Quantum momentum distribution and quantum entanglement in the deep tunneling regime

In this paper, we consider the momentum operator of a quantum particle directed along the displacement of two of its neighbors. A modified open-path path integral molecular dynamics is presented to sample the distribution of this directional momentum distribution, where we derive and use a new estimator for this distribution. Variationally enhanced sampling is used to obtain this distribution for an example molecule, malonaldehyde, in the very low temperature regime where deep tunneling happens. We find no secondary feature in the directional momentum distribution and that its absence is due to quantum entanglement through a further study of the reduced density matrix.