The second term in the Taylor expansion for the energy may be formulated by means of the connectivity matrix (eq. 25), rather than by the Cartesian Hessian; it represents the vibrational energy vib E  . For a system in equilibrium the first term vanishes. The proof has been accomplished: the connectivity matrix represents complete measure for the vibrational energy contribution to the energy of a system. By using the basic properties of the connectivity matrix 0 and