Analytic equation of state for generalized Lennard-Jones solid including lowest-order anharmonic and correlation corrections

Based on the cell model, the general formula for the free energy of solids is derived analytically with the lowest order anharmonic modification and c orrelation effect taken into account. Combining a method of summing over la ttice sites, the analytic equation of state for generalized Lennard-Jones s olid is derived. The calculations show that the agreement between theory an d computer simulation is quite good and is significantly improved as compar ed with the numerical results in literature. The comparison of different ef fects shows the theory including all neighbors but only considering the low est anharmonic and correlation effects may be a good and convenient approxi mation for practical solids. The approximation can be easily extended to th e quantum case and other generalized potentials.