  The interpretation of water line emission from existing observations and
future HIFI/Herschel data requires a detailed knowledge of collisional rate
coefficients. Among all relevant collisional mechanisms, the rotational
(de)excitation of H2O by H2 molecules is the process of most interest in
interstellar space. To determine rate coefficients for rotational de-excitation
among the lowest 45 para and 45 ortho rotational levels of H2O colliding with
both para and ortho-H2 in the temperature range 20-2000 K. Rate coefficients
are calculated on a recent high-accuracy H2O-H2 potential energy surface using
quasi-classical trajectory calculations. Trajectories are sampled by a
canonical Monte-Carlo procedure. H2 molecules are assumed to be rotationally
thermalized at the kinetic temperature. By comparison with quantum calculations
available for low lying levels, classical rates are found to be accurate within
a factor of 1-3 for the dominant transitions, that is those with rates larger
than a few 10^{-12}cm^{3}s^{-1}. Large velocity gradient modelling shows that
the new rates have a significant impact on emission line fluxes and that they
should be adopted in any detailed population model of water in warm and hot
environments.
