  The quantum nature of nuclei plays an important role in the accurate
modelling of light atoms such as hydrogen, but it is often neglected in
simulations due to the high computational overhead involved. It has recently
been shown that zero-point energy effects can be included comparatively cheaply
in simulations of harmonic and quasi-harmonic systems by augmenting classical
molecular dynamics with a generalized Langevin equation (GLE). Here we describe
how a similar approach can be used to accelerate the convergence of path
integral (PI) molecular dynamics to the exact quantum mechanical result in more
strongly anharmonic systems exhibiting both zero point energy and tunnelling
effects. The resulting PI-GLE method is illustrated with applications to a
double-well tunnelling problem and to liquid water.
