Convergence characteristics of Monte Carlo-Metropolis computer simulations on liquid water Abstract: Very long (5000 K) Monte Carlo computer simulations are reported for liquid water described in terms of the analytical potential functions of Matsuoka, Clementi, and Yoshimine and Rahman and Stillinger's empirical ST2 potential. The convergence characteristics of both realizations are fully developed in terms of internal energy, heat capacity molecular distribution functions, and structural indices. A hierarchy in the calculated properties emerges with respect to the degree of computational effort required to obtain reproducible results. Mean energy and radial distribution functions are the most accessible quantities. Fluctuation properties such as heat capacity require roughly twice as many configurations to stabilize as simple orientational averaged quantities. The structural changes over the equilibrated segments of the realization were examined in terms of quasicomponent distribution functions and found to be small in chemical terms.