  Upon hydrogen bond formation, electronic charge density is transferred
between the donor and acceptor, impacting processes ranging from hydration to
spectroscopy. Here we use ab initio path integral simulations to elucidate the
role of nuclear quantum effects in determining the charge transfer in a range
of hydrogen bonded species in the gas and liquid phase. We show that the
quantization of the nuclei gives rise to large changes in the magnitude of the
charge transfer as well as its temperature dependence. We then explain how a
single geometric parameter determines the charge transfer through the hydrogen
bond. These results thus demonstrate that nuclear quantum effects are vital for
the accurate description of charge transfer and offer a physically transparent
way to understand how hydrogen bonding gives rise to it.
