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.

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.

We report an original method that provides a new insight into the reaction mechanism by direct observation of bond breaking and formation. Variations of the diagonal elements of the Hessian along the IRC are shown to reflect the anharmonic properties of the system that are induced by electron density modifications upon the reaction. This information is presented in the form of the reaction spectrum, demonstrating how particular atoms engage in the reorganization of bonds. The test reactions are: HCOF synthesis and HONS isomerization.

The concept of a connectivity matrix, essential for the reaction fragility (RF) spectra technique for monitoring electron density evolution in a chemical reaction, has been supported with a novel formulation for the diagonal matrix elements; their direct link to the electron density function ρ­(r) has been demonstrated. By combining the concept with the atomization energy of a system, the separation of the potential energy into atomic and/or bond contributions has been achieved. The energy derivative diagrams for atoms and bonds that are variable along a reaction path provide new insight into the reaction mechanism. Diagonalization of the connectivity matrix resulted in the eigenvectors that provide information on a role of individual atoms in the development of structural changes along a reaction path.