Numerical Calculations by the Hellmann—Feynman Procedure

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

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.