Interdisciplinary Applied Mathematics

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The PPC Model


The polarizable point charge (PPC) model is an efficient polarizable model that retains most of the simplicity of the popular classical three-site potentials while incorporating the polarization response of the water molecule to a local electric field as determined from ab initio calculations (Svishchev et al., 1996). Studies (Kusalik et al., 1995) have shown that the PPC potential accurately describes both the virial equation of state for steam and the liquid properties, including the local structure, dielectric constant, the selfdiffusion coefficient, and the Debye relaxation time (Kusalik et al., 1995), over a wide range of temperatures. The distance between O and H (i.e., гон) in the    PPC    model    is equal    to    0.943    A and ZHOH    = 106°.    The    ge-


TABLE 11.2. Monomer geometry and parameters for the TIPnP potential functions (Mahoney and Jorgensen, 2000).


Parameters


TIP3P


TIP4P


TIP5P


<?H (e)


0.417


0.520


0.241


c^o (A)


3.15061


3.15365


3.12


eo (kcal/mol)


0.1521


0.1550


0.16


гон (A)


0.9572


0.9572


0.9572


#hoh (deg)


104.52


104.52


104.52


roh (A)



0.15


0.70


#lol (deg)




109.47

ometry of the PPC water model is similar to the geometry of the three-site water model shown in Figure 11.2. The values of the hydrogen charges are given by (Kusalik et al., 1995)


q+ = 0.486 ± 0.03Ex + 0.02Ez,


where for the second term a “ + ” sign is used for one of the hydrogens and a “ — ” sign is used for the other hydrogen, and the electric field is given in V/A. The charge on the negative site follows from charge neutrality. The short-range interaction of the PPC model is taken to be an LJ potential centered on the oxygen. The LJ parameters, eLJ = 0.6 kJ/mol and a = 3.234 A, are optimized to give the correct energy, self-diffusion coefficient, and structure    for    water    at    25°C.    It is observed    by    (Kusalik    et    al.,    1995)

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