Finite-size corrections to the chemical potential

The particle-insertion method of Widom (1963) has been widely used in numerical simulations for the purpose of calculating the excess chemical potential, mu _ex. It is known, however, that values of mu _ex obtained by Widom's method are strongly dependent on N, the number of particles in the system. The authors use the formalism of the grand-canonical ensemble to derive an expression for the leading term in the finite-size correction to mu _ex. The new expression reduces to the exact result for hard rods and gives numerical results in good agreement with those of simulations of hard-disk and hard-sphere fluids. It is, in both respects, an improvement over an expression previously derived by Smit and Frenkel via a thermodynamic argument.