Computational Study on the Boundary Between the Concerted and Stepwise Mechanism of Bimolecular SNAr Reactions

The text-book mechanism of bimolecular nucleophilic aromatic substitutions (SNAr) reactions is a stepwise process that proceeds via a so-called Meisenheimer intermediate. Only recently the alternative, concerted version of this mechanism has gained acceptance as more and more examples thereof have been reported. But so far only isolated examples of concerted SNAr reactions have been described and a coherent picture of when a SNAr reaction proceeds via a stepwise and when via a concerted mechanism has not yet been established. Here key factors are identified that influence the mechanistic choice of SNAr reactions. Moreover, the electron affinity is used as a simple descriptor to make a prediction on whether a given aryl fluoride substrate favors a concerted or stepwise mechanism.

The software used was Gaussian09 [1] (both Revisions A.02 or D.01 were used) in combination with GaussView 5.0.9 [2] for all calculations.

Methods
The DFT methods employed the functional as specified in combination with Pople triple-ζ basis set 6-311++G(d,p) [3][4][5][6] for all atoms up to the atomic number Z=18. For larger atoms (these mainly applied to counter cations K + , Rb + and Cs + and the halogen atoms bromine and iodine) the appropriate MWB relativistic pseudo-potential and associated basis set was used. [7] Solvation effects were accounted for by the solvent reaction field method using the conductor-like polarisable continuum model (CPCM) unless mentioned otherwise. [8,9] 1.3. The Applied σ p -Scale The σ p values were taken form the landmark review by Hansch et al. [10] A selection of para-substituents and their associated σ p constants that are used in this chapter are listed in Table SI-1-1 below. The less commonly encountered structures are drawn out next to the table.

General Procedure
For all S N Ar reactions reported in this chapter the rate limiting transition state ('TS1') was optimised. The

Results
In this chapter a detailed descriptions is given of how the results discussed in the paper were obtained.
Further, additional results are presented and discussed. The log files can be found in the accompanying archive under DOI: 10.15129/254ecae8-9c72-4bb9-9319-b16eada94f9c. To help efficiently retrieve a file of interest, a list of all log files is given in Chapter 3. The structure of Chapter 3 mirrors the structure of this chapter.

Computational Model Benchmarking DFT Functionals
All log files of the calculations presented in this section are listed in Table SI-3-1 (page 25).
The computational model was chosen and validated by comparing the performance of a variety of DFT functionals against the results of a high-level wavefunction-based method for a test-set of S N Ar reactions.
A satisfactorily well performing functional was identified for the further study of S N Ar reaction mechanisms. The S N Ar reaction shown in Figure  Plesset perturbation theory method MP2. MP2 is a wave-function based method and was the most reliable method that was affordable in terms of computational resources (memory requirements and time) for the studied system (number of atoms, electrons, and size of the basis set). The method predicted a sharp turning point for the S N Ar mechanism from stepwise to concerted with t p -= 0.92 ± 0.08. Importantly, the result was the same if either basis set, 6-311++G(d,p) or aug-cc-pVTZ, was used.
A number of DFT functionals was then applied to the same S N Ar model reactions. For all DFT calculations the 6-311++G(d,p) basis set was used. In Figure 4-2 the DFT functionals were clustered into four groups: hybrid functionals based on Becke's three parameter and/or Lee-Yang-Parr functional, members from the Minnesota family, representatives of the Perdew-Burke-Ernzerhof functional class, and methods derived from Becke's B97 functional.
None of the tested DFT methods was able to reproduce the MP2 result exactly and to predict the same mechanistic turning point. Most functionals, however, gave a result that was satisfactorily close to the MP2 result. Three functionals predicted a mechanistic turning point that was two increments or more (Δt p -≥ 0.22) away from the MP2 turning point. Importantly, from the investigated functionals, the widely used functional B3LYP with D3-dispersion correction -B3LYP-D3(BJ), as used, for example, by Jacobsen et al. [11] -and the M06-2X functionals were among the worst-performing ones.
Four functionals were not able to predict the mechanistic turning point as sharply as the MP2 method, i.e.
they produced an alternating pattern of concerted and stepwise mechanisms as the electronic nature of the para-substituent changes. These were the BHandHLYP, M06, PBE0-D3(BJ) and ωB97 functionals. These were consequently ruled out as suitable functionals for the following study.
As an additional measure of the performance of the DFT functionals, their ability to correctly reproduce  basis set and cpcm solvent model for DMF was used, unless mentioned otherwise. 's' stands for 'stepwise S N Ar mechanism', 'c' stands for 'concerted S N Ar mechanism'. [a] The aug-cc-pVTZ basis set was used. The M06-2X functional showed a standard deviation close to 2 kcal/mol, while the range-separated hybrid functional M11 showed a standard deviation of less than 1 kcal/mol. The functionals in the PBE0 and B97 group all showed good to excellent performance.
In conclusion, from the nine DFT functionals that were found to predict the mechanistic turning point t satisfactorily well (see Figure SI-2), four also gave a good prediction of the rate limiting energy barrier with a standard deviation of < 2 kcal/mol. Overall, the M11 and ωB97XD functionals were the two top-runners and the more modern M11 functional was selected for the further study.

Table SI-2-1 Statistical Evaluation of the Functional Performance
The table gives a more detailed analysis of the results shown Figure  [a] The same basis set -6-311++G(d,p) -was used as for the DFT methods.

Validating the Procedure
The log files of the calculations presented in this section are included in Table SI-3-1 (page 25).
The method to test for the presence of a Meisenheimer intermediate so far was to start an optimisation from the transition state geometry that was slightly distorted along the imaginary mode. The optimisation can either converge to a Meisenheimer intermediate or directly to the product complex. Although experience showed that this method is able to detect very shallow local minima on the potential energy surface, it was necessary to establish its validity for the situation at hand. The question of particular concern was whether this method might fail to detect very fleeting Meisenheimer intermediates.
The mechanistic classification based on the M11 functional from Figure SI  [d] The energy barrier of the second transition state is given relative to the Meisenheimer intermediate.
[e] Imaginary modes were found in a frequency calculation for the stationary point structure identified by the IRC.
[f] Bond scans were performed with a step size of 0.00125 Å to search for a candidate structure for the transition state, but no maxima along the expected reaction coordinate were found. the stationary points found by the IRC scan for these two examples are better described as inflection points rather than as true local minima on the potential energy surface. For the example with -R = -CO 2 Me, the result from the IRC scan is in agreement with the initial classification of the reaction.
It can be concluded that the approach of optimising a transition state geometry towards the product complex is a sufficiently sensitive method for finding Meisenheimer intermediates. The method has the advantage over IRC scans that it is computationally more effective and does not falsely classify very flat regions on the potential energy surface as intermediates. Indeed, the results from the IRC scans demonstrated that the potential energy surface of S N Ar reactions close to the mechanistic turning point is -not surprisinglyvery flat.

Comparison to Experiments
All log files of the calculations presented in this section are listed in Table SI-3-2 (page 30).
In addition to benchmarking the DFT functionals against the results from high-level ab initio calculations (i.e. the MP2 results), their predictions were compared with experimental data. First, the activation energy as calculated by the M11/6-311++G(d,p)/cpcm method was compared to the activation energy measured experimentally for one example [12a] (Scheme SI-1). The predicted activation energy deviated by only 1 kcal/ mol from the experimental [12a] value. Similarly, we calculated the activation energy of the S N Ar reaction between potassium methoxide and para-methoxyfluorobenzene (Scheme SI-2 respect. [13][14][15][16] Therefore it was an obvious step to calculate energy profiles for some of the reactions, which Williams et al. suggested to proceed via a concerted mechanism. The displacement of phenolates 15 from a triazine-derivative 11 with amine nucleophiles 12 [15] was chosen as a reference case (Table SI-2-3). In apparent contradiction to the claim of these reactions to be concerted, [15]  the Meisenheimer intermediate and are of major concern for the following discussion.
The reaction was performed in an aqueous solvent system of water-dioxane 9:1. [15] There are no parameters available to model this solvent system directly. As a reasonable approximation, the solvent model for water was chosen in the calculation.  [b] Measured with respect to the Meisenheimer intermediate.
[c] Measured with respect to the substrate complex.
[d] Four explicit molecules of water were included in the calculation.
[e] The energy profiles with two different attack angles of the nucleophile were modelled for the same reaction. Ar: The computational results stand in apparent contradiction to the interpretation of the kinetic studies that were performed by Williams et al. for this class of S N Ar reactions. [15] Closer inspection of the computational results showed, however, that in the majority of cases the relative stability of the Meisenheimer intermediate is lower than 2 kcal/mol -thus below the typically accepted threshold of chemical accuracy. [17] In that sense, the computational results support the interpretation of Williams' kinetic data. Following conventional experimental approaches, these S N Ar reactions appear to proceed via a concerted mechanism. With computational tools, however, it is possible to detect much shallower minima on the potential energy surface than with conventional experiments. Thereby, a reaction that appears to be concerted in the experiment can correctly be revealed to exhibit fleeting intermediates along its path.

Initial Studies
To gain a broad overview of the two mechanistic domains, three classes of S N Ar reactions were investigated. These are the halide displacement with potassium methoxide (Figure 1 in the main text), halide-halide exchange reactions (Table SI- [2][3][4] and the analogous chalcogen-chalcogen exchange reactions (Table  SI- [2][3][4][5]. The log files of these calculations can be found in Table SI In the halide displacement with potassium methoxide in Figure 1, only for the fluoride series was the mechanistic turning point identified, with t p -= 1.05. For the displacement of chloride, bromide and iodide the mechanistic turning point could not be identified. These reactions all showed a concerted energy profile even with the most electron-withdrawing para-nitroso substituent that was included in the σ p scale. A similar picture was obtained for the halide exchange reactions (Table SI- [a] The S N Ar reaction mechanism changes from stepwise to concerted when going from the para-substituent -CF 3 (σ p -= 0.65) to -CCH (σ p -= 0.53).
[b] The para-nitroso substituent marks the upper limit (σ p -= 1.63) of the applied σ p scale. Clearly, a concerted mechanism is favoured for the chalcogen exchange reaction by the participation of larger (i.e. softer) chalcogens. The analogous statement holds true for the halide exchange reaction. The halides chloride, bromide and iodide all strongly favour a concerted mechanism, either in the halide exchange reaction or in an exchange reaction with potassium methoxide. Only for the S N Ar reactions involving fluoride was a stepwise energy profile found to have significant importance.

Counter-Cation and Explicit Solvent Effects
The ability of the alkali counter cation to coordinate to the leaving fluoride anion can have an effect on the mechanistic turning point as became apparent from Figure 2 in the main text and the corresponding discussion. The log files of these calculations are listed in Table SI-3-7 (page 37). In order to refine the understanding of coordination effects, explicit solvent molecules were added to the computational model as ligands of the alkali metal cation ( Figure SI-4). It was assumed that the ability of the counter cation to coordinate the fluoride leaving group may decrease if its coordination sphere gets increasingly saturated with other ligands. It was found that the addition of one explicit solvent molecule in the model system did not evoke any shift in t p -. The addition of a second molecule of DMF led to a significant blurring of the mechanistic turning point, which manifests in an increase of Δσ p from 0.05 to 0.22. Also, the value t p decreased slightly by 0.18 units. However, since the mechanistic turning point is no longer sharp, it is not clear whether this decrease of t p is actually significant. The log files of these calculations are listed in Table   SI-3-8 (page 40).
Overall, including explicit solvent molecules did not produce a dramatically different prediction of the mechanistic turning point. A similar observation has already been made previously (Table SI- . This result also has practical implications. It suggests that relying on the implicit solvation model alone is a reasonable -and computationally much more effective -approximation.

Effect of the Nucleophile
In Figure   favours a concerted mechanism more (t p -= 1.36) than the other investigated reaction series (t p -= 1.05).
The log files of these calculations are listed in Table SI-3-9 (page 41). Closer inspection of the geometries of the rate limiting transition states including nucleophile 2e-K showed that steric repulsion may be at the heart of this pronounced tendency to follow a concerted mechanism (Figure SI-5). One of the hydrogen atoms of the phenyl group of the nucleophile approaches the plane of the aromatic system of 1a-R-F (here shown for R = NO 2 ) as closely as 2.3 Å in the transition state. This steric clash makes a Meisenheimer intermediate less energetically favourable and pushes the reaction towards a concerted pathway.

The SN(ET)Ar Pathway as an Alternative to the Bimolecular S N Ar Pathway
During the reviewing process it was pointed out that the highly activated substrates 1a-R-F with R = NO, NO 2 and CHC(CN) 2 may react with the nucleophiles 2b-K, 2d-K, 2e-K and 2f-K alternatively via an SN(ET) Ar process. Along this reaction coordinate, first an electron would be transferred from the nucleophile to the electrophile in a single electron transfer (SET) step. In order to judge the accessibility of the SN(ET)Ar pathway the Gibbs free energy was calculated for the initial SET and compared to the energy profile of the SNAr reaction.
For isolated examples, also the activation energy of the SET was calculated according to the modified Nelsen-four-point method. [19] The results are summarised in Table SI    . For the pyridine series 28, the variation of t p among the four nucleophiles 2a -d was somewhat larger than in the benzene series. The average was slightly lower with a value of 0.93 ± 0.14. The log files of these calculations are listed in Table SI-3-11 (page 43). For the naphthalene series 29, the three nucleophiles 2a -c showed a similar value of t p with an average t p of 0.77 ± 0.10. The nucleophile 2d, in contrast, massively deviated from this average value. In fact, the S N Ar reaction with this nucleophile favoured a stepwise S N Ar reaction even with electron-donating substituents such as para-methyl or para-NHAc residues. Presumably, π-π-stacking interactions or steric effects between the nucleophile and the aromatic system lead to this pronounced difference to the other nucleophiles. Therefore the reaction series of 2d with 29 was regarded as an anomaly and not included in the calculation of t p -. The log files of these calculations are listed in Table SI-3-13 (page 45).
With the exception of the reactions between 2d and 29 it can be noted that there is relatively little variation between different nucleophiles attacking the same aromatic substrate, i.e. the observation made for the system 1a-R-F was essentially reproduced with 28 and 29. The mechanistic turning point does not seem to depend on the nucleophile strongly, i.e. the value t p is mainly characteristic for the aromatic system (with a fluoride leaving group).

Steric Effects
For two cases so far, indication was found that, in addition to the electronic characteristics of the system, steric effects may influence the mechanistic turning point (see Figure  . This allows us to investigate steric effects by choosing a bulky and a slim nucleophile. Any significant difference in t p between these two nucleophiles for the attack at the same series of substrates can then be attributed to steric effects. Such a comparison was made for the nucleophiles 2c-K and 2d-K based on the aromatic substrates 1a-F, 30 and 31 ( Figure SI-8). When going from 1a-F to 30 to 31, the small nucleophile 2c-K does not show any response to the increasing steric bulk and slightly more electron-rich aromatic core. The value t p remains constant throughout this series. With the sterically more bulky nucleophile 2d-K, the situation is different. While there is no difference in t p between 2c-K and 2d-K for the substrates 1a-F and 30, the value of t p sharply decreases for the reaction of 2d-K when a second ortho-methyl group is present as in 31. The log files of these calculations are listed in Table SI-3-14 (page 47).
This result shows that steric bulk on the aromatic system can force the S N Ar reaction to follow a stepwise mechanism even if a concerted reaction profile would be expected based on the electronic nature of the substrate. As follows from the combination of the nucleophile 2d-K and the aromatic system 31, the steric bias on the mechanism can be massive. The introduction of the second methyl group induced a larger change in t p than did the expansion of the aromatic core from benzene to anthracene, for example ( Figure   4 in the main text). While changes of the electronic nature of the aromatic system affect the S N Ar reaction of various nucleophiles approximately equally, steric changes affect mainly bulky nucleophiles like 2d-K.

2.5.
Effect of the Aryl Fluoride Electrophile As illustrated in Figure 4 in the main text, both, an additional fused ring and a nitrogen atom in the ring, help to stabilise the negative charge that accumulates on the aromatic system during the addition of the nucleophile. The better the aromatic core on its own is able to stabilise this negative charge, the less the stabilisation of a (potential) Meisenheimer intermediate depends on the electron-withdrawing nature of the para-substituent. The log files of these calculations are listed in Table SI The electron affinity of a given aromatic system can be used to estimate whether a S N Ar displacement of the fluoride substituent proceeds via a concerted or stepwise mechanism as shown in Figure 5 in the main text. The log files of these calculations are listed in Table SI-3-16 (page 50).

S N Ar Mechanism and the Hammett Correlation
As has been seen in Figure 6 in the main text, there does not seem to be a connection between the slope of the Hammett correlation and the mechanistic preference of an S N Ar reaction series.
To further investigate what information about the overall reaction mechanism is contained in the structure of the rate-limiting transition state, the changes in the geometry of the rate-limiting transition states of the S N Ar displacement for the series 1a-R-X (for X = F, Cl) with potassium methoxide was analysed ( Figure   SI-9). It can be seen that the investigated distances and angles change in a very similar way between the two series (i.e. the slopes of the correlations of the four investigated parameters are nearly the same).
Further, also the absolute values of d 1 , a 1 and a 2 are very similar (as expected, there is a large difference in the distance d 2 between the two series, which reflects the length difference {ca. 0.4 Å} [18] between the carbon-fluorine and the carbon-chlorine bond). Again, the change of mechanism from stepwise to concerted is not reflected in the change of any of the investigated parameters. The log files for these calculations can be found in Table SI The log files for these calculations can be found in Table SI For three examples, also the overall free energy ΔG° was analysed in detail (series 2c-K, 2d-K and 2e-K in Figure

Predicting the S N Ar Mechanism of Substrates with a Simple Descriptor
As illustrated in Figure 6 in the main text, the S N Ar mechanism a given aryl fluoride would follow, can be predicted based on its gas-phase electron affinity (EA). Alternatively descriptors to the EA were investigated. The Mulliken charge ( Figure

Computational Model Benchmarking DFT Functionals
The names of the .log files of the calculations used to compile Figure

Validating the Procedure
The log files for the IRC scans shown in Table SI-2-2 are included in Table SI-3-1 under the method 'M11' and marked as 'IRC' in the 'Reaction Coordinate' column.

Comparison to Experiments
All files for the calculation shown in Scheme SI-1 and Scheme SI-2 are listed in Table SI

Initial Studies
The The log files for the calculations shown in Figure 1 in the main text for the displacement of the halides fluoride, chloride, bromide and iodide by potassium methoxide are listed in below in Table SI-3-4.

Counter-Cation and Explicit Solvent Effects
The log files for the calculations shown in Figure 2 in the main text investigating the effect of the counter cation on the mechanistic turning point are listed in below in Table SI-3-7.

Effect of the Nucleophile
The .log files for the calculations of different nucleophiles shown in Figure 3 in the main text are listed in below in Table SI-3-9. For the examples with potassium methoxide as the nucleophile see Table SI-3-7.    Table SI-3-11.  The log files for the calculations of different nucleophiles with naphthalene shown in Figure SI-7 are listed in below in Table SI-3-13.

Steric Effects
The log files for the calculations shown in Figure SI-8 are listed in below in Table SI-3-14. For the examples with the aromatic system 1a-F see Table SI-3-7.

Effect of the Aryl Fluoride Electrophile
The log files for the calculations of different aromatic systems with the potassium methoxide nucleophile shown in Figure 4 in the main text are listed in below in Table SI  The log files for the calculations used to correlate electron affinities and the mechanistic turning points shown in Figure 5 in the main text are listed in below in Table SI

S N Ar Mechanism and the Hammett Correlation
The log files for the Hammett correlation studies shown in Figure 6, and Figure SI-9 can be found in Table  SI-3-7.