We have determined the optimized structures, relative energies and intramolecular reactions for two anionic forms of malonic acid, anion malonate(-1) (HO2CCH2CO2-) and malonate(-2) (-O2CCH2CO2-).For this purpose we employed accurate quantum chemistry calculations using second-order Moller-Plesset perturbation theory and Density Functional Theory with an aug '-cc-p-VTZ basis set to determine the structures and energies, and a novel metadynamics method based on Car-Parrinello molecular dynamics for the thermal reactions. For both malonates, we found new isomers (keto and enol structures) characterized by CO2 rotations and intramolecular proton transfers. These proton transfers characterize the keto-enol tautomerism that takes place both in the monoanion and dianion. In all cases, the keto tautomer is the more stable configuration. The metadynamics method allows the system to explore the potential energy surface in a few picoseconds, crossing activation barriers of 20-50 kcal/mol.