In order to explore the dynamic problem of the electronic structure in the ground state for the Creutz-Taube ion, the calculations on the electronic potential surfaces along the totally symmetric vibrational difference coordinate of the Ru-N stretch and the net charge distribution on the Ru atoms are carried out by using the density functional theory in the two schemes with or without the Ru-N(pyz) vibration. It is shown that the vibration associated with the totally symmetric vibrational difference coordinate Q(-) can be regarded as a harmonic oscillation with 123.16 eV Angstrom(-2) of the force constant, and 430 cm(-1) of the fundamental frequency is obtained on the basis of the five-body vibrator model. From the electronic structure calculated in the ground state it is concluded that the asymmetric net distribution on the Ru atoms in the Creutz-Taube ion occurs in the vibration associated with the totally symmetric vibrational difference coordinate, and the charge transfer between the Ru atoms and the ligands is responsible for the asymmetric charge distribution. The total symmetric vibrations of Ru-N for the related monomer [(NH3)(5)Ru(pyz)](2+/3+) are further examined. It is found that the reduction of Ru(III) to Ru(II) corresponds to 0.05 Angstrom of the difference in Ru-N distance between the two Ru-subunits under the asymmetric distortion and to 0.012 eV of the potential energy over the zero point energy, which is comparable with kT. The Born-Oppenheimer approximation and the neglected coupling effect between the electronic and nuclear motion in the present paper are briefly discussed.