# Interdisciplinary Applied Mathematics

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The ST2 model

The ST2 potential developed by (Stillinger and Rahman, 1974) is based on a rigid four-point-charge model for each water molecule. The ST2 water model is shown in Figure 11.3. The positive charges +q are identified as partially shielded protons, and they have been located precisely 1 A from the oxygen nucleus, O. The distance l from O to each of the negative charges —q is 0.8 A in the ST2 model. Pairs of vectors connecting O to the point charges are all disposed at an angle 9t,

9t = 2cos-1(3-1/2) « 109°28b

The ST2 molecules interact with each other through a potential function consisting of a Lennard-Jones central potential acting between oxygens, plus a    Coulombic    potential    for    the    16    (4×4)    pairs    of point    charges. The

ST2 model has a dipole moment of 2.353 D (Stillinger and Rahman, 1974).

The TIPraP Model

The geometry of the TIP5P model is shown in Figure 11.4, and its parameters are presented in Table 11.2, along with those for the TIP3P and TIP4P models. For all TIPraP models, the O-H bond length гон and H-O-H bond angle 0HOH have been set to the experimental gas-phase values, i.e., 0.9572 A and 104.52°. For TIP5P, the negatively charged interaction sites are located symmetrically along the lone-pair directions with an intervening

*

4

#### +q

-q

FIGURE 11.3. A sketch of an ST2 water model.

angle, 0LOL , of 109.47°. A charge of +0.241 e is placed on each hydrogen site, and charges of equal magnitude and opposite sign are placed on the lone-pair interaction sites. The dipole moments are 2.35 D, 2.18 D, and 2.29 D for TIP3P, TIP4P, and TIP5P, respectively. There is no charge on oxygen for TIP5P. The Lennard-Jones potential acts on only the oxygens with a сто    of    3.12    A and an e0    of    0.16    kcal/mol.    The    potential    energy    be

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