The potential energy Surfaces of the neutral and anionic thymine-water complexes are investigated using high-level ab initio calculations. Both dipole-bound (DB) and valence-bound (VB) anionic forms are considered. Four minima and three first-order stationary points are located, and binding energies are computed. All minima, for both anions, are found to be vertically and adiabatically stable. The binding energies are much higher for valence-bound than for dipole-bound anions. Adiabatic electron affinities are in the 66-287 meV range for VB anions and the 4-60 meV range for DB anions, and vertical detachment energies are in the 698-977 meV and 10-70 meV range for VB and DB anions, respectively. For cases where literature data are available, the computed values are in good agreement with previous experimental and theoretical studies. It is observed that electron attachment modifies the shape of the potential energy surfaces of the systems, especially for the valence-bound anions. Moreover, for both anions the size of the energy barrier between the two lowest energy minima is strongly reduced, rendering, the coexistence of different structures more probable.