Inelastic neutron scattering from liquid para-hydrogen by ring polymer molecular dynamics

We investigate the use of the ring polymer molecular dynamics (RPMD) method to calculate the incoherent dynamic structure factor of liquid para-hydrogen at a temperature of 14 K. Two different approximation schemes are considered: the RPMD approximation to the self relaxation function F˜s(κ,t) and the Gaussian approximation to the intermediate scattering function Fs(κ, t). We find that both approximations give similar results for low momentum transfer, but that their predictions differ appreciably for κ > 1.5 Å−1. Exact moment constraints are then used to differentiate between the two approximations. These constraints suggest that the Gaussian approximation to Fs(κ, t) employing the RPMD velocity autocorrelation function is the more accurate of the two approximations for large κ. We end by comparing the results of this approximation with those of a recent inelastic neutron scattering experiment involving two different kinematic lines in the (κ, ω) (momentum and energy transfer) plane.