4-Cyano-4'-pentylbiphenyl (5CB, Fig. ) is perhaps the most well-studied nematic liquid crystal, both experimentally and in silico, and so is a logical demonstrator for our CDF code. We performed a 50 ns long simulation of 3600 molecules of 5CB at a temperature of 293 K, giving a nematic phase with an orientational order parameter (<P2>) of 0.56. We computed the CDF (Fig. ) as well as the radial distribution function (RDF, Fig. ) for the production MD run. The CDF shows a region of zero probability centred at h=r=0 Å, which results from steric repulsion of molecules. High probability regions at h=±10, r=0 Å result from antiparallel pairs of molecules, and at h=0, r ~ 5.5 Å from side-by-side pairs. A series of arcs centred on h=0 Å occur every r ~5.5 Å as a consequence of side-by-side packing of molecules; the diffusivity indicates a lack of positional order, as expected for the nematic state Contrast this with the conventional RDF plot, shown in Figure . Each of the features present in the CDF can be located in the RDF; the region of zero probability at r < 3.5 Å, the large peak at r ~ 5.5 Å, and sequential shells occurring every 5.5 Å. However, owing to the radial binning procedure information about anisotropy and orientation is lost. In the present case, calculation of the RDF took around 5 minutes using the Gromacs tool gmx rdf, whereas the CDF was computed in around 7 minutes using cylinder.py, both on a single Intel E5-2650v4 CPU core on the ARC3 computer at the University of Leeds. So-called ferroelectric nematics (NF) are an exciting recent discovery, in which the orientational order of conventional nematics (such as 5CB) is augmented with polar order. Polar nematic order gives rise to extremely large ferroelectric polarisations, which are of interest to both fundamental and applied science. We simulated a polar nematic configuration of the NF material RM554 (Figure ) by taking an isotropic configuration of 680 molecules with liquid-like density of 1.1 g cm and applying a static electric field (0.1 V nm -1 ) along the y-axis; this gives a large polar order parameter (<P1>) of ~ 0.9 and an orientational order parameter (<P2>) of ~ 0.65. Following this, a production MD simulation (without biasing field) of 250 ns was performed from this polar configuration at a temperature of 375 K with anisotropic pressure coupling; note that, as with prior simulations, the polar order is essentially constant over the entire production run. Comparison of the CDF of the polar nematic phase of RM554 with the conventional nematic phase of 5CB reveals significant differences. Polar nematic phases predictably feature significant head-to-tail intermolecular associations, leading to arc-like features centred on r=0 and h ~ ± 20 Å (i.e. the molecular length). Off-axis features correspond to staggered (h ~ ± 11 Å and ± 6 Å) and side-by-side (h = 0 Å) pairing modes. We now consider nematic phases formed by bent core molecules, specifically the oxadiazole C5-Ph-ODBP-Ph-OC12 (Fig. ). Our simulation consists of 1000 molecules at 483 K; a non-polar nematic phase forms spontaneously giving a <P2> of 0.61±0.019, which compares favourably with experimental data and earlier MD simulations. We compute the CDF, using a slightly larger length cut-off of 50 Å to account for the end-to-end molecular length of this material (~ 45 Å). The most prominent feature in the CDF is at h=0, r = 5 Å, and results from side-by-side pairs of molecules which are themselves likely to be consequence by dipole-dipole interactions between neighbouring 1,3,4-oxadiazole units; the lack of repeats indicates these interactions to be short-range in nature. A pair of diffuse features at h ~ ±40 Å result from the end-to-end separation of molecules, while diffuse features at h ~ ±9 Å are a consequence of staggered pairs of molecules with the 1,3,4oxadiazole being proximal to the carboxylate ester. We now turn to analysis of simulations of mesophases with some degree of positional order (layers, columns etc.). We simulated1500 molecules of 8OCB at a temperature of 365 K; visual inspection reveals the formation of a smectic A mesophase after around 180 ns (Figure ); the production MD run was continued for a further 250 ns from this point, and only the smectic portion of the trajectory was utilised in our subsequent analysis. For the smectic portion of the trajectory we find <P2> = 0.66±0.022, close to both experimental and prior MD simulations. We confirmed the formation of a smectic A phase by dividing the simulation into 75 slices of equal thickness (with the slice plane being perpendicular to the director) and computing the number of centres-of-mass (COM) in each slice; a plot of COM density vs thickness gives the layer spacing as the distance between the maxima (Figure ). For our simulation we find an average layer spacing of 3.42 nm, which compares with an experimental value 3.2.