Interdisciplinary Applied Mathematics

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tween two water molecules a and b is then given by the following equation (Mahoney and Jorgensen, 2000):


v„„ = £



2


qiqje


nj



+ 4eo



сто



roo,



12



CTQ


roo



6″



(11.5)


where i and j are the charged sites on a and b, respectively, and rOO is the oxygen-oxygen distance.


The geometry    of    the    TIP4P    water    model    is    shown    in Figure    11.5.    The


TIP4P model is based on four interaction sites located in a planar configuration. Two of those are labeled M and O, which are associated with the oxygen nucleus, and the other two (which are labeled H) are the protons. The two distances and one angle required to fully specify the site coordinates are rOH = 0.957 A, rOM = 0.15 A (M lies on the axis of symmetry between O and the line joining the H sites), and ZHOH = 104.5°.


The potential energy between two TIP4P water molecules consists of a double sum over the interaction sites of both molecules; the terms in the sum allow for Coulombic interactions between the electric charges assigned to the sites as well as an LJ-type contribution (equation (11.5)). The charge on the H site is equal to 0.52e, on the oxygen site is zero, and on the M site is equal to —1.04e (Rapaport, 1997). The physical properties of water based


O


FIGURE 11.5. A sketch of the planar TIP4P water molecule.


on the    TIP4P    model    are    summarized in    Table    11.3,    and    the    geometrical


and interaction parameters of the TIP4P model are summarized in Table 11.2.

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