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The Diffusion Monte Carlo (DMC) method is applied to the water monomer,dimer, and hexamer, using q-TIP4P/F, one of the most simple, empirical watermodels with flexible monomers. The bias in the time step ($\Delta\tau$) andpopulation size ($N_w$) is investigated. For the binding energies, the bias in$\Delta\tau$ cancels nearly completely, while a noticeable bias in $N_w$ stillremains. However, for the isotope shift, (e.g, in the dimer binding energiesbetween (H$_2$O)$_2$ and (D$_2$O)$_2$) the systematic errors in $N_w$ docancel. Consequently, very accurate results for the latter (within $\sim 0.01$kcal/mol) are obtained with relatively moderate numerical effort ($N_w\sim10^3$). For the water hexamer and its (D$_2$O)$_6$ isotopomer the DMC resultsas a function of $N_w$ are examined for the cage and prism isomers. For a givenisomer, the issue of the walker population leaking out of the correspondingbasin of attraction is addressed by using appropriate geometric constraints.The population size bias for the hexamer is more severe, and in order tomaintain accuracy similar to that of the dimer, the population size $N_w$ mustbe increased by about two orders of magnitude. Fortunately, when the energydifference between cage and prism is taken, the biases cancel, thereby reducingthe systematic errors to within $\sim 0.01$ kcal/mol when using a population of$N_w=4.8\times 10^5$ walkers. Consequently, a very accurate result for theisotope shift is also obtained. Notably, both the quantum and the isotopeeffects for the prism-cage energy difference are small.

Assessing the Performance of the Diffusion Monte Carlo Method as Applied to the Water Monomer, Dimer, and Hexamer