Solvent Molecules Play a Role in an SNAr Reaction
Reaction between 4-nitrobenzonitrile and sodium methoxide (MeONa) exhibits unexpectedly low conversion and puzzling kinetics behavior, which is in sharp contrast to the prediction that reaction would be rapid and thorough made by density functional theory (DFT) calculations under implicit solvation. Free energy surfaces (FES) obtained by explicit solvation model including 62 solvent molecules differ greatly from those with implicit solvation. The real nucleophile is not methoxide anion but methanol-methoxide complex, and it is the entropy effect due to solvent molecules that modifies the FES. It is the first work revealing the significant modification of FES by explicit solvation for small molecule reactions.
Introduction<!>Results and Discussions<!>Entry
<p>Quantum chemistry computations have been used widely and successfully to gain both insights and numbers into chemical reactions. Nearly all quantum chemistry calculations for reactions in solution are based on implicit solvation model, which considers solvents as continuous medium, and no dynamics of solvents is included. In 2016 Singleton reported that implicit solvation model is insufficient to explain the regioselectivity of toluene nitration 1 . To the best of our knowledge it is the only research revealing the importance of explicit solvation for small molecular reaction. In this communication, the significant influence of explicit solvation on free energy surface (FES) is observed. Implicit solvation gave completely wrong prediction for a seemingly simple SNAr reaction, the reaction between sodium methoxide and 4-nitrobenzonitrile (1) in dimethyl sulfoxide (DMSO) (Figure 1). The experimentally observed low conversion and "strange" kinetics behaviors originate from the entropy effect due to the dynamics of solvation molecules, which modified the FES in an astonishing extent.</p><!><p>The work commenced with an incidentally performed reaction of 4-nitrobenzonitrile (1) and sodium methoxide. The reaction gave cleanly a mixture of unreacted 1 and SNAr product 2, which will be stated in detail later. There seems to be nothing interesting at the first look. However, when the calculated free energy surface (FES) was examined (Figure 2), a puzzling inconsistence came to appear. Under SMD implicit solvation model the reaction is fast and irreversible. Compound 1 undergoes a rapid addition by methoxide anion with barrier of 2.6 kcal/mol, leading to a Messenheimer complex Int2. The transition state (TS) for elimination of NO2is lower in energy than Int2 after including correction to Gibbs free energy, indicating a dynamical dominating behavior 2 . In a summary, the reaction was predicted to proceed smoothly and thoroughly. Pathway involving benzyne is highly disfavored. Experiments gave a very different picture. All reactions gave a clean mixture of 1 and 2, with no detectable byproducts. Reaction with 1 eq MeONa gave no conversion of 1. Yield of 2 became higher with large excess of MeONa, although even with 10 eq MeONa there is still 30% of substrate unconverted (Figure 3a). Small amount of methanol raised final yields, but the yields dropped sharply with more than 40 eq of methanol (equivalents calculated with respect to 1). According to these observations, 5 eq of MeONa appeared to be a proper condition for kinetics measurement. Reaction profile is depicted in Figure 3e. Initially the reaction was rapid and 25.1% of 1 converted to 2 in the first 30 s. Order of MeONa was determined to be 2 by measuring initial rates (Figure 3d). However, the reaction profile deviated significantly from what expected from an r=k [1][MeONa] 2 pattern. The kinetics equation was determined to be r=k [1]( [1]0- [1]final-( [1]0- [1])). Some experiments were employed to determine whether the final mixture is in equilibrium. Adding extra 3 eq of MeONa to a mixture with 2 eq of MeONa that has been stirred for 2 h after mixed led to final yield comparable to that with 5 eq MeONa directly added (Table 1). However, adding NaNO2 did not reduce the final yield, indicating no equilibrium involving NO2 -. This observation, along with the kinetic equation above, strongly suggested that the real nucleophile is not MeONa but some species irreversibly generated from MeONa and with an initial concentration of [1]0- [1]final.</p><!><p>Variation on conditions Final yield (%)</p><p>2 eq MeONa, then add 3 eq MeONa 2 h later 43 3 5 eq MeONa and 5 eq NaNO2 49 4</p><p>5 eq MeONa and 5 eq 15-crown-5 71 5</p><p>MeOLi instead of MeONa 0 Table 1. Influence of additives on final yields.</p><p>Obviously the calculated FES based on implicit solvation model was unable to give even qualitatively correct insight into the experimental observations. Then we turned our attention to explicit solvation. DFT-derived transition state TS1 was placed at the center of a sphere on 62 DMSO molecules. Solvent molecules were treated by PM7 and the TS1 part was treated with M06-2X/6-31+G(d). A two-dimensional potential mean field (2D-PMF) calculation was performed to obtain the FES for the addition of MeOto 1 (Figure 4a). The PMF surface indicated a concerted addition-elimination process, in agreement with the extremely low energy of TS2 shown in Figure 2. Most importantly and surprisingly, the FES exhibited a barrier larger than 40 kcal/mol, in sharp contrast to the rapid reaction implied from Figure 2. Some factors possible to cause wrong PMF surface were precluded by careful examination of the calculated results. Then it came to the problem why it shows such a large difference from that calculated from implicit solvation model. There may be several reasons. One is that the insufficiency of SMD solvation model itself, and the other is the harmonious approximation used in conventional DFT calculations. Anharmonic free energies were obtained under implicit solvation model with VPT2 method (Figure 2, grey). Anharmonicity made an unexpected difference on the relative free energies and could not be corrected using correction factors, which is widely used for convenient inclusion of anharmonicity. However, the anharmonic FES based on implicit solvation model also exhibits a very low barrier. Thus there must be other factors contributing to the PMF FES. By comparing PMF-FES and xtb electronic energies and PM7 enthalpies, we concluded that the 62 DMSO molecules modified the shape of FESs through entropy. Detailed discussions, as well as the origin of entropy effect, can be seen in Supporting Information.</p><p>The involvement of MeOas nucleophile is precluded by the calculation results above, and then came the problem what the true nucleophile is. We found that in the trajectories obtained, MeOdid not exist in its free form. Instead, it always extracted a proton from DMSO (Figure 4d-f). Methanol has been considered to show acidity 10 6 stronger than DMSO for a long time, and it looks impossible that sodium methoxide can exist in such a form in DMSO solvation. However, after diving deeply into the literature, we found that the acidity measurement of alchohols in DMSO is actually scarce 3 , as well as the experimental studies about existing form of sodium methoxide in solution 4 . Then it came to be a crucial problem how MeONa actually exists in a DMSO solution.</p><p>MeONa dimer was chosen as a model. 49 trajectories were generated starting from equilibrated cluster with a DFT optimized MeONa dimer surrounded by 62 DMSO molecules. Each of them dissociated rapidly with O-Na distance longer than 8 angstrom. These trajectories with 98 methoxide anion in total gave two products, 68 MeOH (after proton transfer with DMSO) and 32 MeOrespectivel. These species are stable in a time period of 2 ps. On the other hand, all 39 trajectories from MeONa monomer in DMSO cluster gave MeOH with proton extracted from DMSO, and average O-Na distance of 12 angstrom. Although surprising, the results were validated by high accuracy methods (see Supporting Information). The involvement of methanol as primary product for dissociation of MeONa prompted us to consider of methanol-methoxide complex. This complex is stable toward proton extraction from DMSO in a trajectory of 8 ps, giving the possibility of its presence in real solution and we proposed that the fate of MeOproduced in dissociation of MeONa dimer is either to form MeOH by extracting a proton from DMSO, or form methanol-methoxide complex with another methanol molecule in a non-equilibrium manner. The conversion of two MeOH molecules (together with two CH2SOCH3and two Na + ) into methanol-methoxide complex has a barrier of 26 kcal/mol (Figure 4g), indicating that methanol cannot be in equilibrium with methanol-methoxide complex. In a summary, in our mechanistic model, sodium methoxide exists as two species unable to interconvert in DMSO solution, namely MeOH and methanol-methoxide complex. The ratio of them is determined upon the irreversible dissociation of MeONa aggregations or crystal. Some NMR evidences were discussed in Supporting Information. This insight gave us a hint that the actual nucleophile is possible to be methanol-methoxide complex.</p><p>An experimental kinetics isotopic effect (KIE) of 2.3 given by initial rate measurement in DMSO-d6 gave us confidence on this proposal. TS for this process under implicit solvation was located (Figure 1) and the predicted KIE is exactly 2.30. The PMF surface for the SNAr involving methanolmethoxide complex exhibits a barrier of 24 kcal/mol. Although acceptable considering the error of PMF, this pathway cannot explain the experimentally observed second order kinetics on MeONa.</p><p>After including one CH2SOCH3anion, however, the barrier was reduced to 18 kcal/mol. It has to be carefully treated because there might be some hidden "resting state" since any trajectory with finite length cannot promise there is no configuration of the cluster with lower energy than B. However, this model shows best consistence with experiments. Thus it is suggested that in real solvation environment the SNAr reaction between 1 and MeONa proceeds with involvement of a methanol-methoxide complex and a CH2SOCH3anion.</p><p>According to the discussion above, the initial concentration of methanol-methoxide complex is determined during the solvation process, and is proportional to the amount of MeONa. Furthermore, this complex cannot be in equilibrium with other species once MeONa has been fully solvated. Thus the final yield of the SNAr reaction should reflect the concentration of this complex. This accounts for the low conversion, since most methoxide anion is converted into MeOH during solvation. The experimentally observed r=k [1]( [1]0- [1]final-( [1]0- [1])) kinetics has r=k [1][methanolmethoxide][CH2SOCH3 -] as its real form, where [CH2SOCH3 -], generated also during the solvation of MeONa, is constant. The observed second-order dependence of initial rate on amount of MeONa is reflected in the [methanol-methoxide][CH2SOCH3 -] part. Our mechanistic model is shown in Scheme 1. Scheme 1. Summary of our mechanistic model.</p><p>In conclusion, we examined an SNAr reaction by combining experimental and computational methods. The DFT calculated FES based on implicit solvation model gave an over-simplified and qualitatively wrong picture. FESs obtained in the presence of 62 DMSO molecules showed huge difference from those obtained under implicit solvation model. It is not electronic energy, but entropy due to solvent molecules, that modified the shape of FES. Keeping this in mind, we found that the real existing form of MeONa in DMSO is a mixture of MeOH and methanol-methoxide complex which are not in equilibrium, and the latter is the true nucleophile. This work exhibits that in some case solvent can influence the reaction in a way that is very different from what people used to think. There is actually no method to fully account for entropy effect of solvent molecules except molecular dynamics. Although this work is the first work revealing the huge influence of explicit solvation on the shape of FES for reactions of small organic molecules to the best of our knowledge, it is possible that there are more such cases unrealized, in which people were misled by implicit solvation. Also it is still an open question how to explain the origin of this effect in detail, and how to account for it in a way less time-consuming than molecular dynamics simulations.</p>