Modification of the Mayer Sampling Method for the Calculation of High-Order Virial Coefficients


  • M. V. Ushcats Admiral Makarov National University of Shipbuilding



virial coefficient, irreducible cluster integral, Mayer’s function, Mayer sampling, Monte Carlo method


A technique for the calculation of high-order virial coefficients, which combines the quadrature integration and the Mayer sampling Monte Carlo method (MSMC), is proposed. Unlike the original MSMC, this technique does not require to know the reference coefficients for the hard-sphere potential and can be used in a wide range of temperatures and for various interaction potentials. In addition, the proposed method has a higher accuracy at lower computational costs. It has been used to obtain some new data on the seventh virial coefficient of the Lennard-Jones (12-6) model.


A. Isihara, Statistical physics (Academic Press, New York, 1971).

J.E. Mayer and M.G. Mayer, Statistical Mechanics (Wiley, New York, 1977).

M.V. Ushcats and S S. Koval, Fiz. Aerodispers. Sist. 46, 64 (2009).

M.V. Ushcats, Visn. Kharkiv. Nats. Univ. 17, 6 (2012).

M.V. Ushcats, Phys. Rev. Lett. 109, 040601 (2012).

M.V. Ushcats, Phys. Rev. E 87, 042111 (2013).

M.V. Ushcats, J. Chem. Phys. 138, 094309 (2013).

J.A. Barker, P.J. Leonard, and A. Pompe, J. Chem. Phys. 44, 4206 (1966).

M.V. Ushcats, S.S. Koval, and S.V. Koval, MOTROL 14, 119 (2012).

M.V. Ushcats, Ukr. Fiz. Zh. 59, No. 2, 173 (2014).

J.K. Singh and D.A. Kofke, Phys. Rev. Lett. 92, 220601 (2004).

A.J. Schultz and D.A. Kofke, Mol. Phys. 107, 2309 (2009).

A.J. Schultz, N.S. Barlow, V. Chaudhary, and D.A. Kofke, Mol. Phys. 111, 535 (2013).

D. Frenkel and B. Smit, Understanding Molecular Simulation – From Algorithms to Applications (Academic Press, New York, 2002).

W.G. Hoover and A.G. De Rocco, J. Chem. Phys. 36, 3141 (1962).

C.H. Bennett, J. Comput. Phys. 22, 245 (1976).

V.I. Krylov, Approximate Calculation of Integral s (Dover, Mineola, NY, 2006).

P. L'Ecuyer, Math. Comput.65, 203 (1996).



How to Cite

Ushcats, M. V. (2018). Modification of the Mayer Sampling Method for the Calculation of High-Order Virial Coefficients. Ukrainian Journal of Physics, 59(7), 737.



General problems of theoretical physics