We present a semi-classical theory of the impact polarization due to a quadrupolar electric excitation, well-suited to this forbidden line. In addition, this line is also radiatively forbidden being a triplet-singlet transition. This is overcome by scaling the semi-classical result to a full quantum calculation at a single energy value. The cross-section and impact polarization are thus obtained as a function of energy (with good agreement with the quantum calculated cross-section), and the behavior of the impact polarization is found quite different of the usual one of the dipolar electric interaction. Denoting as radial the polarization parallel to the incident beam or magnetic field, and as tangential the perpendicular polarization, the dipolar interaction (permitted lines) leads to radial polarization at low energy, and tangential polarization at high energy, the polarization vanishing at energy about twelve times the threshold energy. In the case of the quadrupolar electric interaction, we get a quite different behavior, the vanishing point being much closer to the threshold energy. This leads to reanalyze the auroræ red line polarization observation by Lilensten et al. (2008), and to conclude that the line is only weakly radially polarized and only during the auroral events. The weak polarization level leads to consider the competing depolarization by collisions with the neighboring O atoms, whose density could then be diagnosed with further measurements and calculations.