Grand Molecular Dynamics: A Method for Open Systems
Cagin, T and Pettitt, BM
MOLECULAR SIMULATION 6,5-26(1991)
ABSTRACT
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.