Molecular electronegativity in density functional theory(VIII) Charge polarization modes in a closed system

Based on the density functional theory and the atom-bond electronegativity equalization model (ABEEM), a method is proposed to construct the softness matrix and to obtain the electron population normal modes (PNMs) for a closed system. Using this method the information about the bond charge polarization in a molecule can be obtained easily. The test calculation shows that the PNM obtained by this method includes all the modes about the bond charge polarization explicitly. And the bond charge polarization mode characterized by the biggest eigenvalue, which is the softest one of all modes related with chemical bonds, can describe the charge polarization process in a molecule as exquisitely as the correspondingab initio method.