Interdisciplinary Applied Mathematics

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that unlike other polarizable models, which typically execute at least three times slower than effective potential models, a comparable calculation with the PPC model runs only 1.5 times slower than a simulation with SPC/E water. The physical properties of the water simulated using the PPC model are summarized in Table 11.3.


The Six-Site Model


(Nada and van der Eerden, 2003) have proposed an intermolecular potential model of a rigid H2O molecule that has six interaction sites. It has been observed that this six-site model is much more suitable for the simulation of ice and water near TM (i.e., melting point of ice) than the TIP4P and TIP5P models. Figure 11.6 shows a sketch of the six-site model. A positive point charge is placed on each hydrogen (H) site, and a negative charge on each lone-pair (L) site, as in the TIP5P model. A negative charge is also placed    on    a    site    M,    which is    located    on    the    bisector    of ZHOH,    as


in the    TIP4P    model.    In    contrast    to    the    TIP4P and TIP5P    models,    the


Lennard-Jones interaction acts not only on the oxygen (O) site but also on the    H    sites    in    the    present    model.    For    the    O-H length    (гон) and H-O-H


angle in this model, intermediate values between those of the real molecule


in the ice and vapor phases are taken (Nada and van der Eerden, 2003). The average of ZHOH and ZLOL in the present model is the tetrahedral angle of 109.5°. The intermolecular interaction between molecules i and jVij, is represented as the sum of the Coulomb interactions acting among the charged points and the Lennard-Jones interactions acting on O and H atoms, in the following way:

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