Atomic Resolution for the Energy Derivatives on the Reaction Path

Abstract

Definite algorithms for calculation of the atomic contributions to the reaction force Fξ and the reaction force constant kξ (the first and the second derivatives of the energy over the reaction path step) are presented. The electronic part in the atomic and group contributions has been separated, and this opened the way to identification of the reactive molecule fragments on the consecutive stages of the reaction path. Properties have been studied for the two canonical test reactions: CO + HF → HCOF and HONS → ONSH.

New Insights into the (A)Synchronicity of Diels-Alder Reactions: A Theoretical Study Based on the Reaction Force Analysis and Atomic Resolution of Energy Derivatives

“…This observation suggests that most of the systems investigated had a normal electron-demand or normal flux. Moreover, in opposition to Domingo and his co-workers who reported a good correlation between the polarity and the activation energy of DA reactions (R 2 =0.99) [27], we did not observe such a significant correlation in our dataset (R 2 = 0.32, Figure S1). This discrepancy can be first ascribed to the high heterogeneity of our dataset as compared to theirs, which was formed of similar DA reactions involving a unique diene (1,3-cyclopentadiene) against twelve substituted ethylenes.…”

“…The reaction force F and reaction force constant 𝜅 were decomposed into 3 pairs of contributions (A1&A6, A2&A3, A4&A5) involving the six atoms in the reactive site using the approach proposed here [27] and implemented in our AMADAR program. Figure 6 depicts these contributions for an illustrate set of six DA reactions covering a range of synchronicity indices from 0.02 to 1.02Å.…”

“…Assessing the individual role of specific atoms or fragments in the (a)synchronicity of DA reactions in the framework of the RFA supposes that energy derivatives along the reaction path, namely the reaction force F and reaction force constant 𝜅, have been decomposed into atomic contributions. In 2016, Ledrzejewski, Ordon and Komorowski (LOK) [27] demonstrated the feasibility of doing such a decomposition by referring to the Hellman-Feynman theorem, which defines the nature of individual forces acting on nuclei in molecular systems [28]. Their promising approach goes beyond the standard reaction force analysis, bringing up the missing breaks for an accurate atomic resolution of the reactive force F and reaction force constant 𝜅.…”

Evolution of the atomic valence observed by the reaction fragility spectra on the reaction path

“…This requires focusing on atoms in the reacting system. Instead of exploring the common population analyses, the Hellman-Feynman (H-F) forces on nuclei have been proposed for a description of an atom-in-molecule with no other arbitrary definition thereof [7].…”

Interacting Quantum Atoms Analysis of the Reaction Force: A Tool to Analyze Driving and Retarding Forces in Chemical Reactions

“…The latter would be clearly available could the E x ð Þ function be partitioned into chemically relevant components. This has been already attempted, and the reaction force has been decomposed into atomic contributions, [17][18][19][20] into terms related to different degrees of freedom, [21] and into terms related to orbital interactions based on the ETS-NOCV decomposition method. [22] In this work, we present a partition of the RF-based on the Interacting Quantum Atoms method (IQA), [23,24] an exact real space energy decomposition that writes the energy of a molecule as a sum of intra-and inter-atomic terms.…”