Conceptual DFT analysis of the fragility spectra of atoms along the minimum energy reaction coordinate

Abstract

Theoretical justification has been provided to the method for monitoring the sequence of chemical bonds' rearrangement along a reaction path, by tracing the evolution of the diagonal elements of the Hessian matrix. Relations between the divergences of Hellman-Feynman forces and the energy and electron density derivatives have been demonstrated. By the proof presented on the grounds of the conceptual density functional theory formalism, the spectral amplitude observed on the atomic fragility spectra [L. Komorowski et al., Phys. Chem. Chem. Phys. 18, 32658 (2016)] reflects selectively the electron density modifications in bonds of an atom. In fact the spectral peaks for an atom reveal changes of the electron density occurring with bonds creation, breaking, or varying with the reaction progress.

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

“…7 is recognized as the energy density of the electrostatic field generated by nucleus A. Thus, observation of the atomic fragility along the reaction path provides a spectrum of changes in the electron density in bonding regions of an atom in question [5].…”

“…We have developed regional chemical potential evolution and identified the most reactive state along the IRC reaction path [4]. Recently, we introduced a new concept of reaction fragility to identify reaction mechanism and to spot electron density modifications along the IRC reaction path [5,6] . We introduced a novel approach, aiming at observation of the electron density flow between atoms, rather than tracing the global parameters of the system.…”

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

“…. This result can be derived from the vector representation of the H-F force as highlighted in previous work by Piotr Ordon et al [105] As a result, the second derivative of the energy (divergence of the H-F force) only depends on electronic contributions.…”

“…[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:…”

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

“…When other sources of electric field are present, for example, other nuclei nearby, C AA > 0 as has been demonstrated by the connectivity matrices. 39 However, the integral in eq 8 calculated for an atom can be finite if, and only if…”