Abstract
This paper presents a theoretical analysis the effect of non-covalent interactions (NCI) in three different SN2 reactions (X–:CH3X → XCH3:X–, X = Cl, Br and I) has been theoretically analysed in the pre-reactive complexes, TS and products. A total of eighteen Lewis acids (LAs: FH, ClH, FCl, I2, SeHF, SeF2, PH2F, PF3, SiH3F, SiF4, BH3, BF3, BeH2, BeF2, LiH, LiF, Au2 and AgCl) interact with the halogen atom of the CH3X molecule. To analyse the strength of the non-covalent interactions, both the independent gradient model tool and electron density maps have been employed. The results reveal that in all cases, the interaction between the anion and the Lewis acid leads to an increase in the transition barriers compared to the parental reaction.
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1 Introduction
Introduced by Hughes and Ingold in 1935 [1,2,3] the binuclear nucleophilic substitution, SN2 reaction is one of the principal backbones in organic chemistry [4], corresponding to a mechanism where one bond is broken and one bond is formed synchronously. The SN2 reaction is closely linked to the Walden inversion [5,6,7] and to the Finkelstein reaction (an SN2 reaction that involves the exchange of one halogen for another) [8]. The SN2 reaction has been much studied over the years [9], especially from a theoretical perspective by Bickelhaupt et al. [10,11,12,13,14,15]. These authors have extensively examined the reaction, particularly focusing on solvent effects [13, 14]. Garver et al. observed that the SN2 reaction between CN– and CH3I proceeds through a double-well energy pathway in gas phase, while the inclusion of solvent effects, transforms the reaction in a unimodal pathway [16]. While the influence of solvent effects has garnered significant attention in the literature with numerous dedicated papers [17,18,19,20,21], the importance of the gas-phase studies cannot be overlooked.These studies offer valuable and intricate insights into the underlying reaction mechanisms. Gas-phase studies contribute to a more comprehensive comprehension of the process [19, 22,23,24,25,26].
Bierbaum et al. have studied the effect of microsolvated anions on SN2 reactions and compared those with gas phase result [16, 24, 25]. In order to model the microsolvated anions, the authors used an explicit solvent molecule interacting with the respective anion and found an enhanced reactivity within solvated anions. Furthermore, in a separate investigation, it was studied how α-nucleophiles (R-Y-X–) enhance the reactivity in SN2 reaction with respect to the normal nucleophiles (R-X–) reducing dramatically the transition barriers [27].
The study of the SN2 reaction has not only been limited to carbon-centred reactions but also expanded into N, O, F, Si, P centres [26, 28,29,30,31,32] and also for both cationic and anionic systems [33,34,35,36]. It is worth mentioning that in addition to the most common experimental and theoretical methodologies, other authors have explored the SN2 reaction by means of the interacting quantum atom methodology [37, 38] and the kinetic isotopic effects [39]. Uggerud et al. studied the steric and electronic effects on SN2 reactions and by using electron density shift (EDS) results, provided an alternative interpretation of the factors that govern the reaction [40, 41]. It is clear that there is a plethora of articles devoted to the SN2 reaction with numerous recent reviews available [13, 19, 41].
The catalysis using Lewis acids (LAs) have been experimentally explored in SN2-type ring openings [42,43,44] and from the theoretical point of view in other reactions, i.e. Diels–Alder [45, 46]. Those LAs interact with the anions through so-called non-covalent interactions (NCI) [47]. Given the importance of the subject, and very intrigued by the effect of a third-party molecule within the SN2 reaction, we decided to study how LAs influence the mentioned reaction.
Herein, to analyse the effect of the LA on the potential energy profiles, the selection of symmetric SN2 reactions allows for the straightforward acquisition and analysis of transition barriers.
In the present article, the effect of a large variety of NCIs [47] (hydrogen [48, 49], halogen [50,51,52], chalcogen [53,54,55], pnictogen [56,57,58], tetrel [59,60,61], triel [62, 63], beryllium [64, 65], lithium [66, 67] and regium bonds [68,69,70]) in three SN2 reactions has been studied where a LA interacts with one of the halogen atoms involved in the reaction. For each system, three stationary points have been characterised along the reaction coordinate: (1) two minima: pre-reaction assembly complex (Scheme 1, l.h.s.) and product complex (Scheme 1, r.h.s.) and (2) the transition state (TS) (at the centre of Scheme 1) linking them. The influence of the NCIs on the geometry, energy and electronic properties of these systems has been analysed.
SN2 reactions studied. X = Cl, Br and I in the present study. The numbering used along the article for the two different X atoms is indicated
2 Computational details
2.1 Ab initio calculations
The systems under study have been optimised using the M06-2X DFT computational method [71] and the 6–311++ G(d,p) basis set [72]. The effective core potential def2-TZVPD basis set [73] has been used for the iodine, gold and silver. These methods have been proved to produce reliable results in SN2 reactions [37] and in LAs within NCIs [74], compared with CCSD and CCSD(T) methodologies [75, 76]. Frequency calculations have been performed to verify that the geometries obtained correspond to energetic minima or true transition states (zero and one imaginary frequencies, respectively) and to obtain the thermodynamic parameters. These calculations have been carried out with the Gaussian-16 program [77]. All the Cartesian coordinates for all the complexes studies can be found in the Electronic Supporting Information.
Binding energies (ΔEb) were calculated as the difference of the electronic energy of the optimised complex minus the electronic energy of each monomer in their optimised geometry. All the binding energies have been corrected with the basis set superposition error (BSSE) [78].
Independent gradient model–intrinsic bond strength index (IGM–IBSI) method: IGM is a recent electron density (ED) overlap-based computational method that enables to detect and quantify covalent and non-covalent chemical interactions [79, 80]. It employs a descriptor, δg, which locally quantifies the electron density clash between two given sources (atoms or fragments or molecules). In other words, δg accounts for the tendency of electrons to be shared between defined fragments. In this study, the ED was calculated from the wave function obtained after the DFT optimisation geometry.
The 2D plot of δg (collected for every node of a three-dimensional grid enclosing the system) as a function of the signed ED leads to a picture where one or more peaks (δgpeak) appear, leading to a specific signature of the interaction; the larger the peak, the more intense the interaction. In the IGM framework, weak NCI hardly exceed a δgpeak of 0.1 a.u. Hydrogen bond generally may extend up to a maximum of δgpeak = 0.1 a.u. (δgpeak = 0.06 a.u. for HB in water dimer), while vdW interactions rarely extend beyond 0.02–0.03 a.u. Pure covalent bonds range from 0.2 up to around 2.5 a.u. Metal coordination δgpeak values range between 0.1 and 0.6 a.u.
Moreover, in this study, the following integration scheme has been used to quantify the interaction between the LA and the SN2 system:
(\(\mathrm{d}v\) is an elementary volume related to the grid enclosing the chemical system).
Furthermore, the IGM–IBSI integrated index [81] has been employed to probe the effect of the LA on the strength of the X–C covalent bond to be broken during the reaction. For an in-depth understanding of various IGM aspects, the reader may refer to the original work [79, 80]. All calculations have been carried out using IGMPlot program [82].
2.2 Electron density shift
The electron density shift maps and the corresponding values were obtained as:
where ρXY, ρX and ρY correspond to the electron density of the complex and both fragments, respectively. EDS+T (total electron density shift) and EDS+0.001 (electron density shift at the 0.001 au. isosurface) are calculated using a numerical grid from the density cubes using the following formula:
where ρEDS+ corresponds to the positive values of the electron density shift on each point of the grid upon complexation, so the sum of all those values corresponds to EDS+T. For the EDS+0.001 term, only those points which fulfil the condition that the density value is equal or less than 0.001 a.u. are considered. The full procedure is described in ref. [83] and the code available in https://github.com/iribirii/EDS_quantification.
Figures were plotted using python and matplotlib [84], CYLview software [84] and VMD [85].
3 Results and discussion
This section has been organised as follows. First, the interaction between the LA and X– with CH3X constituents of the SN2 reaction has been studied. Then, the effects of the LA on the SN2 profile have been analysed and discussed with an emphasis on the geometrical and electronic effects on the reactants, transition states and final products. In each section, the intrinsic bond strength index (IBSI) and EDS analysis of the systems have been considered.
3.1 LA:X– and LA:CH3X complexes
The binding energies of each LA interacting with the isolated X– and with CH3X are shown in Fig. 1 and reported in Table S1. Binding energies for the LA···X– are considerably more negative (between –57 and –262 kJ·mol–1) than the ones found for LA···XCH3 complexes (between −13 and −82 kJ·mol–1). As expected, weak electron acceptors like HF or HCl show the smallest binding energies while strong Lewis acids, like LiH or AgCl present the largest (more negative) Eb values. It is also worth indicating that in LA···XCH3 complexes, the differences between the halogen species are very small, except for Au2 and AgCl in which the Eb for the three halogen derivatives (X = Cl, Br and I) are clearly differentiated. Furthermore, the binding energy values corresponding to X–···H3CX interaction in the binary complex are –49.0, –46.0 and –40.5 kJ·mol–1 (for X = Cl, Br and I, respectively). With all this above, it is clear that when the LA approaches the binary complex, it is expected that it will interact preferentially with the anion, X–. Additionally, the binding energies between the LA and [XCH3X]– moiety, interacting either on the anion side (LA···[X···CH3X]–) or on the XCH3 side (LA···[XCH3···X]–, have been also analysed exhibiting the preferred binding mode mentioned above (Fig. 1).
BSSE corrected electronic binding energies, ΔEb (kJ·mol–1), for the interactions LA···XCH3, LA ···X– and between the LA and the binary complexes in the reactants (LA···X–···CH3X) and products (LA···XCH3···X–) with X = Cl, Br and I at the M06-2X/6–311++G(d,p)/def2-TZVPD computational level
Same behaviour has been found in the electron density shift (EDS) maps (Fig. 2), in which the interaction between the LA and the X– displaces more electron density (EDS+T) that in the interaction with the XCH3 moiety. This also occurs on the 0.001 a.u. electron density isosurfaces as indicated by the EDS+0.001/EDS–0.001 values.
Electron density shift (EDS) maps at the 0.001 a.u. cut-off for the interaction between HF/AgCl with Cl–/CH3Cl. Magenta and green areas correspond to regions of decrease and increase of electron density, respectively. EDS+T indicates the total increment of charge (in e–) displaced, while EDS+0.001/EDS–0.001 corresponds to the increase and decrease of charge at the 0.001a.u. cut-off
This binding mode has been also corroborated by the IGM fingerprint, in which the calculated values of the δgpeak corresponding to the LA···X– interactions complexes are larger than those of the analogous LA···XCH3 ones for the same LA and X groups (Table S2).
Although the LA···X– binding mode is preferred, it is worth shedding some information about the interaction of the LA with the XCH3 for future works. In that regard, it is observed that LA with the XCH3 interaction produces an elongation of the X–C bond as indication of the electron donation from the XCH3 and weakening of this bond. The IGM–IBSI values of the X–C bonds recover this weakening showing smaller values as the X–C is longer. Also, linear relationships between the bond distance and the IBSI value for each halogen (Fig. S1) are obtained with R2 > 0.97. As demonstrated later in this paper, the linear relationships are due to the small range of interatomic distances considered here, and when a wider range of distances are considered, exponential relationship is found.
3.2 Effect of LA on the SN2 profile
3.2.1 Energetics
It has been stated unequivocally that the LA···X– binding mode is preferred over the LA···XCH3 complexation mode. In the following subsection, we monitor the fate of this LA interaction along the reaction path involving the three stationary points. How will the LA affect both sides (reactants and products) of the reaction? Will the LA affect the transition barriers? It is worth noting that the reactants in this study are the molecular complexes (MC), which represent a minimum between the separated reagents (products) and the TS.
The potential energy surfaces for all the cases studied are summarised in Table S3, and some representative systems for X = Cl are plotted in Fig. 3. In the investigated systems, the interaction between the LA and the anion X– increases the stability of the reactant with reference to the parent reaction. It is important to highlight that in the presence of strong LAs, the X– anion binds to the LA causing the resulting molecular complex to deviate from the C–X bond axis. This effect has large implications on the reactivity, since not only the LA binds strongly with the anion (Fig. 1) but also, in those cases, the LA displaces the anion out of the reaction path, i.e. the one aligned with the X–CH3 molecular axis. All these features were observed for the reactions involving the three halogens, X = Cl, Br and I, atoms considered.
Energy profile for some representative systems at the M06-2X/6–311++ G(d,p)/def2-TZVPD computational level. Entrance channel is referred to the sum of the energies of the isolated monomers: E(LA) + E(XCH3) + E(X−)
Regarding the different transition states (TS) obtained, the presence of the LA increases the transition barrier, computed as the energy difference between the pre-reactive (ternary) complex and the TS, in all the cases. The largest increases are found in the ClCH3Cl system, followed by Br and I derivatives. Regarding the nature of the interaction, pnictogen interactions (PH2F) and weak hydrogen bond donors (for instance, HF) present the smallest variations, while BeF2 shows the largest transition barrier (Fig. 4). All the energetic barrier for the systems in the LA presence are under the entrance channel.
Transition barriers, in kJ·mol–1, calculated as the energy difference between the pre-reactive complex and the TS, for the X−CH3X SN2 reactions studied at the M06-2X/6–311++ G(d,p)/def2-TZVPD computational level
The presence of the LA breaks the energetic degeneracy of the different reactions. Thus, even though the presence of LA increases the stability of the reaction products with respect to the parental reaction (−49 mol–1), the reactions are reversible, i.e. the products are less stable than the MC. This is consistent with the interaction energies found on, one hand, between the LA and X–, on the other hand between LA and CH3X. The results indicate that the LA has a stronger binding affinity for the anions than for CH3X. Consequently, based on the calculated data, the LA is expected to inhibit the reaction in principle.
3.2.2 Geometry
In order to study how does the presence of the LA affect the geometry of the stationary points along the X–···CH3X reaction path, the R1 distance will be considered as the distance between the anion X– and the C from CH3X, and R2 as the distance from the same carbon and the leaving X. In the reactants, the R2 distance is elongated about 0.04 Å due to the presence of the X– anion in the MC of the X–··· H3CX reaction. This elongation is reduced in the presence of the LA since the nucleophilicity of the anion is shielded, i.e. the anion has less electron density to interact with the CH3X due to its interaction with the LA. In the same way, the X(1)–C distance increases due to the presence of LA. This increase is up to 0.96, 1.15 and 0.87 Å (Table S4) for the AgCl:[XCH3X]– system (for X = Cl, Br and I, respectively).
Regarding the different TSs, the R1 distance is shorter than in the parental reaction while the R2 one is longer (Table S4), which indicates that the TS tends to resemble the product structure due to the presence of the LAs. In other words, it indicates that the reaction is not favoured by the presence of the LA. According to the Hammond–Leffler postulate, "the transition state resembles that of the structure closest to it in free energy" [86,87,88]; therefore, when the difference in X–C distances increase, the TS structures resemble the products, and consequently, the value of the TS barrier increases.
Finally, in the products the R1 distances found are longer in the presence of LA, consistent with the reduction of the electron density in the X–C bond due to the donation of X towards the LA. Also, in the product, the R2 distance is shorter than in the parental reaction, reinforcing again the idea of the decrease in the electron density on the CH3X moiety and therefore increasing the interaction with the leaving anion X–. These effects are more important for the stronger LAs, indicating their influence on the reaction, particularly in the electron density relocation.
A Steiner–Limbach relationship [89,90,91,92] is obtained for the C–X distances in the complexes using the “R1-R2” and “R1 + R2” parameters (Fig. 5). The “R1-R2” parameter is a measure of the asymmetry of the system. It is 0.0 in the symmetric TS of the LA free X–···CH3X reactions and increases in absolute value for the MC and products. The “R1 + R2” parameter indicates the distance between the two halogen atoms in each structure. Both parameters are useful to show how the presence of LA affect the geometry of MC or products, and particularly the asymmetry in the system. In principle, plotting "R1 + R2" (intramolecular X··X distance) versus "R1-R2" (asymmetry) could show that systems with longer X···X distances exhibit more asymmetry. Figure 5 clearly shows that the distance between the halogen atoms decreases as they tend towards the TS being the "R1 + R2" parameter minimum in the symmetric TS and increases in the MC and products. The strongest the interaction between LA and [XCH3X]– system, the larger R1 + R2 and R1-R2 values. This is an indication of how the LA modifies the structure of [XCH3X]– upon complexation.
Steiner–Limbach plot of the stationary points in the presence/absence of LA
3.2.3 IGMPlot and EDS analysis
Due to the interaction established between the different LAs and the halogen atom X(1), a redistribution of the electron density (ED) in the [XCH3X]– donor counterpart, takes place. This involves the interaction between X(1) and LA, concomitantly with the formation of X(1)–C and dissociation of C–X(2) bonds. Therefore, in order to shed light on the mechanism from the ED perspective, an independent gradient model (IGM) analysis has been undertaken.
The IGM δg descriptor quantifies the electron density clash between two given fragment sources (atoms or molecules). Thus, it accounts for the tendency of electrons to be shared between both interacting moieties. In fact, the two-dimensional (IGM 2D) plot of δg as a function of the signed ED leads to a picture (Fig. 6) where one or more peaks (δgpeak) appear, leading to a characteristic signature of the interaction present in the system. δgpeak values can be associated to a type of interaction (on an absolute scale from non-covalent to covalent). Furthermore, the Δg integrated value assesses the interaction strength (see Computational details section for more details).
IGM approach illustrated on the BeF2···[ClCH3Cl]–, LiH···[ClCH3Cl]–, HF···[ClCH3Cl]– and AgCl···[ClCH3Cl]– complexes: 2D-plot signature in orange colour; 0.02 δg-isosurface associated with the interaction between LA and the reacting system; isosurfaces coloured according to the BGR scheme over the range –0.08 a.u. < sign(λ2)ρ < 0.08 a.u
The IGM 2D-fingerprint of the interaction between two fragments: LA and [XCH3X]– in the reactants, TS and products complexes presents δgpeak values found in a wide range 0.009—0.209 a.u. (Table S5, Fig. 6). As expected, these results disclose very different kinds of interactions from weak interactions to situations involving covalent features. δgpeak values are greater for the pre-reactive MC than for the products, owing to the negative charge on X(1) gradually decreasing along the reaction path. This is also corroborated by the ∆g values (Table S5). The interactions between LA and X– moiety (reactants) present larger integrated values than in the products (LA···XCH3 moiety). At the TS, the strength of the electron density clashes between the LA and the [XCH3X]− fragment decreases, with respect to the reactant one, since the negative charge, initially located on the X(1)– halogen, is progressively transferred to X(2). This can be seen and evaluated using electron density shift (EDS) maps [83]. However, no relationships have been found between Δg and ΔEb value. This may be because while the Δg is focused in a single region of the space, i.e. on a single interaction, the ΔEb, as a whole, accounts for several other factors (for example, electronic repulsion) for the entire system.
In Fig. 7, the electron density shifts maps have been plotted to illustrate the density displacement upon interaction with the LA. As expected from the X–···C interaction, there is an increase on the electron density between both atoms due to the formation of a new bond consistent with the situation in the TS where all the electron density shift is spread along the reaction coordinate. The presence of a LA in the reactant modifies the electron density, increasing the electron density displacement in the whole complex. This is observed (Fig. 7) by the increase of the EDS+T values from 0.163 e– (no LA) to 0.301 and 0.435 e– (HF and AgCl, respectively), which is again aligned to the binding energies and the IGM values. The same effect can be observed at the 0.001 a.u. electron density isosurface (EDS+0.001).
Electron density shift (EDS) maps at the 0.001 a.u. cut-off. Magenta and green areas correspond to regions of decrease and increase of electron density, respectively. EDS+T indicates the total increment of charge (in e–) displaced, while EDS+0.001 corresponds to the increment of charge at the 0.001a.u. cut-off. EDS maps are obtained as: ρ(LA[XCH3X]–) – ρ(LA[XCH3]) –ρ(X–)
Finally, in order to analyse the bond formation/breaking in the reaction, the IGM–IBSI bond index has been calculated. This index does not belong to the class of conventional bond orders (Pauling, Wiberg, Mayer, …)[93,94,95,96] giving the number of electron pairs shared between two atoms, but it is rather closely related to a local bond force constant for a given atom pair. Covering a broad range of bonding cases (from non-covalent to covalent bonds), IBSI is attached to the intrinsic bond strength concept even in situations with imaginary vibrational frequency (TS) where the conventional stretching force constant is no longer connected to the restoring force concept. Therefore, IBSI is particularly suited for following bond formation and breaking in chemical reactions.
The exploration of the three stationary points along the reaction paths with a variety of LA interacting with one of the halogen atoms involved in the reaction provides a large number of IGM–IBSI values for the C–X interaction in a wide range of intermolecular distances. Those IBSI values can be used to estimate the strength of the X(1)–C and C–X(2) bonds within those stationary points. (Figure 8 shows some representative cases.) For example, the IBSI analysis shows the LA strengthening of the X(2)–C bond in the reactants while the LA weakens the same bond in the TS with respect to the reaction without the LA (Table S6) which is in agreement with associated X(2)–C elongation observed in the MC. For instance, the Cl(1)–C bond strength rises from 0.168 to 0.298 a.u. in the presence of AgCl at the TS, constituting an increase by 77% (Fig. 8).
Representation of the X(1)–C bond, C–X(2) distances (black, Å) and IBSI values (red italics, a.u.) in the reactants, TS and products for the [ClCH3Cl]−, HF···[ClCH3Cl]− and AgCl···[ClCH3Cl]− systems
Above all, the representation of these values (IBSI and intermolecular distances) provides excellent exponential relationships between them, as shown in Fig. 9. It is worth mentioning that while in small subsets of data (Fig S1) linear relationship is found, considering longer intermolecular distances leads to exponential relationship due to the larger data set. This relationship confirms the utility of the IBSI parameter to identify the strength of the contact which is connected in the literature with the interatomic distance.
IBSI values (a.u.) vs. the corresponding distance (Å) in reactants, TSs and products
4 Conclusions
The effect of the presence of LAs on a series of SN2 reactions [XCH3X]– (X = Cl, Br and I) has been thoroughly examined. The presence of LAs stabilise the nucleophile, MC, TS and products compared to the parental system, disrupting the energetic degeneracy of the reaction. Notably, the LA exhibits a more favourable interaction with the anionic halogen in the pre-reactive complex than with the CH3X molecule resulting in two important energetic consequences. Firstly, the reaction is reversible since the MC are more stable than the products. Secondly, the barrier, computed as the energetic difference between the MC and the TS, increases with the presence of LAs; however, all of them are under the entrance channel in contrast with the parental one.
The nature of the interaction established between the LA and [XCH3X]– is mainly non-covalent, though certain LAs exhibit some covalent characteristics that impact the binding energies and barriers. LA interacting through hydrogen or halogen bonds presents weak interactions with the reactants, and therefore, their influence on the pre-reaction MC, transition barriers and products is relatively mild. However, the interaction with metals, alkali, alkali earth and transition metals forming regium bonds causes larger binding energies increasing transition barriers dramatically with reference to the parent reaction. This observation is consistent across all the halogen derivatives explored.
The structural data, X(1)–C and C–X(2) features, along with the electron density analysis carried out with IGM and EDS interpreting tools, support unequivocally the energy profiles obtained and the different results obtained. Particularly, it is worth noting that IGM–IBSI values have been proved to be a good indicator of both the strength of the weak interactions, combined with the EDS and δg values, but also, they are able to quantify the bond strength in more complex situations, e.g. bond creating/breaking situations shown in the SN2 reaction.
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Acknowledgements
The research was financially supported by the Spanish Ministerio de Ciencia e Innovación (Project PID2021-125207NB-C32) and Science Foundation of Ireland (SFI), Grant Number 18/SIRG/5517. Thanks are given to the CTI (CSIC), the Irish Centre for High-End Computing (ICHEC), the MaSCA (Maison de la Simulation de Champagne-Ardenne, France) and the CRIANN computational centre for their continued computational support.
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Iribarren, I., Trujillo, C., Sánchez-Sanz, G. et al. Influence of Lewis acids on the symmetric SN2 reaction. Theor Chem Acc 142, 81 (2023). https://doi.org/10.1007/s00214-023-03013-9
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DOI: https://doi.org/10.1007/s00214-023-03013-9