How Oriented External Electric Fields Modulate Reactivity

Abstract A judiciously oriented external electric field (OEEF) can catalyze a wide range of reactions and can even induce endo/exo stereoselectivity of cycloaddition reactions. The Diels–Alder reaction between cyclopentadiene and maleic anhydride is studied by using quantitative activation strain and Kohn–Sham molecular orbital theory to pinpoint the origin of these catalytic and stereoselective effects. Our quantitative model reveals that an OEEF along the reaction axis induces an enhanced electrostatic and orbital interaction between the reactants, which in turn lowers the reaction barrier. The stronger electrostatic interaction originates from an increased electron density difference between the reactants at the reactive center, and the enhanced orbital interaction arises from the promoted normal electron demand donor–acceptor interaction driven by the OEEF. An OEEF perpendicular to the plane of the reaction axis solely stabilizes the exo pathway of this reaction, whereas the endo pathway remains unaltered and efficiently steers the endo/exo stereoselectivity. The influence of the OEEF on the inverse electron demand Diels–Alder reaction is also investigated; unexpectedly, it inhibits the reaction, as the electric field now suppresses the critical inverse electron demand donor–acceptor interaction.


Introduction
Recently,t he study of electrostatically catalyzed non-redoxr eactions has become at hriving field in chemistry. [1] The reactivity,a sw ell as selectivity,o fn on-redoxr eactions can be manipulated by orientingt he electric field in as pecific directionw ith respectt ot he interacting reactants. In nature,f or example, electric fields have been proposed to play ar ole in enzymecatalyzed reactions. [2] In the last decade, artificially designed electric fields have also been utilized to mediate non-redox reactions through, for example, the electrode/electrolyte interface, [3] av oltage-biased STM tip, [4] and the active site under the electric field possibly created by charged functional groups [5] or catalysts. [6] From at heoretical point of view,alarge number of studies have been dedicated to the understanding and predictiono ft he effect of an oriented external electric field (OEEF) on various chemical transformations [7] such as CÀHb ond activationr eactions, [6a-c, 7a-c] Diels-Alder reactions, [5e, 6d, 7d,e] methyl transfer reactions, [7f] electrophilic aromatic substitution reactions, [7g] nucleophilic substitutions of halogen-bond complexes, [7h] and oxidative addition reactions. [7i] The pioneering theoretical predictionsm ade by Shaik et al. in 2010 on the effect of the OEEF on Diels-Alder (DA) reactions [7d] were proveni nc utting-edgee xperimental studies by Coote andc o-workerss ix years later. [4a] Shaik et al. discovered that, for the DA reactionb etween cyclopentadiene and maleic anhydride (Scheme 1a), an electric field directed along the reaction axis, that is, the electric fielda long the forming bonds, can catalyze( positive field) or inhibit( negative field) the reaction, whereas an electric field perpendiculart ot he reaction axis and the bond-forming plane will lead to an enhanced endo (negative field) or exo (positive field) selectivity. Furthermore,a nelectric field along the C=Cd ouble bond of maleic anhydride shows negligible effect on the reactivity or selectivity of the reaction. [7d] Coote and co-workers probed as inglemolecule DA reactionb etween furan and an orbornylogous bridge, which were separately tethered to ag old STM tip and gold surface, respectively (Scheme 1b). [4a] In this way,t he orientation of the electric field was aligneda long the reaction axis, leading to af ivefold increase in the frequency of the formationo ft he single-molecule junction,o bserved through a so-called "blinking" technique. [4a] In addition, Honga nd coworkers confirmed, by using an electric-field-mediated singlemolecule reaction, that the reactivityo ft he studied DA reaction remains unaltered undera ne lectric field aligned to the C=Cdoublebond of the dienophile (Scheme 1c). [8] The molecular dipole momenth as long been considered critical to understanding the effect of an OEEF on the reactivity and selectivity of aD Ar eaction. [7d,e] As the reactants and transition state of aD Ar eactionhave distinct dipole momentsa long ap articular direction, an OEEF is ablet o( de)stabilize the reactants and transition state, depending on the direction of the electric field, and hence,has an immediate effect on the activation barrier of the reaction. On the other hand, qualitative valence bond (VB) theory [9] has also been utilized to understand the catalytic effect of an OEEF alignedt ot he reaction axis on the DA reaction. This model revealed that the charget ransfer state along the reactionp athway is significantlys tabilized by a positive electric field, which, as ac onsequence, mixes into the wavefunctiona ta nd aroundt he transition state. This phenomenon stabilizes the transition state, and therefore lowers the activationb arrier. [7d] On the other hand, the OEEF-induced endo/exo selectivity has been understood solely by the interaction between the OEEF and the molecular dipole moment in a specifics tereoisomer,b ut has not been explained within the framework of VB theory.
In this study,f or the first time, we aim to investigate the OEEF-mediated DA reaction within the context of Kohn-Sham molecular orbital (KS-MO) theory.T he ultimate physicalf actors dictating the catalytic, as well as endo/exo selective, effects of an OEEF on the Diels-Alder reactiona re elucidated using quantitative KS-MO analyses. The results obtained herein, together with the VB study of Shaik et al.,e ffectively provide a complete framework for understanding the effects of the OEEF, and hence,w ill act as at oolbox fort he design of novel electric-field-catalyzed organic reactions. To this end, we have performed as ystematic computational study on OEEF-mediated Diels-Alder reactions between cyclopentadiene (Cp), acting as ad iene, and maleic anhydride( MA), acting as the dienophile (Scheme 2a), at the BP86/TZ2P level. The activation strain model (ASM) [10] of reactivity in combination with quantitative KS-MO theory and amatching canonical energy decomposition analysis( EDA) [11] have been employedt op erform analyses on the Diels-Alder reactions under the OEEF along different axes. This methodology has been utilized to investigate various types of cycloaddition reactions, and has proven to be valuable for understanding the trends in reactivity. [12] Computational Methods All calculations were performed in ADF2017 [13] using the BP86 [14] functional with the TZ2P basis set. [15] The exchange-correlation (XC) functional has been proven to be accurate in calculating the relative trends in activation and reaction energies for this reaction. [7d, 12a, 16] Geometries and energies were recomputed at COS-MO(DCM)-BP86/TZ2P [17] to assess the effect of the solvation on the reactivity trends. Additionally,s ingle-point energies were computed at B3LYP/TZ2P [18] and M06-2X/TZ2P [19] on the optimized BP86/ TZ2P geometries to evaluate the effect of the hybrid and metahybrid functional on the reactivity trends. Frequency calculations were performed to characterize the nature of the stationary points. Local minima present only real frequencies, whereas transition structures have one imaginary frequency.T he potential energy surface (PES) was calculated using the intrinsic reaction coordinate (IRC) method, [20] which follows the imaginary eigenvector of the transition structure toward the reactant and product. The resulting PES was analyzed with the aid of the PyFrag 2019 program. [21] All chemical structures were illustrated using CYLview. [22] Quantitative analyses of the activation barriers associated with the studied reactions were obtained by means of the activation strain model (ASM) of reactivity. [10] Herein, the PES, DE(z), was decomposed into the strain energy, DE strain (z), and the interaction energy, DE int (z)[ Eq. (1)].I nt his study,t he reaction coordinate was projected on the length of the newly forming C···C bond, which undergoes aw ell-defined change throughout the reaction and has been used in the past in analyses of similar reactions. [12] DEðzÞ¼DE strain ðzÞþDE int ðzÞð 1Þ The DE strain (z)v alue is associated with the rigidity as well as the structural deformation of the reactants from their equilibrium geometry to the geometry acquired along the reaction coordinate. The DE int (z)v alue is related to the electronic structure of the reactants and their spatial orientation, and takes the mutual interaction between the deformed reactants into account. To obtain ad eeper insight into the physical mechanism behind the interaction energy, we employed canonical energy decomposition analysis (EDA). [11] This analysis method decomposes the interaction energy between the two deformed reactants, within the framework of Kohn-Sham DFT,i nto three physically meaningful terms [Eq. (2)].
DE int ðzÞ¼DV elstat ðzÞþDE Pauli ðzÞþDE oi ðzÞð 2Þ The electrostatic interaction, DV elstat (z), corresponds to the classical electrostatic interaction between the unperturbed charge distributions of the deformed reactants. The Pauli repulsion, DE Pauli (z), comprises the repulsion between closed-shell occupied orbitals, and is, therefore, destabilizing. The orbital interaction, DE oi (z), accounts for the stabilizing orbital interactions such as electron-pair bonding, charge transfer (interaction between the occupied orbitals of fragment Aw ith the unoccupied orbitals of fragment B, and vice versa), and polarization (e.g.,o ccupied-unoccupied orbital mixing on fragment Ao wing to the presence of fragment B, and vice versa). Ad etailed step-by-step protocol on how to perform the activation strain and energy decomposition analysis can be found in ref. [10e].

Results and Discussion
Definition of the oriented external electric field The effect of an oriented external electric field (OEEF) on the reactivity and endo/exo selectivityo ft he Diels-Alder (DA) reactions between cyclopentadiene (Cp)a nd maleic anhydride (MA)i sh ighly dependento nt he direction of the field. [7d] For this reason, we applied an electric field (F) individually from three distinct directions (Scheme 2b), namely,F x ,F y ,a nd F z . These axes are defined as follows:F x is along the C=Cd ouble bond of MA,F y is perpendicular to the reaction axis, that is, perpendicular to the plane of the newly formingC ÀCb onds, and F z is aligned alongt he reaction axis, that is, alongt he axis of an ewly forming CÀCb ond. For the isolated reactants, the F z is perpendicular to the molecular plane of Cp and MA.S haik et al. revealed that as witch in the reactionm echanism, from a concerted to as tepwise reaction mode, will occur in solution if F z is above 0.008 au.
[7d] Therefore, we limit the strength of the electric field applied in this study to AE 0.008 au (1 au = 514 Vnm À1 ), to ensure that the reactionm echanism remains concerted for all studied electric field strengths. Note that applying an electric fieldw ill, as discussedl ater,m ake the reaction slightly asynchronous;h owever,t his has an egligible effect on the activation barrier.I na ddition, this range of electric field strengths is also accessible in the laboratory. [23] Ta ble 1d isplays the computed activation energies, DE°,a nd reactione nergies, DE rxn ,o ft he endo/exo Diels-Alder reactions between Cp and MA under the strongest electric fields (F = AE 0.008 au) along the different axes. [24] An electric field alongt he x axis was found to have negligible impacto nDE°and DE rxn of both the endo and exo reactionp athways. An electric field along the y axis, however,a lters the endo/exo selectivity, namely,anegative fieldf avors the endo pathway whereas a positive field goes via the exo pathway.F urthermore, an electric field along the z axis can either inhibit( negative field) or catalyze( positivef ield) both endo and exo reaction pathways. In the following sections, we will discusst he effects of the electric field along the various axes individually.

Orientedexternal electric field in the z direction
First, we focus on the effect of the electric field in the z direction (F z ;a long the reaction axis) on the DA reactions studied herein. An electric field in the z direction has, as shown previously, [7d] as ignificant catalytic (positive field) or inhibitive (negative field) effect on the DA reaction( Figure 1). An egative F z (i.e.,p ositive end at Cp,n egative end at MA)l eads to an increase in activation barrier( DDE°= 6kcal mol À1 for F z = À0.008 au), whereas ap ositive F z (i.e., positive end at MA,n egative end at Cp)r esults in ad ecrease in activation barrier (DDE°= À9kcal mol À1 for F z = 0.008 au), for both the endo and Table 1. Activation barriers (DE°,k cal mol À1 )a nd reaction energies (DE rxn , kcal mol À1 ) [24] of the endo/exo Diels-Alder reaction between Cp and MA without the electric fields(F = 0) and under the electric fields( F = AE 0.008 au) alongd ifferent axes. [ In line with the work of Shaik et al., [7d] the inclusion of implicit solvationi no ur variable OEEF calculations has no effect on reactivity trends and endo/exo selectivity (Table S1, Supporting Information).
To gain quantitative insight into the driving force leadingt o the catalytic or inhibitive effect of F z on the DA reaction between Cp and MA,w eturned to the activation strain model (ASM) of reactivity. [10] In Figure 2a,w ef ocus on the activation strain diagram (ASD) of the energeticallyp referred endo pathway. [25] The DA reaction is catalyzed by ap ositive F z owing to both al ess destabilizing DE strain as well as am ore stabilizing DE int (Figure 2a). Increasing F z from À0.008 to 0.008 au leads to a DE strain at the transition state that becomes 5.0 kcal mol À1 less destabilizing. The individual reactants undergo ad eformation and reorientation over the course of the reaction, (Figure S5,Supporting Information), which results in am ore favorable alignment of the dipolem oment of distorted reactants with ap ositive F z and hence as tabilization of these distorted reactants. As aresult, the total strain energy along this reaction pathway will become less destabilizing. Thes tabilization of the DE int at the transition state, upon increasing the F z from À0.008 to 0.008 au, is, on the other hand, more significant, that is, DDE int = À10.6 kcal mol À1 ,i ndicatingt hat the DE int term is the predominant driving force leading to thec atalytic or inhibitive effect of the F z on the DA reaction.
The decisive role of DE int on the reactivity prompted the analysiso ft he different contributors to the interaction energy DE int by using ac anonical energy decomposition analysis (EDA). [11] The corresponding EDA resultsf or the endo DA reaction between Cp and MA under the F z ranging from À0.008 to 0.008 au are presented in Figure 2b.W eh ave found that the consistently more stabilizing DE int ,a sF z is varied from À0.008 to 0.008 au, originates from both am ore stabilizing DV elstat and DE oi .T he DE Pauli value, on the other hand, is hardly affected by the F z ,and thus, has no effect on the observed trend in reactivity.
To understand the origin of the systematically more stabilizing DV elstat upon going from the negative to positiveF z ,w ea nalyzed the molecular electrostatic potential map (MEP) of the distorted fragments in their transition state geometry (Figure 3). From these MEPs, together with the computed dipole moment in the z direction (m z ), it becomes cleart hat the enhanced stabilization of the DV elstat originatesf rom a larger (more favorable) difference in charged ensity between  the reactive side of the reactants going from F z = À0.008 au (left) to F z = 0au( middle) to F z = 0.008 au (right) (Figure 3). For the field-free reaction, Cp and MA have ac harges eparation that leads to anet negative and positive potential, respectively, on the carbon atomsi nvolved in the formation of the new CÀCb onds. These features are also reflected by their positive values of the dipole moment m z (Cp: m z = 0.5 D, MA: m z = 0.7 D). By applying ap ositive F z ,t he intramolecular charge separation increases anda mplifies the m z (Cp: m z = 1.3 D, MA: m z = 1.4 D), leadingt oastronger electrostatic attraction between reactants and hence am ore stabilizing DV elstat .Anegative F z ,o nt he contrary,s uppresses the m z (Cp: m z = À0.2 D, MA: m z = 0.1 D), which results in as maller difference in the charged ensity between reactants in the reactive regions, and thus, al ess stabilizing DV elstat term.
Next, Kohn-Sham molecular orbital (KS-MO) analyses were performed to understand why DE oi becomes increasingly more stabilizing from F z = À0.008 au to F z = 0.008 au. [11b, 26] The normale lectrond emand (NED) between the HOMO Cp and LUMO MA is the dominant orbitali nteraction contributing to the DE oi .A nalysis of the MOs reveals that the HOMO Cp is predominantly located on the two C=Cd oubleb onds of Cp,w hereas the LUMO MA is centered on the C=Cd ouble bond of the five-membered ring of MA (Figure 4a). During the NED interaction, the HOMO Cp mixes with the LUMO MA to give am ore stabilized bondingM O. The energy gain of formingt his two-center-twoelectron interaction (i.e.,o rbitals tabilization) relates to the energy difference between the HOMO Cp and bonding MO (De NED ). [26] The electron density deformation associated with the NED interaction involves the flow of electrons from the HOMO Cp to LUMO MA and is stabilized under ap ositive F z owing to the fact that the electrons move towardt he positive side of the electric field (Figure 4b), ap rocess that goes with negative (stabilizing) work. As ar esult,t he NED interaction is strengthened by the external electrical force, which leads to am ore stabilized bondingM O, or increased De NED ,a nd hence,amore stabilizing DE oi (Figure 4a). On the contrary,anegative F z counteracts the electron flow from the HOMO Cp to LUMO MA because the electron is forced to move toward the negative side of the electric field, ap rocess that resultsi np ositive (destabilizing) work. For this reason, the corresponding De NED becomes smaller,quenching the NED interaction. These effects can be quantified by lookinga tt he charge transfer from the HOMO Cp to LUMO MA ,w hichi ncreasesf rom 0.39 et o0 .50 e À by changing the F z from À0.008 to 0.008 au. Figure 3. Molecular electrostatic potential maps (at 0.01 Bohr À3 )f rom À0.03 (red) to 0.1 (blue) Hartreee À1 and dipole moments (m z ;inDebye) of isolated reactants for the endo Diels-Alder reactionsb etween Cp and MA in the F z at À0.008 au (left), 0au( middle),a nd 0.008 au (right), computed at the transition-state structures at BP86/TZ2P. Orientedexternale lectric field in the y direction After providing ac ausal modelt ou nderstand how the rate of the DA reactionb etween Cp and MA can be tuned by an electric field along the reaction axis (F z ), we examined the effect of an electric field perpendicular to the reactionaxis (F y ). In analogy with the work of Shaik et al., [7d] we found that F y has as ignificant impact on the endo/exo selectivity of the herein studied DA reaction ( Figure 5). The activation barrier of the endo pathway remains nearly unaffected in both an egative or positive F y ,w hereas the barrierf or the exo pathway becomes systematically stabilized on going from F y = À0.008 au to F y = 0.008 au. This resultsi naswitch in the endo/exo selectivity,b ecause an F y of 0.003 au or higher stabilizes the exo pathway to such an extent that the activation barrier becomes lower than the endo analog.
To revealw hy F y influences the exo activation barrier, and thus, induces as witch in the endo/exo selectivity,w ea gain turn to the ASM. The activation barrier of the endo pathway remains unaltered upon applying F y because the DE strain and DE int are nearly unaffected by this field (Figures 6a). Along the exo

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Full Paper doi.org /10.1002/chem.202004906 pathway,t he DE int is increasingly more stabilizing and lowers the activation barrier as F y increases from À0.008 to 0.008 au (Figure 6c). Our quantitative EDA results reveal the stabilization of DE int for the exo pathway,along this series,c an be attributed to both am ore stabilizing DE oi and DV elstat (Figure 6d). In the next section, we will discuss why the differentE DA terms along the endo and exo pathway are affectedi nadifferent manner, which ultimately explains the switch in endo/exo selectivity.
First, we discuss DE oi ,w hich is the major contributor to the stabilization of DE int for the exo pathway going from F y = À0.008 au to F y = 0.008 au.T ot his end, we performed aK S-MO analysisa nd identified that the NED interactions between the previously discussed HOMO Cp and LUMO MA are much more stabilizing than the inverse electron demand (IED) interaction HOMO MA and LUMO Cp .T he direction of the NED charget ransfer with respect to the F y determines if the electric field affects this interaction and hence catalyzes or inhibits the Diels-Alder reaction( Figure 7a). For the endo pathway, both ap ositive and negative F y have little effect on the electron donation capability of HOMO Cp into LUMO MA as F y is nearly perpendicular (808) to the direction of NED charge transfer between reactants (Figure 7a). As ar esult, the DE oi ,a long the endo pathway,r emains nearly unaffected upon applying an electric field in the y direction (Figure 7b). In contrast, the charge transfer,a nd thus DE oi , along the exo pathway does becomed iminished (negative F y ) or enhanced (positive F y )u pon application of an electric field (Figure 7b). The charge transfer accompanyingt he exo pathway is aligned more parallelt oF y (658) ( Figure 7a), and therefore, the electron donation fromt he HOMO Cp to the LUMO MA is increased from 0.41 to 0.44 e À upon varying F y from À0.008 to 0.008 au (Figure 7b). This amplified charget ransfer stabilizes more effectively the bonding MO and leads to al arger De NED (i.e.,e nergy gap between the HOMO Cp and bonding MO;s ee Figure S6, Supporting Information), and ultimately,am ore favorable DE oi along the exo pathway.
Next, we analyzed DV elstat ,w hich becomes increasingly less stabilizing for the endo,b ut more stabilizing for the exo,p athway on going from an egative to positive F y .T he MEPs of the individual reactants in the geometries they obtain in the endo (Figure 8a)a nd exo (Figure 8b)t ransition states were generated for F y = À0.008 au (left), F y = 0au( middle), and F y = 0.008 au (right). From these MEPs, together with the computed dipole moment in the y direction (m y ), it becomes clear that ap ositive F y tends to shift the charge density toward the left (Ày direction), whereas an egative F y polarizes the charge density toward the right (+ y direction). Thus, for the endo pathway (Figure 8a), as F y varies from 0t o0 .008 au, the dipole momentso ft he reactants become morep ositive (Cp: m y = 1.8 D; MA: m z = 5.1 D). The larger intramolecular charge separation leads to an enhanced electrostatic repulsion between the reactants, as both reactants have am ore electron-deficient area in the reactive center. An egative F y ,o nt he other hand, induces an electrostatic attraction between the reactants, because the dipole momentso ft he reactants become smaller( Cp: m y = À0.9 D; MA: m z = 3.1 D), resulting in an electron-deficient (on MA)a nd accumulated( on Cp)a rea in the reactive region. For the exo pathway (Figure 8b), however,t he oppositeb ehavior is observed. In this case, ap ositive F y stabilizes the electrostatic attraction between the reactants, whereas an egative F y ,i n turn, suppresses this interaction.
The less stabilizing DV elstat of the endo Diels-Alder reaction under ap ositive F y ,o nt he other hand, is compensated by a less destabilizing DE Pauli ,a st he F y changes the shape of the MOs that participate in the two-center-four-electron orbital interaction, reducing the corresponding orbital overlap (see Figure S7,Supporting Information). [27] The total interaction energy, DE int ,a long the endo pathway,t herefore, remainsn early invariant under application of af ield F y .F or the exo pathway,o nt he contrary,t he progressively more stabilizing DV elstat and DE oi lead to am ore favorable DE int of this reactionu nder ap ositive F y ,w hich, in turn, lowers the activation barrier height of the exo pathway.

Orientedexternale lectric field in the x direction
An oriented externale lectric field in the x direction (F x ) changes the Diels-Alder reactionf rom ac oncerted synchronous to ac oncerted slightly asynchronous reactionm ode (endo: Dr TS C···C = 0.07 and exo: Dr TS C···C = 0.09 ,w here Dr TS C···C is the difference between the newly forming C···C bonds in the TS;F igure S1, SupportingI nformation). This electric field, however,d oes not affect the reactivity or endo/exo selectivity of the DA reactions tudied herein (Table S1), [7d, 8] because it is unable to either promote the charge transfer or induce a change in electrostatic interaction between the reactants, because the reactants do not have ad ipole moment along the x axis. Shaik and co-workersd id find that an F x induces an enantioselectivity in DA reactions between Cp and various asymmetric substituted ethenes such as haloethene or cyanoethene,b ys uppressing the formationo fo ne of the enantiomers, which becomes highly destabilized along the pathway. [7e] Despite the fact that F x does not affect the reactivity or selectivity of the DA reaction, it is of interest to understand how this electric field alters the reactionm ode (i.e.,s ynchronicity) of this reaction. In our recent study, we established that the driving force behind the asynchronicity of Diels-Alder reactions is the asymmetry in the occupied orbitals of the reactants and the accompanied relief of destabilizing Pauli repulsion. [28] This asymmetry introduces ab ias towardt he formation of one C···C bond later than the other,h ence making the reaction asynchronous. Unsurprisingly,w ea lso found this exact behavior in the DA reactions studied herein (Figure 9). In the absence of an electric field, the carbon2 p p atomico rbitals (AOs) constructing the HOMOÀ1o fCp,i nw hich 2p p AOs on the reacting C=Cd ouble bonds and the s CÀH (pseudo-p)o nt he methylene bridge are out-of-phase, are distributed symmetrically (C1 2pp andC 4 2pp = 0.22;C 2 2pp and C3 2pp = 0.46). Applying an F x introduces an asymmetry in the HOMOÀ1 Cp ,b yp olarizing HOMOÀ1 Cp towardt he positive side of the electric field. This effect of an external electric field on the spatial distribution of am olecular orbitalh as also been shown experimentally by using various laser-spectroscopy techniques. [27] As ar esult, Cp experiences,d uring the course of the Diels-Alder reaction, more Pauli repulsion with the incoming MA at either C1 and C2 (positive F x )o rC 3a nd C4 (negative F x ). To relieve this larger Figure 8. Molecular electrostatic potential maps (at 0.01 Bohr À3 )from À0.03(red) to 0.1 (blue)Hartree e À1 with dipole moments (m y ,D)ofthe isolatedreactants of a) endo and b) exo Diels-Alder reactions between Cp and MA in the F y at À0.008 au, 0au, and 0.008 au, computed at the transition-state structures at BP86/TZ2P. Figure 9. Key occupied p-MO( isovalue = 0.03Bohr À3/2 )computed at the equilibrium geometries of Cp in the F x at À0.008 au, 0au, and 0.008au, in which the MO coefficients of the carbon 2p p atomic orbitals,c ontributing to the occupied orbitals, are shown in the schematic p-MO.
Pauli repulsion, the newly forming bond between Cp and MA at C1 (positive F x )o rC 4( negative F x )r emains longert han the other new bond, making the DA reaction in an electric field in the x direction asynchronous.

Inverse electron demand Diels-Alder reactions
In the final section, we investigate the effect of an OEEF in the z direction on an inverse electron demandD iels-Alder (IED-DA) reaction. [29] The reactivity of this class of DA reactions is controlled by the IED interaction, that is, the interaction between the LUMO of diene and HOMO of dienophile. [29] Based on the insightt hat emerged from the study of the normal electron demand DA reaction above, we expect that the F z will have ac ompletely opposite effect on the reactivity for the IED-DA reaction. In other words, ap ositive F z will destabilize the activation barrier by suppressing the IED interaction, and a negativeF z will now enhance the IED interaction, and therefore, lower the activation barrier.
To this end, we chose the typicalI ED-DAr eactionb etween an electron-deficientd iene, 3,6-bis(trifluoromethyl)tetrazine (Tz), and cyclopentene (Ce)a so ur model (Table 2). [16, 29a, 30] For the first time, we show that the IED-DAr eaction between Tz and Ce is catalyzed by anegative F z and inhibited by apositive F z .A st he F z goes from À0.008 to 0.008 au, the DE°increases from À1.8 to 15.4 kcal mol À1 (Table 2). Our ASM results reveal that the increase in activation barrier is caused predominantly by the increasingly less stabilizing DE int (DDE int = 10.6 kcal mol À1 ), followed by am ore destabilizing DE strain (DDE strain = 6.6 kcal mol À1 ). Next, we performed an energy decomposition analysist op inpoint the origin of the changing DE int .W ef ound that the positive F z destabilizes the DV elstat and DE oi ,a nd hence, leads to al ess favorable DE int .T he less stabilizing DV elstat under am ore positive F z arises from as maller charge density difference between reactants in the reactive center( see FigureS8, Supporting Information, for MEPs). The less favorable DE oi term under the positive F z ,a se xpected, results from aw eakeningo f the IED interaction:t he positive F z suppresses the charge transfer within the IED interaction (CT IED ), namely,t he electron donation from HOMO Ce to LUMO Tz (Table2), and therefore, destabilizes the DE oi term. This case, again,c onfirms the critical role of both the electrostatic and orbital interactions in determiningt he effect of electric fields on the reactivity of DA reactions.

Conclusions
Aj udiciously oriented external electric field can modulate the reactivity as well as endo/exo selectivity of the Diels-Alder reaction between cyclopentadiene (Cp)a nd maleic anhydride (MA). Ap ositive electric field along the forming bonds (F z > 0: positive end at MA,n egative enda tCp)a ccelerates this reaction, whereas one oriented perpendicular to the plain of the forming bonds (F y > 0: positive end at the doubleb ondo fMA, negative end at the anhydride group of MA)m akes the fieldfree endo-selectiveD iels-Alder reaction exo-selective. These findings emerge from our quantum chemical activation strain and Kohn-Sham molecular orbital analysesb ased on density functional theory calculations.
The rate enhancement provoked by F z is caused by both enhanced electrostatic and orbital interactions between the reactants. The former originates from an increased charge density difference between the reactants in the reactive region directly induced by the electric field. The positiveF z also enhances the orbitali nteractions by promoting the electron transfer within the normale lectron demand donor-acceptor interaction between the HOMO Cp and LUMO MA .I na ddition, for the exo pathway,apositive F y can strengthen the orbital interactions by promoting charget ransfer from HOMO Cp to LUMO MA .T he endo pathway,o nt he other hand, remains nearly unaffected, owing to am ismatch between the orientation of the reactants and the electric field. As ar esult,t he endo-selective field-freeD iels-Alder reactionb ecomesa nexo-selective Diels-Alder reaction under an adequately positive F y .
Interestingly,w eh ave established that an F z has an opposite effect on inverse electron demand Diels-Alder reactions, in which the most dominanto rbital interaction occurs between the LUMO of the diene and HOMO of the dienophile. This orbital interaction, in contrast with the normal electron demand Diels-Alder reactionb etween Cp and MA,b ecomes strengthened by an egative F z .T he results obtained herein display,f or the first time, the physicalf actorsd ictating the reactivity and selectivity of Diels-Alder reactions under an external oriented electric field within the framework of Kohn-Sham molecular orbital( KS-MO)t heory,w hich can be applied fort he understandinga nd design of electrostatically catalyzed reactions. Table 2. The Diels-Alder reaction between 3,6-bis(trifluoromethyl)tetrazine (Tz)a nd cyclopentene (Ce)w ith the bonding MO of the IED interaction; and the ASM and EDA results for this reaction under the F z at À0.008au, 0au, and0 .008 au, computed at the transition-state structures at BP86/ TZ2P.