Velocity autocorrelation by quantum simulations for direct parameter-free computations of the neutron cross sections. II. Liquid deuterium

Very recently we showed that quantum centroid molecular dynamics (CMD) simulations of the velocity autocorrelation function provide, through the Gaussian approximation (GA), an appropriate representation of the single-molecule dynamic structure factor of liquid H2, as witnessed by a straightforward absolute-scale agreement between calculated and experimental values of the total neutron cross section (TCS) at thermal and epithermal incident energies. Also, a proper quantum evaluation of the self-dynamics was found to guarantee, via the simple Sköld model, a suitable account of the distinct (intermolecular) contributions that influence the neutron TCS of para-H2 for low-energy neutrons (below 10 meV). The very different role of coherent nuclear scattering in D2 makes the neutron response from this liquid much more extensively determined by the collective dynamics, even above the cold neutron range. Here we show that the Sköld approximation maintains its effectiveness in producing the correct cross section values also in the deuterium case. This confirms that the true key point for reliable computational estimates of the neutron TCS of the hydrogen liquids is, together with a good knowledge of the static structure factor, the modeling of the self part, which must take into due account quantum delocalization effects on the translational single-molecule dynamics. We demonstrate that both CMD and ring polymer molecular dynamics (RPMD) simulations provide similar results for the velocity autocorrelation function of liquid D2 and, consequently, for the neutron double differential cross section and its integrals. This second investigation completes and reinforces the validity of the proposed quantum method for the prediction of the scattering law of these cryogenic liquids, so important for cold neutron production and related condensed matter research.