Biomedical Engineering Reference
In-Depth Information
g
oo
2
(r)
3
2
1
σ
r/
0
1
1.5
2
2.5
3
Figure 10.8
O-O pair distribution function
10.6.1 Other Water Potentials
Over the years, a number of authors have tackled the problem of finding a suitable pair
potential for liquid water. All involve a rigid water monomer with a number of interaction
sites. The original TIPS 3-site model proposed by Jorgensen (1981) has positive charges on
the hydrogens and a negative charge (
q
O
=−
2
q
H
) on the oxygen. The interaction potential
is taken as the sum of all intermolecular Coulomb terms together with a single L-J 12-6
term between the oxygens:
1
4πε
0
q
i
q
j
R
ij
+
A
R
1
OO
−
B
R
OO
U
AB
=
(10.16)
i
on A
j
on B
The parameters
q
i
,
A
and
B
were chosen to give reasonable energetic results for gas-phase
complexes of water and alcohols.
The author subsequently reoptimized the parameters to give TIP3P, an improved three-
site model.
Four-site models have also been used. The oldest is that due to Bernal and Fowler (1933),
with a more modern version referred to as TIP4P by Jorgensen
et al.
(1983). In this case,
the negative charge is moved off the oxygen and towards the hydrogens at a point along the
bisector of the HOH angle. The pair potential is still calculated according to the equation
above but more distances have to be evaluated.
Stillinger and Rahman's ST2 potential is widely used; this is an improved version of
the one discussed above, but adds a L-J 12-6 term between the oxygen atoms. In all, 17
distances have to be evaluated.
10.7 Different Types of Molecular Dynamics
When Newton's equations of motion are integrated, the energy is conserved. Since the
energy and temperature are related by the equipartition of energy principle, the temperature
should also be constant. Slow temperature drifts do occur as a result of the numerical
