Introduction

The solvent effect on chemical reactions has a long history in chemistry [1, 2]. Solvents are widely used for improving reaction yield and can be critical for a successful reaction [2]. In the present time, the inclusion of solvent effects is mandatory for reliable modeling of condensed phase reactions. Indeed, with the development of theoretical methods and practical solvation models based on the continuum approach [3,4,5,6,7,8], fast theoretical solvent screening has become possible [9]. This approach has been applied for interesting problems such as solvent selection for some chemical reactions [10, 11] and separation processes via extraction [12, 13]. However, continuum solvation models have limitations and are not adequate for modeling reactions in situations that microsolvation plays a role [14,15,16], neither describing the solvation of many ionic species in protic solvents [17, 18]. In these cases, inclusion of explicit solvent is essential [19].

Among the different reaction types with important solvent effects, ion–molecule SN2 and E2 reactions can be singled-out [20]. The first solvating shell has the main influence on these reactions. Thus, the microenvironment around the solute can be used for controlling the reaction rate and selectivity [21]. These ideas have led to the design of supramolecular catalysts for nucleophilic fluorination, mainly based on macrocycles such as crown ethers [22,23,24,25], cryptands [26, 27], calixarenes [28,29,30,31], thiourea-crown-ether [32], and similar structures [33,34,35].

Some years ago, Kim and co-workers [36, 37], followed by Gouverneur and co-workers [38], have reported the use of tetrabutylammonium fluoride (TBAF) in acetonitrile solvent and added stoichiometric amount of bulky alcohols as tert-butanol for performing nucleophilic fluorination. They observed an important effect of tert-butanol on the selectivity of the reaction. In fact, it is long known that fluoride ion in aprotic solvents can act as strong base, reacting with alkyl halides to generate much E2 product and decreasing the SN2 yield [39, 40]. With the addition of stochiometric amount of molecules with hydroxyl groups such as water [41] or bulky alcohols [37, 38], a substantial increase of the SN2 product is observed. However, the microscopic details on how the additional bulky alcohols combined with TBAF control the reaction rate and selectivity were not reported to date. Thus, the aim of this report is to conduct a theoretical analysis of this reaction system to provide more insights on the detailed mechanism. As a model system, we have used the ethyl bromide substrate reacting with TBAF and including up to three explicit tert-butanol molecules. Such problem involves modeling the reaction in a complex microsolvated environment [42]. We hope that this analysis can be useful for inducing more advances in the design of nucleophilic fluorination reactions.

Theoretical methods

The reaction system presented in Scheme 1 was investigate by electronic structure calculations and continuum solvation (acetonitrile solvent), also including explicit tert-butanol molecules. Geometry optimization calculations of the minima and transition states investigated in this work were done using density functional theory method, with the PBE functional [43] and resolution of identity approximation. These calculations were performed with the ma-def2-SVP basis set [44, 45]. The optimizations were followed by harmonic frequency calculations to obtain thermodynamics data. However, because ORCA 3 program [46, 47] used in this study does not include frequencies below of 35 cm−1 in the calculation of thermodynamics properties, which can lead to unbalanced description of the system, these contributions were included manually [48]. Additional correction for symmetry number and from standard state from 1 atm to 1 mol L−1, necessary for modeling liquid phase processes, were also done. To obtain reliable free energies, the accurate M06-2X functional [49] with the extended ma-def2-TZVPP basis set was used for single point energy calculation. It is worth to observe that this functional was ranked among the top 10% better functionals for activation barrier and reaction energies in a recently comparative study involving 200 functionals [50].

Scheme 1
scheme 1

Microsolvation effect of the reaction selectivity. In the present study, R = H

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The bulk solvent effect (acetonitrile) was included by the continuum SMD model [6]. This part of the calculations was done with the GAMESS program [51], using the X3LYP functional [52] and the 6–31( +)G(d) basis set. The final free energy for each species X in solution phase can be written as:

$${\mathrm{G}}_{\mathrm{sol}}(\mathrm{X}) = {\mathrm{E}}_{\mathrm{el}}(\mathrm{X}) + {\mathrm{G}}_{\mathrm{N}}(\mathrm{X}) +\Delta {\mathrm{G}}_{\mathrm{solv}}(\mathrm{X})$$
(1)

where the term in the left side is the free energy in liquid phase; the first term in the right side is the electronic energy obtained at M06-2X level; the second term is translational, rotational, and vibrational contribution to the free energy; and the third term is the solvation free energy in acetonitrile. The GN term includes the correction for the standard state of 1 mol−1. All calculations were performed with the ORCA 3 [46, 47] and GAMESS program [51] systems.

Results and discussion

Previous work of our group involving tetramethyl ammonium fluoride (TMAF) in a similar polar aprotic solvent dimethylformamide has indicated that the SNAr reaction proceeds via ion pair [53]. In this report, the presence of TBAF and stoichiometric amount of tert-butanol in acetonitrile solution should lead to the formation of aggregates of the kind TBAF(t-butanol)N, like that reported for a similar system: KF complexed with 18-crown-6 in acetonitrile solution with stoichiometric tert-butanol [24]. In that study, both molecular dynamics calculations and quantum chemistry with continuum solvation calculations have provide the same picture, which one tert-butanol molecule associated with the fluoride ion is the main species. Thus, the present theoretical approach for this system must provide a realistic picture of the problem under investigation.

The first part of the study was to analyze the formation of aggregates of TBAF with t-butanol. The optimized structures of TBAF interacting with up to three t-butanol molecules are presented in the Fig. 1. We can notice that the TBAF supports three t-butanol molecules solvating the fluoride ion in the first solvation shell. Although these structures are minima, only the complex with one t-butanol has a favorable ΔG for its formation. This thermodynamics data is presented in the Fig. 2, the free energy profile of the SN2 reaction. Thus, TBAF(t-butanol) is only 0.6 kcal mol−1 below of the TBAF + t-butanol reference. The complex with two t-butanol molecules is 2.0 kcal mol−1 above of the free reactants and reaches 3.6 kcal mol−1 for the complex with three t-butanol molecules. These are slightly negative and positive ΔG, indicating that all these species, including free TBAF, can be present in the equilibrium. The exact concentration of each species depends on the concentration of the added t-butanol. Because it is not clear the ΔG‡ for each complex, all the species were included in the analysis.

Fig. 1
figure 1

Minima and transition states structures of TBAF reaction with ethyl bromide in the presence of stoichiometric t-butanol obtained by the PBE/ma-def2-SVP method

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Fig. 2
figure 2

Free energy profile for the nucleophilic fluorination reaction (SN2) of ethyl bromide with tetrabutylammonium fluoride in acetonitrile solvent and in the presence of tert-butanol. Units in kcal mol−1. Standard state of 1 mol L−1, 298.15 K. Calculations at M06-2X/ma-def2-TZVPP//X3LYP/ma-def2-SVP level and SMD solvation

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In the activation step, the TBAF can react with ethyl bromide via four SN2 transition states and four E2 transition states (Fig. 1). The direct reaction of TBAF with ethyl bromide has ΔG‡ = 22.9 kcal mol−1 for both SN2 and E2 pathways (Figs. 2 and 3). This finding indicates that both the fluorination and elimination products are formed in 50% selectivity, in agreement with experimental observations of high E2 product (22% SN2: 78% E2, using true anhydrous TBAF) [37]. Consequently, the sole TBAF is not a good reactant for selective fluorination of alkyl halides [54]. With the participation of one t-butanol molecule, the free energy profile has an important modification. The free energy of the SN2 pathway becomes 21.7 kcal mol−1, whereas the free energy for the E2 pathway becomes 27.3 kcal mol−1. These values correspond to the overall ΔG and consider the initial reactants as reference. Thus, the inclusion of just one t-butanol has an important effect on the selectivity and would be able to produce exclusively SN2 product. Nevertheless, the reaction leading to E2 via free TBAF remains competitive (22.9 kcal mol−1) and any conclusion on the observed selectivity requires a complete analysis of the equilibrium and kinetics.

Fig. 3
figure 3

Free energy profile for the elimination reaction (E2) of ethyl bromide with tetrabutylammonium fluoride in acetonitrile solvent and in the presence of tert-butanol. Units in kcal mol−1. Standard state of 1 mol L−1, 298.15 K. Calculations at M06-2X/ma-def2-TZVPP//X3LYP/ma-def2-SVP level and SMD solvation

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The addition of the second t-butanol rises the ΔG of the SN2 transition state to 27.5 kcal mol−1, turning the kinetics by this pathway too slow. The third t-butanol molecule makes the free energy even higher, 31.9 kcal mol−1. In the case of E2 pathway, the addition of the second and third t-butanol molecules also produces barriers above of 27 kcal mol−1 (Fig. 3). Consequently, reaction kinetics via these transition states with two or three t-butanol molecules are slow and should not contribute meaningfully to the overall reaction rate and selectivity. However, it is important to observe that increasing the concentration of t-butanol produces more complexes, decreasing the concentration of free TBAF. This fact should improve the selectivity. In the next section, a detailed kinetics analysis is presented.

In order to ensure that the PBE/ma-def2-SVP geometries are enough to produce reliable barriers at M06-2X level, we have done additional M06-2X/ma-def2-SVP geometry optimizations for the species involved in the activation step of the SN2 reaction involving TBAF(t-butanol), followed of single point energy calculation at M06-2X/ma-def2-TZVPP level. We have found that ΔE‡ is 11.9 kcal mol−1 using the PBE geometries and becomes 12.7 kcal mol−1 using M06-2X geometries. This result supports the good quality of the present calculations.

Analysis of the complexation equilibrium and reaction kinetics

In order to obtain more detailed and clearer view of the effect of t-butanol addition to the reaction system, the equilibria and kinetics equations with the free energy data from Figs. 2 and 3 were resolved. Thus, the equilibrium equations for formation of the complexes are given by:

$${\mathrm{K}}_{1}=\frac{[\mathrm{TBAF}\left(\mathrm{tboh}\right)]}{\left[\mathrm{TBAF}\right][\mathrm{tboh}]}={\mathrm{e}}^{-\Delta {\mathrm{G}}_{1}/\mathrm{RT}}=2.7$$
(2)
$${\mathrm{K}}_{2}=\frac{[\mathrm{TBAF}{\left(\mathrm{tboh}\right)}_{2}]}{\left[\mathrm{TBAF}\right]{[\mathrm{tboh}]}^{2}}={\mathrm{e}}^{-\Delta {\mathrm{G}}_{2}/\mathrm{RT}}=3.4\times {10}^{-2}$$
(3)
$${\mathrm{K}}_{3}=\frac{[\mathrm{TBAF}{\left(\mathrm{tboh}\right)}_{3}]}{\left[\mathrm{TBAF}\right]{[\mathrm{tboh}]}^{3}}={\mathrm{e}}^{-\Delta {\mathrm{G}}_{3}/\mathrm{RT}}=2.3\times {10}^{-3}$$
(4)

and the mass balance requires:

$${\mathrm{C}}_{\text{t-butanol}}=\left[\mathrm{tboh}\right]+\left[\mathrm{TBAF}\left(\mathrm{tboh}\right)\right]+2.[\mathrm{TBAF}{\left(\mathrm{tboh}\right)}_{2}]+3.[\mathrm{TBAF}{\left(\mathrm{tboh}\right)}_{3}]$$
(5)
$${\mathrm{C}}_{\text{TBAF}}=\left[\mathrm{TBAF}\right]+\left[\mathrm{TBAF}\left(\mathrm{tboh}\right)\right]+[\mathrm{TBAF}{\left(\mathrm{tboh}\right)}_{2}]+[\mathrm{TBAF}{\left(\mathrm{tboh}\right)}_{3}]$$
(6)

where CTBAF and Ct-butanol correspond to the total (analytic) concentration of TBAF and t-butanol, respectively, and tboh = t-butanol. The system of Eqs. (2) to (6) (five equations and five incognitos) was resolved using Excel with the conditions: CTBAF = 0.50 mol L−1, and Ct-butanol was varied from 0.0 to 2.0 mol L−1 to evaluate the concentration effect. The results are presented in the Fig. 4a. We can observe that the increase of Ct-butanol up to 2.0 mol L−1 leads to decrease of the concentration of free TBAF (close to 0.1 mol L−1) and the increase of the concentration of the TBAF(t-butanol) up to 0.4 mol L−1. The higher complexes have concentrations calculated to be below of 0.01 mol L−1 even when using 2.0 mol L−1 of Ct-butanol and were not included in the graphics. As a consequence of this analysis, the E2 product should decrease with the increase of Ct-butanol, because this pathway must proceed via free TBAF.

Fig. 4
figure 4

Effect of the total concentration of t-butanol on the concentration of each species (a) and on the selectivity (b) based on the theoretical free energy profile from Figs. 2 and 3

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In the kinetics analysis, we consider the pathways involving TBAF and TBAF(t-butanol) for SN2 process, and TBAF for E2 because the free energy profile indicates that other pathways have remarkably high barriers (Figs. 2 and 3). Thus, the reaction rates are:

$${\mathrm{Rate}}_{\mathrm{SN}2}={\mathrm{k}}_{0-\mathrm{SN}2}\left[\mathrm{RBr}\right]\left[\mathrm{TBAF}\right]+{\mathrm{k}}_{1-\mathrm{SN}2}\left[\mathrm{RBr}\right]\left[\mathrm{TBAF}(\mathrm{tboh})\right]$$
(7)
$${\mathrm{Rate}}_{\mathrm{E}2}={\mathrm{k}}_{0-\mathrm{E}2}\left[\mathrm{RBr}\right]\left[\mathrm{TBAF}\right]$$
(8)

With k0-SN2 and k0-E2 related to ΔG‡ = 22.9 kcal mol−1 and k1-SN2 related to ΔG‡ = 21.7 – (− 0.6) = 22.3 kcal mol−1. Based on this data calculated at 25 °C, we can predict that the selectivity of the SN2 product is given by Fig. 4b. In this analysis, we are considering 100% conversion with the rate given by Eqs. (7) and (8). In the case that [t-butanol] = 0, there is 50% selectivity of the SN2 product. Increasing the analytic concentration of t-butanol leads to increase of the selectivity up to 93% when Ct-butanol = 2.0 mol L−1, and the graphics suggest a plateau at this concentration. This occurs because there is increase of the concentration of [TBAF(t-butanol)], resulting in low concentration of free TBAF able to react via E2. For comparison, the experiments of Gouverneur and co-workers have used CRBr = 0.25 mol L−1, CTBOH = 0.50 mol L−1 and Ct-butanol = 2.0 mol L−1 and observed 67% selectivity using a primary alkyl bromide [38]. However, in [t-butanol] = 0 conditions, the experimental selectivity is only 22% [37]. Thus, this important increase in the selectivity is well reproduced in our calculations. The exact value is difficult to reproduce because this is a complex system, and the theoretical methods have limitations in the description of the solvation effect.

Further comparison can be done. Thus, our total reaction rate corresponds to 3.26 × 10−5 mol L−1 s−1 using the experimental conditions. Defining a pseudo-second-order rate constant as suggested by Gouverneur and co-workers [38], given by:

$${\mathrm{Rate}}_{\mathrm{total}}={\mathrm{k}}_{\mathrm{t}}{\mathrm{C}}_{\mathrm{RBr}}{\mathrm{C}}_{\mathrm{TBAF}}$$
(9)

leads to kt = 2.61 × 10−4 M−1 s−1, which corresponds to ΔG‡ = 22.3 kcal mol−1 at 25 °C. The experiments of Gouverneur have resulted in ΔG‡ = 23.1 kcal mol−1 at 70 °C. This is a particularly good agreement between theory and experiments. Thus, the present study provides a realist description of this complex system.

Based on the present results, the addition of t-butanol leads to the formation of TBAF(t-butanol) complex. Increasing the concentration of t-butanol does not produce appreciable concentration of higher aggregates such as TBAF(t-butanol)2 or TBAF(t-butanol)3, neither the reaction takes place via these higher aggregates. Thus, improving the selectivity of SN2 fluorination with adequate reaction rate could be achieved with the use of diols or tetraols with the right position of hydroxyls [23]. Such approach may lead to higher reaction rate and selectivity if stable aggregates, able to inhibit the reaction, are not formed.

Conclusion

The present theoretical study indicates that micro-heterogeneous environment in the solution of TBAF dissolved in acetonitrile with stoichiometric tert-butanol has an important effect on the selectivity in the reaction of TBAF with alkyl bromide. There is considerable formation of the TBAF(t-butanol) complex, which react selectively with alkyl bromide to produce SN2 product. The free TBAF in equilibrium is responsible for formation of the E2 product. The increase of the concentration of t-butanol does not lead to appreciable formation of higher aggregates. Rather, its effect is reducing the free TBAF species, decreasing the E2 product. Our analysis suggests that further improvement in the selectivity and reaction rate could be achieved with the use of diols or tetraols.