Curly arrows, electron flow, and reaction mechanisms from the perspective of the bonding evolution theory

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

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, and (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.

Unveiling the Stereoselectivity and Regioselectivity of the [3+2] Cycloaddition Reaction between N-methyl-C-4-methylphenyl-nitrone and 2-Propynamide from a MEDT Perspective

[3+2] cycloaddition reactions play a crucial role in synthesizing complex organic molecules and have significant applications in drug discovery and materials science. In this study, the [3+2] cycloaddition (32CA) reactions of N-methyl-C-4-methyl phenyl-nitrone 1 and 2-propynamide 2, which have not been extensively studied before, were investigated using molecular electron density theory (MEDT) at the B3LYP/6-311++G(d,p) level of theory. According to an electron localization function (ELF) study, N-methyl-C-4-methyl phenyl-nitrone 1 is a zwitterionic species with no pseudoradical or carbenoid centers. Conceptual density functional theory (CDFT) indices were used to predict the global electronic flux from the strong nucleophilic N-methyl-C-4-methyl phenylnitrone 1 to the electrophilic 2-propynamide 2 functions. The 32CA reactions proceeded through two pairs of stereo- and regioisomeric reaction pathways to generate four different products: 3, 4, 5, and 6. The reaction pathways were irreversible owing to their exothermic characters: -136.48, -130.08, -130.99, and -140.81 kJ mol^-1, respectively. The enthalpy of the 32CA reaction leading to the formation of cycloadduct 6 was lower compared with the other path owing to a slight increase in its polar character, observed through the global electron density transfer (GEDT) during the transition states and along the reaction path. A bonding evolution theory (BET) analysis showed that these 32CA reactions proceed through the coupling of pseudoradical centers, and the formation of new C-C and C-O covalent bonds did not begin in the transition states.

On the Notation of Catastrophes in the Framework of Bonding Evolution Theory: the Case of Normal and Inverse Electron Demand Diels-Alder Reactions

This paper generalizes very recent and unexpected findings [ J. Phys. Chem. A , 2021 , 125 , 5152-5165] regarding the known "direct- and inverse-electron demand" Diels-Alder mechanisms. Application of bonding evolution theory evidence that the key electron rearrangement associated with significant chemical events (e.g., the breaking/forming processes of bonds) can be characterized via the simplest fold polynomial. To the CC bond formation, neither substituent position nor the type of electronic demand induces a measurable cusp-type signature. On the opposite to the case of [4+2] cycloaddition between 1,3-butadiene and ethylene where the two new CC single bonds occur beyond the transition state (TS), in the activated cases, the first CC bond formation occurs in the domain of structural stability featuring the TS, whereas the second one remains located in the deactivation path connecting the TS with the cycloadduct.

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

The double proton transfer (DPT) reaction between pyrazole and guanidine, a concerted reaction but strongly asynchronous and presenting a "plateau transition region", has been theoretically reinvestigated in the presence of an external uniform electric field. First, we computed the reaction path by DFT and proposed a very detailed description of the constitutive electronic events, based on the ELF topology and the bond evolution theory. Then, we studied the effect of an oriented external electric field (OEEF) on the reaction mechanism, for an OEEF oriented along the proton transfer axis. We observe that in one direction, the DPT reaction can be transformed into a stepwise reaction, going through a stabilized single proton transferred intermediate. Contrarily, the two proton transfers occur simultaneously when the electric field is applied in the opposite direction. In the latter case, the order in which the two protons are transferred in the same elementary step can even be reversed if the OEEF is intense enough. Finally, it has been shown that the evolution of the double proton transfer reaction in the presence of an electric field could be quantitatively anticipated by analyzing the ELF value at the bifurcation point between V(A, H) proton donor and V(B) proton acceptor of the double hydrogen bonded complex in the entrance channel.

Decoding the reaction mechanism of the cyclocondensation of ethyl acetate2-oxo-2-(4-oxo-4H-pyrido [1.2-a] pyrimidin-3-yl) polyazaheterocycle and ethylenediamine using bond evolution theory

We investigated the flow of electron density along the cyclocondensation reaction between ethyl acetate 2-oxo-2-(4-oxo-4H-pyrido[1.2-a]pyrimidin-3-yl) polyazaheterocycle (1) and ethylenediamine (2) at the ωB97XD/6-311++G(d,p)computational method within of bond evolution theory (BET). The exploration of potential energy surface shows that this reaction has three channels (1-3) with the formation of product 3 via channel-2 (the most favorable one) as the main product and this is in good agreement with experimental observations. The BET analysis allows identifying unambiguously the main chemical events happening along channel-2. The mechanism along first step (TS2-a) is described by a series of four structural stability domains (SSDs), while five SSDs for the last two steps (TS2-b and TS2-c). The first and third steps can be summarized as follows, the formation of N1-C6 bond (SSD-II), then, the restoration of the nitrogen N1 lone pair (SSD-III), and finally, the formation of the last O1-H1 bond (SSD-IV). For the second step, the formation of hydroxide ion is noted, as a result of the disappearance of V(C6,O7) basin and the transformation of C6-N1 single bond into double one (SSD-IV). Finally, the appearance of V(O7,H2) basin lead to the elimination of water molecule within the last domain is observed.

Unraveling the role of the electron-pair density symmetry in reaction mechanism patterns: the Newman–Kwart rearrangement

There is an underlying intimate relationship between Thom's catastrophe theory and the electron-pair density evidenced along a reaction pathway.

Electron Density Geometry and the Quantum Theory of Atoms in Molecules

A novel form of charge density analysis, that of isosurface curvature redistribution, is formulated and applied to the toy problem of carbonyl oxygen activation in formaldehyde. The isosurface representation of the electron charge density allows us to incorporate the rigorous geometric constraints of closed surfaces toward the analysis and chemical interpretation of the charge density response to perturbations. Visual inspection of 2D isosurface motion resulting from applied external electric fields reveals how the isosurface curvature flows within and between atoms and that a molecule can be uniquely and completely partitioned into chemically significant regions of positive and negative curvatures. These concepts reveal that carbonyl oxygen activation proceeds primarily through curvature and charge redistribution within rather than between Bader atoms. Using gradient bundle analysis─the partitioning of formaldehyde into infinitesimal volume elements bounded by QTAIM zero-flux surfaces─the observations from visual isosurface inspection are verified. The results of the formaldehyde carbonyl analysis are then shown to be transferable to the substrate carbonyl in the ketosteroid isomerase enzyme, laying the groundwork for extending this approach to the problems of enzymatic catalysis.

Tracking the Transition from Pericyclic to Pseudopericyclic Reaction Mechanisms Using Multicenter Electron Delocalization Analysis: The [1,3] Sigmatropic Rearrangement

Herein, the power of multicenter electron delocalization analysis to elucidate the intricacies of concerted reaction mechanisms is brought to light by tracking the transition of [1,3] sigmatropic rearrangements from the high-barrier pericyclic mechanism in 1-butene to the barrierless pseudopericyclic mechanism in 1,2-diamino-1-nitrosooxyethane. This transition has been progressively achieved by substituting the migrating group, changing the donor and acceptor atoms, and functionalizing the alkene unit with weak and strong electron-donating and electron-withdrawing groups. Fourteen [1,3] sigmatropic reactions with electronic energy barriers ranging from 1 to 89 kcal/mol have been investigated. A very good correlation has been found between the barrier and the four-center electron delocalization at the transition state, the latter calculated for the atoms involved in the four-centered ring adduct formed along the reaction path. Surprisingly, the barrier has been found to be independent of the bond strength between the migrating group and the donor atom so that only the changes induced in the multicenter bonding control the kinetics of the reaction. Additional insights into the effect of atom substitution and group functionalization have also been extracted from the analysis of the multicenter electron delocalization profiles along the reaction path and qualitatively supported by the topological analysis of the electron density.

On the nature of bonding in the photochemical addition of two ethylenes: C-C bond formation in the excited state?

In this work, the 2s + 2s (face-to-face) prototypical example of a photochemical reaction has been re-examined to characterize the evolution of chemical bonding. The analysis of the electron localization function (as an indirect measure of the Pauli principle) along the minimum energy path provides strong evidence supporting that CC bond formation occurs not in the excited state but in the ground electronic state after crossing the rhombohedral S₁/S₀ conical intersection.

Exploring The Sequence of Electron Density Along The Chemical Reactions Between Carbonyl Oxides And Ammonia/Water Using Bond Evolution Theory

The molecular mechanism of the reactions between four carbonyl oxides and ammonia/water are investigated using the M06-2X functional together with 6-311++G(d,p) basis set. The analysis of activation and reaction enthalpy shows that the exothermicity of each process increased with the substitution of electron donating substituents (methyl and ethenyl). Along each reaction pathway, two new chemical bonds C-N/C-O and O-H are expected to form. A detailed analysis of the flow of the electron density during their formation have been characterized from the perspective of bonding evolution theory (BET). For all reaction pathways, BET revealed that the process of C-N and O-H bond formation takes place within four structural stability domains (SSD), which can be summarized as follows: the depopulation of V(N) basin with the formation of first C-N bond (appearance of V(C,N) basin), cleavage of N-H bond with the creation of V(N) and V(H) monosynaptic basin, and finally the V(H,O) disynaptic basin related to O-H bond. On the other hand, in the case of water, the cleavage of O-H bond with the formation of V(O) and V(H) basins is the first stage, followed by the formation of the O-H bond as a second stage, and finally the creation of C-O bond.

Are There Only Fold Catastrophes in the Diels-Alder Reaction Between Ethylene and 1,3-Butadiene?

This work revisits the topological characterization of the Diels-Alder reaction between 1,3-butadiene and ethylene. In contrast to the currently accepted rationalization, we here provide strong evidence in support of a representation in terms of seven structural stability domains separated by a sequence of 10 elementary catastrophes, but all are only of the fold type (F and F^†), that is, C₄H₆ + C₂H₄:1-7-[FF]F[F^†F^†][F^†F^†][FF]F^†-0: C₆H₁₀. Such an unexpected finding provides fundamental new insights opening simplifying perspectives concerning the rationalization of the CC bond formation in pericyclic reactions in terms of the simplest Thom's elementary catastrophe, namely, the one-(state) variable, one-(control) parameter function.

New insights in chemical reactivity from quantum chemical topology

Based on the quantum chemical topology of the modified electron localization function ELF_x , an efficient and robust mechanistic methodology designed to identify the favorable reaction pathway between two reactants is proposed. We first recall and reshape how the supermolecular interaction energy can be evaluated from only three distinct terms, namely the intermolecular coulomb energy, the intermolecular exchange-correlation energy and the intramolecular energies of reactants. Thereafter, we show that the reactivity between the reactants is driven by the first-order variation in the coulomb intermolecular energy defined in terms of the response to changes in the number of electrons. Illustrative examples with the formation of the dative bond B-N involved in the BH₃ NH₃ molecule and the typical formation of the hydrogen bond in the canonical water dimer are presented. For these selected systems, our approach unveils a noticeable mimicking of E_dual onto the DFT intermolecular interaction energy surface calculated between the both reactants. An automated reaction-path algorithm aimed to determine the most favorable relative orientations when the two molecules approach each other is also outlined.

Energetics of Electron Pairs in Electrophilic Aromatic Substitutions

The interacting quantum atoms approach (IQA) as applied to the electron-pair exhaustive partition of real space induced by the electron localization function (ELF) is used to examine candidate energetic descriptors to rationalize substituent effects in simple electrophilic aromatic substitutions. It is first shown that inductive and mesomeric effects can be recognized from the decay mode of the aromatic valence bond basin populations with the distance to the substituent, and that the fluctuation of the population of adjacent bonds holds also regioselectivity information. With this, the kinetic energy of the electrons in these aromatic basins, as well as their mutual exchange-correlation energies are proposed as suitable energetic indices containing relevant information about substituent effects. We suggest that these descriptors could be used to build future reactive force fields.

Topological investigation of the reaction mechanism of glycerol carbonate decomposition by bond evolution theory

The reaction mechanisms of the decomposition of glycerol carbonate have been investigated at the density functional theory level within the bond evolution theory. The four reaction pathways yield to 3-hydroxypropanal (TS1), glycidol (TS2a and TS2b), and 4-methylene-1,3-dioxolan-2-one (TS3). The study reveals non-concerted processes with the same number (four) of structural stability domains for each reaction pathway. For the two decarboxylation mechanisms, the two first steps are similar. They correspond to the cleavage of two single CO bonds to the detriment of the increased population of the lone pairs of two O atoms. These are followed, along TS1, by the transformation of a CO single bond into a double bond together with a proton transfer to create a CH bond. For TS2a and TS2b, the last step is a cyclization by CO bond formation. For the TS3 pathway, the first stage consists in the cleavage of a CH bond and the transfer of its electron population to both a proton and a C atom, the second step corresponds to the formation of an OH bond, and the last one describes the formation of a CC double bond. Moreover, the analysis of the energies, enthalpies, and free enthalpies of reaction and of activation leads to the conclusion that 3-hydroxypropanal is both the thermodynamic and kinetic product, independent of the method of calculation.

ELFs of glycerol carbonate and of its kinetic and thermodynamic decomposition product, 3-hydroxypropanal (+CO₂).

Deciphering the Curly Arrow Representation and Electron Flow for the 1,3-Dipolar Rearrangement between Acetonitrile Oxide and (1S,2R,4S)-2-Cyano-7-oxabicyclo[2.2.1]hept-5-en-2-yl Acetate Derivatives

This study is focused on describing the molecular mechanism beyond the molecular picture provided by the evolution of molecular orbitals, valence bond structures along the reaction progress, or conceptual density functional theory. Using bonding evolution theory (BET) analysis, we have deciphered the mechanism of the 1,3-dipolar rearrangement between acetonitrile oxide and (1S,2R,4S)-2-cyano-7-oxabicyclo[2.2.1]hept-5-en-2-yl acetate derivatives. The BET study revealed that the formation of the C-C bond takes place via a usual sharing model before the O-C one that is also formed in the halogenated species through a not very usual sharing model. The mechanism includes depopulation of the electron density at the N-C triple bond and creation of the V(N) and V(C) monosynaptic basins, depopulation of the former C-C double bond with the creation of V(C,C) basins, and final formation of the V(O,C) basin associated with the O-C bond. The topological changes along the reaction pathway take place in a highly synchronous way. BET provides a convenient quantitative method for deriving curly arrows and electron flow representation to unravel molecular mechanisms.

Real-Space Approach to the Reaction Force: Understanding the Origin of Synchronicity/Nonsynchronicity in Multibond Chemical Reactions

In this article, we present a complementary analysis based on the reaction force F(ξ)/reaction force constant κ(ξ) and noncovalent interactions (NCI) index to characterize the energetics (kinetic and thermodynamics) and mechanistic pathways of two sets of multibond chemical reactions, namely, two double-proton transfer and two Diels-Alder cycloaddition reactions. This approach offers a very straightforward and useful way to delve into a deeper understanding of this type of process. While F(ξ) allows the partition of the whole pathway into three regions or phases, κ(ξ) describes how orchestrated are the bond-breaking and bond-formation events. In turn, NCI indicates how the inter- and intramolecular bonds evolve. The most innovative aspect is the inclusion of the formation of the reactant complex along the pathway, which, by means of NCI, unveils the early molecular recognition and the comprehension of its role in determining the degree of the synchronicity/nonsynchronicity of one-step processes. This approach should be a useful and alternative tool to characterize the energetics and the mechanism of general chemical reactions.

Bonding rearrangements in organometallic reactions: from orbitals to curly arrows

Reaction mechanisms include a description of both the nuclear and electronic rearrangements along the energetically most favourable pathway. Extracting the nuclear rearrangements from the outcome of quantum chemical calculations is straightforward, while it is more intricate for the electronic rearrangements. This is particularly true when changes in the bonding pattern are of interest, just as in the arrow-pushing formalism used in chemical schemes. Here, we report on our use of a simple and highly visual procedure to recover the bonding rearrangements along a reaction pathway from DFT calculations and to draw curly arrows. We show that the procedure allows us discern among mechanistic proposals in the context of organometallic reactions featuring the forming and breaking of bonds.

Epoxidation of Alkenes by Peracids: From Textbook Mechanisms to a Quantum Mechanically Derived Curly-Arrow Depiction

Using the intrinsic bond orbital (IBO) analysis based on accurate quantum mechanical calculations of the reaction path for the epoxidation of propene using peroxyacetic acid, we find that the four commonly used curly arrows for representing this reaction mechanism are insufficient and that seven curly arrows are required as a result of changes to σ and π bonding interactions, which are usually neglected in all textbook curly arrow representations. The IBO method provides a convenient quantitative method for deriving curly arrows in a rational manner rather than the normal ad hoc representations used ubiquitously in teaching organic chemistry.

Resonance Natural Bond Orbitals: Efficient Semilocalized Orbitals for Computing and Visualizing Reactive Chemical Processes

We describe a practical algorithm for calculating NBO-based "resonance natural bond orbitals" (RNBOs) that can accurately describe the localized bond shifts of a reactive chemical process. Unlike conventional NBOs, the RNBOs bear no fixed relationship to a particular Lewis-structural bonding pattern but derive instead from the natural resonance theory (NRT)-based manifold of all bonding patterns that contribute significantly to resonance mixing (and associated multichannel reactivity) at a chosen point of the potential energy surface. The RNBOs typically retain familiar localized Lewis-structural character for stable near-equilibrium species, yet they freely adopt multicenter character as required to satisfy Pople's prerequisite that no allowed computational basis set should be inherently biased toward a particular nuclear arrangement or bonding pattern. A simple numerical application to intramolecular Claisen rearrangement demonstrates the computational and conceptual advantages of describing reactive bond-shifts with RNBOs rather than other conventional NBO- or MO-based expansion sets.

Using the Relative Energy Gradient Method with Interacting Quantum Atoms to Determine the Reaction Mechanism and Catalytic Effects in the Peptide Hydrolysis in HIV-1 Protease

The reaction mechanism in an active site is of the utmost importance when trying to understand the role that an enzyme plays in biological processes. In a recently published paper [Theor. Chem. Acc. 2017, 136, 86], we formalised the Relative Energy Gradient (REG) method for automating an Interacting Quantum Atoms (IQA) analysis. Here, the REG method is utilised to determine the mechanism of peptide hydrolysis in the aspartic active site of the enzyme HIV-1 Protease. Using the REG method along with the IQA approach we determine the mechanism of peptide hydrolysis without employing any arbitrary parameters and with remarkable ease (albeit at large computational cost: the system contains 133 atoms, which means that there are 17 689 individual IQA terms to be calculated). When REG and IQA work together it is possible to determine a reaction mechanism at atomistic resolution from data directly derived from quantum calculations, without arbitrary parameters. Moreover, the mechanism determined by this novel method gives concrete insight into how the active site residues catalyse peptide hydrolysis.