Interdisciplinary Applied Mathematics

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+ V7(rij, «г, «j)



(11.1)


where rij is the distance between the molecular centers, rij is the separation vector between two molecular centers, and « is the orientation of the water molecule, which is determined by both the orientation of the dipole moment vector and the orientation of the molecular plane. The first term in equation (11.1) is the Lennard-Jones potential (see Section 16.1 for more details),


VijJ (rij) = 4ew


FIGURE 11.2. Schematic representation of a three-site water model. This particular model corresponds to the geometry of SSD. M is the molecular center of mass, which is taken as the origin.


12    / x 6-


rijJ    V Vij )    ’


where aw = 3.051 A and ew = 0.152 kcal/mol (Liu and Ichiye, 1996). The second term in equation (11.1) is the point dipole-point dipole potential,


Vdp(rij, Qi, Qj)



Vi ■ Vi    3(Vi



rij)(Vj ■ rij)



r



r



5


where Vi and Vj are the dipole moment vectors, each of whose magnitude is 2.35 D. Note that the factor 1/4^eo has been omitted for simplicity in defining the potential due to electrostatic charges. The last term in equation (11.1) is the tetrahedral sticky potential,


Vj (rij, Qi, Qj ) = V°


[s(rij )wij (rij , Qi, Qj ) + s (rij )wij №j ^ ,


where = 3.7284 kcal/mol determines the strength of the sticky potential. The function wij (rij, Qi, Qj) is given by


wij (ri



) Qi, Qj )

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