# 8.4.3. TIP4P water model¶

The four-point TIP4P rigid water model extends the traditional three-point TIP3P model by adding an additional site, usually massless, where the charge associated with the oxygen atom is placed. This site M is located at a fixed distance away from the oxygen along the bisector of the HOH bond angle. A bond style of harmonic and an angle style of harmonic or charmm should also be used.

A TIP4P model is run with LAMMPS using either this command for a cutoff model:

or these two commands for a long-range model:

For both models, the bond lengths and bond angles should be held fixed using the fix shake command.

These are the additional parameters (in real units) to set for O and H atoms and the water molecule to run a rigid TIP4P model with a cutoff (Jorgensen). Note that the OM distance is specified in the pair_style command, not as part of the pair coefficients.

O mass = 15.9994
H mass = 1.008
O charge = -1.040
H charge = 0.520
$$r_0$$ of OH bond = 0.9572
$$\theta$$ of HOH angle = 104.52$$^{\circ}$$
OM distance = 0.15
LJ $$\epsilon$$ of O-O = 0.1550
LJ $$\sigma$$ of O-O = 3.1536
LJ $$\epsilon$$, $$\sigma$$ of OH, HH = 0.0
Coulomb cutoff = 8.5

For the TIP4/Ice model (J Chem Phys, 122, 234511 (2005); https://doi.org/10.1063/1.1931662) these values can be used:

O mass = 15.9994
H mass = 1.008
O charge = -1.1794
H charge = 0.5897
$$r_0$$ of OH bond = 0.9572
$$\theta$$ of HOH angle = 104.52$$^{\circ}$$
OM distance = 0.1577
LJ $$\epsilon$$ of O-O = 0.21084
LJ $$\sigma$$ of O-O = 3.1668
LJ $$\epsilon$$, $$\sigma$$ of OH, HH = 0.0
Coulomb cutoff = 8.5

For the TIP4P/2005 model (J Chem Phys, 123, 234505 (2005); https://doi.org/10.1063/1.2121687), these values can be used:

O mass = 15.9994
H mass = 1.008
O charge = -1.1128
H charge = 0.5564
$$r_0$$ of OH bond = 0.9572
$$\theta$$ of HOH angle = 104.52$$^{\circ}$$
OM distance = 0.1546
LJ $$\epsilon$$ of O-O = 0.1852
LJ $$\sigma$$ of O-O = 3.1589
LJ $$\epsilon$$, $$\sigma$$ of OH, HH = 0.0
Coulomb cutoff = 8.5

These are the parameters to use for TIP4P with a long-range Coulombic solver (e.g. Ewald or PPPM in LAMMPS):

O mass = 15.9994
H mass = 1.008
O charge = -1.0484
H charge = 0.5242
$$r_0$$ of OH bond = 0.9572
$$\theta$$ of HOH angle = 104.52$$^{\circ}$$
OM distance = 0.1250
LJ $$\epsilon$$ of O-O = 0.16275
LJ $$\sigma$$ of O-O = 3.16435
LJ $$\epsilon$$, $$\sigma$$ of OH, HH = 0.0

Note that the when using the TIP4P pair style, the neighbor list cutoff for Coulomb interactions is effectively extended by a distance 2 * (OM distance), to account for the offset distance of the fictitious charges on O atoms in water molecules. Thus it is typically best in an efficiency sense to use a LJ cutoff >= Coulomb cutoff + 2*(OM distance), to shrink the size of the neighbor list. This leads to slightly larger cost for the long-range calculation, so you can test the trade-off for your model. The OM distance and the LJ and Coulombic cutoffs are set in the pair_style lj/cut/tip4p/long command.

Wikipedia also has a nice article on water models.

(Jorgensen) Jorgensen, Chandrasekhar, Madura, Impey, Klein, J Chem Phys, 79, 926 (1983).