Prediction and Refinement of High-Order Virial Coefficients for a Hard-Sphere System

The n^th virial coefficient for a hard-sphere system is expressed as the sum of n² and a remainder. When n≥3, the remainders of the virials can be accurately expressed with Pade-type functions of n. The maximum deviations are only 0.039-0.053%, which are much better than the existing approaches. By using the predicted virials, the compressibility factors of the hard-sphere system can be predicted very accurately in the whole stable fluid region, and those in the metastable fluid region can also be well predicted up to a packing fraction of 0.545. The simulated B₇ and B₁₀ are found to be inconsistent with the other known virials, and thus they are refined to be 53.2467 and 105.042, respectively.