- Write the Fortran program to calculate the chemical potential for a Lennard-Jones fluid in the canonical (N, V, T)-constant ensemble using the Widom test particle insertion method. Include the long-range correction for the chemical potential.
- Run the simulation at kT/epsilon=1.0 and 1.5 for a range of reduced densities (0.2, 0.4, 0.6, 0.8).
- Compare the values of chemical potential obtained from the simulation with the values from the Nicolas equation of state and the Johnson equation of state.
- Discuss the results.

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