Light nuclei at room temperature and below exhibit a kinetic energy which significantly deviates from the predictions of classical statistical mechanics. This quantum kinetic energy is responsible for a wide variety of isotope effects of interest in fields ranging from chemistry to climatology. It also furnishes the second moment of the nuclear momentum distribution, which contains subtle information about the chemical environment and has recently become accessible to deep inelastic neutron scattering experiments. Here we show how, by combining imaginary time path integral dynamics with a carefully designed generalized Langevin equation, it is possible to dramatically reduce the expense of computing the quantum kinetic energy. We also introduce a transient anisotropic Gaussian approximation to the nuclear momentum distribution which can be calculated with negligible additional effort. As an example, we evaluate the structural properties, the quantum kinetic energy, and the nuclear momentum distribution for a first-principles simulation of liquid water.
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