvent in the calculation of the DN parameter improved the correlation with the experimental data, we expected a similar response. This result suggests that the donor and acceptor molecules behave hardly different. We think that a more universal quantum chemical model incorporates second-order effects, including polarizability effects. Work along this line is under development in our group.

Following a similar approach to determine AN and DN numbers for the ionic liquid, the donicity of DES was determined by UV–Vis spectroscopy. The results are summarized in Table 3. When compared to ILs, DES studied show, in general, higher AN, falling within the range of 30–40, compared to IL series which show variations within the range 20–30. It is also noted that the variability within the series is, in general, low. The DN values for DES also have less variability than the IL examined having a range from 35 to 45, while ILs have a much higher range with values ranging from 8 to 70. This result can be traced to the short series used because it contains only three HBD examined; two of them bearing alcohol groups as the main site of interaction, in contrast to IL where the anion changed within a larger series, varying much more in size and nature of the interacting groups.

From Table 3, the following observations are pertinent: the change in HBA from choline chloride to betaine has the effect of lower AN for the betaine-based DES as compared to the corresponding choline-based DES. This result may be traced to the presence of the carboxylate group of betaine because choline has an alcohol group further away in the side chain and a completely detached chlorine ion that can move to accommodate the extra electron density with much more ease than the betaine group can accommodate.

On the other hand, the changes in HBD show that an increase in alcohol groups does not necessarily leads to a higher DN as one could expect, but a decrease as is shown in Table 3 after comparing propanediol and glycerol. On the other hand, the DN remains constant when comparing DES of betaine and ethylene glycol (37,1) and betaine with glycerol (37,1). These inconsistencies could arise from the fact that the probe is measuring the average effect of multiple possible donating centers in the bulk solvent instead of the easily localized negative charges associated with the anion in the case of IL. This effect could put into jeopardy the proposal of this scale as an appropriate measure of the donicity of DES, since little correlation is found when changing the nature of the HBD in a series of similar molecules. A wider exploration of DES with HBD of different types of interacting moieties may show differences of donicity between families of compounds, but at present, the proposed scale clearly offers qualitative and relative criteria but not an absolute and quantitative model for DN index for DES.

For the DES choline chloride–1,2-propanediol, the effect of the proportion between the components and the donicity number of the resulting solvent was also analyzed. The ratio 1:1 could not be measured at room temperature because it took the form of a solution of propylene glycol with undissolved crystals of choline. For the remaining proportions, the results are shown in Table 4. The eutectic ratio 1:2 has higher donicity of the series, and beyond this point, the donicity remains relatively constant, probably due to the saturation of the probe chosen.

A major difference in the approach taken when analyzing the polarity of DES and ILS is the effect that water may have as an impurity in the solvent. Therefore, it is required to evaluate the role that water may have in the polarity of the solvent after increasing water composition. The results are summarized in Figure 6. As it can be seen, when the mole fraction of water is small, the absorption maxima of the probe remains relatively stable being very close to the value of the pure DES, and as the mole fraction of water is increased, both values of the absorption maxima of the probes shifted to lower values, getting away from the normal value of the water-free DES. This result gives a little flexibility in the handling of the DES since even if a little amount of water may be present, the properties of the solvent should not change to a significant extent. Also, since choline is highly hygroscopic, one could reasonably expect to find a small amount of water in this solvent. The variation of light absorption with increasing water content is depicted in Figure 6.

Finally, experimental DN values were compared with theoretical ones, using the binding enthalpy model already applied to IL series. Since DES are usually in a molar ratio of 1:2, this relationship was maintained in the simulation, although a water molecule was not considered in the case of betaine even when the reactive used was a monohydrate. In the IL case, we had a three-component system (cation, anion, and probe) with a clear separation of charges and, therefore, a clear zone of interaction between the probe and the solvent. In the DES case, we have four or five bodies interacting (two HBD molecules, the HBA and the detached chlorine contra anion in the case of choline, and the probe) with the added complexity of a partial charge separation; after all, both choline chloride and betaine have their own electron donor groups that could interact with the probe.

This increase in complexity in the possible configurations that the system could adopt made the previously successful method of calculating binding enthalpies ineffective as it often gave negatives energies and no correlation at all. Since not all possible configurations were explored, it could be the case that a further exploration of the system could show the correlation between the donor number and the binding enthalpy of the system, but it would be more sensible to approach the problem from a different perspective, as is currently being worked by the research team.

The DN scales obtained for ILs and DES were used to study solvent effects in a model and the reaction between 2,4,6-trinitro phenyl phenyl ether (TNPPE) and a secondary alicyclic amine (piperazine) (Ormazabal–Toledo et al., 2013). S_NAr reactions are a good model to analyze solvent effect because these reactions are significantly affected by the reaction media. S_NAr involves the stabilization of species associated to the potential energy surface (PES) determining selectivity, reaction rates, and mechanisms (Glossman–Mitnik et al., 2020; Alarcón–Espósito et al., 2016; Newington et al., 2007; D’Anna et al., 2010) Figure 7 shows the accepted mechanism for this S_NAr reaction. It occurs in activated aromatic substrates bearing strong electron withdrawing groups (-NO₂ groups in this case) and a good leaving group (2,4,6-trinitro phenol for this reaction) through an addition–elimination process (Crampton et al., 2004; Terrier 2013). The first step for a stepwise mechanism is the nucleophilic attack to the substrate (k ₁ channel in Scheme 3a) leading an anionic σ-adduct named the Meisenheimer complex (MC in Scheme 3a). Then, two processes for its decomposition have been postulated: 1) expulsion of the leaving group (LG) followed a fast proton loss to give the reaction product (k ₂ in Scheme 3a) and 2) the base-catalyzed deprotonation of the MC that lost the LG to give the reaction product (k ₃ channel in Scheme 3a). The pseudo-first-order rate constant (k _obs) can be expressed as shown in Eq. 1, in which [Nu] represents the concentration of nucleophile. k o b s = k 2 k 1 [ N u ] + k 1 k 3 [ N u ] 2 k − 1 + k 2 + k 3 [ N u ] (1)

If pathway k ₂ is faster than k ₃ [Nu], then k ₂ >> k ₃ [Nu]; therefore, the expression simplifies to k o b s = k 2 k 1 [ N u ] k − 1 + k 2 (2)

It is noted that the values of k _obs are in accordance with Eq. 2, and the rate of solvolysis (k ₀) and the nucleophilic rate of the reaction (k _N) are obtained as the intercept (k ₀) and slope (k _N) of linear plots of the following equation: k o b s = k N [ N u ] + k 0 (3)

The straight lines of these plots in all the solvents tested suggest that the k ₃ channel can be discarded as a rate-determining step (RDS) in the reaction mechanism.

The studied reaction in ILs showed a low donicity for C₂C₁IM PF₆ and C₂C₁IM BF₄. In these solvents under the same experimental conditions, no significant amount of product was detected after 3 h. On the other hand, in ILs with high donicity such as C₂C₁IM DCA, the solvent established a competitive reaction with the nucleophile for the same reaction site. This fact was evidenced with a change on the reaction product spectra and the kinetic profile, in this case, changing λ_max from 416 to 441 nm and changing the color associated to the reaction product. This behavior was not observed in DES in comparison to the ILs studied. In this context, the behavior of the reaction in DES was found to be consistent with the general mechanism for S_NAr reaction.

It is noted that this kind of specific interactions between the solvent and reagents cannot be described only by a simple polarity model, so it is important to keep in mind that even when the Gutmann numbers scale can be used to predict reactivity of a system, it only describes one aspect of the interaction between the solvent and solute and no scale and due to the complexity of the possible interactions between the pair, no single scale can describe all the interactions.

Table 5 shows the k _N values and the molar ratio of the reagents used to prepare the studied DES. It is noted that the donicity trend and the nucleophilic rate coefficients decrease with the increase in the propanediol ratio; however, the constant decrease in the reaction rate even when the DN remained constant, thereby, indicated that the donor capabilities of the solvents are not the only factor that affects the reaction. Since in DES, we have neutral components that have lower nucleophilicity, the problems encountered with IL were not found, yet it is important to indicate that the other DES that were attempted (such choline–urea and choline–glycerol) were not suitable to the kinetic measurements since the high viscosity of the liquid prevented the mixing of the reactants in the cuvette. In the case of choline–glycerol, an increase in temperature decreased enough the viscosity of the solvent to enable the measurement of the reaction rates. However, for choline–urea, even this increase was not enough to overcome the difficulties encountered.

Since temperature affects the reaction rate of the system, to compare the rates between propanediol and glycerol, the test with propanediol was repeated at higher temperature in which case we can see that the DES with propanediol has a higher reaction rate than the DES with glycerol. Unfortunately, difficulties in dissolving the solvatochromic dyes in the choline–glycerol mixture prevented us from measuring the Gutmann numbers of this solvent. The viscosity problem in DES is an important issue worth considering. It is noted that the change in the composition of DES (either in the molar ratio of the components or the nature of the HBD and HBA) did have a significant effect on the reactivity derived from the experimental results obtained about the kinetics of these systems. These results cannot be explained by changes in the donicity of the solvent as explained earlier.

Since the previous reaction was not a suitable model for ionic liquids, another reaction was chosen to prove the prediction capabilities of the donicity model. The reaction between 2-chloro-5-nitro-pyrimidine (CNP) and morpholine was tested in 11 ILs as shown in Table 6. All solvents showed a linear relationship between the nucleophile concentration and the apparent reaction rate that indicates that the mechanism goes through a k₂ path with no catalysis of a second nucleophile molecule. Since all the solvents had the same reaction mechanism, it is possible to compare them with the donicity of each solvent to see if a trend appears. When plotting the k_N of each system against the DN in Figure 8, a general upward trend can be seen where a higher donor number gives a faster reaction rate. The IL C₂C₁IM SCN has a reaction rate lower than expected when compared to the remaining elements of the series.

When the reaction was run in DES (choline chloride with propanediol, glycerol, and urea), the presence of the nucleophile destabilized the solvent, thereby forcing it to precipitate, so no kinetic data could be recorded. This result is a reminder that specific interactions between the solute and solvents are to be incorporated via a super molecule-like approach, and therefore, the implicit third-body effects are important. As a result, a simple model based only on solvent polarity is not suitable enough when dealing with the kinetics of these model reactions.