  We report calculations of the surface tension of the water-air interface
using ab initio molecular dynamics (AIMD) simulations. We investigate the
simulation cell size dependence of the surface tension of water from force
field molecular dynamics (MD) simulations, which show that the calculated
surface tension increases with increasing simulation cell size, thereby
illustrating that a correction for finite size effects is required for the
small system used in the AIMD simulation. The AIMD simulations reveal that the
double-{\xi} basis set overestimates the experimentally measured surface
tension due to the Pulay stress, while the triple and quadruple-{\xi} basis
sets give similar results. We further demonstrate that the van der Waals
corrections critically affect the surface tension. AIMD simulations without the
van der Waals correction substantially underestimate the surface tension, while
van der Waals correction with the Grimme's D2 technique results in the value
for the surface tension that is too high. The Grimme's D3 van der Waals
correction provides a surface tension close to the experimental value. Whereas
the specific choices for the van der Waals correction and basis sets critically
affect the calculated surface tension, the surface tension is remarkably
insensitive to the details of the exchange and correlation functionals, which
highlights the impact of long-range interactions on the surface tension. These
simulated values provide important benchmarks, both for improving van der Waals
corrections, and AIMD simulations of aqueous interfaces.
