Describing the Molecular Mechanism of Organic Reactions by Using Topological Analysis of Electronic Localization Function

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.

Three-Dimensional Convolutional Neural Networks Utilizing Molecular Topological Features for Accurate Atomization Energy Predictions

Deep learning methods provide a novel way to establish a correlation between two quantities. In this context, computer vision techniques such as three-dimensional (3D)-convolutional neural networks become a natural choice to associate a molecular property with its structure due to the inherent 3D nature of a molecule. However, traditional 3D input data structures are intrinsically sparse in nature, which tend to induce instabilities during the learning process, which in turn may lead to underfitted results. To address this deficiency, in this project, we propose to use quantum-chemically derived molecular topological features, namely, localized orbital locator and electron localization function, as molecular descriptors, which provide a relatively denser input representation in a 3D space. Such topological features provide a detailed picture of the atomic and electronic configuration and interatomic interactions in the molecule and hence are ideal for predicting properties that are highly dependent on the physical or electronic structure of the molecule. Herein, we demonstrate the efficacy of our proposed model by applying it to the task of predicting atomization energies for the QM9-G4MP2 data set, which contains ∼134k molecules. Furthermore, we incorporated the Δ-machine learning approach into our model, which enabled us to reach beyond benchmark accuracy levels (∼1.0 kJ mol^-1). As a result, we consistently obtain impressive mean absolute errors of the order 0.1 kcal mol^-1 (∼0.42 kJ mol^-1) versus the G4(MP2) theory using relatively modest models, which could potentially be improved further in a systematic manner using additional compute resources.

A Theoretical Evaluation of the Behavior of Nitrosoamidine upon Reacting with Methoxy Butadiene, as Potential Heterodiene or Heterodienophile

Abstract:

The molecular mechanism of experimentally observed regio- and chemoselectivity of the cycloaddition reaction of nitrosoamidine 1 and 1-methoxy butadiene 2 has been investigated using DFT calculations at M06-2X/cc-pVDZ level. Accordingly, the possible reaction pathways and factors, which govern selectivity are investigated systematically. Analysis of the calculated results show that the most favorable cyclization reaction takes place through the [2+4] endo-proximal pathway, which is under kinetically and thermodynamically controls. Moreover, analysis of the global and local reactivity indices correctly explains the source of the experimentally observed regio- and chemoselectivity. The electron localization function (ELF) analysis of some selected points along the IRC profile of the most preferred pathway suggests that the reaction takes place via a two-stage one-step mechanism. NCI topological analysis of the possible pathways of [2+4] cycloaddition reaction of 1-E and 2-Z reveals the roles of the attractive interactions between reaction sites, the weak noncovalent interactions in the endo approaches, and the repulsive interactions in the regio- and stereoselectivity of the reaction.

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.

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.

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.

Evaluation and understanding the performances of various derivatives of carbonyl-stabilized phosphonium ylides in CO2 transformation to cyclic carbonates

The kinetic and mechanism evaluations of the formation of cyclic carbonates by carbonyl-stabilized phosphonium ylides as an efficient and new class of organocatalysts are the main purposes of this research.

A reaction energy profile and fragment attributed molecular system energy change (FAMSEC)-based protocol designed to uncover reaction mechanisms: a case study of the proline-catalysed aldol reaction

A REP-FAMSEC (reaction energy profile-fragment attributed molecular system energy change) protocol designed to explain each consecutive energy change along the reaction pathway is reported. It mainly explores interactions between meaningful polyatomic fragments of a molecular system and, by quantifying energetic contributions, pin-points fragments (atoms) leading to or opposing a chemical change. Its usefulness is tested, as a case study, on the proline-catalysed aldol reaction for which a number of mechanisms have been debated for over four decades. The relative stability of S-proline conformers, their catalytic (in)activity and the superior affinity of the higher energy conformer to acetone is fully explained at atomic and molecular fragment levels, but still appealing to general chemist knowledge. We found that (i) contrary to the generally accepted view, CN-bond formation cannot be explained by the N^δ-, C^δ+ atom pair, but rather by the O-atom of acetone and its strongest inter-molecular attractive interactions with the N-atom as well as the C-atom of the COO group of proline (at this initial stage the lower energy conformer of proline is eliminated) and (ii) the following 'first' H-transfer from N to O atoms of the proline moiety is nearly energy-free even though initially the H-atom interacts three times stronger with the N- than O-atom; a full explanation of this phenomenon is provided.

Transient and intermediate carbocations in ruthenium tetroxide oxidation of saturated rings

The ruthenium tetroxide-mediated oxidation of cyclopentane, tetrahydrofuran, tetrahydrothiophene and N-substituted pyrrolidines has been studied computationally by DFT and topological (analysis of the electron localization function, ELF) methods. In agreement with experimental observations and previous DFT calculations, the rate-limiting step of the reaction takes place through a highly asynchronous (3 + 2) concerted cycloaddition through a single transition structure (one kinetic step). The ELF analysis identifies the reaction as a typical one-step-two-stages process and corroborates the existence of a transient carbocation. In the case of pyrrolidines, the carbocation is completely stabilized as an energy minimum in the form of an iminium ion and the reaction takes place in two steps.

Analyzing Fluxional Molecules Using DORI

The Density Overlap Region Indicator (DORI) is a density-based scalar field that reveals covalent bonding patterns and noncovalent interactions in the same value range. This work goes beyond the traditional static quantum chemistry use of scalar fields and illustrates the suitability of DORI for analyzing geometrical and electronic signatures in highly fluxional molecular systems. Examples include a dithiocyclophane, which possesses multiple local minima with differing extents of π-stacking interactions and a temperature dependent rotation of a molecular rotor, where the descriptor is employed to capture fingerprints of CH-π and π-π interactions. Finally, DORI serves to examine the fluctuating π-conjugation pathway of a photochromic torsional switch (PTS). Attention is also placed on postprocessing the large amount of generated data and juxtaposing DORI with a data-driven low-dimensional representation of the structural landscape.

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

Despite the usefulness of curly arrows in chemistry, their relationship with real electron density flows is still imprecise, and even their direct connection to quantum chemistry is still controversial. The paradigmatic description - from first principles - of the mechanistic aspects of a given chemical process is based mainly on the relative energies and geometrical changes at the stationary points of the potential energy surface along the reaction pathway; however, it is not sufficient to describe chemical systems in terms of bonding aspects. Probing the electron density distribution during a chemical reaction can provide important insights, enabling us to understand and control chemical reactions. This aim has required an extension of the relationships between the concepts of traditional chemistry and those of quantum mechanics. Bonding evolution theory (BET), which combines the topological analysis of the electron localization function (ELF) and Thom's catastrophe theory (CT), provides a powerful method that offers insight into the molecular mechanism of chemical rearrangements. In agreement with the laws of physical and aspects of quantum theory, BET can be considered an appropriate tool to tackle chemical reactivity with a wide range of possible applications. In this work, BET is applied to address a long-standing problem: the ability to monitor the flow of electron density. BET analysis shows a connection between quantum mechanics and bond making/forming processes. Likewise, the present approach retrieves the classical curly arrows used to describe the rearrangements of chemical bonds and provides detailed physical grounds for this type of representation. We demonstrate this procedure using the test set of prototypical examples of thermal ring apertures, and the degenerated Cope rearrangement of semibullvalene.

BET & ELF Quantum Topological Analysis of Neutral 2-Aza-Cope Rearrangement of γ-Alkenyl Nitrones

The 2-Aza-Cope rearrangement of γ-alkenyl nitrones is a rare example of the neutral thermal 2-aza-Cope process that usually takes place with cationic species. During the rearrangement, a redistribution of bonds and electronic density occurs in one kinetic step. However, the introduction of substituents with different steric requirements and electronic features might alter the activation energies and the synchronicity of the reaction. The electron localization function (ELF) analysis and its application to Bonding Evolution Theory (BET) analysis within the context of Molecular Electron Density Theory (MEDT) is an excellent tool to monitor the electron density along the reaction coordinate and thus investigate in detail bond breaking and formation and the corresponding energy barriers. By analyzing topological ELF calculations of seventeen 2-aza-Cope nitrone rearrangements with selected substituents, the main factors influencing the synchronicity of the process were investigated. This MEDT study results revealed that the rearrangement is a non-polar process mostly influenced by steric factors rather than by electronic ones, and confirms the pseudoradical character of the process rather than any pericyclic electron-reorganization.

On the outside looking in: rethinking the molecular mechanism of 1,3-dipolar cycloadditions from the perspective of bonding evolution theory. The reaction between cyclic nitrones and ethyl acrylate

Understanding the molecular mechanism of 1,3-dipolar cycloadditions using the bonding evolution theory.

Introducing topology to assess the synchronicity of organic reactions. Dual reactivity of oximes with alkenes as a case study

Quantum chemical topology analyses provide a new way of understanding the synchronicity of organic reactions.

New mechanistic interpretations for nitrone reactivity

The reactivity of nitrones in cycloadditions and related reactions is revisited by introducing a topological perspective.

Torquoselectivity in Cyclobutene Ring Openings and the Interatomic Interactions That Control Them

Torquoselectivity has explained diasteromeric preferences of a number electrocyclic ring openings. The quantum theory of atoms in molecules (QTAIM), the electron localizability indicator (ELI-D), and the interacting quantum atoms (IQA) energy partition method are used to evaluate qualitatively and quantitatively the atomic interactions behind the torquoselectivity of a series of 3-substituted cyclobutenes. ELI-D topology and IQA energies show that the interaction between the distal terminus carbon atom of cyclobutene (C4) with the substituent at C3 (R5) in the transition state governs torquoselectivities. In the case of 3-borylcyclobutene, this interaction is so strong that a protocovalent bond is actually formed between B5 and C4. The evaluation of the interatomic energies allowed us to identify an additional interaction that contribute to a minor extent to the stabilization of the TS. Despite the fact that C4,R5 interaction is the main cause of the torquoselectivity, a bonding path (BP) between these two atoms was not observed. However, the lack of a BP between C4 and R5 does not mean that the topology of the electron density was not affected by the interaction of these two atoms. Surprisingly, we found a strong correlation between the density at the bond critical point (BCP) and the BP shape of C3-C4 breaking bond with the observed activation energies and torquoselectivities.

A mechanistic insight into the effect of piperidine as an organocatalyst on the [3 + 2] cycloaddition reaction of benzalacetone with phenyl azide from a computational study

Several transition structures (TSs) for catalyst-free [3 + 2] cycloaddition and two plausible mechanistic pathways for the organocatalyzed [3 + 2] cycloaddition (32CA) between benzalacetone and phenyl azide were located by quantum chemistry methods. Calculations were carried out with B3LYP, MPWB1K and M06-2X functionals using 6-31G(d) and 6-311G(d,p) basis sets in gas and solvent phases. The calculated activation barriers imply that the lowest barrier pathway is the catalyzed process producing 3-regioisomers through the iminium intermediate and not through the dienamine route. Electronic displacements along the reaction path have been examined using a topological analysis of the electron-localization function (ELF). ELF topological analyses along the intrinsic reaction coordinates (IRC) of both catalyzed and uncatalyzed 32CA reactions indicated that while the first C1-N1 single bond is formed as a dative bond, the formation of the second C2-N3 bond takes place via a C-to-N coupling between the interacting centers of the reagents. Moreover, the ELF analyses imply that the reaction mechanism is a two-stage one-step process in the presence of a piperidine organocatalyst, while bond formation in an uncatalyzed process is almost synchronous.

Curly arrows meet electron density transfers in chemical reaction mechanisms: from electron localization function (ELF) analysis to valence-shell electron-pair repulsion (VSEPR) inspired interpretation

The displacement of the nuclei along the reaction path provides an explanatory interpretation of the electron density transfers making possible to understand chemical reactions.

Theoretical study of the regio- and stereoselectivity of the intramolecular Povarov reactions yielding 5H-chromeno[2,3-c] acridine derivatives

The intramolecular Povarov (IMP) reactions involved in the synthesis of 5H-chromeno[2,3-c] acridine derivatives [Tetrahedron Lett., 2010, 51, 3071–3074] have been studied using density functional theory (DFT) methods.

Inquiry of the electron density transfers in chemical reactions: a complete reaction path for the denitrogenation process of 2,3-diazabicyclo[2.2.1]hept-2-ene derivatives

A detailed study on all stages associated with the reaction mechanisms for the denitrogenation of 2,3-diazabicyclo[2.2.1]hept-2-ene derivatives (DBX, with X substituents at the methano-bridge carbon atom, X = H and OH) is presented. In particular, we have characterized the processes leading to cycloalkene derivatives through migration-type mechanisms as well as the processes leading to cyclopentil-1,3-diradical species along concerted or stepwise pathways. The reaction mechanisms have been further analysed within the bonding evolution theory framework at B3LYP and M05-2X/6-311+G(2d,p) levels of theory. Analysis of the results allows us to obtain the intimate electronic mechanism for the studied processes, providing a new topological picture of processes underlying the correlation between the experimental measurements obtained by few-optical-cycle visible pulse radiation and the quantum topological analysis of the electron localization function (ELF) in terms of breaking/forming processes along this chemical rearrangement. The evolution of the population of the disynaptic basin V(N1,N2) can be related to the experimental observation associated with the N=N stretching mode evolution, relative to the N2 release, along the reaction process. This result allows us to determine why the N2 release is easier for the DBH case via a concerted mechanism compared to the stepwise mechanism found in the DBOH system. This holds the key to unprecedented insight into the mapping of the electrons making/breaking the bonds while the bonds change.