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

Revisiting the bonding evolution theory: a fresh perspective on the ammonia pyramidal inversion and bond dissociations in ethane and borazane

This work offers a comprehensive and fresh perspective on the bonding evolution theory (BET) framework, originally proposed by Silvi and collaborators [X. Krokidis, S. Noury and B. Silvi, Characterization of elementary chemical processes by catastrophe theory, J. Phys. Chem. A, 1997, 101, 7277-7282]. By underscoring Thom's foundational work, we identify the parametric function characterizing bonding events along a reaction pathway through a three-step sequence to establish such association rigorously, namely: (a) computing the determinant of the Hessian matrix at all potentially degenerate critical points, (b) computing the relative distance between these points, and (c) assigning the unfolding based on these computations and considering the maximum number of critical points for each unfolding. In-depth examination of the ammonia inversion and the dissociation of ethane and ammonia borane molecules yields a striking discovery: no elliptic umbilic flag is detected along the reactive coordinate for any of the systems, contradicting previous reports. Our findings indicate that the core mechanisms of these chemical reactions can be understood using only two folds, the simplest polynomial of Thom's theory, leading to considerable simplification. In contrast to previous reports, no signatures of the elliptic umbilic unfolding were detected in any of the systems examined. This finding dramatically simplifies the topological rationalization of electron rearrangements within the BET framework, opening new approaches for investigating complex reactions.

A simple topology-based model for predicting the activation barriers of reactive processes at 0 K

This work reveals an underlying correlation between the topology and energetic features of matter configurations/rearrangements by exploiting two topological concepts, namely, structural stability and persistency, leading thus to a model capable of predicting activation energies at 0 K. This finding provides some answers to the difficulties of applying Thom's functions for extracting energetic information of rate processes, which has been a limitation for exact, biological, and technological sciences. A linear relationship between the experimental barriers of 17 chemical reactions and both concepts was found by studying these systems' topography along the intrinsic reaction coordinate. Such a procedure led to the model , which accurately predicts the activation energy in reacting systems involving organic and organometallic compounds under different conditions, e.g., the gas-phase, solvent media, and temperature. This function was further recalibrated to enhance its predicting capabilities, generating the equation for this procedure, characterized by a squared Pearson correlation coefficient (r² = 0.9774) 1.1 times higher. Surprisingly, no improvement was observed.

Calculation of the ELF in the excited state with single-determinant methods

Since its first definition, back in 1990, the electron localization function (ELF) has settled as one of the most commonly employed techniques to characterize the nature of the chemical bond in real space. Although most of the work using the ELF has focused on the study of ground-state chemical reactivity, a growing interest has blossomed to apply these techniques to the nearly unexplored realm of excited states and photochemistry. Since accurate excited electronic states usually require to account appropriately for electron correlation, the standard single-determinant ELF formulation cannot be blindly applied to them, and it is necessary to turn to correlated ELF descriptions based on the two-particle density matrix (2-PDM). The latter requires costly wavefunction approaches, unaffordable for most of the systems of current photochemical interest. Here, we compare the exact, 2-PDM-based ELF results with those of approximate 2-PDM reconstructions taken from reduced density matrix functional theory. Our approach is put to the test in a wide variety of representative scenarios, such as those provided by the lowest-lying excited electronic states of simple diatomic and polyatomic molecules. Altogether, our results suggest that even approximate 2-PDMs are able to accurately reproduce, on a general basis, the topological and statistical features of the ELF scalar field, paving the way toward the application of cost-effective methodologies, such as time-dependent-Hartree-Fock or time-dependent density functional theory, in the accurate description of the chemical bonding in excited states of photochemical relevance.

Elucidating the N-N and C-N Bond-breaking Mechanism in the Photoinduced Formation of Nitrile Imine

In this study, we revealed the significance of chemical bonding for the photochemically induced mechanism of 2-phenyl tetrazole derivatives generating nitrile imines. The correlated electron localization function shows that the formation of imine nitrile involves two key bond events: (i) the heterolytic C-N breakage taking place in the T₁ state and (ii) the homolytic N-N rupture occurring in the T₂ excited state. In particular, a cation-radical specie results from the C-N cleavage, whereas the N-N rupture creates a biradical resonant form of imine nitrile. Additionally, we noticed that the substantial pair delocalization of the C-C-N bonded structure could play a significant role in the conversion of the biradical imine nitrile into both the propargylic and allenic forms via the T₁ →S₀ deactivation.

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.

Photochemically Induced 1,3-Butadiene Ring-Closure from the Topological Analysis of the Electron Localization Function Viewpoint

The electronic rearrangement featuring the photochemically-induced 1,3-cis-butadiene is discussed within a bonding evolution theory (BET) perspective based on the topological analysis of the electron localization function and Thom's catastrophe theory. The process involves the vertical singlet-singlet excitation S₀ →S₂ , and the subsequent deactivation implying the S₂ /S₁ and S₁ /S₀ conical intersection regions. BET results reveal that the new CC bond is finally formed on the S₀ surface, as also recently found in the photochemical addition of two ethylenes [Phys. Chem. Chem. Phys. 23, 20598, (2021)].

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.