Family of tunable spherically symmetric potentials that span the range from hard spheres to waterlike behavior

We investigate the equation of state, diffusion coefficient, and structural order of a family of spherically symmetric potentials consisting of a hard core and a linear repulsive ramp. This generic potential has two characteristic length scales: the hard and soft core diameters. The family of potentials is generated by varying their ratio, λ. We find negative thermal expansion (thermodynamic anomaly) and an increase of the diffusion coefficient upon isothermal compression (dynamic anomaly) for 0≤λ<6/7. As in water, the regions where these anomalies occur are nested domes in the (T,ρ) or (T,P) planes, with the thermodynamic anomaly dome contained entirely within the dynamic anomaly dome. We calculate translational and orientational order parameters (t and Q6), and project equilibrium state points onto the (t, Q6) plane, or order map. The order map evolves from waterlike behavior to hard-sphere-like behavior upon varying λ between 4/7 and 6/7. Thus, we traverse the range of liquid behavior encompassed by hard spheres (λ=1) and waterlike (λ∼4/7) with a family of tunable spherically symmetric potentials by simply varying the ratio of hard to soft-core diameters. Although dynamic and thermodynamic anomalies occur almost across the entire range 0≤λ≤1, waterlike structural anomalies (i.e., decrease in both t and Q6 upon compression and strictly correlated t and Q6 in the anomalous region) occur only around λ=4/7. Waterlike anomalies in structure, dynamics and thermodynamics arise solely due to the existence of two length scales, with their ratio λ being the single control parameter, orientation-dependent interactions being absent by design.