Influence of solvent mixture on nucleophilicity parameters: the case of pyrrolidine in methanol–acetonitrile

The course of organic chemical reactions is efficiently modelled through the concepts of “electrophiles” and “nucleophiles” (meaning electron-seeking and nucleus-seeking reactive species). On the one hand, an advanced approach of the correlation of the nucleophilicity parameters N and electrophilicity E has been delivered from the linear free energy relationship log k (20 °C) = s(N + E). On the other hand, the general influence of the solvent mixtures, which are very often employed in preparative synthetic chemistry, has been poorly explored theoretically and experimentally, to date. Herein, we combined experimental and theoretical studies of the solvent influence on pyrrolidine nucleophilicity. We determined the nucleophilicity parameters N and s of pyrrolidine at 20 °C in CH3OH/CH3CN mixtures containing 0, 20, 40, 60, 80 and 100% CH3CN by kinetic investigations of their nucleophilic substitution reactions to a series of 2-methoxy-3-X-5-nitrothiophenes 1a–e (X = NO2, CN, COCH3, CO2CH3, CONH2). Depending on the resulting solvation medium, the N parameters range from 15.72 to 18.32 on the empirical nucleophilicity scale of Mayr. The nucleophilicity parameters N first evolve linearly with the content of acetonitrile up to 60% CH3CN by volume, but is non linear for higher amounts. We designed a general computation protocol to investigate the solvent effect at the atomistic scale. The nucleophilicity in solvent mixtures was evaluated by combining classical molecular dynamic (MD) simulations of solvated pyrrolidine and a few density functional theory (DFT) calculations of Parr nucleophilicity. The pyrrolidine theoretical nucleophilicity 1/ω obtained in various CH3OH/CH3CN mixtures are in excellent agreement with Mayr's nucleophilicity (N) parameters measured. Analyses of the molecular dynamic trajectories reveal that the decrease of the nucleophilicity in methanol rich mixtures arises predominantly from the solvation of the pyrrolidine by methanol molecules through strong hydrogen bonds. Last, we proposed a simple model to predict and accurately reproduce the experimentally obtained nucleophilicity values.


Introduction
The course of organic chemical reactions is efficiently modelled through the concepts of "electrophiles" and "nucleophiles". 1 These important concepts were quickly embraced by the chemical community, and empirical approaches were proposed by many authors both experimentally 2-4 and theoretically 5,6 to obtain quantitative scales.
In particular, the nucleophilicity parameters N and electrophilicity E, as introduced by Mayr group, allows to quantitatively predict the rate constant between an electrophile and a nucleophile based on a linear free energy relationship eqn (1) (ref. [4][5][6][7][8][9][10] in which k corresponds to the second-order rate constant, N and s are nucleophile-specic parameters, and E is the electrophilicity parameter. While the electrophilicity of a molecule is almost independent of the solvent, the nucleophilicity can strongly inuenced by it. 11 For example, the nucleophilicity parameter N of 4-(dimethylamino)pyridine jumps from 13.19 in water to 15.80 in dichloromethane. 12 Being quantitative, Mayr's approach (eqn (1)) is an attractive entrance to study the general inuence of solvent mixtures which are classically employed in preparative synthetic chemistry and was recently used for the synthesis of nanolympiadane. 13 Previous studies have shown that the dependence of the nucleophilicity parameter N on the solvent mixture can be greatly non linear 14 so that it appears difficult to predict the rate of a nucleophile-electrophile reaction in a new solvent or a new solvent mixture. Therefore, a careful study of solvent inuence appeared to us indispensable for providing further advances to the general effort of scaling and predicting nucleophilic and electrophilic parameters.
As a starting point to develop a general approach, we choose to study electrophile/nucleophile reactivity of thiophenes and pyrrolidine into two miscible solvents (acetonitrile, methanol), prepared in mixture at various ratio.
On one hand, pyrrolidine and imidazolidinone derivatives are the object of current interest as organocatalysts used in contemporary organic synthesis. 15 Their intrinsic reactivity has been examined in relation with bioactive compounds of natural or synthetic origin, which incorporate such nucleophilic scaffolds. [16][17][18][19] Recently, Mayr group investigated the kinetics of the reactions of several pyrrolidine derivatives and they integrated the resulting constitutive parameters of pyrrolidines into the socalled Mayr's nucleophilicity scale. 16 On the other hand, thiophenes are heterocycles of industrial interest, 20,21 and substituted thiophenes are scaffold found within pharmaceuticals, conductive polymers, photochromic molecular switches, liquid crystals, etc. 20 Regarding the general studies on nucleophilic and electrophilic parameters of heterocycles, Boubaker group investigated the reactions of 2-methoxy-3-X-5-nitrothiophenes electrophiles 1a-e (where X ¼ NO 2 , CN, COCH 3 , CO 2 CH 3 and CONH 2 ) with a variety of N-based nucleophiles, in different solvents at 20 C. 22,23 The derived second-order rate constants have been employed to determine the reactivity parameters of these series of thiophenes 1a-e, according to the Mayr's linear free energy relationship. The electrophilic parameter E values of 1a-e have been found ranging from À19.09 to À15.26, going respectively, from 1e (X ¼ CONH 2 ) the least reactive thiophene derivative, to 1a (X ¼ NO 2 ), the most reactive specimen.
This set of results and collected data has been of high interest for the understanding of both individual intrinsic organic reactivity and mutual interaction of pyrrolidine and thiophene derivatives. 17,22,23 The present work aimed at determining the nucleophile specic parameters N and s of pyrrolidine, as a model, in CH 3 OH/CH 3 CN mixtures. The changes in nucleophilicity parameters N values as a function of acetonitrile content was used to investigate the solvent-mixture overall effect at the atomistic level by combining experimental and theoretical approaches. As methanol and acetonitrile dielectric constant are rather close, a continuum model is not sufficient to properly describe the solvation effect on the nucleophilicity. To appreciate the effects of solvent on the parameters of nucleophilicity of pyrrolidine, we performed classical molecular dynamic simulations of a pyrrolidine molecule solvated by a mixture of methanol and acetonitrile solvent molecules.
Our studies conrmed the strong dependence of the nucleophilicity (and thus reaction rate) on the nature of the solvation medium. In the present case it comes from a gradual methanol desolvation to pyrrolidine involving four to zero molecules when the acetonitrile amount is gradually increased. Our study provides a relevant model for the more systematic inclusion of varied solvent into the reactivity studies of valuable electrophile/nucleophile organic reagents such the present heteroaromatics.

Materials
The thiophenes 1a-e were prepared as previously described. [24][25][26] Pyrrolidine was received from commercial source and distilled before use. Acetonitrile and methanol HPLC grade >99.9% were used without further purication.

Kinetic measurements
The kinetic study was performed using a spectrophotometer (UV-1650 Shimadzu) equipped with a Peltier temperature controller (TCC-240 A), which is able to keep constant temperature within 0.1 K. The reactions were carried out under pseudo-rst order conditions in which the pyrrolidine concentration (6 Â 10 À4 to 8 Â 10 À1 mol L À1 ) was at least 20 times greater than the substrate concentration (about 3 Â 10 À5 mol L À1 ). The rstorder rate constants measured, k obsd , values, together with detailed reaction conditions, are summarized in Tables S1-S6 in the ESI. † Reproducible kinetics constants were measured from several consistent experimental runs within AE3-5% standard deviation ( Table S7 in the ESI †).

Theoretical models and computational details
All quantum calculations were performed in the framework of density functional theory (DFT) by using the Gaussian 09 soware package. 27 Energies and forces were computed with the B3LYP functional 28,29 empirically corrected for dispersion effects using the D3 scheme of Grimme with the Becke-Johnson damping. 30 The bulk effect of the solvent was described using a polarizable continuum model as implemented in Gaussian09. Geometry optimizations without symmetry constraints and the corresponding frequency calculations were conducted with the 6-311+G(d,p) basis set for all atoms. 31 Methanol and acetonitrile dielectric constant are fairly close with 3 r ¼ 32.613 for methanol and 3 r ¼ 35.688 for acetonitrile, thus a continuum model is not sufficient to properly describing the solation effect on the nucleophilicity. To more precisely appreciate the effects of solvent on the parameters of nucleophilicity of pyrrolidine, we performed molecular dynamic simulations with the Amber simulation suite of a pyrrolidine molecule explicitly solvated by a mixture of methanol and acetonitrile solvent molecules. 32 Pure methanol, pure acetonitrile and mixture containing 9%, 20%, 40%, 50%, 60%, 80% and 90% of acetonitrile in methanol were simulated. The force eld parameters and the technical details of the simulation are given in ESI Fig. S2 and S3. † For each simulation, we computed the distribution methanol molecules in the rst solvation sphere or pyrrolidine. All calculation results were grouped in Tables S11 and S12 in the ESI. † These simulations showed that the rst layer of solvation contains between zero and four methanol molecules.
We computed the Parr nucleophilic indices u À1 of pyrrolidine surrounded by n ¼ 0, 1, 2, 3 and 4 explicit methanol molecules while the bulk solvation effects were described by a continuum. According to Parr, 5 the nucleophilicity index is the inverse of the electrophilicity index u that can be estimated using: In which m is the chemical potential and h the global hardness 6 of pyrrolidine. Both can be evaluated in the context of DFT: The pyrrolidine nucleophilicity are given in Table 1. These values are averaged using the distribution of methanol molecules in the rst solvation layer of pyrrolidine obtained in the MD simulations (see ESI Table S10, Fig. S4 and S5 †).

Kinetics of the reactions of thiophenes 1a-e with pyrrolidine
The kinetics of the reactions of the series of thiophenes 1a-e employed as reference electrophiles with pyrrolidine (Scheme 1) are collected in Table 2. 22,23 The reactions of 2-methoxy-3-X-5-nitrothiophenes 1a-e with pyrrolidine were followed spectrophotometrically by monitoring the formation of the products 3a-e at their absorption maxima (432-540 nm). An illustrative example is given in Fig. 1, which shows the set of UV-visible absorption spectra describing the progressive conversion of 1e to the product 3e (X ¼ CONH 2 ) resulting of the nucleophilic addition of pyrrolidine.
In all experiments, only one relaxation time was observed when the substitution products 3a-e were generated in the presence of a large excess of pyrrolidine. Typical results are given in Fig. 2a. The observed rst-order rate constants k obsd   determining (Scheme 1). 22,23,[33][34][35] The second-order rate constants k 1 (mol À1 L s À1 ) for all reactions, which are listed in Table 3, can be readily derived from eqn (5).
This behaviour might rst seem in contradiction with the fact that this reaction is known to proceed via a dipolar transition state (TS I, Scheme 2), which should be more stabilized in methanolic solutions. 36,37 However, as will be further shown later, it results from the progressive desolvation of pyrrolidine with decreasing CH 3 OH content upon addition of CH 3 CN. 38,39 A comparable effect has been reported by Mayr and co-workers in the reactions of benzhydrylium cation (Scheme 2) with OH À in H 2 O-CH 3 CN mixtures. 40 We further examined the solvation medium effect on the nucleophilic reactivity in terms of changes in solvent nucleophilicity parameters N 1 using CH 3 OH/CH 3 CN mixtures.
We employed the linear dependence of the solvent nucleophilicity N 1 on the amount of % CH 3 CN volume to interpolate the values of N 1 for 40% and 60% of acetonitrile in methanol from the values reported in literature 41 (see ESI †). N 1 values are collected in Table 4.
In contrast to the nonlinear relationships observed between log k 1 and %CH 3 CN volume, excellent correlation coefficients (R 2 > 0.9931) were found in all systems when the log k 1 values were plotted versus the solvent nucleophilicity parameter N 1 , 41 for solutions having N 1 > 6.04 (i.e. less than 80% vol. CH 3 CN, Fig. 4). This result implies that the effect of solvent nucleophilicity is practically independent of the electronic nature of the substituent X. Most importantly, these linear correlations can be used to predict the unknown second-order rate constants, k 1 , values for reactions of thiophenes 1a-e with pyrrolidine in a given CH 3 OH/CH 3 CN mixture. This is particularly the case in CH 3 OH/CH 3 CN mixtures containing 9, 33, 50 and 67% CH 3 CN where the values of k 1 for all thiophenes 1a-e have thus been obtained by extrapolation of the corresponding N 1 data reported by Minegishi and co-worker 41 (see Table S8 in the ESI †).

Mayr's nucleophilicity (N) parameters of pyrrolidine in methanolic acetonitrile solutions
The electrophilicity parameters E for the ve thiophenes 1a-e, 22,23 were employed to quantify the nucleophilicity parameters N and s of pyrrolidine in methanol/acetonitrile solutions.
Using the data given in Tables 1 and 2, plots of log k 1 versus electrophilicity parameters E of 1a-e have been constructed. As can be seen in Fig. 5, linear correlations were obtained, which yield the nucleophilicity parameters N and s, as dened by the linear free energy relationship (1). The nucleophilicity parameters N and s for pyrrolidine in various methanol/acetonitrile mixtures at 20 C are reported in Table 5.
The N value of 18.32 experimentally found in pure acetonitrile is consistent with the value of 18.64 reported by Kanzian and co-workers in the same solvent. 42 It appears that adding   This journal is © The Royal Society of Chemistry 2020 RSC Adv., 2020, 10, 28635-28643 | 28639 Paper acetonitrile to a methanolic solution of pyrrolidine resulted in only small changes in nucleophile specic parameter s. The transfer from CH 3 CN to CH 3 OH corresponds to a relatively important decrease in the nucleophilicity of pyrrolidine (Table 5, DN ¼ 2.60). This decrease of the nucleophilicity values in the CH 3 OH rich solvation medium could be attributed to a stronger solvation of pyrrolidine in this protic solvent, as conrmed below.
Literature data indicated a nucleophilicity parameter for piperidine of 17.35 in CH 3 CN, 42 whereas the piperidine appears more nucleophilic in pure water (N ¼ 18.13). 43 For morpholine the N value is essentially the same in pure CH 3 CN and H 2 O: 42 The changes in nucleophilicity parameter of pyrrolidine observed herein were also examined as a function of the variation in volume fraction of acetonitrile (%CH 3 CN). As seen from the Fig. 6, N linearly correlates with the vol% of CH 3 CN up to approximately 60% vol. CH 3 CN, following the eqn (6) with R 2 ¼ 0.9972: Eqn (6) validity is supported by comparing with the experimental N value in the mixture of 91% CH 3 OH/9% CH 3 CN as reported by Phan et al., 44 to the interpolated value according eqn (6), as shown in Table 5. There is an excellent agreement between experimentally determined and calculated values with the average absolute error being only 0.12 N units.

Theoretical nucleophilicity (1/u) parameters of pyrrolidine in methanolic mixtures with acetonitrile
In the simulation process the number of methanol molecules n varies, and we found that on average one pyrrolidine molecule is surrounded by two molecules in pure methanol. This number decreases to zero when the content of the acetonitrile mixture is increased (Fig. S5 †). In Table 6 is collected the theoretical nucleophilicity 1/u of pyrrolidine in various methanolic CH 3 CN solutions, together with the Mayr's nucleophilicity (N) parameters measured in this study. A very good correlation was found, R 2 ¼ 0.9988, between theoretical 1/u and experimental N values (Fig. 7), 45-47 which is dened by eqn (7).
Chamorro and co-workers have observed a linear correlations between the Mayr's nucleophilicity (N) parameters for a series of primary and secondary amines and the theoretical nucleophilicity index (u À ) obtained at the DFT level. 45  The validity of eqn (7) was checked by estimating the nucleophilicity parameters N of pyrrolidine in CH 3 OH/CH 3 CN mixtures containing 9 and 91% CH 3 CN that had been experimentally measured. 44 The detailed results are listed in Table 6. These results clearly show that the predicted values of N are in excellent agreement with the experimental data.

Modelling inuence of the solvation
Our simulations reveal that the evolution of the pyrrolidine nucleophilicity on the composition of the methanol/ acetonitrile mixture mainly comes from the fact that methanol forms a strong hydrogen bonds with the nitrogen lone pair and the NH bond of the pyrrolidine. Solvated molecules are much less nucleophilic: bare pyrrolidine nucleophilicity is 18.32 while it is only 15.67 for the bis-methanol pyrrolidine and 15.01 for the pyrrolidine solvated by ve methanol. The proportion of pyrrolidine solvated by 0, 1, 2, 3 and 4 methanol molecules is shown in Fig. 8 as a function of the acetonitrile molar fraction.
As the amount of methanol in the mixture is decreased, the amount of bare pyrrolidine molecule increases and so does the observed nucleophilicity. In particular, for molar fraction greater than 60%, the bare pyrrolidine is more abundant than the bis-methanol pyrrolidine. As a consequence, the average pyrrolidine nucleophilicity parameter N rises steeply, following the amount of unsolvated pyrrolidine.
It is interesting to note that solvated molecules have similar nucleophilicities, so that we could model the solvation process as a two states system: The equilibrium constant of eqn (8) ðNðPyrÞ À NðM À PyrÞÞ (9) Results from N mod are reported in Table 6. The very good agreement with the experimental values conrmed that the inuence of the solvent on nucleophilicity can be modelled by our two states approach.

Conclusions
The reactions of 2-methoxy-3-X-5-nitrothiophenes 1a-e with pyrrolidine were studied kinetically by UV-visible spectroscopy in CH 3 OH, CH 3 CN and various CH 3 OH/CH 3 CN vol/vol. mixtures at 20 C. The nucleophilicity parameters N and s for pyrrolidine in CH 3 OH/CH 3 CN mixtures of different compositions as dened by Mayr Equation log k (20 C) ¼ s(E + N) have been determined and found to cover a range from 15.72 to 18.32. We have shown that the nucleophilicity parameters N for pyrrolidine are linearly related to the amount of acetonitrile (in % CH 3 CN volume) for ratio less than 60%. Finally, with the N and s values determined, it becomes possible to make predictions of second-order rate constants for reactions of pyrrolidine with others electrophiles of known E parameters. The nucleophilicity index 1/u for pyrrolidine in solvent mixture of  acetonitrile and methanol have been determined by combining DFT resampling of classical MD simulations. The theoretical values agree with the experimental ones, and the experimental dependence of the nucleophilicity parameters of pyrrolidine on mixture solvent methanol/acetonitrile was conrmed and supported by the simulation. The net dependence of the nucleophilicity parameter of pyrrolidine on solvent is mainly explained by a gradual methanol desolvation when the amount of acetonitrile is increased. The correlation between the experimental and theoretical values obtained herein indicates that this theoretical approach could be further processed to predict the nucleophilicity parameters of other nucleophiles in solvent mixtures and ultimately an automated tool for tuning electrophilic-nucleophilic reactivity as a function of a precise mixture of binary solvent. Further extension might concern ternary mixture of solvents.

Conflicts of interest
There are no conicts to declare.