The properties of excess hydrated electrons in liquid water, at room temperature, are studied via coupled quantum-classical simulations. In these simulations, the system evolves dynamically on the adiabatic potential energy surface with the electron maintained in the ground state throughout the process. The diffusion constant of the hydrated electron under field-free conditions is found to be the same as that obtained, via the Nernst-Townsend-Einstein relation, from the electron mobility simulated for a system under an electric field of 3.2x106 V/cm, acting on the electron. For larger electric fields, the electron mobility is found to be field dependent. The mode of migration of the excess electron is polaronic in nature and the influence of the intramolecular degrees of freedom of the water molecules on the hydrated electron transport properties is investigated. It is shown that the electron diffusion constant obtained in simulations under field-free conditions with rigid-water molecules [De0 = (3.7 ± 0.7)x10 -5 cm2/s] is larger than that obtained from simulations where a flexible-water model potential is employed De0 = (1.9 ± 0.4)x10-5] cm2/s] and smaller than the experimental estimated value obtained from conductivity measurements (4.9x10-5 cm2/s). The difference between the diffusion constants calculated for the two models is correlated with a marked enhancement of the probability of reversal of the direction of motion of the migrating electron in flexible water. The self-diffusion constant of water using the rigid-molecules model [Ds = (3.6 ± 0.4)x10-5 cm2/s] is also larger than that found for the flexible-water molecule model Ds = (2.3 ± 0.2)x10-5] cm2/s], with the latter in agreement with the experimental value (Ds = 2.3x10-5 cm2/s). Structural and dynamical aspects of hydrated electron transport are discussed.