  We show by means of ab-initio calculations that the organic molecular crystal
TTF-CA is multiferroic: it has an instability to develop spontaneously both
ferroelectric and magnetic ordering. Ferroelectricity is driven by a Peierls
transition of the TTF-CA in its ionic state. Subsequent antiferromagnetic
ordering strongly enhances the opposing electronic contribution to the
polarization: it is so large that it switches the direction of the total
ferroelectric moment. Within an extended Hubbard model we capture the essence
of the electronic interactions in TTF-CA, confirm the presence of a
multiferroic groundstate and clarify how this state develops microscopically.
