Nuclear zero-point energy and quantum delocalization effects of water molecules
So, what was actually said in the paper1 with respect to AIMD simulations of water is the following:


  Nuclear zero-point energy and quantum delocalization effects are neglected making classical water overbound.


To understand the meaning of this statement we first need to know how AIMD works. Ab Initio Molecular Dynamics (AIMD) is a molecular dynamics simulation in which potential energy surfaces for nuclear motion are obtained from first principles (ab initio) rather than represented by a force field. The quantum chemical calculation of potential energy surfaces are done in the Born–Oppenheimer approximation in which nuclei are considered to be stationary classical particles. 

As its very name signifies, it is, of course, just an approximation. It ignores that nuclei move and aren't perfectly localized in space. The nuclear motion can be approximately separated into vibrational and rotational the first of which energetically dominates the second. Taking the vibrational motion on the nuclei into account results in some additional so-called zero-point vibrational energy that rises the total energy. Other quantum effects (tunneling, delocalization) can be also taking into account for the nuclei which results in some further changes in energy. 

Altogether, the more and more quantum effects are taking into account, the closer are the results of the simulations to the physical reality. AIMD simulations ignore few quantum effects, and thus, do not quite match the reality. For instance, water tends to be overbound in such simulations comparing to what we have in the real world. That is, essentially, the meaning of the statement quoted above.



1) A.D. Hammerich, V. Buch, F. Mohamed, Ab initio simulations of sulfuric acid solutions, Chemical Physics Letters, 2008, 460, 423-431, http://dx.doi.org/10.1016/j.cplett.2008.06.053.