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Accurate knowledge of the single-molecule (self-) translational dynamics of liquid para-${\mathrm{H}}_{2}$ is an essential requirement for the calculation of the neutron scattering properties of this important quantum liquid. We show that, by using centroid molecular dynamics (CMD) quantum simulations of the velocity autocorrelation function, calculations of the total neutron cross section (TCS) remarkably agree with experimental data at the thermal and epithermal incident neutron energies where para-${\mathrm{H}}_{2}$ dynamics is actually dominated by the self-contributions. This result shows that a proper account of the quantum nature of the fluid, as provided by CMD, is a necessary and very effective condition to obtain the correct absolute-scale cross section values without the need of introducing any empirically adjusted quantity. At subthermal incident energies, appropriate modeling of the para-${\mathrm{H}}_{2}$ intermolecular (distinct) dynamics also becomes crucial, but quantum simulations are not yet able to cope with it. Existing simple models which account for the distinct part provide an appropriate correction of self-only calculations and bring the computed results in reasonable accord with TCS experimental data available until very recently. However, if just published cross section measurements in the cold range are considered, the agreement turns out to be by far superior and very satisfactory. The possible origin of slight residual differences will be commented on and suggests further computational and experimental efforts. Nonetheless, the ability to reproduce the total cross section in the wide range between 1 and 900 meV represents an encouraging and important validation step of the CMD method and of the present simple algorithm.