  It is now established that nuclear quantum motion plays an important role in
determining water's hydrogen bonding, structure, and dynamics. Such effects are
important to include in density functional theory (DFT) based molecular
dynamics simulation of water. The standard way of treating nuclear quantum
effects, path integral molecular dynamics (PIMD), multiplies the number of
energy/force calculations by the number of beads required. In this work we
introduce a method whereby PIMD can be incorporated into a DFT simulation with
little extra cost and little loss in accuracy. The method is based on the many
body expansion of the energy and has the benefit of including a monomer level
correction to the DFT energy. Our method calculates intramolecular forces using
the highly accurate monomer potential energy surface developed by
Partridge-Schwenke, which is cheap to evaluate. Intermolecular forces and
energies are calculated with DFT only once per timestep using the centroid
positions. We show how our method may be used in conjunction with a multiple
time step algorithm for an additional speedup and how it relates to ring
polymer contraction and other schemes that have been introduced recently to
speed up PIMD simulations. We show that our method, which we call "monomer
PIMD", correctly captures changes in the structure of water found in a full
PIMD simulation but at much lower computational cost.
