Interdisciplinary Applied Mathematics

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sin(ftjj) sin(2ftjj) cos(2^jj) + sin(0ji) sin(20ji) cos(2^ji),

where (0ij,    ) is the set of spherical polar angles of the position of molecule

j in    the    frame fixed    on    molecule i and    with    an    orientation    such that    the

Z-axis is parallel to the dipole moment of i and the X-axis is perpendicular to the molecular plane of i. In addition, wx (dj) is an empirical correction form added to the sticky potential; s(rij) and s'(vij) are the modulating functions, which interpolate between 0 and 1. The properties of water modeled by SSD are given in Table 11.3.

Evaluation of the interaction between two SSD water molecules requires computing only one distance between the two centers of mass, four spherical angles, and the angle between the dipole vectors. On the other hand, three-site models like TIP3P and SPC/E require computing nine intermolecular distances, while five-site models like ST2 and TIP5P require computing 17 intermolecular distances. Simulations with the SSD potential are about 4 times and 7 times faster compared with the three-site models in molecular dynamics (Tan et al., 2003) and Monte Carlo (Tan et al., 2003), respectively.    The    original parameters    of    the SSD    water    model    give    low    water

density (0.977 g/cm3) and low heat of vaporization energy at room temperature and 1 atmosphere. However, these issues have been addressed by (Tan et al., 2003) by optimizing the parameters used in the SSD potential.

The SPC Model

The simple point charge (SPC) model is also a three-site model. It consists of a tetrahedral water model with an OH distance of 0.1 nm, H-O-H angle of 109.47°, point charges on the oxygen and hydrogen positions of —0.82e and +0.41e (electronic charge units), respectively, and a Lennard-Jones interaction on the oxygen positions given by

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