Bond Fragility Spectra for the Double Proton-Transfer Reaction in the Formic Acid-Type Dimers

Abstract

The newly developed method of fragility spectra for observation of bond breaking and formation upon a reaction has been applied to the canonical reaction series of the double proton transfer (DPT). Formic acid and its thio-analogues HCXYH (X, Y = O, S) have been chosen for the analysis. Very accurate linear correlations have been determined between the nondiagonal elements of the connectivity matrix, essential for the method, and the Wiberg bond orders for the corresponding bonds. Relation of the slope of this correlation to the global softness and to the atomic numbers of the bonded atoms has been proved, thus corroborating the c-DFT formula describing the fragility spectra. The electron density changes in bonds, as observed by the fragility spectra, are in harmony with the curvature diagrams reported by other authors.

Intramolecular proton transfer in the isomerization of hydroxyacetone: Characterization based on reaction force analysis and the bond fragility spectrum

“…(2) The magnitude of changes in O-H bonds are higher in magnitude than changes in C-H bonds, this is consistent to previous data from Piotr Ordon and coworkers when studying the isomerization in the HCOSH molecule. [74] The DPT mechanism in R3, while still asynchronous in nature, shows more synchronicity than the DPT steps of R1. The two bonds that rupture in the process (H1-O2 and H5-C3) both begin weakening before the transition state region at around ξ = 2.5 and both are completely broken by the end of the transition state region.…”

“…Recent work has utilized these properties in order to track the modification of electron densities around atoms and bonds respectively throughout a chemical reaction. [74,77] It has been proven that the changes to the H-F force derivative throughout a chemical reaction should primarily be attributable to the modulation in electron density in the internuclear region between atoms A and B. [105] This derivative throughout the reaction coordinate is termed the "bond fragility spectrum" (a AB ξ ), if a connectivity matrix is calculated for every point along the reaction coordinate the bond fragility spectrum can be calculated as:…”

“…However it should be stressed that this is not limited to bonded atoms, the definition of the H-F force gradient is general and calculated for all pairs of atoms. Extensive benchmark studies on proton transfer reactions have shown a strong correlation between the elements of the connectivity matrix and the Widberg bond indices, [74] thus the interpretation of the fragility spectrum can be seen as similar to analyzing bond order derivatives.…”

“…[72,73] Additionally, a recent method developed by Piotr Ordon and coworkers called the bond fragility spectrum aims to analyze the sequence of bond breaking/formation for a reaction by investigating the derivative of properties based on the molecular Hessian. [74][75][76][77] In the present study, we utilize all of these theoretical tools in order to characterize the proton transfer reactions involved in the isomerization of hydroxyacetone to 2-hydroxypropanal. Specifically we will characterize the nature of each elementary reaction step as SPT or DPT, and for all DPT mechanisms we will classify their relative synchronicity.…”

The Connectivity Matrix: A Toolbox for Monitoring Bonded Atoms and Bonds

“…Persuasive pictures for bond formating/breaking along IRC have already been demonstrated for several reactions as the reaction fragility (RF) spectra for atoms and bonds. 39,40,43,44 The aim of this work is to review briefly the properties of the divergences (eq 2) collected in the connectivity matrix for a system, in order to demonstrate their new explicit relation to the electron density function (section 2). Application of the concept to tentative separation of the potential energy of a system into atomic contributions and their observation in a system undergoing a reaction has been presented in sections 3 and 4.…”