\(\renewcommand{\AA}{\text{Å}}\)

8.4.4. 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 these commands for a cutoff model:

or these commands for a long-range model:

The bond lengths and bond angles should be held fixed using the fix shake or fix rattle command, unless a parameterization for a flexible TIP4P model is used. The parameter sets listed below are all for rigid TIP4P model variants and thus the bond and angle force constants are not used and can be set to any legal value; only equilibrium length and angle are used.

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).