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Fast and Simple Evaluation of the Catalysis and Selectivity Induced by External Electric Fields
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Fast and Simple Evaluation of the Catalysis and Selectivity Induced by External Electric Fields
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  • Pau Besalú-Sala
    Pau Besalú-Sala
    Institut de Química Computacional i Catàlisi and Departament de Química, Universitat de Girona, Campus de Montilivi, 17003 Girona, Catalonia, Spain
  • Miquel Solà
    Miquel Solà
    Institut de Química Computacional i Catàlisi and Departament de Química, Universitat de Girona, Campus de Montilivi, 17003 Girona, Catalonia, Spain
    More by Miquel Solà
  • Josep M. Luis*
    Josep M. Luis
    Institut de Química Computacional i Catàlisi and Departament de Química, Universitat de Girona, Campus de Montilivi, 17003 Girona, Catalonia, Spain
    *Email: [email protected]
  • Miquel Torrent-Sucarrat*
    Miquel Torrent-Sucarrat
    Department of Organic Chemistry I, Centro de Innovación en Química Avanzada (ORFEO-CINQA), Universidad del País Vasco/Euskal Herriko Unibertsitatea (UPV/EHU) and Donostia International Physics Center (DIPC), P Manuel Lardizabal 3, E-20018 Donostia/San Sebastián, Euskadi, Spain
    Ikerbasque, Basque Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Euskadi, Spain
    *Email: [email protected]
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ACS Catalysis

Cite this: ACS Catal. 2021, 11, 23, 14467–14479
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https://doi.org/10.1021/acscatal.1c04247
Published November 17, 2021

Copyright © 2021 The Authors. Published by American Chemical Society. This publication is licensed under

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Abstract

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In the oriented external electric-field-driven catalysis, the reaction rates and the selectivity of chemical reactions can be tuned at will. The activation barriers of chemical reactions within external electric fields of several strengths and directions can be computationally modeled. However, the calculation of all of the required field-dependent transition states and reactants is computationally demanding, especially for large systems. Herein, we present a method based on the Taylor expansion of the field-dependent energy of the reactants and transition states in terms of their field-free dipole moments and electrical (hyper)polarizabilities. This approach, called field-dependent energy barrier (FDBβ), allows systematic one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) representations of the activation energy barriers for any strength and direction of the external electric field. The calculation of the field-dependent FDBβ energy barriers has a computational cost several orders of magnitude lower than the explicit electric field optimizations, and the errors of the FDBβ barriers are within the range of only 1–2 kcal·mol–1. The achieved accuracy is sufficient for a fast-screening tool to study and predict potential electric-field-induced catalysis, regioselectivity, and stereoselectivity. As illustrative examples, four cycloadditions (1,3-dipolar and Diels–Alder) are studied.

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Introduction

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The interaction between molecules and external electric fields (EEFs) generates a broad range of effects. (1) Common observed phenomena are the changes in molecular geometry, vibrational structure, Stark effect, spin polarization, triggered electron transfer, chirality, and modification of absorption and emission properties. (2) Among them, the interest of the EEF effects on reactivity and selectivity is growing hugely since several practical applications of EEF-aided control on reactivity are being developed. (3) Since the field-induced change on regioselectivity in Diels–Alder (DA) reactions predicted by Shaik and co-workers (4) was experimentally validated, (3d) this chemistry is becoming more tangible and there has been a reborn of the topic also from the theoretical perspective. (5) Additionally, examples of the application of EEF on very diverse topics as the tuning of photo- and excited-state chemistry, (6) switch molecular diodes, (7) quantum tunneling, (8) and homo- and heterogeneous catalysis have been successfully investigated. (7,9)
One of the basic principles ruling the EEF potential applications is the control over the alignment between the molecule and the applied EEF. Currently, this new chemistry framework is investigated with the aid of very specific equipment as scanning tunneling microscopes, (10) and using laser-induced oscillating fields, (11) plasmonic modes in nanocavities, (12) and tribo- or piezoelectricity. (13) Therefore, improvements toward this direction are advancing by leaps and bounds.
The electric-field-induced chemistry can also be studied in the electrochemical double layer, (14) the interface layer between the electrode and the electrolyte. In this region, the molecular electron density of the reactants and their reactivity can be altered by the electric fields generated by the electrode. (15) The characterization of the electric field generated in the electrochemical double layer is a complex task, although the combination of the vibrational stark shift spectroscopy (16) and computational modeling is paving the way. (2a,17)
From another perspective, nature has been using electric fields to tailor its reactivity ubiquitously. Since the shape of the binding pockets of enzymes presents a well-defined structure of polar and charged amino acids, a local electric field (LEF) is generated in the active site of enzymes. (18) The LEFs can, thus, promote electrostatic-induced catalysis in enzymes. Several works have already been reported, mainly focused on heme and nonheme iron proteins, (19) illustrating the LEFs potential utility in the control of reactivity and, more interestingly, selectivity.
Head-Gordon and co-workers (5e,20) and Hammes-Schiffer and co-workers (21) have used a bond dipole and electric field theoretical model to project the field onto the relevant bonds that are broken and formed along the reaction pathway. The difference between native and modified protein scaffolds allows the suggestion of possible mutations that tune the LEF to improve the enzyme efficiency. (22) For instance, this computational directed evolution has allowed an artificial Kemp Eliminase with a 43-fold improvement in the reaction rate of the enzyme. (23)
The main challenge of the computational evaluation of EEF effects on reactivity is the high amount of computational time requested since the number of calculations grows arithmetically with the number of electric-field strengths and directions investigated. (24) In this regard, the development of new computational methods is required to predict the reactivity and selectivity induced by EEFs at a feasible computational cost even when large chemical systems are involved. In this work, we present a new methodology to efficiently screen the effect on the reactivity and selectivity of an EEF applied with any strength and direction that can be used as a fast semiquantitative tool for the modeling, designing, and understanding of EEF-aided chemistry.

Theory

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The in-depth study of the field-dependent energy barriers (FDB) for one specific reaction involves computation of the reactants and the corresponding transition states (TSs) within external electric fields of several different strengths and directions. Consequently, it requires a tedious task that involves huge quantities of central processing unit (CPU) time even for medium-sized molecular systems.
For a given chemical system, the exact energy in the presence of an electric field can be expressed as a Taylor expansion around free-field energy
(1)
where F is the external electric field strength vector and μ, α, β, and γ are the permanent dipole moment, the electrical polarizability matrix, and the first and second electrical hyperpolarizability tensors, respectively, defined as
(2)
where the indices i, j, k, and l indicate Cartesian axes x, y, or z. Using eq 2 to express the field-dependent energy of the reactants and TS, the field-dependent energy barrier (FDB) of a reaction, ΔE(F), is given by
(3a)
(3b)
where P = μ, α, β, and γ, and ETS(PTS) and ER(PR) are the electronic energies (molecular electrical properties) of the transition state and reactants, respectively.
For practical implementation of eq 3a, such expansion must be truncated. For instance, the truncation at the first term models the linear response of the barrier with respect to the EEF applied. Nevertheless, we can anticipate here that the neglect of the field-dependent nonlinear response of the barrier may lead to important quantitative or even qualitative errors in the predictions of the field-induced regioselectivity. Thus, the nonlinear terms are required to describe correctly the EEF effect on the energy barriers of chemical reactions. Conversely, the truncation of eq 3a at the third-order correction (given by β) yields an expression flexible enough to properly evaluate the perturbation of the energy barriers induced by EEFs of any strength and direction at a low computational cost.
(4)
Equation 4 is used throughout this work if not stated otherwise. It only requires the calculation of the field-free energy, μ, α, and β tensors for the reactants and transition states, which can be calculated analytically using several quantum chemistry packages. We refer to this approach to compute the FDB based on eq 4 as FDBβ. The benefits of including higher-order terms in eq 4 were also explored, but the changes in energy barrier due to the higher-order terms were usually below density functional theory (DFT) intrinsic errors. It is important to remark that the truncation at the linear term of eq 4 has been used in the literature to estimate the changes in the energy barriers induced by EEFs and light-emitting diodes (LEDs). (1c,5e,25)
The total electric polarizabilities and hyperpolarizabilities can be divided into the electronic contribution (Pel), the nuclear relaxation (nr) contribution (Pnr), and the curvature contribution (Pcurv). (26)
(5)
where Pel describes the response of the electrons to an external electric field at the equilibrium geometry, whereas Pnr and Pcurv arise from the change of the electronic and vibrational energies due to the field-induced change of the equilibrium geometry and the shape of the potential energy surface (PES), respectively. The nuclear relaxation contribution contains all of the harmonic and lowest-order anharmonic terms, whereas the curvature contribution includes the rest of the higher-order vibrational anharmonicity. Pcurv contribution is usually smaller than Pel and Pnr, and far more expensive to compute, and it has not been evaluated in this work. (27)
Finally, it is worth noting that the field-induced changes in the thermodynamics of the reactions can be also easily computed and represented from an approximation homologous to FDBβ, expanding in a Taylor series the field-dependent reaction energies (for more details, see Figure SI8).

Computational Details

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All electronic structure calculations have been performed using Gaussian16 software package. (28) For three studied cycloadditions, the geometries were optimized with the B3LYP exchange–correlation functional (29) using a 6-31+G(d,p) basis set (30) to span the atomic orbitals. Empirical dispersion corrections were added using the Grimme D3 correction (31) with Becke–Johnson damping factor. (32) Then, energy corrections, dipole moments, and (hyper)polarizabilities were obtained using the B3LYP functional and the 6-311+G(2d,2p) basis set, i.e., B3LYP-D3BJ/6-311+G(2d,2p)//B3LYP-D3BJ/6-31+G(d,p). For the Diels–Alder cycloaddition between maleic anhydride and cyclopentadiene and to facilitate the direct comparison with the study of Shaik et al., (4) the optimizations were performed using the BP86 functional, (33)i.e., the computational level used for this reaction was B3LYP/6-311++G(d,p)//BP86/6-31+G(d). All stationary points on the potential energy surface (PES) were characterized through analytical vibrational frequency calculations.
To validate our approach, we have also computed the effect of explicit external static electric fields on the energy barriers. Several field strengths (F) were considered in the range F = [−10–2,10–2] au (1 au = 51.4 V·Å–1) for all of the studied reactions; this range spans the order of magnitude of intrinsic LEF present in enzyme pockets or mitochondrial membrane interfaces. (34) It is important to remark that the positive direction of the electric field vector is defined from the negative to the positive charge, following the Gaussian16 convention (contrary to the conventional physics definition). (25) Notice that all of the calculations have been performed in the gas phase (for the solvent-phase electric field effect on a reaction, see the recent work of Dubey et al. (35)).
The field-free reactants were oriented by defining the z-axis as the reaction axis, i.e., the axis along which the bonds are formed or broken. To avoid undesired field-induced rotations of the chemical systems during the geometry optimizations in the presence of explicit electric field, an in-house code was set up. The field-dependent equilibrium geometry is considered aligned to the original field-free equilibrium geometry when the rotation between them is smaller than 0.1° for the x, y, and z-axes. It is worth noticing that these constraints were added to ensure the formation of a reactant complex would correspond to an experimental scenario where one reactant is immobilized, for example, by being absorbed on a surface. (4,9f) The activation energy barriers for any strength and direction of the EEFs using the FDBβ approach can be generated using an open-access script available at https://github.com/pau-besalu/FDB.
Preferably, the Pnr contribution should be computed at the same level of calculation as the electronic contribution. However, the energies and electronic contributions to the molecular electrical properties were computed using a triple-ζ basis (6-311++G(d,p) or 6-311+G(2d,2p)), while the equilibrium geometry and frequency calculations required to calculate the nuclear relaxation contribution were performed using a double-ζ basis (6-31+G(d,p)). Therefore, Pnr was computed using double-ζ basis, although we have checked that calculating Pnr with the triple-ζ basis leads to very similar results for the field-dependent energy barriers (for more details, see Table SI1).

Results and Discussion

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Initially, two 1,3-dipolar cycloadditions and one Diels–Alder (DA) cycloadditions involving small/medium-sized organic molecules are studied. For these first three reactions, the chemical barriers are computed using both FDBβ and through the explicit optimization of equilibrium geometries of reactant complexes and TSs under EEF of several strengths and directions. After that, taking advantage of the computational benefits of the FDBβ methodology, we have studied the DA cycloaddition between C60 fullerene and a diene. For this reaction, the determination of the geometries of reactant complexes and TSs under an electric field of several strengths and directions become computationally demanding. On the other hand, the FDBβ methodology only requires the evaluation of field-free dipole moments and (hyper)polarizabilities of the reactant complexes and TSs at their stationary points. Additionally, we introduce the two-dimensional (2D) representations (36) of the activation energy barriers, which allow the easy determination of the oriented EEF conditions requested to switch between kinetic control selectivities. In practice, this novel visual tool can “only” be generated using the FDBβ methodology (otherwise, it becomes computationally prohibitive even for medium-sized systems).
Finally, another benefit of this research has been the analysis of the viability (37) of the oriented EEF as a synthetic strategy to obtain elusive cycloadducts. For instance, the exo′/endo′ cycloadducts in the (3 + 2) cycloadditions and the [5,6]-bond attack DA product between C60 and a diene.

(3 + 2) Cycloaddition between Azomethine Ylide and Nitrostyrene

The 1,3-dipolar cycloadditions, also known as Huisgen cycloadditions, have become a versatile route for the regio- and stereoselective construction of five-membered rings. (38) As the first test of our FDBβ methodology, we selected the (3 + 2) cycloaddition between N-benzylidene-glycinate and β-nitrostyrene, which has been thoroughly studied both experimentally and computationally. (39) Depending on the experimental conditions, two ylides can be formed from the imide, yielding to four possible cycloadducts, namely, endo, exo, endo′, and exo′ (see Scheme 1). With usual heating and solvent, only the stereoisomers endo and exo are formed. (40) When the reaction is carried out without solvent, both in thermal or microwave conditions, a mixture of exo, endo, and endo′ cycloadducts is obtained. (40) Finally, the exo′ product has been synthesized catalyzing the reaction with consensus tetratricopeptide repeat proteins in tetrahydrofuran solution, which generates the four pyrrolidine stereoisomers in equimolar ratio. (41)

Scheme 1

Scheme 1. Studied (3 + 2) Cycloaddition Reaction between Azomethine Ylide and Nitrostyrene with the Four Possible Cycloadducts
Our computational results for this reaction are fully consistent with previous studies. (40,41) Without the presence of an EEF, using a Boltzmann distribution over the activation energy barriers of the different cycloadducts obtained, the ratios 5.3:2.9:1.8:0 for the endo, exo, endo′, and exo′ are predicted, respectively.
Herein, the orientation of the nitrostyrene is fixed, and the two ylides are placed in the proper orientation to deliver each of the four possible cycloadducts. The z-axis is defined as the reaction axis; the olefinic double bond delimits the y-axis, and the direction where the phenyl group of the nitrostyrene is located indicates the positive region for both the x and y-axes (see Scheme 1).
Turning on an oriented EEF along the z-axis, the reaction can be either catalyzed or inhibited; see Figure 1. The field-induced catalysis/inhibition is controlled by the nucleophilicity–electrophilicity of the reactants triggered by the electronic density changes that the molecules suffer caused by the EE. As Shaik and co-workers have reported in several articles, (1c) the aforementioned field-induced changes in the electronic density are sometimes easily tracked by measuring the dipole moment of the transition-state geometries. For instance, for the endo pathway, when an EEF with Fz > 0 is applied, the reaction energy barrier decreases and the dipole moment module of the TS increases from 2.10 to 2.96 au. The increase in field-induced TS dipole moment illustrates the increase of the electron transfer from the highest occupied molecular orbital (HOMO) of the diene to the lowest unoccupied molecular orbital (LUMO) of the dienophile, which is the cause of the reduction of the cycloaddition activation barrier. The opposite is true when Fz < 0 is applied, and the dipole moment module of the TS decreases, resulting in an increase of the energy barrier. This rationalization can also be performed for all of the studied reactions (see Figures SI1 and SI2).

Figure 1

Figure 1. Activation energy barriers for the (3 + 2) cycloaddition between azomethine ylide and nitrostyrene (kcal·mol–1) in terms of the applied EEF z-axis. Dashed lines represent the prediction using FDBβ. Solid lines correspond to the explicit optimization of the reactants, products, and TSs in the presence of an EEF. Calculations were performed at the B3LYP-D3BJ/6-311+G(2d,2p)//B3LYP-D3BJ/6-31+G(d,p) level of theory.

In Figure 1, for field strengths between −5 × 10–3 and 5 × 10–3 au, we found excellent agreement between the predictions obtained with the FDBβ methodology and the results obtained reoptimizing the geometry of the reactants and TSs for each given value of EEFs. As expected, higher deviations are found using large field strengths, although the FDBβ approach still provides reliable and fast estimations of the field-dependent energy barriers.
The four TSs present different polarities along the y-axis, and thus, this (3 + 2) cycloaddition may present electric-field-induced selectivity switches (EFISSs) when an EEF is placed along this axis. The activation energy barriers for all of the isomers, except exo′, increase when a positive or negative EEF is applied along the y-axis (Figure 2). Conversely, the energy barrier of the exo′ cycloadduct decreases (increases) for positive (negative) EEF. Then, for a Fy = 5 × 10–3 au, an EFISS occurs and the elusive exo′ cycloadduct can be achieved as the major product. Consequently, at 120 °C, the aforementioned field-free 5.3:2.9:1.8:0 ratio for the endo, exo, endo′, and exo′ cycloadducts, respectively, completely switches into 0.1:0.1:0:9.8 at Fy = 1 × 10–2 au. Additionally, the oriented EEF along the x-axis also presents some interesting reactivity features (see Figure SI3). For instance, for Fx > 0, the endo (major product under free-field conditions) selectivity increases. On the other hand, at Fx = −19 × 10–4 au, an EFISS occurs between the activation energy barriers of the endo and exo (the second major product under free-field conditions) cycloadducts, which leads to an exo selectivity. Then, the oriented EEF could be used for the regio- and stereo-controlled synthesis of the five-membered rings obtained from 1,3-dipolar cycloadditions.

Figure 2

Figure 2. Activation energy barriers for the (3 + 2) cycloaddition between azomethine ylide and nitrostyrene (kcal·mol–1) in terms of the applied EEF y-axis. See Figure 1 caption for additional details.

From a computational cost point of view, the evaluation of the kinetic barriers for four regioisomers with N EEFs of different strengths and orientations (positive and negative) along all three directions of space implies the optimization of 24N + 8 stationary points. On the other hand, using the FDBβ methodology, the same information can be generated computing only the corresponding electrical properties of the field-free reactants and TSs stationary points. Thus, using the FDBβ methodology, 24N optimization of the geometry of the field-dependent stationary points is avoided, implying a considerable computational reduction cost. Nevertheless, it is important to note that the FDBβ approach considers that the same reaction mechanism holds for any combination of EEF strengths placed in the x, y, and z-axes. For instance, it does not take into account the possibility that a concerted cycloaddition mechanism can become a stepwise process. The stabilization of the zwitterionic or radical intermediate and the mechanistic crossover usually occur with strong oriented EEF. In these situations, the valence bond model can be a useful tool to provide physical insight to rationalize the mechanistic crossover. (1c,25)
Figure 3 illustrates the accuracy obtained using different possible truncations of eq 4 for the exo cycloadduct in terms of the strength of a y-axis EEF. The consideration of only the linear term leads to a wrong prediction of the activation barrier in the presence of Fy, which shows a clear nonlinear dependence. However, it is worth noting that the absolute errors are <3 kcal·mol–1 (see Figure SI4). The incorporation of αel into the model improves substantially the prediction, and a reasonable semiquantitative picture is already obtained. In this particular case, the improvement of the βel term in the Taylor series is negligible. Nevertheless, we recommend including this term routinely in the Taylor series, especially, when α and β can be analytically calculated with an acceptable computational cost.

Figure 3

Figure 3. Activation energy barriers for the (3 + 2) cycloaddition between azomethine ylide and nitrostyrene (kcal·mol–1) for the exo cycloadduct in terms of y-axis EEF. Dotted and dashed lines represent several levels of truncation of eq 4. See Figure 1 caption for additional details.

Up to this point, only electronic terms were considered in the definition of μ, α, and β of eq 4. However, the inclusion of nuclear relaxation (nr) contribution to α leads to an improved description of the field-dependent barriers, reducing the error down to <0.5 kcal·mol–1 (see Figures 3 and SI4). Thus, and as expected, a progressive and systematic enhancement of the prediction can always be achieved owing to the addition of new terms to the Taylor expansion. As an illustrative example, at Fy = −5 × 103 au, the individual percentage contributions to the activation barrier energy for the μ, αel, αnr, and β terms are −150, 184, 60, and 6%, respectively (see Figure SI5).
As a method based on the Taylor expansion, the FDBβ approximation validity is reduced when the EEF strength increases. Nevertheless, the studies of the reactivity and selectivity induced by EEF often use intensities of the electric fields below 1000 mV·Å–1. Usually, the energy barrier discrepancies between the optimized EEF and the FDBβ approach could be attributed to the nuclear relaxation of the TSs and reactant complexes, which may be partially taken into account by the FDBβ approach including the nuclear relaxation contribution to the polarizability in the Taylor expansion. An indication of the nuclear relaxation relevance is given by the presence of low frequencies in the infrared spectrum.
Overall, the FDBβ approximation including only the electronic contributions to of μ, α, and β provides a mean error for activation energy barriers of all four cycloadducts lower than 1.0 kcal·mol–1. Therefore, this methodology has been selected to study the field-catalyzed reactivity throughout this work.

Diels–Alder Reaction between Maleic Anhydride and Cyclopentadiene

In 1928, Diels and Alder’ seminal work (42) introduces the (4 + 2) cycloaddition between 1,3-dienes and a substituted alkene, the Diels–Alder (DA) reaction. This cycloaddition allows the regio- and stereo-controlled synthesis of cyclohexene derivatives. (43) One of the archetypal DA cycloadditions is the reaction between maleic anhydride and cyclopentadiene (Scheme 2). (44) For this reaction, the effects of oriented EEFs have thoroughly been studied both from theoretical (4,45) and experimental (3d) points of view. Then, for comparison purposes, this reaction has been selected to check the FDBβ performance and to introduce the 2D representation of the chemical barriers for the kinetic product of the reaction.

Scheme 2

Scheme 2. Studied DA Reaction between Maleic Anhydride and Cyclopentadiene
As Shaik and co-workers reported, (4) under free-field conditions, the formation of both endo and exo cycloadducts is exergonic by −15.4 and −16.1 kcal·mol–1, respectively, and the activation energy barriers for the formation of these products are 15.5 and 16.7 kcal·mol–1, respectively. Assuming that the reaction is kinetically driven, the endo cycloadduct is obtained as the major product under free-field conditions.
In a similar way to the previous example, applying an EEF along the reaction axis (z-axis) catalyzes (Fz < 0) or inhibits (Fz > 0) the endo and exo pathways (Figure 4). At large Fz strengths, the energy barrier discrepancies found between the optimized EEF and the FDBβ approximation are due to the stabilization of a zwitterionic intermediate. (4) If a y-axis EEF is applied, an EFISS is found at Fy ≤ −5 × 10–3 au (0.257 V·Å–1 or 1.29 × 1012 W·cm–2), where the DA reaction presents exo selectivity (Figure 5). The endo barrier is barely affected within the scanned range of electric field strengths, whereas the exo one is modified by almost 6 kcal·mol–1. As reported elsewhere, (46) the secondary orbital interactions (SOI) play a key role in the endo product stabilization at free field. At Fy ≤ 0 au, the destabilization of the endo product with respect to the exo occurs due to the energy increase of the orbital responsible for the stabilizing SOI (for more details, see Figure SI6 and the discussion therein). For this reaction, the FDBβ approach also presents a robust performance, i.e., the mean absolute error (MAE) with respect to the energy profile obtained optimizing with explicit EEFs is <1 kcal·mol–1 and the maximum error is <2 kcal·mol–1.

Figure 4

Figure 4. Activation energy barriers for the endo and exo DA pathways between maleic anhydride and cyclopentadiene (kcal·mol–1) in terms of z-axis EEF. Calculations performed at the B3LYP/6-311++G(d,p)//BP86/6-31+G(d) level of theory. See Figure 1 caption for additional details.

Figure 5

Figure 5. Activation energy barriers for the endo and exo DA cycloaddition between maleic anhydride and cyclopentadiene (kcal·mol–1) in terms of y-axis EEF. See Figure 4 caption for additional details.

Taking advantage of the low FDBβ computational cost, it is possible to generate 2D representations summarizing the effects of the combination of any strength of the y- and z-axis EEFs (Figure 6). The red (green) region corresponds to the range of Fz and Fy for which the endo (exo) barrier is lower than the exo (endo) barrier. The intensity of the color and the isocontour lines indicate the magnitude of the activation energy barriers of the kinetically most favored reaction in kcal·mol–1. Isocontour lines are not equidistant, indicating a nonlinear dependence of the chemical barrier with respect to EEF. For the same reason, the border from endo to exo selectivity regions is not linear (see Figure SI7 for the 2D representation using only the linear μ term in eq 4).

Figure 6

Figure 6. Two-dimensional representation of the chemical barriers for the major kinetic product of the DA reaction between maleic anhydride and cyclopentadiene in terms of EEFs along the y and z-axes using the FDBβ approach. Green and red zones indicate exo and endo kinetic selectivities, respectively. Calculations are performed at the B3LYP/6-311++G(d,p)//BP86/6-31+G(d) level of theory. Isoenergy barrier lines in kcal·mol–1.

In addition, it is worth noting that the endo energy barriers are barely affected by the value of Fy (in agreement with Figure 5), as expected considering the small dipole moment along the y-axis of the endo TS structure.
From this 2D representation, it is also possible to define some novel reactivity EEF concepts. For instance, the EFISS curve defines the set of all vectors that switch the selectivity. In this particular case, the EFISS curve is given by all (Fy,Fz) vectors that switch from endo to exo selectivities. Additionally, it is possible to determine the vector with the minimum module within the set, MEFISS. In Figure 6, MEFISS is represented as a black dot at Fz = 0 au and Fy = −5.8 × 10–3 au. Another important point to remark is that the three-dimensional (3D) representations are also easy to achieve, for instance, performing several (Fy,Fz) 2D plots with different constant Fx values (for an illustrative example, see Figure SI8).
To catalyze or inhibit a reaction, usually, the most relevant orientation is the reaction coordinate. (47) However, the reaction pathways can become quite complex and their regioselectivity, stereoselectivity, and enantioselectivity cannot be controlled by placing the electric field in only one direction. For these systems, the 2D and 3D representations using the FDBβ approach are valuable tools to predict the electric-field-induced reactivity. Additionally, external electric fields can be used to simulate the local electric fields induced by charged functional groups and metal ions, which increases the reaction rate and controls the selectivity of organocatalytic reactions catalyzed by enzymes and zeolites. (1)
Representing these 2D (or 3D) plots using explicit field-dependent optimizations of the reactants and TSs requires an enormous computational cost. For instance, the optimization of (4N)2 + 4 field-dependent stationary points is required to plot the corresponding version of Figure 6, where N is the number of selected EEF strengths (positive and negative). On the other hand, using the FDBβ approximations, representing Figure 6 only requires the optimization of four field-free stationary points and the calculation of their corresponding electrical properties, which implies a (4N2 + 1)-fold computational cost reduction. In addition, here, is important to remark that for such kind of 2D plots, N should be somewhat large to obtain an acceptable resolution.
Finally, the representation of the homologous eq 4 but expanding in a Taylor series, the field-dependent reaction energies instead of the energy barriers shows that the exothermicity of both reactions (endo and exo) increases for the same EEFs for which the corresponding energy barrier decreases, i.e., Fz < 0 (see Figure SI9). Thus, the relationship between field-dependent kinetics and thermodynamics follows the trend given by the Bell–Evans–Polanyi principle. (48)

(3 + 2) Cycloaddition between Methoxyethene and Phenyl Diazomethane

As another example to illustrate the potential of the FDBβ approach, we select a (3 + 2) cycloaddition for which oriented EFFs are potentially able to tune the selectivity between four possible cycloadducts (endo, endo′, exo, and exo′). For this purpose, we choose as reactants a 1,3-diene and a dipolarophile with clear polar characters, i.e., the 1,3-dipolar reaction between phenyl diazomethane and methyl vinyl ether (Scheme 3). The molecular orientation is defined as follows: z-axis was set to be the reaction axis, y-axis to be parallel to the olefin double bond and positive in the direction of the methoxy substituent, and the x-axis is negative in the zone where the methoxy group is located.

Scheme 3

Scheme 3. Studied 1,3-Dipolar Cycloaddition between Phenyl Diazomethane and Methoxyethene and the Four Possible Cycloadducts; Definition of the Cartesian Coordinates for the Reaction
Under free-field conditions, the exo pathway presents the lowest activation energy barrier (19.8 kcal·mol–1), while the endo, exo′, and endo′ pathways are located at 0.2, 1.4, and 1.7 kcal·mol–1 above it, respectively. Then, at room temperature, the four cycloadducts present the 5.4:3.8:0.5:0.3 (exo/endo/exo′/endo′) ratios.
For Fx > 0, the endo kinetic selectivity is enhanced, whereas the activation energy barriers increase for the other regioisomers (Figure 7). On the contrary, for 0 > Fx > −6.2 × 10–3 au, the exo energy barrier is the lowest one, whereas exo′ cycloadduct becomes the kinetic product of the reaction for Fx < −6.2 × 10–3 au. In this manner, only by varying the intensity of the EEF in the x-axis, one achieves as the major product the endo, exo, or exo′ cycloadducts, passing through two different EFISSs along the path.

Figure 7

Figure 7. Activation energy barriers for (3 + 2) dipolar reactions between phenyl diazomethane and methoxyethene (kcal·mol–1) in terms of the applied x-axis EEF. See Figure 1 caption for additional details.

For Fy > 0, the exo selectivity is enhanced with respect to endo pathway (Figure 8), whereas the change with respect to the strength of the EEF of endo′ and exo′ activation energy barriers is very small. On the other hand, for Fy < 0, the endo and exo pathways are inhibited, and then at Fy = −102 au, the endo′ and exo′ become the only kinetically feasible cycloadducts. Finally, the EEF along the reaction axis (Fz) catalyzes or inhibits the endo and exo pathways in a similar way (for more details, see Figure SI10).

Figure 8

Figure 8. Activation energy barriers for the (3 + 2) dipolar reaction between phenyl diazomethane and methoxyethene (kcal·mol–1) in terms of the applied y-axis EEF. See Figure 1 caption for additional details.

A visual summary 2D representation of the activation energy barriers for the major kinetic cycloadduct using any combination of any Fx and Fy strengths is displayed in Figure 9. Under field-free conditions, the exo and endo energy barriers are almost isoenergetic and present the lowest activation energy barriers. From a general perspective, the exo selectivity can be enhanced by negative Fx and positive Fy. The kinetic endo selectivity can be obtained using positive Fx. On the other hand, using negative Fx and Fy electric fields, the major kinetic cycloadduct becomes the exo′ product. Finally, the endo′ cycloadduct, which is the most elusive product under field-free conditions, can be obtained as a major kinetic product applying Fy < −5.0 × 10–3 au and moderate positive Fx.

Figure 9

Figure 9. Two-dimensional representation of the activation energy barriers for the major kinetic product of the (3 + 2) dipolar reaction between phenyl diazomethane and methoxyethene in terms of the applied EEFs along the x- and y-axes using the FDBβ approach. Green, red, blue, and orange zones indicate exo, endo, exo′, and endo′ kinetic selectivities, respectively. Black dots indicate the MEFISS points. Calculations are performed at the B3LYP-D3BJ/6-311+G(2d,2p)//B3LYP-D3BJ/6-31+G(d,p) level of theory. Isoenergy barrier lines in kcal·mol–1.

Figure 9 also shows five EFISS curves corresponding to the exo/endo, exo/exo′, endo/endo′, endo/exo′, and exo′/endo′ selectivity switches and four MEFISSs (indicated as black dots). Herein, it is important to underline that the exo, endo, exo′, and endo′ selectivities can be tuned at will using relatively small EEF window values, i.e., −25 × 10–4 < Fx < 10–4 and −60 × 10–4 < Fy < 0 au. Additionally, the 2D plot generated with the FDBβ approach also illustrates that the dependence of the barriers in terms of the strength of the applied EEF is nonlinear (see also Figure SI11) since both the displayed isocontour lines and the EFISS curves are not straight lines.
As in the previous example, it is also possible to generate several (Fx,Fy) 2D plots with different constant Fz strengths. As indicated previously, the EEF along the reaction coordinate modifies the magnitude of the activation energy barrier (catalyze or inhibit) but not the selectivity. Consequently, not relevant differences are found with respect to Figure 9 (see Figure SI12). Again, it is important to remark that the generation of Figure 9 using explicit field-dependent equilibrium geometry optimizations requires the calculation of (8N)2 + 8 stationary points, where N is the number of selected positive and negative EEF strengths. On the other hand, the FDBβ approximations only requires the optimization of eight field-free stationary points and the calculation of their corresponding electrical properties. Therefore, for a reaction with four possible products, FDBβ is (8N2 + 1)-fold cheaper in terms of CPU time than the usual methodology. A detailed summary of the computational cost benefits of the FDBβ approximation can be found in Table SI2.

Diels–Alder Reaction between C60 and Cyclopentadiene

As a last example, we select a reaction involving 65 carbon atoms, the DA reaction between C60 fullerene and cyclopentadiene. (49) Under field-free conditions, the energy barrier of this DA cycloaddition is lower for [6,6]- than for [5,6]-bonds (Scheme 4). (50) The Diels–Alder [5,6] functionalization has never been reported experimentally for the DA cycloadditions to C60, although theoretically it was found possible in highly reduced C60 (51) or in the high-spin states of C60. (52) Herein, we explore the potential of the oriented EEF as a synthetic strategy to obtain the elusive [5,6]-bond cycloadduct.

Scheme 4

Scheme 4. Schematic Representation of DA Reaction over a [6,6]- (Top) or [5,6]-Bond (Bottom) of a C60 Fullerene Represented by One of Its Corannulene Unit, Respectively
The reactant complex is oriented so that the z-axis is parallel to the reaction coordinate, and either the attacked [5,6]- or the [6,6]-bond defines the y-axis (Scheme 4). The reactivity is almost not changing when an EEF is applied either along the x- or y-axis (see Figures SI13 and S14 for more details); therefore, only the z-axis results are discussed herein. For Fz > 0 (Fz < 0) au, the FDBβ approach predicts that the activation energy barriers are increasing (decreasing) for both pathways (Figure 10). The role of the EEF on this reaction can be rationalized by analyzing the effect of the electric field on the HOMO and LUMO. The presence of a negative (positive) pole of the EEF located above (below) the diene (C60) destabilizes (stabilizes) the HOMO (LUMO) mainly located in the cyclopentadiene (C60), which favors the reaction and then decreases the energy barrier.

Figure 10

Figure 10. Activation energy barriers of the DA between C60 and cyclopentadiene (kcal·mol–1) in terms of the applied z-axis EEF. Solid lines are calculated at the B3LYP-D3BJ/6-311+G(2d,2p)//B3LYP-D3BJ/6-31+G(d,p) level of theory using the FDBβ approximation. Color dots correspond to explicit field-dependent geometrical optimizations performed for a specific EEF.

For Fz < 0, the decrease of the activation energy barriers is more pronounced for the [5,6]-bond than for the [6,6]-bond pathway, implying a reduction of the gap between the two activation barriers, although no EFISS is observed in the studied range. At Fz = 10–2 au, the FDBβ approach estimates a gap difference between both pathways of only 3 kcal·mol–1, a reduction of 9 kcal·mol–1 with respect to the free-field conditions. To check the validity of this conclusion, optimizations of the reactants and TSs at Fz = −10–2 au were performed. The results displayed in Figure 10 confirm the FDBβ results, although there is a difference of 2.5 kcal·mol–1 between the difference in the energy barriers obtained with both methodologies. Thus, we conclude that for Fz < −10–2 au and high temperatures, some traces of the [5,6]-cycloadduct in the product mixture could be found.

Conclusions

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A novel methodology to estimate activation energy barriers in the presence of external electric fields (EEFs) is reported herein. The FDBβ approach is based on the Taylor expansion of the field-dependent energy of the reactants and transition states (TSs) in terms of their dipole moments and electrical (hyper)polarizabilities. As illustrative examples, to assess the reliability and validity of the proposed method, we have studied the effect of EEFs on four reactions (two 1,3-dipolar and two Diels–Alder cycloadditions).
The FDBβ approach only requires the geometry optimizations of the reactants and TSs under free-field conditions, and the calculation of their (hyper)polarizabilities. Thus, no explicit EEF calculations are required. The obtained results indicate that estimations of the activation energy barriers for different EEF strengths can be obtained with errors usually smaller than 1 kcal·mol–1. Additionally, the consideration of only the electronic contribution to the electrical (hyper)polarizabilities is sufficient to recover most of the changes in the activation energy barriers. Nevertheless, if it is required, the inclusion of nuclear relaxation contribution to the polarizability, which can be obtained from a single frequency calculation, further improves the quality of the energy barrier estimations.
The benefits of the FDBβ methodology are its simplicity and the massive reduction of the CPU-time cost with respect to the explicit optimizations of the reactant complexes and transition states for several EEF strengths. The FDBβ approach permits systematic 1D, 2D, and 3D representations of the activation energy barriers for any strength and direction of the EEFs. Furthermore, one can determine which is the optimum strength and direction of an EEF required to induce a particular selectivity switch. Thus, the FDBβ approach can be used to “seek and identify” the potential synthesis using EEF of elusive regioisomers, which cannot be obtained under other experimental conditions. For instance, for the studied 1,3-dipolar reaction between methoxyethene and phenyl diazomethane, the four possible cycloadducts can be obtained as major kinetic control products by changing only the magnitudes and directions of Fx and Fy.
To conclude, we believe that the FDBβ approach can be used as a fast-screening tool to predict novel potential field-induced catalysis and regioselectivities, especially for systems of organocatalytic and biocatalytic interests that involve a large number of atoms.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acscatal.1c04247.

  • Nuclear relaxation contribution assessment; dipole moment changes in TS structures; MAE for several FDB approaches; 1D representations of the EEF-induced chemical barriers for the remaining directions and cycloadditions indicated but not reported in the manuscript; DA secondary orbital interaction analysis; 2D maps for different FDB approaches and for several Fz EEFs for the DA maleic anhydride and cyclopentadiene and the (3 + 2) cycloaddition between azomethine ylide and nitrostyrene; CPU time required using the explicit optimization of reactant complexes and transition states in the presence of an EEF and using the FDBβ approach; and Cartesian coordinates (PDF)

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Author Information

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  • Corresponding Authors
    • Josep M. Luis - Institut de Química Computacional i Catàlisi and Departament de Química, Universitat de Girona, Campus de Montilivi, 17003 Girona, Catalonia, SpainOrcidhttps://orcid.org/0000-0002-2880-8680 Email: [email protected]
    • Miquel Torrent-Sucarrat - Department of Organic Chemistry I, Centro de Innovación en Química Avanzada (ORFEO-CINQA), Universidad del País Vasco/Euskal Herriko Unibertsitatea (UPV/EHU) and Donostia International Physics Center (DIPC), P Manuel Lardizabal 3, E-20018 Donostia/San Sebastián, Euskadi, SpainIkerbasque, Basque Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Euskadi, SpainOrcidhttps://orcid.org/0000-0003-2689-0278 Email: [email protected]
  • Authors
    • Pau Besalú-Sala - Institut de Química Computacional i Catàlisi and Departament de Química, Universitat de Girona, Campus de Montilivi, 17003 Girona, Catalonia, SpainOrcidhttps://orcid.org/0000-0002-0955-9762
    • Miquel Solà - Institut de Química Computacional i Catàlisi and Departament de Química, Universitat de Girona, Campus de Montilivi, 17003 Girona, Catalonia, SpainOrcidhttps://orcid.org/0000-0002-1917-7450
  • Author Contributions

    M.T.-S., M.S., and J.M.L. devised and supervised the project. P.B-S. performed all calculations and analyzed the results. The manuscript was written through the contributions of all authors. All authors approved the final version of the manuscript.

  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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This work was supported with funds from the Ministerio de Economía y Competitividad (MINECO) of Spain (project CTQ2017-85341-P to M.S.), the Spanish government MICINN (projects PGC2018-098212-B-C22 to J.M.L, PID2020-113711GB-I00 to M.S., and PID2019-104772GB-I00 to M.T.S.), the Generalitat de Catalunya (project 2017SGR39 to M.S. and J.M.L.), and Gobierno Vasco (project IT1346-19 to M.T.S.). The authors thank the Spanish government for the predoctoral grant to P.B.-S. (FPU17/02058). They are also grateful for the computational time financed by the Consorci de Serveis Universitaris de Catalunya (CSUC). They thank the reviewers for their comments and helpful suggestions.

References

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  • Abstract

    Scheme 1

    Scheme 1. Studied (3 + 2) Cycloaddition Reaction between Azomethine Ylide and Nitrostyrene with the Four Possible Cycloadducts

    Figure 1

    Figure 1. Activation energy barriers for the (3 + 2) cycloaddition between azomethine ylide and nitrostyrene (kcal·mol–1) in terms of the applied EEF z-axis. Dashed lines represent the prediction using FDBβ. Solid lines correspond to the explicit optimization of the reactants, products, and TSs in the presence of an EEF. Calculations were performed at the B3LYP-D3BJ/6-311+G(2d,2p)//B3LYP-D3BJ/6-31+G(d,p) level of theory.

    Figure 2

    Figure 2. Activation energy barriers for the (3 + 2) cycloaddition between azomethine ylide and nitrostyrene (kcal·mol–1) in terms of the applied EEF y-axis. See Figure 1 caption for additional details.

    Figure 3

    Figure 3. Activation energy barriers for the (3 + 2) cycloaddition between azomethine ylide and nitrostyrene (kcal·mol–1) for the exo cycloadduct in terms of y-axis EEF. Dotted and dashed lines represent several levels of truncation of eq 4. See Figure 1 caption for additional details.

    Scheme 2

    Scheme 2. Studied DA Reaction between Maleic Anhydride and Cyclopentadiene

    Figure 4

    Figure 4. Activation energy barriers for the endo and exo DA pathways between maleic anhydride and cyclopentadiene (kcal·mol–1) in terms of z-axis EEF. Calculations performed at the B3LYP/6-311++G(d,p)//BP86/6-31+G(d) level of theory. See Figure 1 caption for additional details.

    Figure 5

    Figure 5. Activation energy barriers for the endo and exo DA cycloaddition between maleic anhydride and cyclopentadiene (kcal·mol–1) in terms of y-axis EEF. See Figure 4 caption for additional details.

    Figure 6

    Figure 6. Two-dimensional representation of the chemical barriers for the major kinetic product of the DA reaction between maleic anhydride and cyclopentadiene in terms of EEFs along the y and z-axes using the FDBβ approach. Green and red zones indicate exo and endo kinetic selectivities, respectively. Calculations are performed at the B3LYP/6-311++G(d,p)//BP86/6-31+G(d) level of theory. Isoenergy barrier lines in kcal·mol–1.

    Scheme 3

    Scheme 3. Studied 1,3-Dipolar Cycloaddition between Phenyl Diazomethane and Methoxyethene and the Four Possible Cycloadducts; Definition of the Cartesian Coordinates for the Reaction

    Figure 7

    Figure 7. Activation energy barriers for (3 + 2) dipolar reactions between phenyl diazomethane and methoxyethene (kcal·mol–1) in terms of the applied x-axis EEF. See Figure 1 caption for additional details.

    Figure 8

    Figure 8. Activation energy barriers for the (3 + 2) dipolar reaction between phenyl diazomethane and methoxyethene (kcal·mol–1) in terms of the applied y-axis EEF. See Figure 1 caption for additional details.

    Figure 9

    Figure 9. Two-dimensional representation of the activation energy barriers for the major kinetic product of the (3 + 2) dipolar reaction between phenyl diazomethane and methoxyethene in terms of the applied EEFs along the x- and y-axes using the FDBβ approach. Green, red, blue, and orange zones indicate exo, endo, exo′, and endo′ kinetic selectivities, respectively. Black dots indicate the MEFISS points. Calculations are performed at the B3LYP-D3BJ/6-311+G(2d,2p)//B3LYP-D3BJ/6-31+G(d,p) level of theory. Isoenergy barrier lines in kcal·mol–1.

    Scheme 4

    Scheme 4. Schematic Representation of DA Reaction over a [6,6]- (Top) or [5,6]-Bond (Bottom) of a C60 Fullerene Represented by One of Its Corannulene Unit, Respectively

    Figure 10

    Figure 10. Activation energy barriers of the DA between C60 and cyclopentadiene (kcal·mol–1) in terms of the applied z-axis EEF. Solid lines are calculated at the B3LYP-D3BJ/6-311+G(2d,2p)//B3LYP-D3BJ/6-31+G(d,p) level of theory using the FDBβ approximation. Color dots correspond to explicit field-dependent geometrical optimizations performed for a specific EEF.

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