Diagonalization of the Cartesian Hessian is subject of the classical analysis and leads to the 3n-6 (or 3n-5) vibrational normal modes for a molecule () and their frequencies. Analogous procedure for C matrix yields (n-1) modes, hereby referred to as the atomic fragility modes (   ): 77 The relation between these two solutions, the normal modes () and the atomic modes (), is indirect, but has been implied by the frequency sum rule described by King, Wilson et al. In the framework of this present work the sum rule reads: