  Free energy differences $\Delta F:=F-F_{\text{prism}}$ are computed for
several isomers of water hexamer relative to the "prism" isomer using the
self-consistent phonons method. %$\Delta F:=F-F({prism})$ We consider the
isotope effect defined by the quantity $\delta F_{D_2O}:=\Delta F_{\rm
D_2O}-\Delta F_{\rm H_2O}$, and the quantum effect, $\delta F_{\hbar=0}:=\Delta
F_{\hbar=0}-\Delta F_{\rm H_2O}$, and evaluate them using different flexible
water models. While both $\delta F_{D_2O}$ and $\delta F_{\hbar=0}$ are found
to be rather small for all of the potentials, they are especially small for two
of the empirical models, q-TIP4P/F and TTM3-F, compared to q-SPC/Fw and the two
{\it abinitio}-based models, WHBB and HBB2-pol. This qualitative difference in
the properties of different water models cannot be explained by one being "more
accurate" than the other. We speculate as to whether the observed anomalies are
caused by the special properties of water systems, or are an artifact of either
the potential energy surface form/parametrization or the numerical
approximation used.
