Using the second virial coefficient as physical criterion to map the hard-sphere potential onto a continuous potential

In the same sense as in the extended law of corresponding states M. Noro and D. Frenkel, J. Chem. Phys. 113, 2941 (2000), we propose the use of the second virial coefficient to map the hard-sphere potential onto a continuous potential. We show that this criterion provides accurate results when the continuous potential is used, for example, in computer simulations to reproduce the physical properties of systems with hard-core interactions. We also demonstrate that this route is straightforwardly applicable to any spatial dimension, does not depend on the particle density and, from a numerical point of view, is easy to implement.