Convergence acceleration in Monte Carlo computer simulation on water and aqueous solutions Abstract: The convergence characteristics of standard Metropolis Monte Carlo calculations on liquid water and aqueous solutions are described, and documentation of the need for convergence acceleration procedures is presented. The acceleration procedures are additional importance sampling schemes added to the Metropolis method. The recently proposed ``forced bias'' and ``preferential sampling'' procedures are specifically considered. Comparative studies on liquid water at T=25 °C using the force bias method show that convergence is improved by a factor of 2-3 over standard Metropolis results. For aqueous solutions, force bias and preferential sampling procedures used separately and together were studied on a prototype aqueous solution problem based on the liquid water simulation. Neither method alone was found to be adequate for describing structural characteristics of solutions in realizations of the length presently used for simulations on pure liquids. A combination of the force bias and preferential sampling methods was found to be quite successful, and makes aqueous solutions accessible to simulation studies at levels of rigor commensurate with that obtained for pure liquids. Preliminary convergence acceleration results on [CH₄]_aq using the combined force bias-preferential sampling acceleration methods are also presented.