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*Fig. 1. **Temperature dependence of liquid binding energy at normal pressure. Red and blue curves correspond to quantum and classical MD simulations, respectively; the cyan curve represents classical simulations with the rigid molecules. For all of the curves the statistical errors are comparable with the marker sizes except of the leftmost points for classical curves. The crosses represent the experimental data (**16**).*

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*Fig. 2. **Temperature dependence of water diffusivity. Red and blue curves correspond to quantum and classical MD results, respectively. The crosses represent the experimental data (**17**).*

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*Fig. 3. **Temperature dependence of water density at normal pressure. Red and blue curves correspond to quantum and classical MD with QMPFF2, respectively; the cyan curve represents results (**6**) for the TIP5P empirical water potential. For all of the curves the statistical errors are comparable with or less than the marker sizes. The crosses represent the experimental data (**16**).*

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*Fig. 4. **Radial distribution functions for HH (Bottom), OH (Middle), and OO (Top) pairs in liquid water at room temperature and pressure. Blue and red curves correspond to classical and quantum MD simulations with QMPFF2, respectively. Black curves represent experiment (**21**).*

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*Fig. 5. **The QMPFF2 model of a representative molecule. Atomic cores are shown for three atoms labeled as a, b, and c; the electron cloud is shown only for atom a (proportions are distorted). The cloud is attached by a nonharmonic spring to a reference point shifted with respect to the atomic core by vector ***t**_{a}^{0}, which is the sum of the partial shifts t_{ab} and t_{ac}. Each partial shift vector is directed along a bond to atom a, with a length that depends on the types of the bonded atoms. In the presence of an external field (the force vector, F), the cloud shifts by t_{a} relative to its reference position so as to minimize the total energy of the molecular system (generally t_{a} is not parallel with F because of anisotropic polarizability).

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