Monitoring Evolution of Atoms and Bonds on a Reaction Path by the Reaction Fragility Method

. The theoretic foundations of the novel method for the comprehensive studies on the mechanism of the evolution of the electronic structure in a chemical reaction have been presented. Our method provides quantification for both the sequence of bond forming and breaking and the degree of bond (order) modifications along the chemical reaction path. The new Density Functional Connectivity Matrix has been introduced: its elements are the divergences of the Hellmann–Feynman forces for atoms in a molecule over the atomic displacements. They have been proved to describe to what extend atoms in a molecule are actually connected with chemical bonds or bonding interactions. The matrix provided foundation for the Reaction Fragility Method. (i) With the use of the Conceptual Density Functional Theory we have completed the road map to characterization of the properties of atoms and bonds in a molecule. We have derived the new gradient theorem, essential for demonstrating the direct link between divergences of the Hellman-Feynman forces on the nuclei and the linear response function of electron density. (ii) The vibrational energy of a system has been decomposed into the atomic fragility modes through diagonalization of the DF Connectivity Matrix, by analogy with the formalism of the normal modes. We present numerical results for the evolution of the atomic fragility modes on the reaction path in the test reaction of the internal proton transfer in H2N-CHO molecule. The visualization of the involvement of bonds and/or contacts between individual atoms on consecutive steps of the reaction has been demonstrated. (iii) The bond fragilities introduced in previous works clearly deliver description of the anharmonic effects for all bonds/contacts in the reacting system. Here we demonstrate how the bond fragilities provide a unique measure of the anharmonic effects in the system, reflecting the response of the vibrational electronic energy to changes in the distances between atoms. The additive contributions from all bonds are combined to the unique global anharmonicity parameter, the third electron energy derivative over the reaction progress. This quantity can be used as a measure of the global changes in a molecule, when they are triggered step by step along a specific reaction path.