The molecular structure and vibrational spectra of the different oxidation states of tetrakis(dimethylamino)ethylene (TDAE) are calculated using structural optimization and normal-mode calculations. The predictions are compared with x-ray structural data and infrared spectra of TDAE, TDAE-C-60 and (TDAE)(Cl)(2). The C-N stretch vibration frequency and axial torsional angle are shown to be sensitive indicators of the charge state of the molecule. TDAE(+), which occurs in TDAE-C-60 is found to have a near-degenerate configurational ground state.