How to search for and reveal a hidden intermediate? The ELF topological description of non- synchronicity in double proton transfer reactions under oriented external electric field

How to search for and reveal a hidden intermediate? 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The ELF topological description of non- synchronicity in double proton transfer reactions under oriented external electric field Vanessa Labet, Antoine Geoffroy-Neveux, Mohammad Esmaïl Alikhani This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4612227/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 04 Oct, 2024 Read the published version in Journal of Molecular Modeling → Version 1 posted 9 You are reading this latest preprint version Abstract · Context: The nature of double intermolecular proton transfer was studied with the ELF topological approach in two model dimers (the formic acid homodimer and the 1,2,3-triazole–guanidine heterodimer) under an oriented external electric field. It has been shown that each of the two dimers can have either a one-step (one transition state structure) or two-step (two transition state structures) reaction path, depending on the intensity and orientation of the external electric field. The presence of a singularly broad shoulder (plateau in the case of homodimer, and plateau-like for heterodimer) around the formal transition state structure results from the strong asynchronicity of the reaction. A careful ELF topological analysis of the nature of protons, hydride (localized) or roaming (delocalized) proton, along the reaction path allowed us to unambiguously classify the one-step mechanisms governing the double-proton transfer reactions into three distinct classes: 1) concerted-synchronous, when two events (roaming proton regions) completely overlap, 2) concerted-asynchronous, when two events (roaming proton regions) partially overlap, 3) two-stage one-step non-concerted, when two roaming proton regions are separated by a “hidden intermediate region”. All the structures belonging to this separatrix region are of the zwitterion form. · Methods: Geometry optimization of the stationary points on the potential energy surface was performed using density functional theory –wB97XD functional– in combination with the 6-311++G(2d, 2p) basis set for all the atoms. All first-principles calculations were performed using the Gaussian 09 quantum chemical packages. We also used the electron localization function (ELF) to reveal the nature of the proton along the reaction path: a bound proton (hydride) becomes a roaming proton (carrying a tiny negative charge ≈ 0.3 e) exchanging with two adjacent atoms via two attractors (topological critical points with (3, -3) signature). The ELF analyses were performed using the TopMod package. Double proton transfer electric field ELF topology hidden intermediate concerted vs stepwise asynchronicity Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction Elucidating and understanding in detail the mechanism of a chemical reaction is particularly important for the chemist, since only then can he or she hope to control it, both in terms of reaction rate and selectivity. In this context, concerted mechanisms, in which several chemical bonds are formed and broken during the same elementary step, have attracted particular interest over the last 50 years [ 1 – 3 ]. Today, it is widely accepted that many textbook reactions can occur either according to a stepwise mechanism or a concerted one, depending on the conditions. A great deal of work has been, and continues to be, devoted to determining the mechanism followed for these reactions, depending on the system of interest (eliminations [ 4 – 7 ], Diels-Alder reactions [ 8 – 11 ], double proton transfers (DPT) [ 12 – 14 ], aromatic nucleophilic substitutions [ 15 ] to name but a few). However, a distinction must be made between two cases. For some reactions, the concerted and stepwise mechanisms coexist on the potential energy surface [ 16 , 17 ]; the system then preferentially follows the mechanism associated with the lowest activation energy. For other reactions – those we are interested in in this work – only one of both mechanisms exists on the potential energy surface of a given system. Depending on the system, the concerted mechanism then has a more or less marked asynchronous character, which More O'Ferrall - Jencks diagrams elegantly highlight [ 18 – 20 ]. This asynchronicity, the origin of which remains open to discussion [ 21 ], generally manifests itself through an asymmetry of the transition state (possibly anticipable from the electronic characteristics of the reactants [ 22 , 23 ]). This undoubtedly explains why, historically, Jencks used the expression "imbalanced transition state" [ 24 ] to refer to this type of mechanism. Taking up the expression originally introduced by Dewar, many authors now speak of a two-stage reaction [ 25 , 26 ] albeit with subtle differences in what this implies in terms of asynchronicity [ 27 , 28 ]. In extreme cases, the coupling between the primitive processes constituting the reaction disappears; the system then follows a stepwise mechanism. Three particularities of asynchronous concerted mechanisms explain why gaining insight on this type of mechanism is interesting: The degree of asynchronicity of a concerted mechanism has a significant impact on the activation energy of the reaction [ 3 , 29 , 30 ]. This point is addressed by Bernasconi's Principle of Non-perfect Synchronization [ 31 ], which has recently gained renewed interest, particularly for PCET reactions [ 32 , 33 ]. Certain structures through which the system passes during an asynchronous concerted mechanism can be converted into a transition state or reaction intermediate under other reaction conditions. Kraka and Cremer call these structures hidden transition state or hidden intermediate [ 34 ]. The degree of asynchrony of a concerted mechanism can be controlled to some extent by modifying certain reaction parameters: substituent [ 35 ], solvent [ 36 ], catalyst [ 22 ] or more recently application of an oriented external electric field [ 37 ]. The work we present here follows on from a recently published computational study dedicated to investigating the mechanism of the DPT reaction between a pyrazole and a guanidine. This reaction is known in the literature to involve a highly asynchronous concerted mechanism [ 38 ]. We showed that in this particular case, under the effect of an external electric field oriented along the proton transfers, the mechanism could be converted into a synchronous concerted mechanism or a stepwise mechanism.[ 39 ]. Our goal here is (1) to study the extent to which these results can be generalized to other DPT reactions and (2) to further unravel the transition from one type of mechanism to the other. To this end, we considered two model DPT reactions: between two formic acid molecules on the one hand (synchronous concerted mechanism model) [ 40 – 44 ] and between 1,2,3-triazole and guanidine on the other hand (highly asynchronous concerted mechanism model) [ 45 ] (see Scheme 1 ). Again, we studied the evolution of the mechanism under the effect of an external electric field oriented in the direction of proton transfer. To quote Shaik, the electric field is used here as a "smart reagent" [ 46 ]. It has the advantage to enable control of bond polarization more finely than by modifying a substituent or changing the polarity of the solvent. It's worth noting, however, that the study of DPT reactions under electric fields is also of real practical interest. In biological systems, DNA, whose three-dimensional structure is ensured by hydrogen bonds between pairs of nucleic bases, can be subjected to relatively intense local electric fields able to affect the tautomeric equilibrium of nucleic bases and thus lead to mutagenic lesions [ 47 , 48 ]. Returning to the work presented here, the mechanisms were analyzed by applying the reaction force model [ 49 ] to identify the different phases of the reaction, and by studying the chemical bond evolution along the intrinsic reaction coordinate within the ELF topology framework [ 50 – 57 ] to account for the electronic reorganizations involved. 2. Computational details 2.1. Electronic structure: DFT computations All first-principles calculations were performed using the Gaussian 09 quantum chemical packages [ 58 ]. Optimization of the stationary points on the potential energy surface was performed using the ωB97X-D exchange-correlation functional [ 59 , 60 ] which accounts for dispersion energy and long-range interaction. The Pople triple- ζ quality basis set extended with polarization and diffuse functions, 6-311 + + G(2d, 2p) has been used for all atoms [ 61 , 62 ]. Calculation of reaction path was performed by following the intrinsic-reaction-coordinate (IRC) [ 63 ] labeled as ξ and expressed in mass-weighted Cartesian coordinates which links the transition state TS (characterized by a single imaginary frequency) to the reactant and product. All IRC calculations have been performed using the local quadratic approximation (LQA) algorithm [ 64 , 65 ], force constants computed only at the first point (CalcFC), and a step-size equal to 4 (StepSize = 4) in units of 0.01 amu 1/2 ·Bohr. 2.2 Analysis of chemical bond evolution In order to analyze the chemical bond evolution along the reaction path, we used the electron localization function (ELF) [ 66 ]. Indeed, the ELF topology [ 67 ] provides a partitioning of the molecular space into chemically representative regions (basins of attractors) [ 68 , 69 ] corresponding to the chemical object in the framework of the Lewis valence theory [ 70 – 73 ] and also in the Valence Shell Electron Pair Repulsion (VSEPR) approach [ 74 , 75 ]. During the last three decades, the ELF topology was successfully applied to study different hydrogen-bonded complexes in the gas phase [ 50 , 51 , 76 – 78 ]. Within the ELF framework, the core–valence bifurcation (CVB) index is proposed to distinguish strength of various kind of hydrogen bonds [ 79 ]. For a hydrogen bond (H-bond) complex (usually noted as A-H···B, where A = proton-donor, H = hydrogen, and B = proton-acceptor), this index is expressed as CVB = η cv – η vv′ . η cv corresponds to the ELF bifurcation value between ELF core domain and valence domain, while the η vv′ stands for the ELF value at the bifurcation point between V(A,H) and V(B). The last point is indeed a second order critical point (3,–1) linking the V(A, H) proton-donor domain to the V(B) proton-acceptor one [ 70 , 77 ]. In this work the partition of the molecular space in terms of nonoverlapping space-filling domains has been performed using the TopMod package. [ 80 ] We used the Multiwfn package [ 81 , 82 ] to evaluate both CVB and η vv′ quantities. As shown recently by Silvi et al. [ 77 ], the η vv′ quantity enables us to estimate the variance of the V(A–H) domain population. Consequently, we use now the η vv′ quantity as a delocalization index. The Bond Evolution Theory (BET) [ 50 – 57 ] based on the ELF topology of reorganization of covalent bonds and lone pairs along the reaction path allowed us to identify and describe most of the electronic events (such as bond breaking/forming and electronic density redistribution) which occur along the reaction path. 3. Results and discussion This section is essentially focused on the study of double proton transfer in two model systems, FAD and TGD illustrated in Scheme 1 , under the influence of an oriented external electric field (OEEF). The static and homogeneous electric field is actually oriented along the “reaction axis” [ 83 ], the direction in which the double proton transfer occurs (see Scheme 1 ). In this work, the F z is expressed in atomic units , with the following conversion rule: 1 au = 5.140 x 10 3 MV.cm -1 = 5.14 x 10 11 V.m -1 . 3.1. FAD under an OEEF Two symmetrically equivalent structures (reactant and product) separated by a barrier estimated at 8.1 kcal/mol form the reaction path of the FAD case when no external electric field is applied [ 44 , 84 ]. Along the reaction path, both proton transfers progress identically (concerted synchronous reaction) and the inter-oxygen distance gets its shortest value at the transition state. A previous careful theoretical study of the FAD isomerization under influence of an oriented external electric field (OEEF) [ 85 ] clearly showed that as the electric field intensity increases: The single imaginary vibrational frequency decreases in absolute value accompanied by a flattening of the potential energy curve around the transition state structure [ 86 ], The isomerization barrier height decreases, Over of two proton-donors, the one opposite to OEEF is transferred first (using the convention and labels indicated in Scheme 1 , H b is transferred first when F z > 0), The two inter-oxygen distances remain equal but increase at the transition state structure. 3.1.1. Energetic, geometric and vibrational analysis In order to take this study further, we have re-investigated at the ωB97X-D/6-311 + + G(2d,2p) level of theory the double proton transfer reaction of the formic acid dimer in varying the external electric field strength from F z = 0 to 200×10 − 4 au. As a reminder, we emphasize that the electric field of strength ≤ 100×10 − 4 au has been identified in the microenvironment of a DNA base-pair, in an enzyme active site [ 87 , 88 ]. Our geometric and energetic results (see ESM-Table 1) are perfectly in line with the aforementioned trends: the acidity of the formic acid whit an O-H oriented in the direction of the electric field decreases, while that of the second formic acid increases. This corroborates with the geometric and energetic changes in the reactant: r1 decreases, r3 increases. The reactive dimer (at TS structure) loses its symmetry, R1 increases then R2 decreases (see ESM-Table 1). The potential energy curve, U(ξ), around TS flattens more and more and its width increases with the increase in F z [ 85 , 86 , 88 ]. At F z = 125×10 − 4 au, this plateau extends from ξ = -0.486 to ξ = +0.486 amu 1/2 .Bohr, when U(ξ) = U(TS) ± 0.04 kcal/mol. In full agreement with a recent work, the more the barrier decreases, the more non-synchronicity increases [ 89 ]. The accentuation of this phenomenon can lead to the appearance of a reaction intermediate (RI) at the TS structure. Our investigation, indeed, showed that the double proton transfer in the FAD is actually a one-step process for 0 ≤ F z ≤ 120×10 − 4 au (one transition state structure), and becomes a stepwise reaction presenting a reaction intermediate (RI) when F z > 120×10 − 4 au (see Fig. 1 ). The reactant–RI isomerization barrier continuously decreases with increasing F z . Especially at F z = 200×10 − 4 au (the strongest electric field studied in this paper), this barrier is close to zero so that the only observable species is the RI compound. Furthermore, it should be noted that the RI compound is no longer a formic acid dimer, but a pair of ions: formate (HCO 2 − ) in interaction with protonated formic acid, [HCOOH]H + (see ESM-Figure 1). 3.1.2. The ELF topological analysis: existence domain of a roaming proton We focus our topological analysis over regions where bound protons (hydride) transform into almost free protons (roaming between two electronegative atoms) [ 90 ]. From topological point of view, a roaming proton does not form a protonated basin with any neighboring atom, but it is curiously exchanging with two adjacent atoms via two attractors (topological critical points with (3, -3) signature). In the studied compounds, the roaming proton carries a tiny negative charge (≈ 0.3 e) [ 54 , 57 , 91 ]. Figure 2 illustrates the ELF representation of these two types of protons in the case of the formic acid dimer. In Fig. 2 -left (reactant structure for F z = 0), we can easily identify two protons forming two disynaptic basins which are engaged in the hydrogen bonding with the other formic acid. By contrast, Fig. 2 -right (transition state structure for F z = 0) illustrates two roaming protons, each of which is sandwiched between two monosynaptic (lone-pair) basins coming from the two (neighboring) heavy atoms. The topological analysis along the reaction path allowed us to identify the region where the proton wanders between two oxygens. This region is now called the “roaming proton region”, and referred to as “RPR”. Table 1 Roaming proton regions (RPR), delimited by ξ 1 and ξ 2 , for the DPT reaction of FAD under four selected electric fields. F z and ξ are in a.u. and amu 1/2 ·Bohr units, respectively. For comparison, extension of the TS region as defined by the reaction force profile [ 49 , 89 ] is also indicated. Two protons are denoted as H a and H b (see Scheme 1 ). Fz = 0 40×10 − 4 80×10 − 4 100×10 − 4 120×10 − 4 ξ 1 ξ 2 ξ 1 ξ 2 ξ 1 ξ 2 ξ 1 ξ 2 ξ 1 ξ 2 H b RPR -0.43 0.43 -0.57 0.39 -0.78 0.11 -0.96 0.0 -1.27 -0.16 H a RPR -0.43 0.43 -0.39 0.57 -0.11 0.78 0.0 0.96 0.16 1.27 TS region -0.30 0.30 -0.35 0.35 -0.50 0.50 -0.61 0.61 -0.79 0.79 For the case of the free-field FAD dimer (concerted synchronous reaction), the two protons (denoted as H a and H b in see Scheme 1 ) both behave as roaming protons in the same region delimited by ξ 1 = -0.426 amu 1/2 ·Bohr and ξ 2 = + 0.426 amu 1/2 ·Bohr, namely over a region of width of 0.852 amu 1/2 ·Bohr. In other words, the overlap between two RPRs is total. This region obviously covers the “TS region” as defined by the reaction force profile [ 49 , 89 ], ranging from − 0.298 to + 0.298 amu 1/2 ·Bohr. Under an electric field (F z > 0), the H b proton begins to behave like a roaming proton before the H a proton. For instance, we note that H b is a roaming proton from − 0.782 to + 0.112 amu 1/2 ·Bohr, while H a is between − 0.112 and + 0.782 amu 1/2 ·Bohr, when F z = 80×10 − 4 au. It is interesting to underline the fact that the two RPRs although being offset, they share a subdomain ranging from − 0.112 to + 0.112 amu 1/2 ·Bohr. In other words, the overlap between two RPRs is partial. The existence of shifted “roaming proton regions” along the reaction path stands for “nonsynchronous processes”, and the existence of a shared domain, with partial overlap, indicates that this is a “concerted reaction”. In other words, we have a "concerted non-synchronous" reaction for the ELF topological situations similar to the case of F z = 80×10 − 4 au. Note that this shared domain only includes one structure, that of TS, for F z = 100×10 − 4 au. (see Fig. 3 -a for 0 100×10 − 4 au, a remarkable change occurs in the topological image of the TS structure: the two protons stop being wandering and form two protonated basins with the two oxygens of the same formic acid partner. In other words, according to the ELF topology, at the TS structure, the formic acid dimer (under F z = 120×10 − 4 au, for instance) is a zwitterionic compound: a formate anion in interaction with a protonated formic acid cation. This situation reminds the “hidden intermediate” suggested two decades ago by Cremer and Kraka [ 92 – 96 ] and also by other researchers [ 97 – 104 ] in the case of Diels-Alder reactions, in particular, and for other types of reactions. Figure 4 illustrates the reaction path and the three distinct domains for F z = 120×10 − 4 au: H b RPR (from − 1.268 to -0.158 amu 1/2 ·Bohr), H a RPR (from 0.158 to 1.268 amu 1/2 ·Bohr), and zwitterion domain ranging from − 0.158 to 0.158 amu 1/2 ·Bohr. The barrier height reduced to 3.5 kcal/mol, almost half of barrier in the absence of electric field (7.4 kcal/mol). It should be emphasized that the “hidden intermediate” is, in the case of FAD, confused with the structure of TS. In other words, it is a stationary point on the reaction path, without being a minimum, unlike the cases mentioned in the literature [ 96 , 98 , 99 , 104 ]. This property is due to the fact that the reactant and product are structurally equivalent in the FAD compound. It is therefore clear that the topological description according to the ELF function is a robust and powerful tool which allows us to unambiguously identify the “hidden intermediate region”, referred to as HIR. In the case of FAD under OEEF, this domain exists for 100×10 − 4 au < F z < 130×10 − 4 au. We emphasize that this HIR is the region that separates the two RPRs. Precisely because of the existence of this separating region, we can no longer consider this reaction as a concerted reaction from a topological point of view. This description fits perfectly with the "two-stage one-step non-concerted mechanism" concept suggested more than one decade ago by Domingo and coworkers [ 27 ]. At this stage, the question that naturally arises is: where is located the hidden TS of this hidden intermediate? In fact, each of the structures located inside the H a RPR (or H b RPR) is indeed a candidate to be a "hidden TS" structure, from the point of view of the ELF topology: each structure is composed of an anion, a roaming proton and a neutral molecule waiting to receive the proton. This is precisely the topological structure of a “Hidden TS”. A new important change appears in the reaction mechanism, when we increase the F z beyond 130×10 − 4 au: the reaction is no longer a one-step reaction, but a two-step one with three minima (reactant, RI, and product) along the potential energy curve. Compared to the reactant, the relative stability of RI increases while the barrier of the reactant–RI transformation decreases when F z increases (see Fig. 1 ). In particular at F z = 200×10 − 4 au, only the RI becomes observable because the reactant–RI barrier is actually close to zero. Consequently, the transformation of Reactant into RI (or RI to product) is a single proton transfer reaction. We therefore have one roaming proton in the transition state region. 3.2. TGD under an OEEF The 1,2,3-triazole–guanidine dimer (TGD) is the second borderline case in our set for which the reactant is fully different from the product, both from a geometrical point of view (2H-1,2,3-triazole–guanidine for reactant, and 1H-1,2,3-triazole–guanidine for product) and from an energetic point of view (the product is by 2.7 kcal/mol less stable than the reactant, at the wB97XD/6311 + + G(2d,2p) level of theory). As shown in a previous theoretical work, [ 45 ] unlike the FAD case studied in the previous paragraph, the calculated DPT reaction path for 1,2,3-triazole–guanidine dimer exhibits a singularly wide shoulder on the reactant side (plateau-like) which results from the strong asynchronicity of the reaction. It has been shown that solvent effects and the electron withdrawing substituents attached to the triazole (cyano-substituent in the 4-position) turn this plateau into reactive intermediate [ 45 ]. Here again, to reveal proton bonding evolution along the reaction path, we carried out the ELF topological analysis in order to identify the different domains of topological stability. Such an ELF cartoon is illustrated in Fig. 5 . The entire reaction path includes 258 structures which were calculated based on the IRC (ξ) which varies from − 7.897 to 3.290 amu 1/2 .Bohr passing through zero for the TS structure. The five regions of a topological stability (same topological structure) are identified along the IRC path (see Fig. 5 ). They are in the following order (from reactant to product): Reactant region is the first domain going from ξ = -7.89 to -4.34 amu 1/2 .Bohr containing 83 structures. These structures are characterized by two protonated disynaptic basins with nitrogen atoms of two molecules, V(H, N). Each of these basins participates in a hydrogen bonding (see Fig. 6 -a). The second region starting with ξ = -4.34 amu 1/2 .Bohr and ending with ξ = -3.04 amu 1/2 .Bohr is characterized, as shown in Fig. 6 -b, by the presence of a roaming proton (H a of 2H-1,2,3-triazole) and a protonated disynaptic basin (H b of guanidine). The roaming proton is sandwiched between two monosynaptic basins V(N) coming from two molecules participating in the DPT reaction. This region is referred as to H a RPR in Fig. 5 and contains 30 structures on the IRC path. The third region referred as to HIR (hidden intermediate region) is a region that contains 58 structures along the reaction path going from ξ = -3.04 to ξ = -0.52 amu 1/2 .Bohr. The ELF topological structure of this region is a zwitterionic form composed of protonated guanidine and deprotonated 1,2,3-triazole (Fig. 8 -c). In the fourth region, the first hydrogen, H a , forms a protonated disynaptic basin with the guanidine’s nitrogen, and the second hydrogen, H b , behaves like a roaming proton. This region goes from − 0.52 to + 0.57 amu 1/2 .Bohr over 25 structures (see Fig. 6 -d). The last region corresponds to the product region where two hydrogens evolving in the DPT reaction are topologically localized on the two molecules forming two protonated disynaptic basins (Fig. 6 -e). We count 62 structures over an interval of ξ which extends from + 0.57 to + 3.29 amu 1/2 .Bohr. In contrast to the FAD compound, the “hidden intermediate” is not confused with the formal TS structure located at ξ = 0 amu 1/2 .Bohr. In other words, all structures included in the HIR domain are representative of the hidden intermediate “hi” structure. For this “hi” structure, as proposed by Kraka and Cramer [ 95 ], we need to identify two hidden transition states “hts” corresponding to two hidden reactions “hr”: one connecting the “hi” to the reactant, and another one connecting the “hi” to the product. These two “hts” are represented respectively by the structures located within the two proton roaming regions. Furthermore, the DPT reaction within the 1,2,3-triazole–guanidine dimer cannot be considered as a concerted reaction, because of the presence of a wide region (HIR) which separates the two roaming proton regions. It is a two-stage reaction, but one-step process because of the presence of only one TS structure along the full IRC path. Consequently, the ELF topological description clearly shows that double proton transfer in the TGD reaction occurs via a "two-stage one-step non-concerted mechanism" [ 27 , 99 ]. Other than solvent and/or substituent effects, an OEEF used as a “smart reagent” can reveal the "hi" or completely inhibit it in transforming the DPT reaction of TGD in a perfectly concerted synchronous reaction. Considering the convention presented in Scheme 1 , we can anticipate the effect of an OEEF: It forces the departure of H a (from triazole to guanidine) if it is negative. If so, it will enable us to optimize a structure on the potential energy surface for the "hi" and the corresponding "hts". It will allow us to move from a non-concerted mechanism to a reaction obeying a concerted mechanism, if F z > 0. 3.2.1. F z > 0 Figure 7 shows three reaction path curves for three values ​​of F z : 0, 40×10 − 4 , and 70×10 − 4 au. As we can see with the naked eye, the barrier height increases, and the width of the plateau-like part of the IRC path decreases when the OEEF intensity increases. The DPT reaction of TGD converges to a concerted synchronous reaction for F z ≈ 70x10 − 4 au. Imaginary vibrational frequency at the TS structure (F z = 70×10 − 4 au) is found to be 1157 \(i\) cm − 1 . Furthermore, an analysis of the ELF topology along the reaction path makes it possible to identify the nature of the reaction mechanisms for different values ​​of F z . A systematic study of the ELF topology on numerous structures on each IRC curve revealed that: The width of the hidden intermediate region shrinks like a skin of sorrow as F z increases incrementally from 0 to 50×10 − 4 au. For comparison, it reduces from 3 to 0.72, then to 0 amu 1/2 .Bohr, when F z goes from 0 to 30×10 − 4 , and then to 50×10 − 4 au. Particularly at F z = 50×10 − 4 au, we no longer have a zone corresponding to the HIR along the reaction path. Consequently, we consider that the double proton transfer reaction takes place according to the “two-stage one-step non-concerted mechanism” for the interval 0 ≤ F z < 50×10 − 4 au. At F z = 50×10 − 4 au, the two corresponding roaming domains of H a and H b are (disjointed) side-by-side. This is precisely the beginning of a “synchronous concerted mechanism”. If the width of the overlap of these two roaming domains is zero at F z = 50×10 − 4 au, it reaches the value of 0.23 amu 1/2 .Bohr when F z = 60×10 − 4 au. More precisely, the roaming H a region extends from − 0.936 to 0 amu 1/2 .Bohr, while that of H b ranges from − 0.233 to 0.655 amu 1/2 .Bohr (see Fig. 8 ). As shown in a previous work [ 91 ], the ELF topological descriptor δη = η 1(vv') – η 2(vv') , related to the core-valence bifurcation index mentioned in section “2. Computational details”, is a good index to evaluate the interaction force of the two hydrogen bonds at the reactant structure of a DPT reaction. We found that δη is very close to zero (δη = 0.002) when F z = 75×10 − 4 au. In other words, we can conclude that the DPT reaction in TGD takes place according to the “concerted synchronous mechanism”, when F z = 75×10 − 4 au. Consequently, the overlap between two roaming H a and H b domains is almost total. 3.2.2. F z < 0 In contrast, the DPT reaction of TGD under a negative OEEF quickly converges to a stepwise reaction: one optimized minimum for an intermediate, and two transition state structures connecting to the reactant and product. In Table 2 are gathered some energetic properties of some stationary structures versus the negative F z strength. Note that the relative energies (ΔE) are calculated with respect to the reactant total energy for each F z . Table 2 Energetic properties (in kcal/mol) of TGD under four selected negative OEEF. F z (au) ΔE(R) ΔE (TS1) ΔE(RI) ΔE(TS2) ΔE(P) -20 x10 -4 0 5.9 5.5 7.1 2.5 -40 x10 -4 0 3.9 2.6 5.2 2.1 -60 x10 -4 0 2.3 -0.5 3.5 1.7 -80 x10 -4 0 1.0 -3.6 2.1 1.1 As expected, the barrier heights, ΔE (TS1) and ΔE (TS2), decreases when the OEEF strength decreases. For F z = -20 x10 -4 au, the reaction intermediate (RI) although well identified on the reaction path, cannot be experimentally observed, because a high barrier. On the other hand, energetic conditions in the case of F z = -80 x10 -4 au allow us to confirm that RI is indeed the most stable compound compared to the reactant (R) and product (P). Furthermore, the required energy for going from R to RI is relatively low and therefore surmountable. 4. Conclusions The main results of this work are summarized as follows: Any DPT reaction can occur by one of the four reaction mechanisms: 1) concerted-synchronous, 2) concerted-asynchronous, 3) two-stage one-step non-concerted, and 4) stepwise mechanism. The first three can be grouped into the so-called "one-step mechanism” which is characterized by the presence of a single transition state structure throughout the reaction path connecting the reactant to the product. The presence of two TS structures along the reaction path following the reactant - TS1 - Intermediate - TS2 – Product sequence is characteristic of a stepwise mechanism. Whatever the mechanism of a DPT reaction in the absence of an OEEF, it has been shown that by applying an OEEF we can modify the mechanism and thus modulate the DPT reaction. The ELF topological analysis of the electronic structures of stationary points along the IRC path has been shown to be a powerful tool for rationalizing the motion of two protons during a DPT reaction. It has been seen that a proton engaged in the proton transfer reaction is either localized forming then a protonated disynaptic basin with a heavy atom, or delocalized (roaming proton) carrying then a tiny negative charge (≈ 0.3 e) and sandwiched between two monosynaptic basins of the two heavy atoms. We can therefore determine the region in which the proton behaves as a roaming proton (referred to as RPR), and the region where the proton is localized (referred to as HIR). In a DPT reaction, involving two protons, the three mechanisms of the "one-step" family can be clearly identified according to the following rules: Rule 1: When two RPRs (relative to the two protons) perfectly overlap, then the DPT reaction takes place following a “concerted-synchronous mechanism”. Rule 2: When two RPRs partially overlap, then the DPT reaction takes place following a “concerted-asynchronous mechanism”. Rule 3: When two RPRs are fully disjointed by the presence of an HIR, then the DPT reaction takes place following a “two-stage one-step non-concerted mechanism”. Declarations Author Contributions Vanessa Labet : Electronic and ELF analysis, and writing the original draft Antoine Geoffroy-Neveux : Optimization calculations, Electronic and ELF analysis Mohammad Esmaïl Alikhani : Optimization calculations, Electronic and ELF analysis, and writing the original draft Conflicts of interest There are no conflicts to declare. Funding The authors declare that no funds, grants, or other support were received during the preparation of this manuscript. Electronic Supplementary Information An ESM (electronic supplementary material) file is available. References Dewar MJS (1984) Multibond reactions cannot normally be synchronous. J Am Chem Soc 106:209–219. https://doi.org/10.1021/ja00313a042 Jencks WP (1981) Ingold Lecture. How does a reaction choose its mechanism? Chem Soc Rev 10:345–375. https://doi.org/10.1039/CS9811000345 Williams A (1994) The diagnosis of concerted organic mechanisms. Chem Soc Rev 23:93–100. https://doi.org/10.1039/CS9942300093 Ortega DE, Ormazábal-Toledo R, Contreras R, Matute RA (2019) Theoretical insights into the E1cB/E2 mechanistic dichotomy of elimination reactions. Org Biomol Chem 17:9874–9882. https://doi.org/10.1039/C9OB02004G Duarte F, Gronert S, Kamerlin SCL (2014) Concerted or Stepwise: How Much Do Free-Energy Landscapes Tell Us about the Mechanisms of Elimination Reactions? J Org Chem 79:1280–1288. https://doi.org/10.1021/jo402702m Alunni S, De Angelis F, Ottavi L, et al (2005) Evidence of a Borderline Region between E1cb and E2 Elimination Reaction Mechanisms: A Combined Experimental and Theoretical Study of Systems Activated by the Pyridine Ring. J Am Chem Soc 127:15151–15160. https://doi.org/10.1021/ja0539138 Mosconi E, De Angelis F, Belpassi L, et al (2009) Merging of E2 and E1cb Reaction Mechanisms: A Combined Theoretical and Experimental Study. Eur J Org Chem 2009:5501–5504. https://doi.org/10.1002/ejoc.200900906 Linder M, Brinck T (2012) Stepwise Diels–Alder: More than Just an Oddity? A Computational Mechanistic Study. J Org Chem 77:6563–6573. https://doi.org/10.1021/jo301176t Houk KN, Liu F, Yang Z, Seeman JI (2021) Evolution of the Diels–Alder Reaction Mechanism since the 1930s: Woodward, Houk with Woodward, and the Influence of Computational Chemistry on Understanding Cycloadditions. Angew Chem Int Ed 60:12660–12681. https://doi.org/10.1002/anie.202001654 Aktah D, Passerone D, Parrinello M (2004) Insights into the Electronic Dynamics in Chemical Reactions. J Phys Chem A 108:848–854. https://doi.org/10.1021/jp036572y De Souza MAF, Ventura E, Do Monte SA, et al (2016) Revisiting the concept of the (a)synchronicity of diels‐alder reactions based on the dynamics of quasiclassical trajectories. J Comput Chem 37:701–711. https://doi.org/10.1002/jcc.24245 Accardi A, Barth I, Kühn O, Manz J (2010) From Synchronous to Sequential Double Proton Transfer: Quantum Dynamics Simulations for the Model Porphine. J Phys Chem A 114:11252–11262. https://doi.org/10.1021/jp103435d Pandey P, Naik S, Keshavamurthy S (2022) Influence of low frequency modes on dynamical concertedness in double proton transfer dynamics. Communications in Nonlinear Science and Numerical Simulation 109:106326. https://doi.org/10.1016/j.cnsns.2022.106326 Schweiger S, Hartke B, Rauhut G (2005) Double proton transfer reactions at the transition from a concerted to a stepwise mechanism: a comparative ab initio study. Phys Chem Chem Phys 7:493. https://doi.org/10.1039/b415528a Rohrbach S, Murphy JA, Tuttle T (2020) Computational Study on the Boundary Between the Concerted and Stepwise Mechanism of Bimolecular S N Ar Reactions. J Am Chem Soc 142:14871–14876. https://doi.org/10.1021/jacs.0c01975 Goldstein E, Beno B, Houk KN (1996) Density Functional Theory Prediction of the Relative Energies and Isotope Effects for the Concerted and Stepwise Mechanisms of the Diels−Alder Reaction of Butadiene and Ethylene. J Am Chem Soc 118:6036–6043. https://doi.org/10.1021/ja9601494 Sakai S (2000) Theoretical Analysis of Concerted and Stepwise Mechanisms of Diels−Alder Reaction between Butadiene and Ethylene. J Phys Chem A 104:922–927. https://doi.org/10.1021/jp9926894 Jencks WP (1972) General acid-base catalysis of complex reactions in water. Chem Rev 72:705–718. https://doi.org/10.1021/cr60280a004 O’Ferrall RAM (1970) Relationships between E2 and E1cB mechanisms of β-elimination. J Chem Soc B 0:274–277. https://doi.org/10.1039/J29700000274 Smedarchina Z, Siebrand W, Fernández-Ramos A (2007) Correlated double-proton transfer. I. Theory. The Journal of Chemical Physics 127:174513. https://doi.org/10.1063/1.2785186 Vermeeren P, Hamlin TA, Bickelhaupt FM (2021) Origin of asynchronicity in Diels–Alder reactions. Phys Chem Chem Phys 23:20095–20106. https://doi.org/10.1039/D1CP02456F Domingo LR, Pérez P, Sáez JA (2012) Origin of the synchronicity in bond formation in polar Diels–Alder reactions: an ELF analysis of the reaction between cyclopentadiene and tetracyanoethylene. Org Biomol Chem 10:3841. https://doi.org/10.1039/c2ob25152c Domingo LR, Aurell MJ, Pérez P, Sáez JA (2012) Understanding the origin of the asynchronicity in bond-formation in polar cycloaddition reactions. A DFT study of the 1,3-dipolar cycloaddition reaction of carbonyl ylides with 1,2-benzoquinones. RSC Adv 2:1334–1342. https://doi.org/10.1039/C1RA00717C Jencks WP (1985) A primer for the Bema Hapothle. An empirical approach to the characterization of changing transition-state structures. Chem Rev 85:511–527. https://doi.org/10.1021/cr00070a001 Goldstein MJ, Thayer GL (1965) The Mechanism of a Diels-Alder Reaction. II. The Structure of the Transition State 1 . J Am Chem Soc 87:1933–1941. https://doi.org/10.1021/ja01087a017 Dewar MJS, Olivella Santiago, Stewart JJP (1986) Mechanism of the Diels-Alder reaction: reactions of butadiene with ethylene and cyanoethylenes. J Am Chem Soc 108:5771–5779. https://doi.org/10.1021/ja00279a018 Domingo LR, Saéz JA, Zaragozá RJ, Arnó M (2008) Understanding the Participation of Quadricyclane as Nucleophile in Polar [2σ + 2σ + 2π] Cycloadditions toward Electrophilic π Molecules. J Org Chem 73:8791–8799. https://doi.org/10.1021/jo801575g Houk KN, Gonzalez J, Li Y (1995) Pericyclic Reaction Transition States: Passions and Punctilios, 1935-1995. Acc Chem Res 28:81–90. https://doi.org/10.1021/ar00050a004 Barrales-Martínez C, Jaque P (2022) A deeper analysis of the role of synchronicity on the Bell–Evans–Polanyi plot in multibond chemical reactions: a path-dependent reaction force constant. Phys Chem Chem Phys 24:14772–14779. https://doi.org/10.1039/D2CP01460B Giraldo C, Gómez S, Weinhold F, Restrepo A (2016) Insight into the Mechanism of the Michael Reaction. ChemPhysChem 17:2022–2034. https://doi.org/10.1002/cphc.201600166 Bernasconi CF (1985) The principle of imperfect synchronization. Tetrahedron 41:3219–3234. https://doi.org/10.1016/S0040-4020(01)96673-6 Costentin C, Savéant J-M (2020) Hydrogen and proton exchange at carbon. Imbalanced transition state and mechanism crossover. Chemical Science 11:1006–1010. https://doi.org/10.1039/C9SC05147C Darcy JW, Kolmar SS, Mayer JM (2019) Transition State Asymmetry in C–H Bond Cleavage by Proton-Coupled Electron Transfer. J Am Chem Soc 141:10777–10787. https://doi.org/10.1021/jacs.9b04303 Kraka E, Cremer D (2010) Computational Analysis of the Mechanism of Chemical Reactions in Terms of Reaction Phases: Hidden Intermediates and Hidden Transition States. Acc Chem Res 43:591–601. https://doi.org/10.1021/ar900013p Sakai S, Okumura T (2004) Theoretical studies on the substituent effects for concerted and stepwise mechanisms of the Diels–Alder reaction between butadiene and ethylene. Journal of Molecular Structure: THEOCHEM 685:89–95. https://doi.org/10.1016/j.theochem.2004.06.052 Yepes D, Martínez-Araya JI, Jaque P (2018) Solvent effect on the degree of (a)synchronicity in polar Diels-Alder reactions from the perspective of the reaction force constant analysis. J Mol Model 24:33. https://doi.org/10.1007/s00894-017-3563-x Shaik S, Ramanan R, Danovitch D, Mandal D (2018) Structure and reactivity/selectivity control by oriented-external electric fields. Chem Soc Rev 47:5125–5145. https://doi.org/10.1039/C8CS00354H Schweiger S, Rauhut G (2003) Plateau Reactions: Double Proton-Transfer Processes with Structureless Transition States. J Phys Chem A 107:9668–9678. https://doi.org/10.1021/jp0350060 Geoffroy-Neveux A, Labet V, Alikhani ME (2022) Influence of an Oriented External Electric Field on the Mechanism of Double Proton Transfer between Pyrazole and Guanidine: from an Asynchronous Plateau Transition State to a Synchronous or Stepwise Mechanism. J Phys Chem A 126:3057–3071. https://doi.org/10.1021/acs.jpca.1c10553 Ivanov SD, Grant IM, Marx D (2015) Quantum free energy landscapes from ab initio path integral metadynamics: Double proton transfer in the formic acid dimer is concerted but not correlated. The Journal of Chemical Physics 143:124304. https://doi.org/10.1063/1.4931052 Farfán P, Echeverri A, Diaz E, et al (2017) Dimers of formic acid: Structures, stability, and double proton transfer. The Journal of Chemical Physics 147:044312. https://doi.org/10.1063/1.4985880 Richardson JO (2017) Full- and reduced-dimensionality instanton calculations of the tunnelling splitting in the formic acid dimer. Phys Chem Chem Phys 19:966–970. https://doi.org/10.1039/C6CP07808G Liu H, Cao J, Bian W (2019) Double Proton Transfer in the Dimer of Formic Acid: An Efficient Quantum Mechanical Scheme. Front Chem 7:676. https://doi.org/10.3389/fchem.2019.00676 Nejad A, Suhm MA (2020) Concerted Pair Motion Due to Double Hydrogen Bonding: The Formic Acid Dimer Case. J Indian Inst Sci 100:5–19. https://doi.org/10.1007/s41745-019-00137-5 Rauhut G (2003) Modulation of reaction barriers by generating reactive intermediates: double proton transfer reactions. Phys Chem Chem Phys 5:791–800. https://doi.org/10.1039/b208960b Shaik S, Mandal D, Ramanan R (2016) Oriented electric fields as future smart reagents in chemistry. Nature Chemistry 8:1091–1098. https://doi.org/10.1038/nchem.2651 Cerón-Carrasco JP, Jacquemin D (2013) Electric-field induced mutation of DNA: a theoretical investigation of the GC base pair. Phys Chem Chem Phys 15:4548. https://doi.org/10.1039/c2cp44066k Cerón-Carrasco JP, Jacquemin D (2013) Electric field induced DNA damage: an open door for selective mutations. Chem Commun 49:7578. https://doi.org/10.1039/c3cc42593b Toro-Labbé A (1999) Characterization of Chemical Reactions from the Profiles of Energy, Chemical Potential, and Hardness. J Phys Chem A 103:4398–4403. https://doi.org/10.1021/jp984187g Berski S, Andrés J, Silvi B, Domingo LR (2003) The Joint Use of Catastrophe Theory and Electron Localization Function to Characterize Molecular Mechanisms. A Density Functional Study of the Diels−Alder Reaction between Ethylene and 1,3-Butadiene. J Phys Chem A 107:6014–6024. https://doi.org/10.1021/jp030272z Polo V, Andres J, Castillo R, et al (2004) Understanding the Molecular Mechanism of the 1,3‐Dipolar Cycloaddition between Fulminic Acid and Acetylene in Terms of the Electron Localization Function and Catastrophe Theory. Chemistry A European J 10:5165–5172. https://doi.org/10.1002/chem.200400161 Krokidis X, Silvi B, Alikhani ME (1998) Topological characterization of the isomerization mechanisms in XNO (X=H, Cl). Chemical Physics Letters 292:35–45. https://doi.org/10.1016/S0009-2614(98)00650-2 Santos JC, Andres J, Aizman A, et al (2005) A Theoretical Study on the Reaction Mechanism for the Bergman Cyclization from the Perspective of the Electron Localization Function and Catastrophe Theory. J Phys Chem A 109:3687–3693. https://doi.org/10.1021/jp0441947 Krokidis X, Vuilleumier R, Borgis D, Silvi B (1999) A topological analysis of the proton transfer in H 5 O + 2 . Molecular Physics 96:265–273. https://doi.org/10.1080/00268979909482959 Ćmikiewicz A, Gordon AJ, Berski S (2018) Characterisation of the reaction mechanism between ammonia and formaldehyde from the topological analysis of ELF and catastrophe theory perspective. Struct Chem 29:243–255. https://doi.org/10.1007/s11224-017-1024-x Andrés J, González-Navarrete P, Safont VS, Silvi B (2017) Curly arrows, electron flow, and reaction mechanisms from the perspective of the bonding evolution theory. Phys Chem Chem Phys 19:29031–29046. https://doi.org/10.1039/C7CP06108K Krokidis X, Goncalves V, Savin A, Silvi B (1998) How Malonaldehyde Bonds Change during Proton Transfer. J Phys Chem A 102:5065–5073. https://doi.org/10.1021/jp9734282 Frisch MJ, Trucks GW, Schlegel HB, et al (2013) Gaussian˜09 Revision D.01 Körzdörfer T, Sears JS, Sutton C, Brédas J-L (2011) Long-range corrected hybrid functionals for π-conjugated systems: Dependence of the range-separation parameter on conjugation length. The Journal of Chemical Physics 135:204107. https://doi.org/10.1063/1.3663856 Chai J-D, Head-Gordon M (2008) Systematic optimization of long-range corrected hybrid density functionals. The Journal of Chemical Physics 128:084106. https://doi.org/10.1063/1.2834918 McLean AD, Chandler GS (1980) Contracted Gaussian basis sets for molecular calculations. I. Second row atoms, Z =11–18. The Journal of Chemical Physics 72:5639–5648. https://doi.org/10.1063/1.438980 Krishnan R, Binkley JS, Seeger R, Pople JA (1980) Self-consistent molecular orbital methods. XX. A basis set for correlated wave functions. The Journal of Chemical Physics 72:650–654. https://doi.org/10.1063/1.438955 Fukui K (1970) Formulation of the reaction coordinate. J Phys Chem 74:4161–4163. https://doi.org/10.1021/j100717a029 Page M, McIver JW (1988) On evaluating the reaction path Hamiltonian. The Journal of Chemical Physics 88:922–935. https://doi.org/10.1063/1.454172 Page M, Doubleday C, McIver JW (1990) Following steepest descent reaction paths. The use of higher energy derivatives with a b i n i t i o electronic structure methods. The Journal of Chemical Physics 93:5634–5642. https://doi.org/10.1063/1.459634 Becke AD, Edgecombe KE (1990) A simple measure of electron localization in atomic and molecular systems. The Journal of Chemical Physics 92:5397–5403. https://doi.org/10.1063/1.458517 Silvi B, Savin A (1994) Classification of chemical bonds based on topological analysis of electron localization functions. Nature 371:683–686. https://doi.org/10.1038/371683a0 Silvi B, Fourré I, Alikhani M (2005) The Topological Analysis of the Electron Localization Function. A Key for a Position Space Representation of Chemical Bonds. Monatshefte für Chemie 136:855–879. https://doi.org/10.1007/s00706-005-0297-8 Grin Y, Savin A, Silvi B (2014) The ELF Perspective of chemical bonding. In: Frenking G, Shaik S (eds) The Chemical Bond, 1st ed. Wiley, pp 345–382 Alikhani ME, Fuster F, Silvi B (2005) What Can Tell the Topological Analysis of ELF on Hydrogen Bonding? Struct Chem 16:203–210. https://doi.org/10.1007/s11224-005-4451-z Zins E-L, Silvi B, Alikhani ME (2015) Activation of C–H and B–H bonds through agostic bonding: an ELF/QTAIM insight. Phys Chem Chem Phys 17:9258–9281. https://doi.org/10.1039/C4CP05728G Alikhani ME (2013) On the chemical bonding features in boron containing compounds: a combined QTAIM/ELF topological analysis. Phys Chem Chem Phys 15:12602. https://doi.org/10.1039/c3cp50396h Michelini MDC, Russo N, Alikhani ME, Silvi B (2004) Energetic and topological analysis of the reaction of Mo and Mo₂ with NH₃, C₂H₂, and C₂H₄ molecules. Journal of Computational Chemistry 25:1647–1655. https://doi.org/10.1002/jcc.20087 Noury S, Silvi B, Gillespie RJ (2002) Chemical Bonding in Hypervalent Molecules: Is the Octet Rule Relevant? Inorg Chem 41:2164–2172. https://doi.org/10.1021/ic011003v Berski S, Gordon AJ, Latajka Z (2014) Electron Localization Function Study on the Chemical Bonding in a Real Space for Tetrahedrane, Cubane, Adamantane, and Dodecahedrane and Their Perfluorinated Derivatives and Radical Anions. J Phys Chem A 118:4147–4156. https://doi.org/10.1021/jp501838g Fuster F, Silvi B (2000) Determination of protonation sites in bases from topological rules. Chemical Physics 252:279–287. https://doi.org/10.1016/S0301-0104(99)00320-1 Silvi B, Ratajczak H (2016) Hydrogen bonding and delocalization in the ELF analysis approach. Phys Chem Chem Phys 18:27442–27449. https://doi.org/10.1039/C6CP05400E Esmaı̈l Alikhani M, Silvi B (2004) A topological analysis of the proton transfer in the HF– and HCl–(OH)− interactions. Journal of Molecular Structure 706:3–6. https://doi.org/10.1016/j.molstruc.2004.02.052 Fuster F, Silvi B (2000) Does the topological approach characterize the hydrogen bond? Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta) 104:13–21. https://doi.org/10.1007/s002149900100 Noury S, Krokidis X, Fuster F, Silvi B (1999) Computational tools for the electron localization function topological analysis. Computers & Chemistry 23:597–604. https://doi.org/10.1016/S0097-8485(99)00039-X Lu T, Chen F (2012) Multiwfn: A multifunctional wavefunction analyzer. J Comput Chem 33:580–592. https://doi.org/10.1002/jcc.22885 Tian L, Fei-Wu C, 北京科技大学化学与生物工程学院, 北京 100083,School of Chemical and Biological Engineering, University of Science and Technology Beijing, Beijing 100083, P. R. China (2011) Meaning and Functional Form of the Electron Localization Function. Acta Physico-Chimica Sinica 27:2786–2792. https://doi.org/10.3866/PKU.WHXB20112786 Shaik S, Ramanan R, Danovich D, Mandal D (2018) Structure and reactivity/selectivity control by oriented-external electric fields. Chem Soc Rev 47:5125–5145. https://doi.org/10.1039/C8CS00354H Li F, Yang X, Liu X, et al (2023) An Ab Initio Neural Network Potential Energy Surface for the Dimer of Formic Acid and Further Quantum Tunneling Dynamics. ACS Omega 8:17296–17303. https://doi.org/10.1021/acsomega.3c02169 Arabi AA, Matta CF (2011) Effects of external electric fields on double proton transfer kinetics in the formic acid dimer. Phys Chem Chem Phys 13:13738. https://doi.org/10.1039/c1cp20175a Arabi AA, Matta CF (2018) Effects of Intense Electric Fields on the Double Proton Transfer in the Watson–Crick Guanine–Cytosine Base Pair. J Phys Chem B 122:8631–8641. https://doi.org/10.1021/acs.jpcb.8b05053 Sowlati-Hashjin S, Karttunen M, Matta CF (2021) Electrostatic Fields in Biophysical Chemistry. In: Shaik S, Stuyver T (eds) Effects of Electric Fields on Structure and Reactivity. The Royal Society of Chemistry, pp 225–262 Matta CF, Bandrauk AD (2021) An Introduction to Laser-field Effects on Chemical Reactivity. In: Shaik S, Stuyver T (eds) Effects of Electric Fields on Structure and Reactivity. The Royal Society of Chemistry, pp 394–419 Gómez S, Rojas-Valencia N, Toro-Labbé A, Restrepo A (2023) The transition state region in nonsynchronous concerted reactions. The Journal of Chemical Physics 158:084109. https://doi.org/10.1063/5.0133487 Bowman JM (2006) Skirting the transition state, a new paradigm in reaction rate theory. Proc Natl Acad Sci USA 103:16061–16062. https://doi.org/10.1073/pnas.0607810103 Geoffroy-Neveux A, Labet V, Alikhani ME (2022) Influence of an Oriented External Electric Field on the Mechanism of Double Proton Transfer between Pyrazole and Guanidine: from an Asynchronous Plateau Transition State to a Synchronous or Stepwise Mechanism. J Phys Chem A 126:3057–3071. https://doi.org/10.1021/acs.jpca.1c10553 Cremer D, Wu A, Kraka E (2001) The mechanism of the reaction FH + H2C=CH2→H3C–CFH2. Investigation of hidden intermediates with the unified reaction valley approach. Phys Chem Chem Phys 3:674–687. https://doi.org/10.1039/b007733j Kraka E, Cremer D (2002) Mechanism and dynamics of organic reactions: 1,2‐H shift in methylchlorocarbene. J of Physical Organic Chem 15:431–447. https://doi.org/10.1002/poc.495 Joo H, Kraka E, Quapp W, Cremer D (2007) The mechanism of a barrierless reaction: hidden transition state and hidden intermediates in the reaction of methylene with ethene. Molecular Physics 105:2697–2717. https://doi.org/10.1080/00268970701620677 Kraka E, Cremer D (2010) Computational Analysis of the Mechanism of Chemical Reactions in Terms of Reaction Phases: Hidden Intermediates and Hidden Transition States. Acc Chem Res 43:591–601. https://doi.org/10.1021/ar900013p Sexton T, Kraka E, Cremer D (2016) Extraordinary Mechanism of the Diels–Alder Reaction: Investigation of Stereochemistry, Charge Transfer, Charge Polarization, and Biradicaloid Formation. J Phys Chem A 120:1097–1111. https://doi.org/10.1021/acs.jpca.5b11493 Rzepa HS, Wentrup C (2013) Mechanistic Diversity in Thermal Fragmentation Reactions: A Computational Exploration of CO and CO 2 Extrusions from Five-Membered Rings. J Org Chem 78:7565–7574. https://doi.org/10.1021/jo401146k Armstrong A, Boto RA, Dingwall P, et al (2014) The Houk–List transition states for organocatalytic mechanisms revisited. Chem Sci 5:2057–2071. https://doi.org/10.1039/C3SC53416B Roca-López D, Polo V, Tejero T, Merino P (2015) Understanding Bond Formation in Polar One-Step Reactions. Topological Analyses of the Reaction between Nitrones and Lithium Ynolates. J Org Chem 80:4076–4083. https://doi.org/10.1021/acs.joc.5b00413 Lillo VJ, Mansilla J, Saá JM (2018) The role of proton shuttling mechanisms in solvent-free and catalyst-free acetalization reactions of imines. Org Biomol Chem 16:4527–4536. https://doi.org/10.1039/C8OB01007B Said RB, Kolle JM, Essalah K, et al (2020) A Unified Approach to CO 2 –Amine Reaction Mechanisms. ACS Omega 5:26125–26133. https://doi.org/10.1021/acsomega.0c03727 Shernyukov AV, Salnikov GE, Rudakov DA, Genaev AM (2021) Noncatalytic Bromination of Icosahedral Dicarboranes: The Key Role of Anionic Bromine Clusters Facilitating Br Atom Insertion into the B–H σ-Bond. Inorg Chem 60:3106–3116. https://doi.org/10.1021/acs.inorgchem.0c03392 Gheorghiu A, Coveney PV, Arabi AA (2021) The influence of external electric fields on proton transfer tautomerism in the guanine–cytosine base pair. Phys Chem Chem Phys 23:6252–6265. https://doi.org/10.1039/D0CP06218A Durán R, Barrales-Martínez C, Matute RA (2023) Hidden intermediate activation: a concept to elucidate the reaction mechanism of the Schmittel cyclization of enyne–allenes. Phys Chem Chem Phys 25:6050–6059. https://doi.org/10.1039/D2CP04684A Scheme 1 Scheme 1 is available in the Supplementary Files section. Additional Declarations No competing interests reported. Supplementary Files Scheme1.jpg Scheme 1. Schematic structure of two model dimers. The convention for the external electric field orientation (in the Z-direction) and polarity (chemists convention used by the Gaussian package) are also illustrated. FAD and TGD stand for formic acid dimer and triazole-guanidine dimer respectively. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4612227","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":326175462,"identity":"dcb93117-1599-4c3b-963c-e3f00b2d0132","order_by":0,"name":"Vanessa Labet","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABRUlEQVRIie3OwUrDMBjA8W8Esktmrimde4aOwOZJn6UUtsscHguOLqNQj14Lis+w08RbQ6C7dPgCHpRdh6y3DoqaysQ6JuhNsH9ISEJ+JABVVX+5AyB6dvVgH0fofS62tcd9BBckSvYQvUfWt0QGZbJtl1jzhXzK8mPA9YVcpjdeq3vlx8szF+zbOmkv3fzIo4DwukSSocMbgQOYDB1LzhRvPsR9HiZg3/mEtxcBY4ZAKPwkhhh0zJpA4wAGHSZnkR0yfdIIXu2pwj1jIhizIqpKHzMuV91Nlo8B01U3k9felrxAQfobkTN2EiFUIlRfAIIV4GIhBdoSURAU1wTWr8AOWXH9jbkmzw5LYsVZM+6ZJAauiTImATNC9YVgOminWX4OlJ7KtTvyWsz0Y5OM4HB6LyepyD1KL/wy+VG/BlVVVVX/vjeWV3FC18728gAAAABJRU5ErkJggg==","orcid":"","institution":"Sorbonne Université CNRS, MONARIS, UMR8233","correspondingAuthor":true,"prefix":"","firstName":"Vanessa","middleName":"","lastName":"Labet","suffix":""},{"id":326175463,"identity":"4024ecd3-50ac-4e84-a13f-23a072356e82","order_by":1,"name":"Antoine Geoffroy-Neveux","email":"","orcid":"","institution":"Sorbonne Université CNRS, MONARIS, UMR8233","correspondingAuthor":false,"prefix":"","firstName":"Antoine","middleName":"","lastName":"Geoffroy-Neveux","suffix":""},{"id":326175464,"identity":"e41ce4f8-2597-4c8f-8c41-da689da9d7fa","order_by":2,"name":"Mohammad Esmaïl Alikhani","email":"","orcid":"","institution":"Sorbonne Université CNRS, MONARIS, UMR8233","correspondingAuthor":false,"prefix":"","firstName":"Mohammad","middleName":"Esmaïl","lastName":"Alikhani","suffix":""}],"badges":[],"createdAt":"2024-06-20 13:55:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4612227/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4612227/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00894-024-06163-0","type":"published","date":"2024-10-04T15:58:24+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":60621095,"identity":"64d6d571-1d27-4396-8efc-85b47968661b","added_by":"auto","created_at":"2024-07-18 20:59:02","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":40837,"visible":true,"origin":"","legend":"\u003cp\u003ePotential energy curves of the DPT reaction in FAD for selected external electric fields oriented along proton transfers.\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4612227/v1/6583805b724ca30449bf5160.jpg"},{"id":60620209,"identity":"ca729d56-95cc-47a8-b3c7-686212f9f4b4","added_by":"auto","created_at":"2024-07-18 20:51:01","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":60191,"visible":true,"origin":"","legend":"\u003cp\u003eThe ELF topological basins of localized and delocalized (roaming) protons at two FAD structures of the DPT reaction in the absence of electric field: reactant (left) and TS structure (right). Note that we used the same ELF values for isosurfaces and for isolines in both cases.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4612227/v1/adff8f8ff346cbf4c8f28285.jpg"},{"id":60620214,"identity":"436e088f-3a52-4d3f-b648-5322e7254a6c","added_by":"auto","created_at":"2024-07-18 20:51:02","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":60239,"visible":true,"origin":"","legend":"\u003cp\u003eExistence ranges for two roaming protons along the reaction path of the FAD under influence of an OEEF of strength 80×10\u003csup\u003e-4\u003c/sup\u003e au (a) and 100×10\u003csup\u003e-4\u003c/sup\u003e au (b).\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4612227/v1/a0d1c0f05874fb8140e494d8.jpg"},{"id":60620216,"identity":"6b637976-bc13-4daf-a0c1-4531cd290121","added_by":"auto","created_at":"2024-07-18 20:51:02","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":73759,"visible":true,"origin":"","legend":"\u003cp\u003eThree ranges of the two protons (two disjoint ranges for two roaming protons and one for two hydridic protons) along the reaction path of the DPT in FAD under influence of an OEEF of strength 120×10\u003csup\u003e-4\u003c/sup\u003e au.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4612227/v1/52b4811d7edd0ab798b6ad17.jpg"},{"id":60621096,"identity":"31d995b5-1e59-4f1d-8a72-083df5d8dddd","added_by":"auto","created_at":"2024-07-18 20:59:02","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":69655,"visible":true,"origin":"","legend":"\u003cp\u003eSuccession of different topological regions along reaction path of DPT for triazole–guanidine with no OEEF.\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4612227/v1/33d8d63355b1b5566c3e83f5.jpg"},{"id":60620219,"identity":"db4fc7c5-fe41-4bc2-bde1-93247cbefcc6","added_by":"auto","created_at":"2024-07-18 20:51:02","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":51894,"visible":true,"origin":"","legend":"\u003cp\u003eThe five topological stability structures characterizing the DPT pathway for TGD with no OEEF. Monosynaptic and protonated disynaptic basins are labelled as V(N) and V(H, N), respectively.\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4612227/v1/8b77de2e194954957aaa8f51.jpg"},{"id":60620217,"identity":"06395441-01e7-4805-b31d-6efd3ffa7195","added_by":"auto","created_at":"2024-07-18 20:51:02","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":55493,"visible":true,"origin":"","legend":"\u003cp\u003eThree pathways for the DPT reaction of Triazole – Guanidine under three selected F\u003csub\u003ez\u003c/sub\u003e: 0, 40×10\u003csup\u003e-4\u003c/sup\u003e, and 70×10\u003csup\u003e-4\u003c/sup\u003e au.\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4612227/v1/99ebcdcb18d07ec5678613a9.jpg"},{"id":60620210,"identity":"01dd23cf-db49-4c2d-b902-240528cc73eb","added_by":"auto","created_at":"2024-07-18 20:51:02","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":84832,"visible":true,"origin":"","legend":"\u003cp\u003eTwo roaming regions (H\u003csub\u003ea\u003c/sub\u003e at left and H\u003csub\u003eb\u003c/sub\u003e at right) with the overlapping region between these two domains along the reaction path: Relative energy (U) and reaction force vs. IRC (ξ).\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4612227/v1/209fd6b9f6ad373ae77b6b33.jpg"},{"id":66097008,"identity":"8d2a8ca1-c5d9-4694-948c-6b912412f2ac","added_by":"auto","created_at":"2024-10-07 16:12:35","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1190074,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4612227/v1/f3571a6a-d39f-4f16-a50e-24a766f3e703.pdf"},{"id":60620211,"identity":"d7b96e82-543d-4f17-8008-dd44179c3400","added_by":"auto","created_at":"2024-07-18 20:51:02","extension":"jpg","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":70180,"visible":true,"origin":"","legend":"\u003cp\u003eScheme 1. Schematic structure of two model dimers. The convention for the external electric field orientation (in the Z-direction) and polarity (chemists convention used by the Gaussian package) are also illustrated. FAD and TGD stand for formic acid dimer and triazole-guanidine dimer respectively.\u003c/p\u003e","description":"","filename":"Scheme1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4612227/v1/ddef46cad072831a68473ecc.jpg"},{"id":60620212,"identity":"2622c0a0-4aee-4ade-9275-7e1658e2385a","added_by":"auto","created_at":"2024-07-18 20:51:02","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":120183,"visible":true,"origin":"","legend":"","description":"","filename":"ESMAsynchronousconcertedmechanisms.docx","url":"https://assets-eu.researchsquare.com/files/rs-4612227/v1/29755c46bf7b07480d6102d9.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"How to search for and reveal a hidden intermediate? The ELF topological description of non- synchronicity in double proton transfer reactions under oriented external electric field","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eElucidating and understanding in detail the mechanism of a chemical reaction is particularly important for the chemist, since only then can he or she hope to control it, both in terms of reaction rate and selectivity. In this context, concerted mechanisms, in which several chemical bonds are formed and broken during the same elementary step, have attracted particular interest over the last 50 years [\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Today, it is widely accepted that many textbook reactions can occur either according to a stepwise mechanism or a concerted one, depending on the conditions. A great deal of work has been, and continues to be, devoted to determining the mechanism followed for these reactions, depending on the system of interest (eliminations [\u003cspan additionalcitationids=\"CR5 CR6\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], Diels-Alder reactions [\u003cspan additionalcitationids=\"CR9 CR10\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], double proton transfers (DPT) [\u003cspan additionalcitationids=\"CR13\" citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], aromatic nucleophilic substitutions [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] to name but a few).\u003c/p\u003e \u003cp\u003eHowever, a distinction must be made between two cases. For some reactions, the concerted and stepwise mechanisms coexist on the potential energy surface [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]; the system then preferentially follows the mechanism associated with the lowest activation energy. For other reactions \u0026ndash; those we are interested in in this work \u0026ndash; only one of both mechanisms exists on the potential energy surface of a given system. Depending on the system, the concerted mechanism then has a more or less marked asynchronous character, which More O'Ferrall - Jencks diagrams elegantly highlight [\u003cspan additionalcitationids=\"CR19\" citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. This asynchronicity, the origin of which remains open to discussion [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], generally manifests itself through an asymmetry of the transition state (possibly anticipable from the electronic characteristics of the reactants [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]). This undoubtedly explains why, historically, Jencks used the expression \"imbalanced transition state\" [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] to refer to this type of mechanism. Taking up the expression originally introduced by Dewar, many authors now speak of a \u003cem\u003etwo-stage reaction\u003c/em\u003e [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] albeit with subtle differences in what this implies in terms of asynchronicity [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. In extreme cases, the coupling between the primitive processes constituting the reaction disappears; the system then follows a stepwise mechanism.\u003c/p\u003e \u003cp\u003eThree particularities of asynchronous concerted mechanisms explain why gaining insight on this type of mechanism is interesting:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe degree of asynchronicity of a concerted mechanism has a significant impact on the activation energy of the reaction [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. This point is addressed by Bernasconi's Principle of Non-perfect Synchronization [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e], which has recently gained renewed interest, particularly for PCET reactions [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eCertain structures through which the system passes during an asynchronous concerted mechanism can be converted into a transition state or reaction intermediate under other reaction conditions. Kraka and Cremer call these structures \u003cem\u003ehidden transition state\u003c/em\u003e or \u003cem\u003ehidden intermediate\u003c/em\u003e [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e].\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe degree of asynchrony of a concerted mechanism can be controlled to some extent by modifying certain reaction parameters: substituent [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e], solvent [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e], catalyst [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] or more recently application of an oriented external electric field [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e].\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eThe work we present here follows on from a recently published computational study dedicated to investigating the mechanism of the DPT reaction between a pyrazole and a guanidine. This reaction is known in the literature to involve a highly asynchronous concerted mechanism [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. We showed that in this particular case, under the effect of an external electric field oriented along the proton transfers, the mechanism could be converted into a synchronous concerted mechanism or a stepwise mechanism.[\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. Our goal here is (1) to study the extent to which these results can be generalized to other DPT reactions and (2) to further unravel the transition from one type of mechanism to the other. To this end, we considered two model DPT reactions: between two formic acid molecules on the one hand (synchronous concerted mechanism model) [\u003cspan additionalcitationids=\"CR41 CR42 CR43\" citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e] and between 1,2,3-triazole and guanidine on the other hand (highly asynchronous concerted mechanism model) [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e] (see Scheme \u003cspan refid=\"Sch1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Again, we studied the evolution of the mechanism under the effect of an external electric field oriented in the direction of proton transfer. To quote Shaik, the electric field is used here as a \"smart reagent\" [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. It has the advantage to enable control of bond polarization more finely than by modifying a substituent or changing the polarity of the solvent. It's worth noting, however, that the study of DPT reactions under electric fields is also of real practical interest. In biological systems, DNA, whose three-dimensional structure is ensured by hydrogen bonds between pairs of nucleic bases, can be subjected to relatively intense local electric fields able to affect the tautomeric equilibrium of nucleic bases and thus lead to mutagenic lesions [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e, \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eReturning to the work presented here, the mechanisms were analyzed by applying the reaction force model [\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e] to identify the different phases of the reaction, and by studying the chemical bond evolution along the intrinsic reaction coordinate within the ELF topology framework [\u003cspan additionalcitationids=\"CR51 CR52 CR53 CR54 CR55 CR56\" citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e] to account for the electronic reorganizations involved.\u003c/p\u003e"},{"header":"2. Computational details","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Electronic structure: DFT computations\u003c/h2\u003e \u003cp\u003eAll first-principles calculations were performed using the Gaussian 09 quantum chemical packages [\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e]. Optimization of the stationary points on the potential energy surface was performed using the ωB97X-D exchange-correlation functional [\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e, \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e] which accounts for dispersion energy and long-range interaction. The Pople triple-\u003cem\u003eζ\u003c/em\u003e quality basis set extended with polarization and diffuse functions, 6-311\u0026thinsp;+\u0026thinsp;+\u0026thinsp;G(2d, 2p) has been used for all atoms [\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e, \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eCalculation of reaction path was performed by following the intrinsic-reaction-coordinate (IRC) [\u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e63\u003c/span\u003e] labeled as ξ and expressed in mass-weighted Cartesian coordinates which links the transition state TS (characterized by a single imaginary frequency) to the reactant and product. All IRC calculations have been performed using the local quadratic approximation (LQA) algorithm [\u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e64\u003c/span\u003e, \u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e65\u003c/span\u003e], force constants computed only at the first point (CalcFC), and a step-size equal to 4 (StepSize\u0026thinsp;=\u0026thinsp;4) in units of 0.01 amu\u003csup\u003e1/2\u003c/sup\u003e\u0026middot;Bohr.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Analysis of chemical bond evolution\u003c/h2\u003e \u003cp\u003eIn order to analyze the chemical bond evolution along the reaction path, we used the electron localization function (ELF) [\u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e66\u003c/span\u003e]. Indeed, the ELF topology [\u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e67\u003c/span\u003e] provides a partitioning of the molecular space into chemically representative regions (basins of attractors) [\u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e68\u003c/span\u003e, \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e69\u003c/span\u003e] corresponding to the chemical object in the framework of the Lewis valence theory [\u003cspan additionalcitationids=\"CR71 CR72\" citationid=\"CR70\" class=\"CitationRef\"\u003e70\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e73\u003c/span\u003e] and also in the Valence Shell Electron Pair Repulsion (VSEPR) approach [\u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e74\u003c/span\u003e, \u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e75\u003c/span\u003e]. During the last three decades, the ELF topology was successfully applied to study different hydrogen-bonded complexes in the gas phase [\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e, \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e, \u003cspan additionalcitationids=\"CR77\" citationid=\"CR76\" class=\"CitationRef\"\u003e76\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e78\u003c/span\u003e]. Within the ELF framework, the core\u0026ndash;valence bifurcation (CVB) index is proposed to distinguish strength of various kind of hydrogen bonds [\u003cspan citationid=\"CR79\" class=\"CitationRef\"\u003e79\u003c/span\u003e]. For a hydrogen bond (H-bond) complex (usually noted as A-H\u0026middot;\u0026middot;\u0026middot;B, where A\u0026thinsp;=\u0026thinsp;proton-donor, H\u0026thinsp;=\u0026thinsp;hydrogen, and B\u0026thinsp;=\u0026thinsp;proton-acceptor), this index is expressed as CVB\u0026thinsp;=\u0026thinsp;η\u003csub\u003ecv\u003c/sub\u003e \u0026ndash; η\u003csub\u003evv\u0026prime;\u003c/sub\u003e. η\u003csub\u003ecv\u003c/sub\u003e corresponds to the ELF bifurcation value between ELF core domain and valence domain, while the η\u003csub\u003evv\u0026prime;\u003c/sub\u003e stands for the ELF value at the bifurcation point between V(A,H) and V(B). The last point is indeed a second order critical point (3,\u0026ndash;1) linking the V(A, H) proton-donor domain to the V(B) proton-acceptor one [\u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e70\u003c/span\u003e, \u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e77\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn this work the partition of the molecular space in terms of nonoverlapping space-filling domains has been performed using the TopMod package. [\u003cspan citationid=\"CR80\" class=\"CitationRef\"\u003e80\u003c/span\u003e] We used the Multiwfn package [\u003cspan citationid=\"CR81\" class=\"CitationRef\"\u003e81\u003c/span\u003e, \u003cspan citationid=\"CR82\" class=\"CitationRef\"\u003e82\u003c/span\u003e] to evaluate both CVB and η\u003csub\u003evv\u0026prime;\u003c/sub\u003e quantities. As shown recently by Silvi et al. [\u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e77\u003c/span\u003e], the η\u003csub\u003evv\u0026prime;\u003c/sub\u003e quantity enables us to estimate the variance of the V(A\u0026ndash;H) domain population. Consequently, we use now the η\u003csub\u003evv\u0026prime;\u003c/sub\u003e quantity as a delocalization index.\u003c/p\u003e \u003cp\u003eThe Bond Evolution Theory (BET) [\u003cspan additionalcitationids=\"CR51 CR52 CR53 CR54 CR55 CR56\" citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e] based on the ELF topology of reorganization of covalent bonds and lone pairs along the reaction path allowed us to identify and describe most of the electronic events (such as bond breaking/forming and electronic density redistribution) which occur along the reaction path.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results and discussion","content":"\u003cp\u003eThis section is essentially focused on the study of double proton transfer in two model systems, FAD and TGD illustrated in Scheme \u003cspan refid=\"Sch1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, under the influence of an oriented external electric field (OEEF). The static and homogeneous electric field is actually oriented along the \u0026ldquo;reaction axis\u0026rdquo; [\u003cspan citationid=\"CR83\" class=\"CitationRef\"\u003e83\u003c/span\u003e], the direction in which the double proton transfer occurs (see Scheme \u003cspan refid=\"Sch1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). In this work, the F\u003csub\u003ez\u003c/sub\u003e is expressed in \u003cem\u003eatomic units\u003c/em\u003e, with the following conversion rule: 1 au\u0026thinsp;=\u0026thinsp;5.140 x 10\u003csup\u003e3\u003c/sup\u003e MV.cm\u003csup\u003e-1\u003c/sup\u003e = 5.14 x 10\u003csup\u003e11\u003c/sup\u003e V.m\u003csup\u003e-1\u003c/sup\u003e.\u003c/p\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.1. FAD under an OEEF\u003c/h2\u003e \u003cp\u003eTwo symmetrically equivalent structures (reactant and product) separated by a barrier estimated at 8.1 kcal/mol form the reaction path of the FAD case when no external electric field is applied [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e, \u003cspan citationid=\"CR84\" class=\"CitationRef\"\u003e84\u003c/span\u003e]. Along the reaction path, both proton transfers progress identically (concerted synchronous reaction) and the inter-oxygen distance gets its shortest value at the transition state. A previous careful theoretical study of the FAD isomerization under influence of an oriented external electric field (OEEF) [\u003cspan citationid=\"CR85\" class=\"CitationRef\"\u003e85\u003c/span\u003e] clearly showed that as the electric field intensity increases:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThe single imaginary vibrational frequency decreases in absolute value accompanied by a flattening of the potential energy curve around the transition state structure [\u003cspan citationid=\"CR86\" class=\"CitationRef\"\u003e86\u003c/span\u003e],\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe isomerization barrier height decreases,\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eOver of two proton-donors, the one opposite to OEEF is transferred first (using the convention and labels indicated in Scheme \u003cspan refid=\"Sch1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, H\u003csub\u003eb\u003c/sub\u003e is transferred first when F\u003csub\u003ez\u003c/sub\u003e \u0026gt; 0),\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe two inter-oxygen distances remain equal but increase at the transition state structure.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e3.1.1. Energetic, geometric and vibrational analysis\u003c/h2\u003e \u003cp\u003eIn order to take this study further, we have re-investigated at the ωB97X-D/6-311\u0026thinsp;+\u0026thinsp;+\u0026thinsp;G(2d,2p) level of theory the double proton transfer reaction of the formic acid dimer in varying the external electric field strength from F\u003csub\u003ez\u003c/sub\u003e= 0 to 200\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au. As a reminder, we emphasize that the electric field of strength \u0026le; 100\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au has been identified in the microenvironment of a DNA base-pair, in an enzyme active site [\u003cspan citationid=\"CR87\" class=\"CitationRef\"\u003e87\u003c/span\u003e, \u003cspan citationid=\"CR88\" class=\"CitationRef\"\u003e88\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eOur geometric and energetic results (see ESM-Table\u0026nbsp;1) are perfectly in line with the aforementioned trends: the acidity of the formic acid whit an O-H oriented in the direction of the electric field decreases, while that of the second formic acid increases. This corroborates with the geometric and energetic changes in the reactant: r1 decreases, r3 increases. The reactive dimer (at TS structure) loses its symmetry, R1 increases then R2 decreases (see ESM-Table\u0026nbsp;1). The potential energy curve, U(ξ), around TS flattens more and more and its width increases with the increase in F\u003csub\u003ez\u003c/sub\u003e [\u003cspan citationid=\"CR85\" class=\"CitationRef\"\u003e85\u003c/span\u003e, \u003cspan citationid=\"CR86\" class=\"CitationRef\"\u003e86\u003c/span\u003e, \u003cspan citationid=\"CR88\" class=\"CitationRef\"\u003e88\u003c/span\u003e]. At F\u003csub\u003ez\u003c/sub\u003e = 125\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au, this plateau extends from ξ = -0.486 to ξ = +0.486 amu\u003csup\u003e1/2\u003c/sup\u003e.Bohr, when U(ξ)\u0026thinsp;=\u0026thinsp;U(TS) \u0026plusmn; 0.04 kcal/mol. In full agreement with a recent work, the more the barrier decreases, the more non-synchronicity increases [\u003cspan citationid=\"CR89\" class=\"CitationRef\"\u003e89\u003c/span\u003e]. The accentuation of this phenomenon can lead to the appearance of a reaction intermediate (RI) at the TS structure. Our investigation, indeed, showed that the double proton transfer in the FAD is actually a one-step process for 0 \u0026le; F\u003csub\u003ez\u003c/sub\u003e \u0026le; 120\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au (one transition state structure), and becomes a stepwise reaction presenting a reaction intermediate (RI) when F\u003csub\u003ez\u003c/sub\u003e \u0026gt; 120\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe reactant\u0026ndash;RI isomerization barrier continuously decreases with increasing F\u003csub\u003ez\u003c/sub\u003e. Especially at F\u003csub\u003ez\u003c/sub\u003e = 200\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au (the strongest electric field studied in this paper), this barrier is close to zero so that the only observable species is the RI compound. Furthermore, it should be noted that the RI compound is no longer a formic acid dimer, but a pair of ions: formate (HCO\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e\u0026minus;\u003c/sup\u003e) in interaction with protonated formic acid, [HCOOH]H\u003csup\u003e+\u003c/sup\u003e (see ESM-Figure 1).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e3.1.2. The ELF topological analysis: existence domain of a roaming proton\u003c/h2\u003e \u003cp\u003eWe focus our topological analysis over regions where bound protons (hydride) transform into almost free protons (roaming between two electronegative atoms) [\u003cspan citationid=\"CR90\" class=\"CitationRef\"\u003e90\u003c/span\u003e]. From topological point of view, a roaming proton does not form a protonated basin with any neighboring atom, but it is curiously exchanging with two adjacent atoms via two attractors (topological critical points with (3, -3) signature). In the studied compounds, the roaming proton carries a tiny negative charge (\u0026asymp;\u0026thinsp;0.3 e) [\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e, \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e, \u003cspan citationid=\"CR91\" class=\"CitationRef\"\u003e91\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates the ELF representation of these two types of protons in the case of the formic acid dimer. In Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e-left (reactant structure for F\u003csub\u003ez\u003c/sub\u003e = 0), we can easily identify two protons forming two disynaptic basins which are engaged in the hydrogen bonding with the other formic acid. By contrast, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e-right (transition state structure for F\u003csub\u003ez\u003c/sub\u003e = 0) illustrates two roaming protons, each of which is sandwiched between two monosynaptic (lone-pair) basins coming from the two (neighboring) heavy atoms.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe topological analysis along the reaction path allowed us to identify the region where the proton wanders between two oxygens. This region is now called the \u0026ldquo;roaming proton region\u0026rdquo;, and referred to as \u0026ldquo;RPR\u0026rdquo;.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRoaming proton regions (RPR), delimited by ξ\u003csub\u003e1\u003c/sub\u003e and ξ\u003csub\u003e2\u003c/sub\u003e, for the DPT reaction of FAD under four selected electric fields. F\u003csub\u003ez\u003c/sub\u003e and ξ are in a.u. and amu\u003csup\u003e1/2\u003c/sup\u003e\u0026middot;Bohr units, respectively. For comparison, extension of the TS region as defined by the reaction force profile [\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e, \u003cspan citationid=\"CR89\" class=\"CitationRef\"\u003e89\u003c/span\u003e] is also indicated. Two protons are denoted as H\u003csub\u003ea\u003c/sub\u003e and H\u003csub\u003eb\u003c/sub\u003e (see Scheme \u003cspan refid=\"Sch1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"11\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eFz\u0026thinsp;=\u0026thinsp;0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e40\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e80\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e100\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e \u003cp\u003e120\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eξ\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eξ\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eξ\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eξ\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eξ\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eξ\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eξ\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003eξ\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eξ\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eξ\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eH\u003csub\u003eb\u003c/sub\u003e RPR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-0.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-1.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-0.16\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eH\u003csub\u003ea\u003c/sub\u003e RPR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1.27\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTS region\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-0.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-0.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-0.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.79\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFor the case of the free-field FAD dimer (concerted synchronous reaction), the two protons (denoted as H\u003csub\u003ea\u003c/sub\u003e and H\u003csub\u003eb\u003c/sub\u003e in see Scheme \u003cspan refid=\"Sch1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) both behave as roaming protons in the same region delimited by ξ\u003csub\u003e1\u003c/sub\u003e = -0.426 amu\u003csup\u003e1/2\u003c/sup\u003e\u0026middot;Bohr and ξ\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;+\u0026thinsp;0.426 amu\u003csup\u003e1/2\u003c/sup\u003e\u0026middot;Bohr, namely over a region of width of 0.852 amu\u003csup\u003e1/2\u003c/sup\u003e\u0026middot;Bohr. In other words, the overlap between two RPRs is total. This region obviously covers the \u0026ldquo;TS region\u0026rdquo; as defined by the reaction force profile [\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e, \u003cspan citationid=\"CR89\" class=\"CitationRef\"\u003e89\u003c/span\u003e], ranging from \u0026minus;\u0026thinsp;0.298 to +\u0026thinsp;0.298 amu\u003csup\u003e1/2\u003c/sup\u003e\u0026middot;Bohr. Under an electric field (F\u003csub\u003ez\u003c/sub\u003e \u0026gt; 0), the H\u003csub\u003eb\u003c/sub\u003e proton begins to behave like a roaming proton before the H\u003csub\u003ea\u003c/sub\u003e proton. For instance, we note that H\u003csub\u003eb\u003c/sub\u003e is a roaming proton from \u0026minus;\u0026thinsp;0.782 to +\u0026thinsp;0.112 amu\u003csup\u003e1/2\u003c/sup\u003e\u0026middot;Bohr, while H\u003csub\u003ea\u003c/sub\u003e is between \u0026minus;\u0026thinsp;0.112 and +\u0026thinsp;0.782 amu\u003csup\u003e1/2\u003c/sup\u003e\u0026middot;Bohr, when F\u003csub\u003ez\u003c/sub\u003e = 80\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au. It is interesting to underline the fact that the two RPRs although being offset, they share a subdomain ranging from \u0026minus;\u0026thinsp;0.112 to +\u0026thinsp;0.112 amu\u003csup\u003e1/2\u003c/sup\u003e\u0026middot;Bohr. In other words, the overlap between two RPRs is partial. The existence of shifted \u0026ldquo;roaming proton regions\u0026rdquo; along the reaction path stands for \u0026ldquo;nonsynchronous processes\u0026rdquo;, and the existence of a shared domain, with partial overlap, indicates that this is a \u0026ldquo;concerted reaction\u0026rdquo;. In other words, we have a \"concerted non-synchronous\" reaction for the ELF topological situations similar to the case of F\u003csub\u003ez\u003c/sub\u003e = 80\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au. Note that this shared domain only includes one structure, that of TS, for F\u003csub\u003ez\u003c/sub\u003e= 100\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au. (see Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e-a for 0\u0026thinsp;\u0026lt;\u0026thinsp;F\u003csub\u003ez\u003c/sub\u003e \u0026le; 100\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au, and Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e-b for F\u003csub\u003ez\u003c/sub\u003e = 100\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au)\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFrom F\u003csub\u003ez\u003c/sub\u003e \u0026gt; 100\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au, a remarkable change occurs in the topological image of the TS structure: the two protons stop being wandering and form two protonated basins with the two oxygens of the same formic acid partner. In other words, according to the ELF topology, at the TS structure, the formic acid dimer (under F\u003csub\u003ez\u003c/sub\u003e = 120\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au, for instance) is a zwitterionic compound: a formate anion in interaction with a protonated formic acid cation. This situation reminds the \u0026ldquo;hidden intermediate\u0026rdquo; suggested two decades ago by Cremer and Kraka [\u003cspan additionalcitationids=\"CR93 CR94 CR95\" citationid=\"CR92\" class=\"CitationRef\"\u003e92\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR96\" class=\"CitationRef\"\u003e96\u003c/span\u003e] and also by other researchers [\u003cspan additionalcitationids=\"CR98 CR99 CR100 CR101 CR102 CR103\" citationid=\"CR97\" class=\"CitationRef\"\u003e97\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR104\" class=\"CitationRef\"\u003e104\u003c/span\u003e] in the case of Diels-Alder reactions, in particular, and for other types of reactions. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e illustrates the reaction path and the three distinct domains for F\u003csub\u003ez\u003c/sub\u003e = 120\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au: H\u003csub\u003eb\u003c/sub\u003e RPR (from \u0026minus;\u0026thinsp;1.268 to -0.158 amu\u003csup\u003e1/2\u003c/sup\u003e\u0026middot;Bohr), H\u003csub\u003ea\u003c/sub\u003e RPR (from 0.158 to 1.268 amu\u003csup\u003e1/2\u003c/sup\u003e\u0026middot;Bohr), and zwitterion domain ranging from \u0026minus;\u0026thinsp;0.158 to 0.158 amu\u003csup\u003e1/2\u003c/sup\u003e\u0026middot;Bohr. The barrier height reduced to 3.5 kcal/mol, almost half of barrier in the absence of electric field (7.4 kcal/mol).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIt should be emphasized that the \u0026ldquo;hidden intermediate\u0026rdquo; is, in the case of FAD, confused with the structure of TS. In other words, it is a stationary point on the reaction path, without being a minimum, unlike the cases mentioned in the literature [\u003cspan citationid=\"CR96\" class=\"CitationRef\"\u003e96\u003c/span\u003e, \u003cspan citationid=\"CR98\" class=\"CitationRef\"\u003e98\u003c/span\u003e, \u003cspan citationid=\"CR99\" class=\"CitationRef\"\u003e99\u003c/span\u003e, \u003cspan citationid=\"CR104\" class=\"CitationRef\"\u003e104\u003c/span\u003e]. This property is due to the fact that the reactant and product are structurally equivalent in the FAD compound. It is therefore clear that the topological description according to the ELF function is a robust and powerful tool which allows us to unambiguously identify the \u0026ldquo;hidden intermediate region\u0026rdquo;, referred to as HIR. In the case of FAD under OEEF, this domain exists for 100\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au\u0026thinsp;\u0026lt;\u0026thinsp;F\u003csub\u003ez\u003c/sub\u003e \u0026lt; 130\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au. We emphasize that this HIR is the region that separates the two RPRs. Precisely because of the existence of this separating region, we can no longer consider this reaction as a concerted reaction from a topological point of view. This description fits perfectly with the \"two-stage one-step non-concerted mechanism\" concept suggested more than one decade ago by Domingo and coworkers [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. At this stage, the question that naturally arises is: where is located the hidden TS of this hidden intermediate? In fact, each of the structures located inside the H\u003csub\u003ea\u003c/sub\u003e RPR (or H\u003csub\u003eb\u003c/sub\u003e RPR) is indeed a candidate to be a \"hidden TS\" structure, from the point of view of the ELF topology: each structure is composed of an anion, a roaming proton and a neutral molecule waiting to receive the proton. This is precisely the topological structure of a \u0026ldquo;Hidden TS\u0026rdquo;.\u003c/p\u003e \u003cp\u003eA new important change appears in the reaction mechanism, when we increase the F\u003csub\u003ez\u003c/sub\u003e beyond 130\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au: the reaction is no longer a one-step reaction, but a two-step one with three minima (reactant, RI, and product) along the potential energy curve. Compared to the reactant, the relative stability of RI increases while the barrier of the reactant\u0026ndash;RI transformation decreases when F\u003csub\u003ez\u003c/sub\u003e increases (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). In particular at F\u003csub\u003ez\u003c/sub\u003e = 200\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au, only the RI becomes observable because the reactant\u0026ndash;RI barrier is actually close to zero. Consequently, the transformation of Reactant into RI (or RI to product) is a single proton transfer reaction. We therefore have one roaming proton in the transition state region.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.2. TGD under an OEEF\u003c/h2\u003e \u003cp\u003eThe 1,2,3-triazole\u0026ndash;guanidine dimer (TGD) is the second borderline case in our set for which the reactant is fully different from the product, both from a geometrical point of view (2H-1,2,3-triazole\u0026ndash;guanidine for reactant, and 1H-1,2,3-triazole\u0026ndash;guanidine for product) and from an energetic point of view (the product is by 2.7 kcal/mol less stable than the reactant, at the wB97XD/6311\u0026thinsp;+\u0026thinsp;+\u0026thinsp;G(2d,2p) level of theory). As shown in a previous theoretical work, [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e] unlike the FAD case studied in the previous paragraph, the calculated DPT reaction path for 1,2,3-triazole\u0026ndash;guanidine dimer exhibits a singularly wide shoulder on the reactant side (plateau-like) which results from the strong asynchronicity of the reaction. It has been shown that solvent effects and the electron withdrawing substituents attached to the triazole (cyano-substituent in the 4-position) turn this plateau into reactive intermediate [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e]. Here again, to reveal proton bonding evolution along the reaction path, we carried out the ELF topological analysis in order to identify the different domains of topological stability. Such an ELF cartoon is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe entire reaction path includes 258 structures which were calculated based on the IRC (ξ) which varies from \u0026minus;\u0026thinsp;7.897 to 3.290 amu\u003csup\u003e1/2\u003c/sup\u003e.Bohr passing through zero for the TS structure. The five regions of a topological stability (same topological structure) are identified along the IRC path (see Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). They are in the following order (from reactant to product):\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eReactant region is the first domain going from ξ = -7.89 to -4.34 amu\u003csup\u003e1/2\u003c/sup\u003e.Bohr containing 83 structures. These structures are characterized by two protonated disynaptic basins with nitrogen atoms of two molecules, V(H, N). Each of these basins participates in a hydrogen bonding (see Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e-a).\u003c/p\u003e \u003c/li\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe second region starting with ξ = -4.34 amu\u003csup\u003e1/2\u003c/sup\u003e.Bohr and ending with ξ = -3.04 amu\u003csup\u003e1/2\u003c/sup\u003e.Bohr is characterized, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e-b, by the presence of a roaming proton (H\u003csub\u003ea\u003c/sub\u003e of 2H-1,2,3-triazole) and a protonated disynaptic basin (H\u003csub\u003eb\u003c/sub\u003e of guanidine). The roaming proton is sandwiched between two monosynaptic basins V(N) coming from two molecules participating in the DPT reaction. This region is referred as to H\u003csub\u003ea\u003c/sub\u003e RPR in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and contains 30 structures on the IRC path.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe third region referred as to HIR (hidden intermediate region) is a region that contains 58 structures along the reaction path going from ξ = -3.04 to ξ = -0.52 amu\u003csup\u003e1/2\u003c/sup\u003e.Bohr. The ELF topological structure of this region is a zwitterionic form composed of protonated guanidine and deprotonated 1,2,3-triazole (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e-c).\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eIn the fourth region, the first hydrogen, H\u003csub\u003ea\u003c/sub\u003e, forms a protonated disynaptic basin with the guanidine\u0026rsquo;s nitrogen, and the second hydrogen, H\u003csub\u003eb\u003c/sub\u003e, behaves like a roaming proton. This region goes from \u0026minus;\u0026thinsp;0.52 to +\u0026thinsp;0.57 amu\u003csup\u003e1/2\u003c/sup\u003e.Bohr over 25 structures (see Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e-d).\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe last region corresponds to the product region where two hydrogens evolving in the DPT reaction are topologically localized on the two molecules forming two protonated disynaptic basins (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e-e). We count 62 structures over an interval of ξ which extends from +\u0026thinsp;0.57 to +\u0026thinsp;3.29 amu\u003csup\u003e1/2\u003c/sup\u003e.Bohr.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eIn contrast to the FAD compound, the \u0026ldquo;hidden intermediate\u0026rdquo; is not confused with the formal TS structure located at ξ\u0026thinsp;=\u0026thinsp;0 amu\u003csup\u003e1/2\u003c/sup\u003e.Bohr. In other words, all structures included in the HIR domain are representative of the hidden intermediate \u0026ldquo;hi\u0026rdquo; structure. For this \u0026ldquo;hi\u0026rdquo; structure, as proposed by Kraka and Cramer [\u003cspan citationid=\"CR95\" class=\"CitationRef\"\u003e95\u003c/span\u003e], we need to identify two hidden transition states \u0026ldquo;hts\u0026rdquo; corresponding to two hidden reactions \u0026ldquo;hr\u0026rdquo;: one connecting the \u0026ldquo;hi\u0026rdquo; to the reactant, and another one connecting the \u0026ldquo;hi\u0026rdquo; to the product. These two \u0026ldquo;hts\u0026rdquo; are represented respectively by the structures located within the two proton roaming regions.\u003c/p\u003e \u003cp\u003eFurthermore, the DPT reaction within the 1,2,3-triazole\u0026ndash;guanidine dimer cannot be considered as a concerted reaction, because of the presence of a wide region (HIR) which separates the two roaming proton regions. It is a two-stage reaction, but one-step process because of the presence of only one TS structure along the full IRC path. Consequently, the ELF topological description clearly shows that double proton transfer in the TGD reaction occurs via a \"two-stage one-step non-concerted mechanism\" [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR99\" class=\"CitationRef\"\u003e99\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eOther than solvent and/or substituent effects, an OEEF used as a \u0026ldquo;smart reagent\u0026rdquo; can reveal the \"hi\" or completely inhibit it in transforming the DPT reaction of TGD in a perfectly concerted synchronous reaction. Considering the convention presented in Scheme \u003cspan refid=\"Sch1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, we can anticipate the effect of an OEEF:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eIt forces the departure of H\u003csub\u003ea\u003c/sub\u003e (from triazole to guanidine) if it is negative. If so, it will enable us to optimize a structure on the potential energy surface for the \"hi\" and the corresponding \"hts\".\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eIt will allow us to move from a non-concerted mechanism to a reaction obeying a concerted mechanism, if F\u003csub\u003ez\u003c/sub\u003e \u0026gt; 0.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e \u003ch2\u003e3.2.1. F\u003csub\u003ez\u003c/sub\u003e \u0026gt; 0\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows three reaction path curves for three values ​​of F\u003csub\u003ez\u003c/sub\u003e: 0, 40\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e, and 70\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au. As we can see with the naked eye, the barrier height increases, and the width of the plateau-like part of the IRC path decreases when the OEEF intensity increases. The DPT reaction of TGD converges to a concerted synchronous reaction for F\u003csub\u003ez\u003c/sub\u003e \u0026asymp; 70x10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au. Imaginary vibrational frequency at the TS structure (F\u003csub\u003ez\u003c/sub\u003e = 70\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au) is found to be 1157\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(i\\)\u003c/span\u003e\u003c/span\u003e cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFurthermore, an analysis of the ELF topology along the reaction path makes it possible to identify the nature of the reaction mechanisms for different values ​​of F\u003csub\u003ez\u003c/sub\u003e. A systematic study of the ELF topology on numerous structures on each IRC curve revealed that:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThe width of the hidden intermediate region shrinks like a skin of sorrow as F\u003csub\u003ez\u003c/sub\u003e increases incrementally from 0 to 50\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au. For comparison, it reduces from 3 to 0.72, then to 0 amu\u003csup\u003e1/2\u003c/sup\u003e.Bohr, when F\u003csub\u003ez\u003c/sub\u003e goes from 0 to 30\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e, and then to 50\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au. Particularly at F\u003csub\u003ez\u003c/sub\u003e = 50\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au, we no longer have a zone corresponding to the HIR along the reaction path. Consequently, we consider that the double proton transfer reaction takes place according to the \u0026ldquo;two-stage one-step non-concerted mechanism\u0026rdquo; for the interval 0 \u0026le; F\u003csub\u003ez\u003c/sub\u003e \u0026lt; 50\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eAt F\u003csub\u003ez\u003c/sub\u003e = 50\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au, the two corresponding roaming domains of H\u003csub\u003ea\u003c/sub\u003e and H\u003csub\u003eb\u003c/sub\u003e are (disjointed) side-by-side. This is precisely the beginning of a \u0026ldquo;synchronous concerted mechanism\u0026rdquo;. If the width of the overlap of these two roaming domains is zero at F\u003csub\u003ez\u003c/sub\u003e = 50\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au, it reaches the value of 0.23 amu\u003csup\u003e1/2\u003c/sup\u003e.Bohr when F\u003csub\u003ez\u003c/sub\u003e = 60\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au. More precisely, the roaming H\u003csub\u003ea\u003c/sub\u003e region extends from \u0026minus;\u0026thinsp;0.936 to 0 amu\u003csup\u003e1/2\u003c/sup\u003e.Bohr, while that of H\u003csub\u003eb\u003c/sub\u003e ranges from \u0026minus;\u0026thinsp;0.233 to 0.655 amu\u003csup\u003e1/2\u003c/sup\u003e.Bohr (see Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e).\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eAs shown in a previous work [\u003cspan citationid=\"CR91\" class=\"CitationRef\"\u003e91\u003c/span\u003e], the ELF topological descriptor δη\u0026thinsp;=\u0026thinsp;η\u003csub\u003e1(vv')\u003c/sub\u003e \u0026ndash; η\u003csub\u003e2(vv')\u003c/sub\u003e, related to the core-valence bifurcation index mentioned in section \u0026ldquo;2. Computational details\u0026rdquo;, is a good index to evaluate the interaction force of the two hydrogen bonds at the reactant structure of a DPT reaction. We found that δη is very close to zero (δη\u0026thinsp;=\u0026thinsp;0.002) when F\u003csub\u003ez\u003c/sub\u003e = 75\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au. In other words, we can conclude that the DPT reaction in TGD takes place according to the \u0026ldquo;concerted synchronous mechanism\u0026rdquo;, when F\u003csub\u003ez\u003c/sub\u003e = 75\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e au. Consequently, the overlap between two roaming H\u003csub\u003ea\u003c/sub\u003e and H\u003csub\u003eb\u003c/sub\u003e domains is almost total.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e \u003ch2\u003e3.2.2. F\u003csub\u003ez\u003c/sub\u003e \u0026lt; 0\u003c/h2\u003e \u003cp\u003eIn contrast, the DPT reaction of TGD under a negative OEEF quickly converges to a stepwise reaction: one optimized minimum for an intermediate, and two transition state structures connecting to the reactant and product. In Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e are gathered some energetic properties of some stationary structures versus the negative F\u003csub\u003ez\u003c/sub\u003e strength. Note that the relative energies (ΔE) are calculated with respect to the reactant total energy for each F\u003csub\u003ez\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eEnergetic properties (in kcal/mol) of TGD under four selected negative OEEF.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF\u003csub\u003ez\u003c/sub\u003e(au)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eΔE(R)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eΔE (TS1)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eΔE(RI)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eΔE(TS2)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eΔE(P)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e-20 x10\u003csup\u003e-4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e-40 x10\u003csup\u003e-4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e5.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e-60 x10\u003csup\u003e-4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e-80 x10\u003csup\u003e-4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e-3.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAs expected, the barrier heights, ΔE (TS1) and ΔE (TS2), decreases when the OEEF strength decreases. For F\u003csub\u003ez\u003c/sub\u003e = -20 x10\u003csup\u003e-4\u003c/sup\u003e au, the reaction intermediate (RI) although well identified on the reaction path, cannot be experimentally observed, because a high barrier. On the other hand, energetic conditions in the case of F\u003csub\u003ez\u003c/sub\u003e = -80 x10\u003csup\u003e-4\u003c/sup\u003e au allow us to confirm that RI is indeed the most stable compound compared to the reactant (R) and product (P). Furthermore, the required energy for going from R to RI is relatively low and therefore surmountable.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"4. Conclusions","content":"\u003cp\u003eThe main results of this work are summarized as follows:\u003c/p\u003e\n\u003col\u003e\n \u003cli\u003e\n \u003cp\u003eAny DPT reaction can occur by one of the four reaction mechanisms: 1) concerted-synchronous, 2) concerted-asynchronous, 3) two-stage one-step non-concerted, and 4) stepwise mechanism. The first three can be grouped into the so-called \u0026quot;one-step mechanism\u0026rdquo; which is characterized by the presence of a single transition state structure throughout the reaction path connecting the reactant to the product. The presence of two TS structures along the reaction path following the reactant - TS1 - Intermediate - TS2 \u0026ndash; Product sequence is characteristic of a stepwise mechanism.\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eWhatever the mechanism of a DPT reaction in the absence of an OEEF, it has been shown that by applying an OEEF we can modify the mechanism and thus modulate the DPT reaction.\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eThe ELF topological analysis of the electronic structures of stationary points along the IRC path has been shown to be a powerful tool for rationalizing the motion of two protons during a DPT reaction. It has been seen that a proton engaged in the proton transfer reaction is either localized forming then a protonated disynaptic basin with a heavy atom, or delocalized (roaming proton) carrying then a tiny negative charge (\u0026asymp;\u0026thinsp;0.3 e) and sandwiched between two monosynaptic basins of the two heavy atoms. We can therefore determine the region in which the proton behaves as a roaming proton (referred to as RPR), and the region where the proton is localized (referred to as HIR).\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eIn a DPT reaction, involving two protons, the three mechanisms of the \u0026quot;one-step\u0026quot; family can be clearly identified according to the following rules:\u003c/p\u003e\n \u003c/li\u003e\n\u003c/ol\u003e\n\u003cdiv\u003e\n \u003cp\u003eRule 1: When two RPRs (relative to the two protons) perfectly overlap, then the DPT reaction takes place following a \u0026ldquo;concerted-synchronous mechanism\u0026rdquo;.\u003c/p\u003e\n \u003cp\u003eRule 2: When two RPRs partially overlap, then the DPT reaction takes place following a \u0026ldquo;concerted-asynchronous mechanism\u0026rdquo;.\u003c/p\u003e\n \u003cp\u003eRule 3: When two RPRs are fully disjointed by the presence of an HIR, then the DPT reaction takes place following a \u0026ldquo;two-stage one-step non-concerted mechanism\u0026rdquo;.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAuthor Contributions\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eVanessa Labet\u003c/em\u003e: Electronic and ELF analysis, and writing the original draft\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eAntoine Geoffroy-Neveux\u003c/em\u003e: Optimization calculations, Electronic and ELF analysis\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eMohammad Esma\u0026iuml;l Alikhani\u003c/em\u003e: Optimization calculations, Electronic and ELF analysis, and writing the original draft\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflicts of interest\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThere are no conflicts to declare.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eThe authors declare that no funds, grants, or other support were received during the preparation of this manuscript.\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eElectronic Supplementary Information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAn ESM (electronic supplementary material) file is available.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eDewar MJS (1984) Multibond reactions cannot normally be synchronous. J Am Chem Soc 106:209\u0026ndash;219. https://doi.org/10.1021/ja00313a042\u003c/li\u003e\n\u003cli\u003eJencks WP (1981) Ingold Lecture. How does a reaction choose its mechanism? Chem Soc Rev 10:345\u0026ndash;375. https://doi.org/10.1039/CS9811000345\u003c/li\u003e\n\u003cli\u003eWilliams A (1994) The diagnosis of concerted organic mechanisms. Chem Soc Rev 23:93\u0026ndash;100. https://doi.org/10.1039/CS9942300093\u003c/li\u003e\n\u003cli\u003eOrtega DE, Ormaz\u0026aacute;bal-Toledo R, Contreras R, Matute RA (2019) Theoretical insights into the E1cB/E2 mechanistic dichotomy of elimination reactions. Org Biomol Chem 17:9874\u0026ndash;9882. https://doi.org/10.1039/C9OB02004G\u003c/li\u003e\n\u003cli\u003eDuarte F, Gronert S, Kamerlin SCL (2014) Concerted or Stepwise: How Much Do Free-Energy Landscapes Tell Us about the Mechanisms of Elimination Reactions? J Org Chem 79:1280\u0026ndash;1288. https://doi.org/10.1021/jo402702m\u003c/li\u003e\n\u003cli\u003eAlunni S, De Angelis F, Ottavi L, et al (2005) Evidence of a Borderline Region between E1cb and E2 Elimination Reaction Mechanisms: A Combined Experimental and Theoretical Study of Systems Activated by the Pyridine Ring. J Am Chem Soc 127:15151\u0026ndash;15160. https://doi.org/10.1021/ja0539138\u003c/li\u003e\n\u003cli\u003eMosconi E, De Angelis F, Belpassi L, et al (2009) Merging of E2 and E1cb Reaction Mechanisms: A Combined Theoretical and Experimental Study. Eur J Org Chem 2009:5501\u0026ndash;5504. https://doi.org/10.1002/ejoc.200900906\u003c/li\u003e\n\u003cli\u003eLinder M, Brinck T (2012) Stepwise Diels\u0026ndash;Alder: More than Just an Oddity? A Computational Mechanistic Study. J Org Chem 77:6563\u0026ndash;6573. https://doi.org/10.1021/jo301176t\u003c/li\u003e\n\u003cli\u003eHouk KN, Liu F, Yang Z, Seeman JI (2021) Evolution of the Diels\u0026ndash;Alder Reaction Mechanism since the 1930s: Woodward, Houk with Woodward, and the Influence of Computational Chemistry on Understanding Cycloadditions. Angew Chem Int Ed 60:12660\u0026ndash;12681. https://doi.org/10.1002/anie.202001654\u003c/li\u003e\n\u003cli\u003eAktah D, Passerone D, Parrinello M (2004) Insights into the Electronic Dynamics in Chemical Reactions. J Phys Chem A 108:848\u0026ndash;854. https://doi.org/10.1021/jp036572y\u003c/li\u003e\n\u003cli\u003eDe Souza MAF, Ventura E, Do Monte SA, et al (2016) Revisiting the concept of the (a)synchronicity of diels‐alder reactions based on the dynamics of quasiclassical trajectories. J Comput Chem 37:701\u0026ndash;711. https://doi.org/10.1002/jcc.24245\u003c/li\u003e\n\u003cli\u003eAccardi A, Barth I, K\u0026uuml;hn O, Manz J (2010) From Synchronous to Sequential Double Proton Transfer: Quantum Dynamics Simulations for the Model Porphine. J Phys Chem A 114:11252\u0026ndash;11262. https://doi.org/10.1021/jp103435d\u003c/li\u003e\n\u003cli\u003ePandey P, Naik S, Keshavamurthy S (2022) Influence of low frequency modes on dynamical concertedness in double proton transfer dynamics. Communications in Nonlinear Science and Numerical Simulation 109:106326. https://doi.org/10.1016/j.cnsns.2022.106326\u003c/li\u003e\n\u003cli\u003eSchweiger S, Hartke B, Rauhut G (2005) Double proton transfer reactions at the transition from a concerted to a stepwise mechanism: a comparative ab initio study. Phys Chem Chem Phys 7:493. https://doi.org/10.1039/b415528a\u003c/li\u003e\n\u003cli\u003eRohrbach S, Murphy JA, Tuttle T (2020) Computational Study on the Boundary Between the Concerted and Stepwise Mechanism of Bimolecular S \u003csub\u003eN\u003c/sub\u003e Ar Reactions. J Am Chem Soc 142:14871\u0026ndash;14876. https://doi.org/10.1021/jacs.0c01975\u003c/li\u003e\n\u003cli\u003eGoldstein E, Beno B, Houk KN (1996) Density Functional Theory Prediction of the Relative Energies and Isotope Effects for the Concerted and Stepwise Mechanisms of the Diels\u0026minus;Alder Reaction of Butadiene and Ethylene. J Am Chem Soc 118:6036\u0026ndash;6043. https://doi.org/10.1021/ja9601494\u003c/li\u003e\n\u003cli\u003eSakai S (2000) Theoretical Analysis of Concerted and Stepwise Mechanisms of Diels\u0026minus;Alder Reaction between Butadiene and Ethylene. J Phys Chem A 104:922\u0026ndash;927. https://doi.org/10.1021/jp9926894\u003c/li\u003e\n\u003cli\u003eJencks WP (1972) General acid-base catalysis of complex reactions in water. Chem Rev 72:705\u0026ndash;718. https://doi.org/10.1021/cr60280a004\u003c/li\u003e\n\u003cli\u003eO\u0026rsquo;Ferrall RAM (1970) Relationships between E2 and E1cB mechanisms of \u0026beta;-elimination. J Chem Soc B 0:274\u0026ndash;277. https://doi.org/10.1039/J29700000274\u003c/li\u003e\n\u003cli\u003eSmedarchina Z, Siebrand W, Fern\u0026aacute;ndez-Ramos A (2007) Correlated double-proton transfer. I. Theory. The Journal of Chemical Physics 127:174513. https://doi.org/10.1063/1.2785186\u003c/li\u003e\n\u003cli\u003eVermeeren P, Hamlin TA, Bickelhaupt FM (2021) Origin of asynchronicity in Diels\u0026ndash;Alder reactions. Phys Chem Chem Phys 23:20095\u0026ndash;20106. https://doi.org/10.1039/D1CP02456F\u003c/li\u003e\n\u003cli\u003eDomingo LR, P\u0026eacute;rez P, S\u0026aacute;ez JA (2012) Origin of the synchronicity in bond formation in polar Diels\u0026ndash;Alder reactions: an ELF analysis of the reaction between cyclopentadiene and tetracyanoethylene. Org Biomol Chem 10:3841. https://doi.org/10.1039/c2ob25152c\u003c/li\u003e\n\u003cli\u003eDomingo LR, Aurell MJ, P\u0026eacute;rez P, S\u0026aacute;ez JA (2012) Understanding the origin of the asynchronicity in bond-formation in polar cycloaddition reactions. A DFT study of the 1,3-dipolar cycloaddition reaction of carbonyl ylides with 1,2-benzoquinones. RSC Adv 2:1334\u0026ndash;1342. https://doi.org/10.1039/C1RA00717C\u003c/li\u003e\n\u003cli\u003eJencks WP (1985) A primer for the Bema Hapothle. An empirical approach to the characterization of changing transition-state structures. Chem Rev 85:511\u0026ndash;527. https://doi.org/10.1021/cr00070a001\u003c/li\u003e\n\u003cli\u003eGoldstein MJ, Thayer GL (1965) The Mechanism of a Diels-Alder Reaction. II. The Structure of the Transition State \u003csup\u003e1\u003c/sup\u003e. J Am Chem Soc 87:1933\u0026ndash;1941. https://doi.org/10.1021/ja01087a017\u003c/li\u003e\n\u003cli\u003eDewar MJS, Olivella Santiago, Stewart JJP (1986) Mechanism of the Diels-Alder reaction: reactions of butadiene with ethylene and cyanoethylenes. J Am Chem Soc 108:5771\u0026ndash;5779. https://doi.org/10.1021/ja00279a018\u003c/li\u003e\n\u003cli\u003eDomingo LR, Sa\u0026eacute;z JA, Zaragoz\u0026aacute; RJ, Arn\u0026oacute; M (2008) Understanding the Participation of Quadricyclane as Nucleophile in Polar [2\u0026sigma; + 2\u0026sigma; + 2\u0026pi;] Cycloadditions toward Electrophilic \u0026pi; Molecules. J Org Chem 73:8791\u0026ndash;8799. https://doi.org/10.1021/jo801575g\u003c/li\u003e\n\u003cli\u003eHouk KN, Gonzalez J, Li Y (1995) Pericyclic Reaction Transition States: Passions and Punctilios, 1935-1995. Acc Chem Res 28:81\u0026ndash;90. https://doi.org/10.1021/ar00050a004\u003c/li\u003e\n\u003cli\u003eBarrales-Mart\u0026iacute;nez C, Jaque P (2022) A deeper analysis of the role of synchronicity on the Bell\u0026ndash;Evans\u0026ndash;Polanyi plot in multibond chemical reactions: a path-dependent reaction force constant. Phys Chem Chem Phys 24:14772\u0026ndash;14779. https://doi.org/10.1039/D2CP01460B\u003c/li\u003e\n\u003cli\u003eGiraldo C, G\u0026oacute;mez S, Weinhold F, Restrepo A (2016) Insight into the Mechanism of the Michael Reaction. ChemPhysChem 17:2022\u0026ndash;2034. https://doi.org/10.1002/cphc.201600166\u003c/li\u003e\n\u003cli\u003eBernasconi CF (1985) The principle of imperfect synchronization. Tetrahedron 41:3219\u0026ndash;3234. https://doi.org/10.1016/S0040-4020(01)96673-6\u003c/li\u003e\n\u003cli\u003eCostentin C, Sav\u0026eacute;ant J-M (2020) Hydrogen and proton exchange at carbon. Imbalanced transition state and mechanism crossover. Chemical Science 11:1006\u0026ndash;1010. https://doi.org/10.1039/C9SC05147C\u003c/li\u003e\n\u003cli\u003eDarcy JW, Kolmar SS, Mayer JM (2019) Transition State Asymmetry in C\u0026ndash;H Bond Cleavage by Proton-Coupled Electron Transfer. J Am Chem Soc 141:10777\u0026ndash;10787. https://doi.org/10.1021/jacs.9b04303\u003c/li\u003e\n\u003cli\u003eKraka E, Cremer D (2010) Computational Analysis of the Mechanism of Chemical Reactions in Terms of Reaction Phases: Hidden Intermediates and Hidden Transition States. Acc Chem Res 43:591\u0026ndash;601. https://doi.org/10.1021/ar900013p\u003c/li\u003e\n\u003cli\u003eSakai S, Okumura T (2004) Theoretical studies on the substituent effects for concerted and stepwise mechanisms of the Diels\u0026ndash;Alder reaction between butadiene and ethylene. Journal of Molecular Structure: THEOCHEM 685:89\u0026ndash;95. https://doi.org/10.1016/j.theochem.2004.06.052\u003c/li\u003e\n\u003cli\u003eYepes D, Mart\u0026iacute;nez-Araya JI, Jaque P (2018) Solvent effect on the degree of (a)synchronicity in polar Diels-Alder reactions from the perspective of the reaction force constant analysis. J Mol Model 24:33. https://doi.org/10.1007/s00894-017-3563-x\u003c/li\u003e\n\u003cli\u003eShaik S, Ramanan R, Danovitch D, Mandal D (2018) Structure and reactivity/selectivity control by oriented-external electric fields. Chem Soc Rev 47:5125\u0026ndash;5145. https://doi.org/10.1039/C8CS00354H\u003c/li\u003e\n\u003cli\u003eSchweiger S, Rauhut G (2003) Plateau Reactions: Double Proton-Transfer Processes with Structureless Transition States. J Phys Chem A 107:9668\u0026ndash;9678. https://doi.org/10.1021/jp0350060\u003c/li\u003e\n\u003cli\u003eGeoffroy-Neveux A, Labet V, Alikhani ME (2022) Influence of an Oriented External Electric Field on the Mechanism of Double Proton Transfer between Pyrazole and Guanidine: from an Asynchronous Plateau Transition State to a Synchronous or Stepwise Mechanism. J Phys Chem A 126:3057\u0026ndash;3071. https://doi.org/10.1021/acs.jpca.1c10553\u003c/li\u003e\n\u003cli\u003eIvanov SD, Grant IM, Marx D (2015) Quantum free energy landscapes from \u003cem\u003eab initio\u003c/em\u003e path integral metadynamics: Double proton transfer in the formic acid dimer is concerted but not correlated. The Journal of Chemical Physics 143:124304. https://doi.org/10.1063/1.4931052\u003c/li\u003e\n\u003cli\u003eFarf\u0026aacute;n P, Echeverri A, Diaz E, et al (2017) Dimers of formic acid: Structures, stability, and double proton transfer. The Journal of Chemical Physics 147:044312. https://doi.org/10.1063/1.4985880\u003c/li\u003e\n\u003cli\u003eRichardson JO (2017) Full- and reduced-dimensionality instanton calculations of the tunnelling splitting in the formic acid dimer. Phys Chem Chem Phys 19:966\u0026ndash;970. https://doi.org/10.1039/C6CP07808G\u003c/li\u003e\n\u003cli\u003eLiu H, Cao J, Bian W (2019) Double Proton Transfer in the Dimer of Formic Acid: An Efficient Quantum Mechanical Scheme. Front Chem 7:676. https://doi.org/10.3389/fchem.2019.00676\u003c/li\u003e\n\u003cli\u003eNejad A, Suhm MA (2020) Concerted Pair Motion Due to Double Hydrogen Bonding: The Formic Acid Dimer Case. J Indian Inst Sci 100:5\u0026ndash;19. https://doi.org/10.1007/s41745-019-00137-5\u003c/li\u003e\n\u003cli\u003eRauhut G (2003) Modulation of reaction barriers by generating reactive intermediates: double proton transfer reactions. Phys Chem Chem Phys 5:791\u0026ndash;800. https://doi.org/10.1039/b208960b\u003c/li\u003e\n\u003cli\u003eShaik S, Mandal D, Ramanan R (2016) Oriented electric fields as future smart reagents in chemistry. Nature Chemistry 8:1091\u0026ndash;1098. https://doi.org/10.1038/nchem.2651\u003c/li\u003e\n\u003cli\u003eCer\u0026oacute;n-Carrasco JP, Jacquemin D (2013) Electric-field induced mutation of DNA: a theoretical investigation of the GC base pair. Phys Chem Chem Phys 15:4548. https://doi.org/10.1039/c2cp44066k\u003c/li\u003e\n\u003cli\u003eCer\u0026oacute;n-Carrasco JP, Jacquemin D (2013) Electric field induced DNA damage: an open door for selective mutations. Chem Commun 49:7578. https://doi.org/10.1039/c3cc42593b\u003c/li\u003e\n\u003cli\u003eToro-Labb\u0026eacute; A (1999) Characterization of Chemical Reactions from the Profiles of Energy, Chemical Potential, and Hardness. J Phys Chem A 103:4398\u0026ndash;4403. https://doi.org/10.1021/jp984187g\u003c/li\u003e\n\u003cli\u003eBerski S, Andr\u0026eacute;s J, Silvi B, Domingo LR (2003) The Joint Use of Catastrophe Theory and Electron Localization Function to Characterize Molecular Mechanisms. A Density Functional Study of the Diels\u0026minus;Alder Reaction between Ethylene and 1,3-Butadiene. J Phys Chem A 107:6014\u0026ndash;6024. https://doi.org/10.1021/jp030272z\u003c/li\u003e\n\u003cli\u003ePolo V, Andres J, Castillo R, et al (2004) Understanding the Molecular Mechanism of the 1,3‐Dipolar Cycloaddition between Fulminic Acid and Acetylene in Terms of the Electron Localization Function and Catastrophe Theory. Chemistry A European J 10:5165\u0026ndash;5172. https://doi.org/10.1002/chem.200400161\u003c/li\u003e\n\u003cli\u003eKrokidis X, Silvi B, Alikhani ME (1998) Topological characterization of the isomerization mechanisms in XNO (X=H, Cl). Chemical Physics Letters 292:35\u0026ndash;45. https://doi.org/10.1016/S0009-2614(98)00650-2\u003c/li\u003e\n\u003cli\u003eSantos JC, Andres J, Aizman A, et al (2005) A Theoretical Study on the Reaction Mechanism for the Bergman Cyclization from the Perspective of the Electron Localization Function and Catastrophe Theory. J Phys Chem A 109:3687\u0026ndash;3693. https://doi.org/10.1021/jp0441947\u003c/li\u003e\n\u003cli\u003eKrokidis X, Vuilleumier R, Borgis D, Silvi B (1999) A topological analysis of the proton transfer in H \u003csub\u003e5\u003c/sub\u003e O \u003csup\u003e+\u003c/sup\u003e \u003csub\u003e2\u003c/sub\u003e. Molecular Physics 96:265\u0026ndash;273. https://doi.org/10.1080/00268979909482959\u003c/li\u003e\n\u003cli\u003eĆmikiewicz A, Gordon AJ, Berski S (2018) Characterisation of the reaction mechanism between ammonia and formaldehyde from the topological analysis of ELF and catastrophe theory perspective. Struct Chem 29:243\u0026ndash;255. https://doi.org/10.1007/s11224-017-1024-x\u003c/li\u003e\n\u003cli\u003eAndr\u0026eacute;s J, Gonz\u0026aacute;lez-Navarrete P, Safont VS, Silvi B (2017) Curly arrows, electron flow, and reaction mechanisms from the perspective of the bonding evolution theory. Phys Chem Chem Phys 19:29031\u0026ndash;29046. https://doi.org/10.1039/C7CP06108K\u003c/li\u003e\n\u003cli\u003eKrokidis X, Goncalves V, Savin A, Silvi B (1998) How Malonaldehyde Bonds Change during Proton Transfer. J Phys Chem A 102:5065\u0026ndash;5073. https://doi.org/10.1021/jp9734282\u003c/li\u003e\n\u003cli\u003eFrisch MJ, Trucks GW, Schlegel HB, et al (2013) Gaussian\u0026tilde;09 Revision D.01\u003c/li\u003e\n\u003cli\u003eK\u0026ouml;rzd\u0026ouml;rfer T, Sears JS, Sutton C, Br\u0026eacute;das J-L (2011) Long-range corrected hybrid functionals for \u0026pi;-conjugated systems: Dependence of the range-separation parameter on conjugation length. The Journal of Chemical Physics 135:204107. https://doi.org/10.1063/1.3663856\u003c/li\u003e\n\u003cli\u003eChai J-D, Head-Gordon M (2008) Systematic optimization of long-range corrected hybrid density functionals. The Journal of Chemical Physics 128:084106. https://doi.org/10.1063/1.2834918\u003c/li\u003e\n\u003cli\u003eMcLean AD, Chandler GS (1980) Contracted Gaussian basis sets for molecular calculations. I. Second row atoms, \u003cem\u003eZ\u003c/em\u003e =11\u0026ndash;18. The Journal of Chemical Physics 72:5639\u0026ndash;5648. https://doi.org/10.1063/1.438980\u003c/li\u003e\n\u003cli\u003eKrishnan R, Binkley JS, Seeger R, Pople JA (1980) Self-consistent molecular orbital methods. XX. A basis set for correlated wave functions. The Journal of Chemical Physics 72:650\u0026ndash;654. https://doi.org/10.1063/1.438955\u003c/li\u003e\n\u003cli\u003eFukui K (1970) Formulation of the reaction coordinate. J Phys Chem 74:4161\u0026ndash;4163. https://doi.org/10.1021/j100717a029\u003c/li\u003e\n\u003cli\u003ePage M, McIver JW (1988) On evaluating the reaction path Hamiltonian. The Journal of Chemical Physics 88:922\u0026ndash;935. https://doi.org/10.1063/1.454172\u003c/li\u003e\n\u003cli\u003ePage M, Doubleday C, McIver JW (1990) Following steepest descent reaction paths. The use of higher energy derivatives with \u003cem\u003ea\u003c/em\u003e \u003cem\u003eb\u003c/em\u003e \u003cem\u003ei\u003c/em\u003e \u003cem\u003en\u003c/em\u003e \u003cem\u003ei\u003c/em\u003e \u003cem\u003et\u003c/em\u003e \u003cem\u003ei\u003c/em\u003e \u003cem\u003eo\u003c/em\u003e electronic structure methods. The Journal of Chemical Physics 93:5634\u0026ndash;5642. https://doi.org/10.1063/1.459634\u003c/li\u003e\n\u003cli\u003eBecke AD, Edgecombe KE (1990) A simple measure of electron localization in atomic and molecular systems. The Journal of Chemical Physics 92:5397\u0026ndash;5403. https://doi.org/10.1063/1.458517\u003c/li\u003e\n\u003cli\u003eSilvi B, Savin A (1994) Classification of chemical bonds based on topological analysis of electron localization functions. Nature 371:683\u0026ndash;686. https://doi.org/10.1038/371683a0\u003c/li\u003e\n\u003cli\u003eSilvi B, Fourr\u0026eacute; I, Alikhani M (2005) The Topological Analysis of the Electron Localization Function. A Key for a Position Space Representation of Chemical Bonds. Monatshefte f\u0026uuml;r Chemie 136:855\u0026ndash;879. https://doi.org/10.1007/s00706-005-0297-8\u003c/li\u003e\n\u003cli\u003eGrin Y, Savin A, Silvi B (2014) The ELF Perspective of chemical bonding. In: Frenking G, Shaik S (eds) The Chemical Bond, 1st ed. Wiley, pp 345\u0026ndash;382\u003c/li\u003e\n\u003cli\u003eAlikhani ME, Fuster F, Silvi B (2005) What Can Tell the Topological Analysis of ELF on Hydrogen Bonding? Struct Chem 16:203\u0026ndash;210. https://doi.org/10.1007/s11224-005-4451-z\u003c/li\u003e\n\u003cli\u003eZins E-L, Silvi B, Alikhani ME (2015) Activation of C\u0026ndash;H and B\u0026ndash;H bonds through agostic bonding: an ELF/QTAIM insight. Phys Chem Chem Phys 17:9258\u0026ndash;9281. https://doi.org/10.1039/C4CP05728G\u003c/li\u003e\n\u003cli\u003eAlikhani ME (2013) On the chemical bonding features in boron containing compounds: a combined QTAIM/ELF topological analysis. Phys Chem Chem Phys 15:12602. https://doi.org/10.1039/c3cp50396h\u003c/li\u003e\n\u003cli\u003eMichelini MDC, Russo N, Alikhani ME, Silvi B (2004) Energetic and topological analysis of the reaction of Mo and Mo₂ with NH₃, C₂H₂, and C₂H₄ molecules. Journal of Computational Chemistry 25:1647\u0026ndash;1655. https://doi.org/10.1002/jcc.20087\u003c/li\u003e\n\u003cli\u003eNoury S, Silvi B, Gillespie RJ (2002) Chemical Bonding in Hypervalent Molecules: Is the Octet Rule Relevant? Inorg Chem 41:2164\u0026ndash;2172. https://doi.org/10.1021/ic011003v\u003c/li\u003e\n\u003cli\u003eBerski S, Gordon AJ, Latajka Z (2014) Electron Localization Function Study on the Chemical Bonding in a Real Space for Tetrahedrane, Cubane, Adamantane, and Dodecahedrane and Their Perfluorinated Derivatives and Radical Anions. J Phys Chem A 118:4147\u0026ndash;4156. https://doi.org/10.1021/jp501838g\u003c/li\u003e\n\u003cli\u003eFuster F, Silvi B (2000) Determination of protonation sites in bases from topological rules. Chemical Physics 252:279\u0026ndash;287. https://doi.org/10.1016/S0301-0104(99)00320-1\u003c/li\u003e\n\u003cli\u003eSilvi B, Ratajczak H (2016) Hydrogen bonding and delocalization in the ELF analysis approach. Phys Chem Chem Phys 18:27442\u0026ndash;27449. https://doi.org/10.1039/C6CP05400E\u003c/li\u003e\n\u003cli\u003eEsmaı̈l Alikhani M, Silvi B (2004) A topological analysis of the proton transfer in the HF\u0026ndash; and HCl\u0026ndash;(OH)\u0026minus; interactions. Journal of Molecular Structure 706:3\u0026ndash;6. https://doi.org/10.1016/j.molstruc.2004.02.052\u003c/li\u003e\n\u003cli\u003eFuster F, Silvi B (2000) Does the topological approach characterize the hydrogen bond? Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta) 104:13\u0026ndash;21. https://doi.org/10.1007/s002149900100\u003c/li\u003e\n\u003cli\u003eNoury S, Krokidis X, Fuster F, Silvi B (1999) Computational tools for the electron localization function topological analysis. Computers \u0026amp; Chemistry 23:597\u0026ndash;604. https://doi.org/10.1016/S0097-8485(99)00039-X\u003c/li\u003e\n\u003cli\u003eLu T, Chen F (2012) Multiwfn: A multifunctional wavefunction analyzer. J Comput Chem 33:580\u0026ndash;592. https://doi.org/10.1002/jcc.22885\u003c/li\u003e\n\u003cli\u003eTian L, Fei-Wu C, 北京科技大学化学与生物工程学院, 北京 100083,School of Chemical and Biological Engineering, University of Science and Technology Beijing, Beijing 100083, P. R. China (2011) Meaning and Functional Form of the Electron Localization Function. Acta Physico-Chimica Sinica 27:2786\u0026ndash;2792. https://doi.org/10.3866/PKU.WHXB20112786\u003c/li\u003e\n\u003cli\u003eShaik S, Ramanan R, Danovich D, Mandal D (2018) Structure and reactivity/selectivity control by oriented-external electric fields. Chem Soc Rev 47:5125\u0026ndash;5145. https://doi.org/10.1039/C8CS00354H\u003c/li\u003e\n\u003cli\u003eLi F, Yang X, Liu X, et al (2023) An \u003cem\u003eAb Initio\u003c/em\u003e Neural Network Potential Energy Surface for the Dimer of Formic Acid and Further Quantum Tunneling Dynamics. ACS Omega 8:17296\u0026ndash;17303. https://doi.org/10.1021/acsomega.3c02169\u003c/li\u003e\n\u003cli\u003eArabi AA, Matta CF (2011) Effects of external electric fields on double proton transfer kinetics in the formic acid dimer. Phys Chem Chem Phys 13:13738. https://doi.org/10.1039/c1cp20175a\u003c/li\u003e\n\u003cli\u003eArabi AA, Matta CF (2018) Effects of Intense Electric Fields on the Double Proton Transfer in the Watson\u0026ndash;Crick Guanine\u0026ndash;Cytosine Base Pair. J Phys Chem B 122:8631\u0026ndash;8641. https://doi.org/10.1021/acs.jpcb.8b05053\u003c/li\u003e\n\u003cli\u003eSowlati-Hashjin S, Karttunen M, Matta CF (2021) Electrostatic Fields in Biophysical Chemistry. In: Shaik S, Stuyver T (eds) Effects of Electric Fields on Structure and Reactivity. The Royal Society of Chemistry, pp 225\u0026ndash;262\u003c/li\u003e\n\u003cli\u003eMatta CF, Bandrauk AD (2021) An Introduction to Laser-field Effects on Chemical Reactivity. In: Shaik S, Stuyver T (eds) Effects of Electric Fields on Structure and Reactivity. The Royal Society of Chemistry, pp 394\u0026ndash;419\u003c/li\u003e\n\u003cli\u003eG\u0026oacute;mez S, Rojas-Valencia N, Toro-Labb\u0026eacute; A, Restrepo A (2023) The transition state region in nonsynchronous concerted reactions. The Journal of Chemical Physics 158:084109. https://doi.org/10.1063/5.0133487\u003c/li\u003e\n\u003cli\u003eBowman JM (2006) Skirting the transition state, a new paradigm in reaction rate theory. Proc Natl Acad Sci USA 103:16061\u0026ndash;16062. https://doi.org/10.1073/pnas.0607810103\u003c/li\u003e\n\u003cli\u003eGeoffroy-Neveux A, Labet V, Alikhani ME (2022) Influence of an Oriented External Electric Field on the Mechanism of Double Proton Transfer between Pyrazole and Guanidine: from an Asynchronous Plateau Transition State to a Synchronous or Stepwise Mechanism. J Phys Chem A 126:3057\u0026ndash;3071. https://doi.org/10.1021/acs.jpca.1c10553\u003c/li\u003e\n\u003cli\u003eCremer D, Wu A, Kraka E (2001) The mechanism of the reaction FH + H2C=CH2\u0026rarr;H3C\u0026ndash;CFH2. Investigation of hidden intermediates with the unified reaction valley approach. Phys Chem Chem Phys 3:674\u0026ndash;687. https://doi.org/10.1039/b007733j\u003c/li\u003e\n\u003cli\u003eKraka E, Cremer D (2002) Mechanism and dynamics of organic reactions: 1,2‐H shift in methylchlorocarbene. J of Physical Organic Chem 15:431\u0026ndash;447. https://doi.org/10.1002/poc.495\u003c/li\u003e\n\u003cli\u003eJoo H, Kraka E, Quapp W, Cremer D (2007) The mechanism of a barrierless reaction: hidden transition state and hidden intermediates in the reaction of methylene with ethene. Molecular Physics 105:2697\u0026ndash;2717. https://doi.org/10.1080/00268970701620677\u003c/li\u003e\n\u003cli\u003eKraka E, Cremer D (2010) Computational Analysis of the Mechanism of Chemical Reactions in Terms of Reaction Phases: Hidden Intermediates and Hidden Transition States. Acc Chem Res 43:591\u0026ndash;601. https://doi.org/10.1021/ar900013p\u003c/li\u003e\n\u003cli\u003eSexton T, Kraka E, Cremer D (2016) Extraordinary Mechanism of the Diels\u0026ndash;Alder Reaction: Investigation of Stereochemistry, Charge Transfer, Charge Polarization, and Biradicaloid Formation. J Phys Chem A 120:1097\u0026ndash;1111. https://doi.org/10.1021/acs.jpca.5b11493\u003c/li\u003e\n\u003cli\u003eRzepa HS, Wentrup C (2013) Mechanistic Diversity in Thermal Fragmentation Reactions: A Computational Exploration of CO and CO \u003csub\u003e2\u003c/sub\u003e Extrusions from Five-Membered Rings. J Org Chem 78:7565\u0026ndash;7574. https://doi.org/10.1021/jo401146k\u003c/li\u003e\n\u003cli\u003eArmstrong A, Boto RA, Dingwall P, et al (2014) The Houk\u0026ndash;List transition states for organocatalytic mechanisms revisited. Chem Sci 5:2057\u0026ndash;2071. https://doi.org/10.1039/C3SC53416B\u003c/li\u003e\n\u003cli\u003eRoca-L\u0026oacute;pez D, Polo V, Tejero T, Merino P (2015) Understanding Bond Formation in Polar One-Step Reactions. Topological Analyses of the Reaction between Nitrones and Lithium Ynolates. J Org Chem 80:4076\u0026ndash;4083. https://doi.org/10.1021/acs.joc.5b00413\u003c/li\u003e\n\u003cli\u003eLillo VJ, Mansilla J, Sa\u0026aacute; JM (2018) The role of proton shuttling mechanisms in solvent-free and catalyst-free acetalization reactions of imines. Org Biomol Chem 16:4527\u0026ndash;4536. https://doi.org/10.1039/C8OB01007B\u003c/li\u003e\n\u003cli\u003eSaid RB, Kolle JM, Essalah K, et al (2020) A Unified Approach to CO \u003csub\u003e2\u003c/sub\u003e \u0026ndash;Amine Reaction Mechanisms. ACS Omega 5:26125\u0026ndash;26133. https://doi.org/10.1021/acsomega.0c03727\u003c/li\u003e\n\u003cli\u003eShernyukov AV, Salnikov GE, Rudakov DA, Genaev AM (2021) Noncatalytic Bromination of Icosahedral Dicarboranes: The Key Role of Anionic Bromine Clusters Facilitating Br Atom Insertion into the B\u0026ndash;H \u0026sigma;-Bond. Inorg Chem 60:3106\u0026ndash;3116. https://doi.org/10.1021/acs.inorgchem.0c03392\u003c/li\u003e\n\u003cli\u003eGheorghiu A, Coveney PV, Arabi AA (2021) The influence of external electric fields on proton transfer tautomerism in the guanine\u0026ndash;cytosine base pair. Phys Chem Chem Phys 23:6252\u0026ndash;6265. https://doi.org/10.1039/D0CP06218A\u003c/li\u003e\n\u003cli\u003eDur\u0026aacute;n R, Barrales-Mart\u0026iacute;nez C, Matute RA (2023) Hidden intermediate activation: a concept to elucidate the reaction mechanism of the Schmittel cyclization of enyne\u0026ndash;allenes. Phys Chem Chem Phys 25:6050\u0026ndash;6059. https://doi.org/10.1039/D2CP04684A\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Scheme 1","content":"\u003cp\u003eScheme 1 is available in the Supplementary Files section.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-molecular-modeling","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jmmo","sideBox":"Learn more about [Journal of Molecular Modeling](https://www.springer.com/journal/894)","snPcode":"894","submissionUrl":"https://submission.nature.com/new-submission/894/3","title":"Journal of Molecular Modeling","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Double proton transfer, electric field, ELF topology, hidden intermediate, concerted vs stepwise, asynchronicity","lastPublishedDoi":"10.21203/rs.3.rs-4612227/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4612227/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e· \u003cstrong\u003eContext:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe nature of double intermolecular proton transfer was studied with the ELF topological approach in two model dimers (the formic acid homodimer and the 1,2,3-triazole–guanidine heterodimer) under an oriented external electric field. It has been shown that each of the two dimers can have either a one-step (one transition state structure) or two-step (two transition state structures) reaction path, depending on the intensity and orientation of the external electric field. The presence of a singularly broad shoulder (plateau in the case of homodimer, and plateau-like for heterodimer) around the formal transition state structure results from the strong asynchronicity of the reaction. A careful ELF topological analysis of the nature of protons, hydride (localized) or roaming (delocalized) proton, along the reaction path allowed us to unambiguously classify the one-step mechanisms governing the double-proton transfer reactions into three distinct classes: 1) concerted-synchronous, when two events (roaming proton regions) completely overlap, 2) concerted-asynchronous, when two events (roaming proton regions) partially overlap, 3) two-stage one-step non-concerted, when two roaming proton regions are separated by a “hidden intermediate region”. All the structures belonging to this separatrix region are of the zwitterion form.\u003c/p\u003e\n\u003cp\u003e· \u003cstrong\u003eMethods:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eGeometry optimization of the stationary points on the potential energy surface was performed using density functional theory –wB97XD functional– in combination with the 6-311++G(2d, 2p) basis set for all the atoms. All first-principles calculations were performed using the Gaussian 09 quantum chemical packages.\u003c/p\u003e\n\u003cp\u003eWe also used the electron localization function (ELF) to reveal the nature of the proton along the reaction path: a bound proton (hydride) becomes a roaming proton (carrying a tiny negative charge ≈ 0.3 e) exchanging with two adjacent atoms via two attractors (topological critical points with (3, -3) signature). The ELF analyses were performed using the TopMod package.\u003c/p\u003e","manuscriptTitle":"How to search for and reveal a hidden intermediate? The ELF topological description of non- synchronicity in double proton transfer reactions under oriented external electric field","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-18 20:50:57","doi":"10.21203/rs.3.rs-4612227/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-07-22T21:49:04+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-07-22T17:12:05+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-07-12T13:26:26+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"113947593562882781410168618033371077346","date":"2024-07-03T21:43:59+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"142488020739191176740770781799546553763","date":"2024-07-02T01:00:20+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-07-01T18:39:30+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-06-24T07:30:08+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-06-24T01:21:44+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Molecular Modeling","date":"2024-06-20T13:53:54+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-molecular-modeling","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jmmo","sideBox":"Learn more about [Journal of Molecular Modeling](https://www.springer.com/journal/894)","snPcode":"894","submissionUrl":"https://submission.nature.com/new-submission/894/3","title":"Journal of Molecular Modeling","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"8f26c6ed-c2c4-4250-b149-0da6a87d4f98","owner":[],"postedDate":"July 18th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-10-07T16:05:27+00:00","versionOfRecord":{"articleIdentity":"rs-4612227","link":"https://doi.org/10.1007/s00894-024-06163-0","journal":{"identity":"journal-of-molecular-modeling","isVorOnly":false,"title":"Journal of Molecular Modeling"},"publishedOn":"2024-10-04 15:58:24","publishedOnDateReadable":"October 4th, 2024"},"versionCreatedAt":"2024-07-18 20:50:57","video":"","vorDoi":"10.1007/s00894-024-06163-0","vorDoiUrl":"https://doi.org/10.1007/s00894-024-06163-0","workflowStages":[]},"version":"v1","identity":"rs-4612227","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4612227","identity":"rs-4612227","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}