Grand Molecular Dynamics: A Method for Open Systems

Cagin, T and Pettitt, BM


We present a new molecular dynamics method for studying the dynamics of open systems. The method couples a classical system to a chemical potential reservoir. In the formulation, following the extended system dynamics approach, we introduce a variable, nu to represent the coupling to the chemical potential reservoir. The new variable governs the dynamics of the variation of number of particles in the system. The fractional part of the new variable is used to scale the potential energy and the kinetic energy of an additional particle: i.e. we introduce a fractional particle. We give the ansatz Lagrangians and equiations of motion for both the isothermal and adiabatic forms of grand molecular dynamics. The averages calculated over the trajectories generated by these equations of motion represent the classical grand canonical ensemble (muVT) and the constant chemical potential adiabatic ensemble (muVL) averages, respectively. The microcanonical phase space densities of the adiabatic and isothermal forms of the molecular dynamics method are shown to be equivalent to adiabatic constant chemical potential adiabatic ensemble, and grand canonical ensemble partition functions. We also discuss extension to multi-component systems, molecular fluids, ionic solutions and the problems and solutions associated with the implementation of the method. The statistical expressions for the thermodynamic functions such as specific heat, adiabatic bulk modulus, Gruneissen parameter and number fluctuations are derived. These expressions are used to analyse trajectories of constant chemical potential systems.