We describe a class of organic molecular magnets based on zwitterionic molecules (betaine derivatives) possessing donor, π bridge, and acceptor groups. Using extensive electronic structure calculations we show the electronic ground-state in these systems is magnetic. In addition, we show that the large energy differences computed for the various magnetic states indicate a high Neel temperature. The quantum mechanical nature of the magnetic properties originates from the conjugated π bridge (only p electrons) in cooperation with the molecular donor-acceptor character. The exchange interactions between electron spin are strong, local, and independent on the length of the π bridge.