Thermodynamic functions as correlation-function integrals

Expressions of some thermodynamic functions as correlation-function integrals, such as the Ornstein-Zernike integral, the Kirkwood-Buff integrals, and the integral formulas for virial coefficients, are recalled. It is noted, as has been remarked before, that the choice of molecular centers from which intermolecular distances are measured is arbitrary and that different choices lead to different forms of the correlation functions but that the integrals must be independent of those choices. This is illustrated with the second virial coefficients of hard spheres in one, two, and three dimensions, with that of gaseous propane in three dimensions, and with computer simulations of the pair correlations in water and in a dilute aqueous solution of propane.