  The isothermal compressibility of water is essential to understand its
anomalous properties. We compute it by ab initio molecular dynamics simulations
of 200 molecules at five densities, using two different van der Waals density
functionals. While both functionals predict compressibilities within ~30% of
experiment, only one of them accurately reproduces, within the uncertainty of
the simulation, the density dependence of the self-diffusion coefficient in the
anomalous region. The discrepancies between the two functionals are explained
in terms of the low- and high-density structures of the liquid.
