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Register a new userEfficient first-principles calculation of the quantum kinetic energy and momentum distribution of nuclei
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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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Even at room temperature, quantum mechanics plays a major role in determining the quantitative behaviour of light nuclei, changing significantly the values of physical properties such as the heat capacity. However, other observables appear to be only weakly affected by nuclear quantum effects (NQEs): for instance, the melting temperatures of light and heavy water differ by less than 4 K. Recent theoretical work has attributed this to a competition between intra and inter molecular NQEs, which can be separated by computing the anisotropy of the quantum kinetic energy tensor. The principal values of this tensor change in opposite directions when ice melts, leading to a very small net quantum mechanical effect on the melting point. This paper presents the first direct experimental observation of this phenomenon, achieved by measuring the deuterium momentum distributions n(p) in heavy water and ice using Deep Inelastic Neutron Scattering (DINS), and resolving their anisotropy. Results from the experiments, supplemented by a theoretical analysis, show that the anisotropy of the quantum kinetic energy tensor can also be captured for heavier atoms such as oxygen.
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