A bonding evolution theory study of the reaction between methylidyne radical, CH(X²Π), and cyclopentadiene, C₅H₆

Abstract

In the present work, bonding evolution theory (BET) is applied to gain insight about the complex reaction between methylidyne radical, CH (X2Π) and cyclopentadiene, C5H6. The novelty of this work is that all reaction pathways take place in the doublet electronic state and an unpaired electron is always present. Therefore, taking the aforementioned reaction as explicative example, we have shown how to apply the BET tool to these kinds of open‐shell systems, by splitting the wavefunctions into the corresponding alpha and beta parts. As an added value, we have included a point‐by‐point description of the algorithm we use to make it available for the readers. Hence, a complete analysis of bond breaking/forming and charge redistribution along the multi‐channels connecting reactants to products via the transition states and intermediates is presented. We show how the BET brings about the representation of the electronic flow in complex molecular rearrangements like the one herein studied, yielding a transparent rationalization based on the electron density redistribution. The present study allows us to conclude that along the different processes giving rise to the benzene product, the breaking of a CC sigma bond initiates the electronic rearrangement in two cases, but not in the third one. The last step in these processes can be described as an initial weakening of the CH bond with a quasi‐hydride formation and a final retro‐transfer of electrons from the quasi‐hydride to the CH bond. On the other hand, in the way to the fulvene product, the breaking of the CC sigma bond takes place after previous electronic redistribution. Neither the last step of the fulvene formation process nor the interesting H transfer described in the second one, can be explained without the wavefunction splitting technique herein detailed and exemplified.

Radical revelations: the pnictogen effect in linear acetylenes

“…36 In fact, ELF analyses have gained a lot of popularity outside the QCT field in recent years due to their simplicity and straightforward interpretation. [37][38][39] Finally, the local expectation values of the squared spin operator, hS A 2 i = S A (S A + 1), attributed to an atom or chemical fragment can be used to provide a description compatible with the more naı ¨ve resonance theory. The local spin concept was introduced by Clark and Davidson in 2001 40 via atomic projection operators as a means to access information about spin localization in singlets (e.g.…”

“…36 In fact, ELF analyses have gained a lot of popularity outside the QCT field in recent years due to their simplicity and straightforward interpretation. 37–39…”

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

“…[19][20][21][22][23] Structures derived from this analysis are specified in the form of critical points (CPs) and their interconnections via gradient paths. [22] Within this framework, QTAIM [25] and ELF, [3] are nowadays useful methodological tools that help us rationalize concepts related to chemical bonding. [15,25,26] Bonding evolution theory, [4] which combines the topological analysis of ELF with Thom's catastrophe theory, [2] has permitted exploring chemical reactions as sequences of SSDs in processes involving rupture/formation bonds.…”

“…[22] Within this framework, QTAIM [25] and ELF, [3] are nowadays useful methodological tools that help us rationalize concepts related to chemical bonding. [15,25,26] Bonding evolution theory, [4] which combines the topological analysis of ELF with Thom's catastrophe theory, [2] has permitted exploring chemical reactions as sequences of SSDs in processes involving rupture/formation bonds. [1,4,[9][10][11]15] Any chemical reaction involving covalent bonds within the BET approach can be represented by a succession of catastrophic bifurcations associated with electron pairing topologies for a simple rationalization of the chemical bonding patterns.…”

A combined BET and IQA–REG study of the activation energy of non-polar zw-type [3+2] cycloaddition reactions

“…As electron populations can be associated with Lewis' bonding model, 22 BET constitutes an appealing way to represent molecular mechanisms with chemically meaningful drawings. BET has been applied to the study of a wide variety of organic chemical reactions, [23][24][25] specifically cycloaddition reactions, [26][27][28] providing accurate descriptions of their molecular mechanisms.…”