  The behavior of liquid water under an electric field is a crucial phenomenon
in science and engineering. However, its detailed description at a microscopic
level is difficult to achieve experimentally. Here we report on the first ab
initio molecular-dynamics study on water under an electric field. We observe
that the hydrogen-bond length and the molecular orientation are significantly
modified at low-to-moderate field intensities. Fields beyond a threshold of
about 0.35 V/\AA are able to dissociate molecules and sustain an ionic current
via a series of correlated proton jumps. Upon applying even more intense fields
(1.0 V/\AA), a 15-20% fraction of molecules are instantaneously dissociated and
the resulting ionic flow yields a conductance of about 7.8
$\Omega^{-1}cm^{-1}$, in good agreement with experimental values. This result
paves the way to quantum-accurate microscopic studies of the effect of electric
fields on aqueous solutions and, thus, to massive applications of ab initio
molecular dynamics in neurobiology, electrochemistry and hydrogen economy.
