A density of states transformation Monte Carlo method: thermodynamics of the Lennard-Jones fluid

The standard NVT ensemble Metropolis Monte Carlo method is modified to include uniformly weighted steps in ln β as well as weighted steps in U, the total potential energy. This simulation is used to sample a soft sphere (r−12 potential) fluid over a very wide range of energies. For each r−12 energy U12, the corresponding r−6 energy U6 is also recorded. Information from the simulation is used to determine relative values of the configurational density of states γ12(U12 ) (i.e., the number of configurations with total potential energy between U12 and U12+dU12) for the soft sphere fluid over a large range in energy. Then using the distribution of U6 at each U12, the configurational density of states for arbitrary linear combinations of U12 and U6 is determined and the equation of state for the Lennard-Jones fluid is evaluated for a wide range of densities and temperatures in a very efficient manner. The generalization to simulations of other linear combinations of potentials is discussed.