Molecular dynamics in the isothermal-isobaric ensemble: the requirement of a "shell" molecule. III. Discontinuous potentials.

Based on the approach of Gruhn and Monson [Phys. Rev. E 63, 061106 (2001)], we present a new method for deriving the collisions dynamics for particles that interact via discontinuous potentials. By invoking the conservation of the extended Hamiltonian, we generate molecular dynamics (MD) algorithms for simulating the hard-sphere and square-well fluids within the isothermal-isobaric (NpT) ensemble. Consistent with the recent rigorous reformulation of the NpT ensemble partition function, the equations of motion impose a constant external pressure via the introduction of a shell particle of known mass [M. J. Uline and D. S. Corti, J. Chem. Phys. 123, 164101 (2005); 123, 164102 (2005)], which serves to define uniquely the volume of the system. The particles are also connected to a temperature reservoir through the use of a chain of Nose-Hoover thermostats, the properties of which are not affected by a hard-sphere or square-well collision. By using the Liouville operator formalism and the Trotter expansion theorem to integrate the equations of motion, the update of the thermostat variables can be decoupled from the update of the positions of the particles and the momentum changes upon a collision. Hence, once the appropriate collision dynamics for the isobaric-isenthalpic (NpH) equations of motion is known, the adaptation of the algorithm to the NpT ensemble is straightforward. Results of MD simulations for the pure component square-well fluid are presented and serve to validate our algorithm. Finally, since the mass of the shell particle is known, the system itself, and not a piston of arbitrary mass, controls the time scales for internal pressure and volume fluctuations. We therefore consider the influence of the shell particle algorithm on the dynamics of the square-well fluid.