Though the electron attachment on the water dimer has been observed, ab initio calculations performed at the Hartree-Fock and post Hartree-Fock levels do not succeed in predicting a bounded (H2O)(2)(-) anion. It is shown that the hybrid density functional approach (B3LYP) yields results in reasonable agreement with experiment, provided a systematic optimization of the basis sets in the variational sense. Neglecting the zero point energy (ZPE) correction, the adiabatic electron affinity (EA) is calculated to be 21.2 meV (30+/-2 experimentally) whereas the vertical detachment energy (VDE) is overestimated by about 10 meV (55.7 against 45). The ZPE correction has been estimated from the frequencies calculated at the harmonic level. It improves noticeably the EA and the VDE which corrected values are 35.6 and 41.9 meV, respectively. The sign and magnitude of the EA and VDE isotopic shifts between the hydrogenated and deuterated species are correctly predicted. The analysis of the electron density difference and of the spin density shows that the electron attachment occurs for one half between the two H2O molecules, the remaining being located outside in the dipole moment direction.