Helmholtz free energy is one of the most important thermodynamic properties for condensed matter systems. It is closely related to other thermodynamic properties such as chemical potential and compressibility. It is also the starting point for studies of interfacial properties and phase coexistence if free energies of different phases can be obtained.

In this thesis, we will use an approach based on the Weeks-Chandler-Anderson (WCA) perturbation theory to calculate the free energy of both solid and liquid phases of Lennard-Jones pair potential systems and the free energy of liquid states of Yukawa pair potentials. Our results indicate that the perturbation theory provides an accurate approach to the free energy calculations of liquid and solid phases based upon comparisons with results from molecular dynamics (MD) and Monte Carlo (MC) simulations.