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A robust and model free Monte Carlo simulation method is proposed to address the challenge in computing the classical density of states and partition function of solids. Starting from the minimum configurational energy, the algorithm partitions the entire energy range in the increasing energy direction ("upward") into subdivisions whose integrated density of states is known. When combined with the density of states computed from the "downward" energy partitioning approach [H. Do, J. D. Hirst, and R. J. Wheatley, J. Chem. Phys. 135, 174105 (2011)], the equilibrium thermodynamic properties can be evaluated at any temperature and in any phase. The method is illustrated in the context of the Lennard-Jones system and can readily be extended to other molecular systems and clusters for which the structures are known. [ABSTRACT FROM AUTHOR]

Accurate virial coefficients BN(λ,ɛ) (where ɛ is the well depth) for the three-dimensional square-well and square-step potentials are calculated for orders N=5-9 and well widths λ=1.1−2.0 using a very fast recursive method. The efficiency of the algorithm is enhanced significantly by exploiting permutation symmetry and by storing integrands for reuse during the calculation. For N=9 the storage requirements become sufficiently large that a parallel algorithm is developed. The methodology is general and is applicable to other discrete potentials. The computed coefficients are precise even near the critical temperature, and thus open up possibilities for analysis of criticality of the system, which is currently not accessible by any other means. [ABSTRACT FROM AUTHOR]