Recently we have exposed the fresh practical power of the application of the vector analysis to the derivatives of the H-F force along a defined reaction path (IRC), meeting the MEC condition. We have found that the divergence of H-F force contains solely the electronic energy of a system, since nuclear-nuclear contributions vanish by the Laplace law. This valuable property has been first mentioned by King et al. as the frequency sum rule. The authors attempted to characterize bond properties with the use force divergencies calling them effective force constants and noticed that the electronic energy contributes exclusively to the divergence of the H-F force. Decius and Wilson also used that sum rule, however, their work has been limited to the isotopic effects. The even earlier deep analysis by Salem contained the clear formulation for the derivatives of the H-F forces. We have established that the H-F force divergences calculated along the reaction path, represent a potential source of quantitative information on evolution of the electron density within a reacting system. This is definitely an approach from atomic and bonding perspective. The H-F force divergences for any system of n atoms form the novel DF Connectivity Matrix C , that describes electronic properties of the system in the long desired atomic resolution. This DF Connectivity Matrix has different meaning than the old, arbitrary concept of the Atomic Connectivity Matrix (ACM) first proposed by Spialter and developed by his followers within the graph theory; the idea has been applied even to an analysis of crystal structures, with appropriate modifications as to reflect the bond valences. Our DF Connectivity Matrix delivers theoretical description of the atomic valences and bond orders providing readily available and exact numerical data. We obtain the elements of the DF Connectivity Matrix elements (CAA, CABcumulative force constants) in the harmonic approximation by appropriate summation of the elements of the Cartesian Hessian. The harmonic oscillator's regime seems to be limiting, however when CAA and CAB are calculated for a sequence of stationary states along the IRC, their step-by-step variations unveil the process beyond the harmonic condition: modification of atomic bonds (and valences) as a result of the ongoing chemical reaction. This straightforward method to picture the mechanism of the chemical reaction leads to the analogous results as observations of the reaction path curvatures provided with the advanced normal modes considerations by Kraka et al., (adiabatic internal vibrational mode AIMO ), within their unified reaction valley approach (URVA). Recently we have investigated in depth the derivatives of the elements of the DF connectivity matrix over reaction progress (dCAA/d, dCAB/d). The working term Reaction Fragility (RF) has been adopted for those derivatives. They were found to reproduce very accurately the evolution of common atomic properties along a reaction path: the evolution of the atomic valence and the bond orders, respectively. 63, The atomic fragilities also provide proper measure for the contribution of an atom to the global reaction force /