Optical control of electron spin states is important for quantum sensing and computing applications, as developed with the diamond nitrogen vacancy centre. This requires electronic excitations, excitons, with net spin. Here we report a molecular diradical where two trityl radical groups are coupled via a meta-linked fluorene bridge. The singlet exciton is at lower energy than the triplet because electron transfer from one of the radical non-bonding orbitals to the other is spin allowed, set by the charging energy for the double occupancy of the non-bonding level, the Hubbard U. Both excitons give efficient photoluminescence at 640 and 700 nm with near unity efficiency. The ground state exchange energy is low, 60 µeV, allowing control of ground state spin populations. We demonstrate spin-selective intersystem crossing and show coherent microwave control. We report up to 8% photoluminescence contrast at microwave resonance. This tuning of the singlet Mott–Hubbard exciton against the ‘bandgap’ exciton provides a new design platform for spin–optical materials.