Several dynamic properties of the 4-n-alkyl-4'-cyanobiphenyls series (nCB) with n = 5, 6, 7, 8 have been studied by atomistic molecular dynamics (MD) simulations in the NVE ensemble adopting an ab initio derived force field (J. Phys. Chem. B 2007, 111, 2130). For each homologue, at least two state points, in the nematic and in the isotropic phase, as determined from lengthy equilibration runs performed in the previous work, have been considered. More than 10 ns have been produced at each state point, allowing us to calculate single-molecule properties as the translational and rotational diffusion coefficients along the series. An oscillating behavior of the diffusion coefficients, similar to the observed odd-even effect in static properties, has been predicted by MD. A good agreement with the results of purposely carried out H-1 NMR measurements is achieved, provided the MD values are increased by a factor that accounts for density overestimation. Spinning and tumbling rotational motions, monitored by calculating the rotational diffusion coefficients for all homologues in both phases, agree well with experimental data, at least for 5CB where NMR measures are reported. Collective properties, such as the isotropic shear viscosity and the rotational viscosity coefficient, have been computed for all homologues, and the MD values agree well with the experimental data reported in the literature. Finally, the origin of the odd-even effect, found for all the computed dynamic properties, is addressed.